Finite Group Databasebeta

← #17199684

Subgroups — #17199684

Order 4352.

2636 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763446C211yesmaximal, characteristic
2#14531951C211yesmaximal, characteristic, complemented
3#14531935C211yesmaximal, characteristic, complemented
4#14531926C211yesmaximal, characteristic, complemented
5#14531922C211yesmaximal, characteristic, complemented
6#14531891C211yesmaximal, characteristic, complemented
7#14531829C211yesmaximal, characteristic, complemented
8#14531827C211yesmaximal, characteristic, complemented
9#14531778C211yesmaximal, characteristic, complemented
10#14531768C211yesmaximal, characteristic, complemented
11#14531722C211yesmaximal, characteristic, complemented
12#14531718C211yesmaximal, characteristic, complemented
13#14531635C211yesmaximal, characteristic, complemented
14#14531632C211yesmaximal, characteristic, complemented
15#14531609C211yesmaximal, characteristic, complemented
16#14531600C211yesmaximal, characteristic, complemented
17#14531591C211yesmaximal, characteristic, complemented
18#14531572C211yesmaximal, characteristic, complemented
19#14531545C211yesmaximal, characteristic, complemented
20#14531541C211yesmaximal, characteristic, complemented
21#14531485C211yesmaximal, characteristic, complemented
22#14531452C211yesmaximal, characteristic, complemented
23#14531443C211yesmaximal, characteristic, complemented
24#14531421C211yesmaximal, characteristic, complemented
25#14531378C211yesmaximal, characteristic, complemented
26#14531371C211yesmaximal, characteristic, complemented
27#14531359C211yesmaximal, characteristic, complemented
28#14531294C211yesmaximal, characteristic, complemented
29#14531220C211yesmaximal, characteristic, complemented
30C2×#11762703C211yesmaximal, characteristic, complemented
31C17×#2321C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C22⋊D17C2211yescharacteristic
34#11763446C4116yescomplemented
35C2×#10587571C2211yescharacteristic
36C2×#10587572C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587564C2211yescharacteristic
39C2×#10587625C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587624C2211yescharacteristic
42C2×#10587623C2211yescharacteristic
43C2×D4×Dic17C2211yescharacteristic
44C2×D4×Dic17C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic, complemented
46C2×#10587567C2211yescharacteristic
47C2×#10587567C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic, complemented
50C2×#10587578C2211yescharacteristic, complemented
51C2×#10587563C2211yescharacteristic, complemented
52C22×#63225C2211yescharacteristic, complemented
53C22×C22⋊Dic17C2211yescharacteristic
54C22×C22⋊Dic17C2211yescharacteristic
55C22×C22⋊Dic17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C22×C4×Dic17C2211yescharacteristic, complemented
59#11762715C2211yescharacteristic, complemented
60#11762714C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762712C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic, complemented
67#11762709C2211yescharacteristic, complemented
68#11762709C2211yescharacteristic, complemented
69#11762707C2211yescharacteristic, complemented
70#11762706C2211yescharacteristic, complemented
71#11762705C2211yescharacteristic, complemented
72#11762705C2211yescharacteristic, complemented
73#11762703C2211yescharacteristic
74#11762703C2211yescharacteristic
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic, complemented
80#11762703C2211yescharacteristic, complemented
81#11762703C2211yescharacteristic, complemented
82#11762703C2211yescharacteristic, complemented
83#11762703C2211yescharacteristic, complemented
84#11762702C2211yescharacteristic
85#11762702C2211yescharacteristic
86#11762701C2211yescharacteristic, complemented
87#11762701C2211yescharacteristic, complemented
88#11762701C2211yescharacteristic, complemented
