Finite Group Databasebeta

← #17199665

Subgroups — #17199665

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×#11763449C211yesmaximal, characteristic
2#14531951C211yesmaximal, characteristic, complemented
3#14531940C211yesmaximal, characteristic, complemented
4#14531928C211yesmaximal, characteristic, complemented
5#14531923C211yesmaximal, characteristic, complemented
6#14531892C211yesmaximal, characteristic, complemented
7#14531835C211yesmaximal, characteristic, complemented
8#14531822C211yesmaximal, characteristic, complemented
9#14531779C211yesmaximal, characteristic, complemented
10#14531762C211yesmaximal, characteristic, complemented
11#14531721C211yesmaximal, characteristic, complemented
12#14531719C211yesmaximal, characteristic, complemented
13#14531632C211yesmaximal, characteristic, complemented
14#14531615C211yesmaximal, characteristic, complemented
15C22⋊C4×C22⋊D17C211yesmaximal, characteristic, complemented
16#14531592C211yesmaximal, characteristic, complemented
17#14531574C211yesmaximal, characteristic, complemented
18#14531546C211yesmaximal, characteristic, complemented
19#14531534C211yesmaximal, characteristic, complemented
20#14531481C211yesmaximal, characteristic, complemented
21#14531451C211yesmaximal, characteristic, complemented
22#14531446C211yesmaximal, characteristic, complemented
23#14531442C211yesmaximal, characteristic, complemented
24#14531425C211yesmaximal, characteristic, complemented
25#14531382C211yesmaximal, characteristic, complemented
26#14531373C211yesmaximal, characteristic, complemented
27#14531360C211yesmaximal, characteristic, complemented
28C4×#10587570C211yesmaximal, characteristic, complemented
29#14531221C211yesmaximal, characteristic, complemented
30D17×#388C211yesmaximal, characteristic, complemented
31C17×#2342C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C22⋊D17C2211yescharacteristic
34#11763449C4116yescomplemented
35C2×#10587571C2211yescharacteristic
36C2×#10587615C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587564C2211yescharacteristic
39C2×#10587616C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587568C2211yescharacteristic
43C2×#10587639C2211yescharacteristic
44C2×C4×D68C2211yescharacteristic, complemented
45C2×C4×D68C2211yescharacteristic, complemented
46C2×#10587579C2211yescharacteristic, complemented
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic, complemented
51C2×#10587567C2211yescharacteristic
52C2×#10587578C2211yescharacteristic, complemented
53C2×C4⋊C4×D17C2211yescharacteristic, complemented
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic, complemented
59#11762715C2211yescharacteristic, complemented
60#11762715C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762710C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic, complemented
69#11762709C2211yescharacteristic, complemented
70#11762709C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762705C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic, complemented
78#11762703C2211yescharacteristic, complemented
79#11762703C2211yescharacteristic, complemented
80#11762702C2211yescharacteristic
81#11762702C2211yescharacteristic
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic
84#11762702C2211yescharacteristic, complemented
85#11762702C2211yescharacteristic, complemented
86#11762702C2211yescharacteristic, complemented
87#11762702C2211yescharacteristic, complemented
88#11762701C2211yescharacteristic, complemented
89#11762701C2211yescharacteristic, complemented
90#11762700C2211yescharacteristic, complemented
91#11762700C2211yescharacteristic, complemented
92#11762700C2211yescharacteristic, complemented
93#11762699C2211yescharacteristic, complemented
94#11762698C2211yescharacteristic, complemented
95#11762698C2211yescharacteristic, complemented
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic, complemented
99#11762697C2211yescharacteristic, complemented
100#11762697C2211yescharacteristic, complemented
101#11762696C2211yescharacteristic, complemented
102#11762696C2211yescharacteristic, complemented
103#11762694C2211yescharacteristic, complemented
104#11762694C2211yescharacteristic, complemented
105#11762693C2211yescharacteristic, complemented
106#11762691C2211yescharacteristic, complemented