89#11762700C2211yescharacteristic, complemented
90#11762700C2211yescharacteristic, complemented
91#11762699C2211yescharacteristic, complemented
92#11762699C2211yescharacteristic, complemented
93#11762698C2211yescharacteristic, complemented
94#11762698C2211yescharacteristic, complemented
95#11762698C2211yescharacteristic, complemented
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic, complemented
99#11762696C2211yescharacteristic, complemented
100#11762694C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762693C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762692C2211yescharacteristic, complemented
105#11762692C2211yescharacteristic, complemented
106#11762691C2211yescharacteristic, complemented
107#11762690C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762689C2211yescharacteristic
110#11762689C2211yescharacteristic, complemented
111#11762689C2211yescharacteristic, complemented
112#11762688C2211yescharacteristic
113#11762688C2211yescharacteristic
114#11762688C2211yescharacteristic
115#11762688C2211yescharacteristic
116#11762688C2211yescharacteristic, complemented
117#11762688C2211yescharacteristic, complemented
118#11762686C2211yescharacteristic
119#11762686C2211yescharacteristic
120#11762686C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762686C2211yescharacteristic
123#11762686C2211yescharacteristic
124#11762686C2211yescharacteristic, complemented
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic, complemented
128#11762684C2211yescharacteristic, complemented
129#11762684C2211yescharacteristic, complemented
130#11762683C2211yescharacteristic, complemented
131#11762681C2211yescharacteristic, complemented
132#11762681C2211yescharacteristic, complemented
133#11762680C2211yescharacteristic, complemented
134#11762680C2211yescharacteristic, complemented
135#11762676C2211yescharacteristic, complemented
136#11762671C2211yescharacteristic, complemented
137#11762670C2211yescharacteristic
138#11762670C2211yescharacteristic
139#11762670C2211yescharacteristic, complemented
140#11762670C2211yescharacteristic, complemented
141#11762668C2211yescharacteristic, complemented
142#11762668C2211yescharacteristic, complemented
143#11762667C2211yescharacteristic
144#11762667C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic, complemented
147#11762666C2211yescharacteristic, complemented
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150#11762664C2211yescharacteristic
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×#63227C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762655C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic, complemented
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#390C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic, complemented
185C17×#385C2211yescharacteristic, complemented
186C17×#379C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C25×C17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17—42no—
197C22×C22⋊D17—42no—
198C22×C22⋊D17C2×C418yescomplemented
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C2×#63254—42no—
215C2×#63254—42no—
216C2×#63254C2×C418yescomplemented
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C17×#120C2×C418yescomplemented
223C4×D4×C17—42no—
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17—42no—
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C22⋊Dic17—42no—
248C2×C22⋊Dic17—42no—
249C2×C22⋊Dic17C2×C418yescomplemented
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266#10587625C2×C418yescomplemented
267#10587625C2×C418yescomplemented
268#10587624C2×C418yescomplemented
269#10587623C2×C418yescomplemented
270D4×Dic17—42no—
271D4×Dic17—42no—
272D4×Dic17C2×C418yescomplemented
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×#63225—42no—
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×C4×Dic17—42no—
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324#10587578—42no—
325#10587572C2×C418yescomplemented
326#10587571C2×C418yescomplemented
327#10587569C2×C418yescomplemented
328#10587567—42no—
329#10587567—42no—
330#10587567—42no—
331#10587567C2×C418yescomplemented
332C22⋊C4×D17—42no—
333C22⋊C4×D17C2×C418yescomplemented
334#10587564C2×C418yescomplemented
335#10587563—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17—22no—
377C24×C17—22no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C23×D17—41no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17—41no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17C22×C414yes—
394C23×D17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C2×D4×C17—22no—
397C2×D4×C17—22no—
398C2×D4×C17—41no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17C22×C414yes—
403C2×D4×C17C22×C414yes—
404C2×D4×C17C22×C414yes—
405C22×C4×C17—22no—
406C22×C4×C17—22no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—416no—
438C2×C22⋊D17C22×C414yes—
439C2×C22⋊D17C22×C414yes—
440C2×C22⋊D17C22×C414yes—
441C2×C22⋊D17C22×C414yes—
442C2×C22⋊D17C22×C414yes—
443C2×C22⋊D17C22×C414yes—
444C22×Dic17—22no—
445C22×Dic17—22no—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—22no—
449C22×Dic17—22no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17C22×C414yes—
468C22×Dic17C22×C414yes—
469C22×Dic17C22×C414yes—
470C22×Dic17C22×C414yes—
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485#63254—416no—
486C2×C4×D17—22no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17C22×C414yes—
497C2×C4×D17C22×C414yes—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C2×Dic34C22×C414yes—
501C4⋊C4×C17—41no—
502C4⋊C4×C17—41no—
503C4⋊C4×C17—41no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—41no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17—41no—
510C22⋊C4×C17—41no—
511C22⋊C4×C17—41no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17C22×C414yes—
518C22⋊C4×C17C22×C414yes—
519C22⋊C4×C17C22×C414yes—
520C42×C17—41no—
521C42×C17—41no—
522C42×C17—41no—
523C22⋊Dic17—22no—
524C22⋊Dic17—22no—
525C22⋊Dic17—22no—
526C22⋊Dic17—22no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17—41no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17C22×C414yes—
535C22⋊Dic17C22×C414yes—
536C22⋊Dic17C22×C414yes—
537C22⋊Dic17C22×C414yes—
538C22⋊Dic17C22×C414yes—
539#63227—22no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227C22×C414yes—
554#63227C22×C414yes—
555#63227C22×C414yes—
556#63227C22×C414yes—
557C4⋊Dic17—22no—
558C4⋊Dic17—41no—
559C4⋊Dic17—41no—
560C4⋊Dic17C22×C414yes—
561C4⋊Dic17C22×C414yes—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570#63225—41no—
571#63225—41no—
572#63225C22×C414yes—
573#63225C22×C414yes—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17—41no—
587C4×Dic17C22×C414yes—
588#34492—171nomaximal, Sylow
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—28no—
612C23×C17—44no—
613C23×C17—44no—
614C23×C17—82no—
615C23×C17—82no—
616C23×C17—82no—
617C23×C17—82no—
618C23×C17C23×C412yes—
619C23×C17C23×C412yes—
620C23×C17C23×C412yes—
621C23×C17C23×C412yes—
622C23×C17H(5,𝔽2)12yes—
623C23×C17H(5,𝔽2)12yes—
624C23×C17C2511yescharacteristic
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—44no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—82no—
641C22×D17—82no—
642C22×D17—82no—
643C22×D17—82no—
644C22×D17C23×C412yes—
645C22×D17C23×C412yes—
646D4×C17—28no—
647D4×C17—44no—
648D4×C17—44no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—44no—
680C2×C4×C17—82no—
681C2×C4×C17—82no—
682C2×C4×C17C23×C412yes—
683C2×C4×C17C23×C412yes—
684C2×C4×C17C23×C412yes—
685C22⋊D17—28no—
686C22⋊D17—28no—
687C22⋊D17—44no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C2×Dic17—28no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—44no—
728C2×Dic17—44no—
729C2×Dic17—44no—
730C2×Dic17—44no—
731C2×Dic17—82no—
732C2×Dic17—82no—
733C2×Dic17—82no—
734C2×Dic17—82no—
735C2×Dic17C23×C412yes—
736C2×Dic17C23×C412yes—
737C2×Dic17C23×C412yes—
738C2×Dic17C23×C412yes—
739C2×Dic17C23×C412yes—
740C2×Dic17C23×C412yes—
741C2×Dic17H(5,𝔽2)12yes—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—82no—
745C4×D17—82no—
746Dic34—44no—
747C2×#546—171no—
748#2378—171no—
749#2377—171no—
750#2376—171no—
751#2375—171no—
752#2372—171no—
753#2364—171no—
754#2363—171no—
755#2359—171no—
756#2358—171no—
757#2353—171no—
758#2353—171no—
759#2342—171no—
760#2342—171no—
761#2339—171no—
762D4×C22⋊C4—171no—
763#2337—171no—
764#2335—171no—
765#2333—171no—
766#2332—171no—
767#2325—171no—
768#2322—171no—
769#2321—171no—
770#2321D1711yescharacteristic, complemented
771#2319—171no—
772#2312—171no—
773#2311—171no—
774#2308—171no—
775C4×#121—171no—
776#2290—171no—
777C2×#388—171no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—22no—
789C22×C17—22no—
790C22×C17—22no—
791C22×C17—22no—
792C22×C17—22no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—88no—
806C22×C17#51814yes—
807C22×C17C24×C411yescharacteristic
808C22×C17C2×H(5,𝔽2)11yescharacteristic
809C22×C17C2×H(5,𝔽2)11yescharacteristic
810C22×C17C2×H(5,𝔽2)11yescharacteristic
811C22×C17#58511yescharacteristic
812C22×C17#58511yescharacteristic
813C22×C17#58511yescharacteristic
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—22no—
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—88no—
829C4×C17—22no—
830C4×C17—22no—
831C4×C17—22no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840Dic17—22no—
841Dic17—22no—
842Dic17—22no—
843Dic17—22no—
844Dic17—22no—
845Dic17—22no—
846Dic17—22no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854C22×#41—171no—
855C23×D4—171no—
856#546—1716no—
857C2×#124—171no—
858C2×#123—171no—
859C2×#123—171no—
860C2×C22⋊Q8—171no—
861C2×#121—171no—
862C2×#121—171no—
863C2×#121—171no—
864C2×#120—171no—
865C2×#120C2×D1711yescharacteristic
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4—171no—
872C2×C4×D4—171no—
873C2×C4×D4C2×D1711yescharacteristic, complemented
874C2×#117—171no—
875C2×#117—171no—
876C22×C4⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C22⋊C4—171no—
879C22×C22⋊C4—171no—
880C22×C22⋊C4—171no—
881C22×C22⋊C4—171no—
882C22×C22⋊C4C2×D1711yescharacteristic
883C22×C42—171no—
884#391—171no—
885#391—171no—
886#391—171no—
887#391—171no—
888#390—171no—
889#390—171no—
890#390—171no—
891#390—171no—
892#390—171no—
893#390—171no—
894#390C2×D1711yescharacteristic
895#390C2×D1711yescharacteristic, complemented
896#389—171no—
897#389—171no—
898#389—171no—
899#389—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388—171no—
922#388—171no—
923#388—171no—
924#388—171no—
925#388—171no—
926#388C2×D1711yescharacteristic
927#388C2×D1711yescharacteristic
928#388C2×D1711yescharacteristic, complemented
929#388C2×D1711yescharacteristic, complemented
930#387—171no—
931#387—171no—
932#387—171no—
933#387—171no—
934#387—171no—
935#387—171no—
936#387—171no—
937#387—171no—
938#387—171no—
939#387—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#386—171no—
955#386—171no—
956#386—171no—
957#386—171no—
958#386—171no—
959#386C2×D1711yescharacteristic
960#386C2×D1711yescharacteristic, complemented
961#386C2×D1711yescharacteristic, complemented
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#385C2×D1711yescharacteristic, complemented
970#383—171no—
971#381—171no—
972#381—171no—
973#381—171no—
974#381—171no—
975#381—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#380—171no—
981#380—171no—
982#380—171no—
983#379—171no—
984#379—171no—
985#379—171no—
986#379C2×D1711yescharacteristic
987C4×C4⋊C4—171no—
988C4×C4⋊C4—171no—
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4—171no—
1002C4×C22⋊C4—171no—
1003C4×C22⋊C4—171no—
1004C4×C22⋊C4C2×D1711yescharacteristic, complemented
1005#376—171no—
1006#376—171no—
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×C17—24no—
1011C2×C17—42no—
1012C2×C17—42no—
1013C2×C17—42no—
1014C2×C17C2×#51811yescharacteristic
1015C2×C17#342811yescharacteristic
1016C2×C17C4×H(5,𝔽2)11yescharacteristic
1017C2×C17#353411yescharacteristic
1018C2×C17#354211yescharacteristic
1019C2×C17#354511yescharacteristic
1020C2×C17#356011yescharacteristic
1021D17—42no—
1022D17—42no—
1023C25—171no—
1024C25C22×D1711yescharacteristic
1025C2×#41—178no—
1026C2×#41—682no—
1027C2×#41—682no—
1028C22×Q8—171no—
1029C22×D4—171no—
1030C22×D4—171no—
1031C22×D4—178no—
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—682no—
1037C22×D4—682no—
1038C22×D4C22×D1711yescharacteristic
1039C22×D4C22×D1711yescharacteristic
1040C22×D4C22×D1711yescharacteristic
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4C22×D1711yescharacteristic
1055C23×C4C22×D1711yescharacteristic
1056C23×C4C22×D1711yescharacteristic
1057#124—178no—
1058#123—178no—
1059#123—178no—
1060C22⋊Q8—178no—
1061#121—178no—
1062#121—178no—
1063#121—178no—
1064#120—178no—
1065#120C4×D1718yescomplemented
1066C4×D4—42no—
1067C4×D4—178no—
1068C4×D4—178no—
1069C4×D4—682no—
1070C4×D4—682no—
1071C4×D4—682no—
1072C4×D4—682no—
1073C4×D4—682no—
1074#117—682no—
1075#117—682no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—682no—
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C4⋊C4C22×D1711yescharacteristic
1096C2×C4⋊C4C22×D1711yescharacteristic
1097C2×C22⋊C4—42no—
1098C2×C22⋊C4—178no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—178no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—682no—
1135C2×C22⋊C4—682no—
1136C2×C22⋊C4—682no—
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C22⋊C4C22×D1711yescharacteristic
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42—171no—
1163C2×C42—171no—
1164C2×C42—171no—
1165C2×C42—171no—
1166C2×C42—171no—
1167C2×C42—682no—
1168C2×C42C22×D1711yescharacteristic
1169C2×C42C22×D1711yescharacteristic
1170C2×C42C22×D1711yescharacteristic
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211C17#3449211yescharacteristic, complemented, Sylow
1212C24—22no—
1213C24—22no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—171no—
1219C24—171no—
1220C24—174no—
1221C24—681no—
1222C24—681no—
1223C24—681no—
1224C24—681no—
1225C24—681no—
1226C24—681no—
1227C24C2×C4×D1714yes—
1228C24C23×D1711yescharacteristic
1229C24C23×D1711yescharacteristic
1230C24C23×D1711yescharacteristic
1231C24C23×D1711yescharacteristic
1232#41—6816no—
1233C2×Q8—174no—
1234C2×Q8—681no—
1235C2×Q8—681no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—174no—
1243C2×D4—174no—
1244C2×D4—174no—
1245C2×D4—174no—
1246C2×D4—174no—
1247C2×D4—174no—
1248C2×D4—342no—
1249C2×D4—342no—
1250C2×D4—342no—
1251C2×D4—342no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4—681no—
1258C2×D4—681no—
1259C2×D4—681no—
1260C2×D4—6816no—
1261C2×D4C2×C4×D1714yes—
1262C2×D4C2×C4×D1714yes—
1263C2×D4C2×C4×D1714yes—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—174no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—174no—
1282C22×C4—174no—
1283C22×C4—174no—
1284C22×C4—174no—
1285C22×C4—174no—
1286C22×C4—171no—
1287C22×C4—171no—
1288C22×C4—171no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—342no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—681no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4C23×D1711yescharacteristic
1327C22×C4C23×D1711yescharacteristic
1328C22×C4C23×D1711yescharacteristic
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—174no—
1341C4⋊C4—174no—
1342C4⋊C4—174no—
1343C4⋊C4—174no—
1344C4⋊C4—342no—
1345C4⋊C4—681no—
1346C4⋊C4—681no—
1347C4⋊C4—681no—
1348C4⋊C4—681no—
1349C4⋊C4—681no—
1350C4⋊C4—681no—
1351C4⋊C4—681no—
1352C4⋊C4—681no—
1353C4⋊C4—681no—
1354C4⋊C4—681no—
1355C4⋊C4—681no—
1356C4⋊C4—681no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—174no—
1371C22⋊C4—174no—
1372C22⋊C4—174no—
1373C22⋊C4—174no—
1374C22⋊C4—174no—
1375C22⋊C4—174no—
1376C22⋊C4—174no—
1377C22⋊C4—174no—
1378C22⋊C4—174no—
1379C22⋊C4—342no—
1380C22⋊C4—342no—
1381C22⋊C4—342no—
1382C22⋊C4—342no—
1383C22⋊C4—342no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4C2×C4×D1714yes—
1405C22⋊C4C2×C4×D1714yes—
1406C22⋊C4C2×C4×D1714yes—
1407C42—41no—
1408C42—41no—
1409C42—41no—
1410C42—174no—
1411C42—342no—
1412C42—342no—
1413C42—681no—
1414C42—681no—
1415C42—681no—
1416C42—681no—
1417C42—681no—
1418C42—681no—
1419C42—681no—
1420C42—681no—
1421C42—681no—
1422C42—681no—
1423C42—681no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—28no—
1447C23—44no—
1448C23—44no—
1449C23—82no—
1450C23—82no—
1451C23—82no—
1452C23—82no—
1453C23—172no—
1454C23—172no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—684no—
1468C23—684no—
1469C23—684no—
1470C23—1362no—
1471C23—1362no—
1472C23—1362no—
1473C23—1362no—
1474C23C22×C4×D1712yes—
1475C23C22×C4×D1712yes—
1476C23C22×C4×D1712yes—
1477C23C22×C4×D1712yes—
1478C23#1058769112yes—
1479C23#1058769612yes—
1480C23C24×D1711yescharacteristic
1481Q8—684no—
1482D4—28no—
1483D4—44no—
1484D4—44no—
1485D4—348no—
1486D4—348no—
1487D4—684no—
1488D4—684no—
1489D4—684no—
1490D4—684no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—44no—
1522C2×C4—82no—
1523C2×C4—82no—
1524C2×C4—172no—
1525C2×C4—172no—
1526C2×C4—172no—
1527C2×C4—172no—
1528C2×C4—172no—
1529C2×C4—172no—
1530C2×C4—172no—
1531C2×C4—348no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—684no—
1568C2×C4—684no—
1569C2×C4—684no—
1570C2×C4—684no—
1571C2×C4—684no—
1572C2×C4—684no—
1573C2×C4—1362no—
1574C2×C4—1362no—
1575C2×C4—1362no—
1576C2×C4—1362no—
1577C2×C4—1362no—
1578C2×C4—1362no—
1579C2×C4C22×C4×D1712yes—
1580C2×C4C22×C4×D1712yes—
1581C2×C4C22×C4×D1712yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—22no—
1596C22—22no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—88no—
1610C22—342no—
1611C22—342no—
1612C22—342no—
1613C22—342no—
1614C22—342no—
1615C22—342no—
1616C22—681no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—1368no—
1625C22#1176328114yes—
1626C22C23×C4×D1711yescharacteristic
1627C22H(5,𝔽2)×D1711yescharacteristic
1628C22C2×#1058769111yescharacteristic
1629C22C2×#1058769611yescharacteristic
1630C22#1176364411yescharacteristic
1631C22#1176364411yescharacteristic
1632C22#1176364411yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—342no—
1645C4—342no—
1646C4—342no—
1647C4—342no—
1648C4—342no—
1649C4—342no—
1650C4—342no—
1651C4—681no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C2—24no—
1659C2—42no—
1660C2—42no—
1661C2—42no—
1662C2—682no—
1663C2—682no—
1664C2C2×#1176328111yescharacteristic
1665C2#1454198211yescharacteristic
1666C2#1454198811yescharacteristic
1667C2#1454297511yescharacteristic
1668C2#1454308711yescharacteristic
1669C2#1454313311yescharacteristic
1670C2#1454333811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2321C2
socle, cosocleC23×C17C25
prime radicalC2×#11763446C2
hypercenter#2321D17
hypocenterC17#34492
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2321

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531951C2semidirect
3. #14531935C2semidirect
4. #14531926C2semidirect
5. #14531922C2semidirect
6. #14531891C2semidirect
7. #14531829C2semidirect
8. #14531827C2semidirect
9. #14531778C2semidirect
10. #14531768C2semidirect
11. #14531722C2semidirect
12. #14531718C2semidirect
13. #14531635C2semidirect
14. #14531632C2semidirect
15. #14531609C2semidirect
16. #14531600C2semidirect
17. #14531591C2semidirect
18. #14531572C2semidirect
19. #14531545C2semidirect
20. #14531541C2semidirect
21. #14531485C2semidirect
22. #14531452C2semidirect
23. #14531443C2semidirect
24. #14531421C2semidirect
25. #14531378C2semidirect
26. #14531371C2semidirect
27. #14531359C2semidirect
28. #14531294C2semidirect
29. #14531220C2semidirect
30. C2×#11762703C2semidirect
31. C17×#2321C2semidirect
34. #11763446C4semidirect
44. C2×D4×Dic17C22semidirect
45. C2×D4×Dic17C22semidirect
49. C2×#10587567C22semidirect
50. C2×#10587578C22semidirect
51. C2×#10587563C22semidirect
52. C22×#63225C22semidirect
58. C22×C4×Dic17C22semidirect
59. #11762715C22semidirect
60. #11762714C22semidirect
61. #11762713C22semidirect
62. #11762713C22semidirect
66. #11762709C22semidirect
67. #11762709C22semidirect
68. #11762709C22semidirect
69. #11762707C22semidirect
70. #11762706C22semidirect
71. #11762705C22semidirect
72. #11762705C22semidirect
79. #11762703C22semidirect
80. #11762703C22semidirect
81. #11762703C22semidirect
82. #11762703C22semidirect
83. #11762703C22semidirect
86. #11762701C22semidirect
87. #11762701C22semidirect
88. #11762701C22semidirect
89. #11762700C22semidirect
90. #11762700C22semidirect
91. #11762699C22semidirect
92. #11762699C22semidirect
93. #11762698C22semidirect
94. #11762698C22semidirect
95. #11762698C22semidirect
98. #11762697C22semidirect
99. #11762696C22semidirect
100. #11762694C22semidirect
101. #11762694C22semidirect
102. #11762693C22semidirect
103. #11762693C22semidirect
104. #11762692C22semidirect
105. #11762692C22semidirect
106. #11762691C22semidirect
107. #11762690C22semidirect
108. #11762690C22semidirect
110. #11762689C22semidirect
111. #11762689C22semidirect
116. #11762688C22semidirect
117. #11762688C22semidirect
124. #11762686C22semidirect
127. #11762685C22semidirect
128. #11762684C22semidirect
129. #11762684C22semidirect
130. #11762683C22semidirect
131. #11762681C22semidirect
132. #11762681C22semidirect
133. #11762680C22semidirect
134. #11762680C22semidirect
135. #11762676C22semidirect
136. #11762671C22semidirect
139. #11762670C22semidirect
140. #11762670C22semidirect
141. #11762668C22semidirect
142. #11762668C22semidirect
144. #11762667C22semidirect
145. #11762667C22semidirect
146. #11762667C22semidirect
147. #11762666C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4×C4⋊Dic17C22semidirect
153. #11762660C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×#63227C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762655C22semidirect
169. #11762654C22semidirect
170. C2×#10587502C22semidirect
171. C2×#10587502C22semidirect
172. C2×#10587502C22semidirect
174. C2×C4×D4×C17C22semidirect
177. C17×#390C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
183. C17×#386C22semidirect
184. C17×#386C22semidirect
185. C17×#385C22semidirect
187. C4×C22⋊C4×C17C22semidirect
198. C22×C22⋊D17C2×C4semidirect
216. C2×#63254C2×C4semidirect
222. C17×#120C2×C4semidirect
249. C2×C22⋊Dic17C2×C4semidirect
266. #10587625C2×C4semidirect
267. #10587625C2×C4semidirect
268. #10587624C2×C4semidirect
269. #10587623C2×C4semidirect
272. D4×Dic17C2×C4semidirect
325. #10587572C2×C4semidirect
326. #10587571C2×C4semidirect
327. #10587569C2×C4semidirect
331. #10587567C2×C4semidirect
333. C22⋊C4×D17C2×C4semidirect
334. #10587564C2×C4semidirect
770. #2321D17semidirect
873. C2×C4×D4C2×D17semidirect
895. #390C2×D17semidirect
928. #388C2×D17semidirect
929. #388C2×D17semidirect
960. #386C2×D17semidirect
961. #386C2×D17semidirect
969. #385C2×D17semidirect
1004. C4×C22⋊C4C2×D17semidirect
1065. #120C4×D17semidirect
1211. C17#34492semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117634462
#145319512
#145319352
#145319262
#145319222
#145318912
#145318292
#145318272
#145317782
#145317682
#145317222
#145317182
#145316352
#145316322
#145316092
#145316002
#145315912
#145315722
#145315452
#145315412
#145314852
#145314522
#145314432
#145314212
#145313782
#145313712
#145313592
#145312942
#145312202
C2×#117627032
C17×#23212
#3449217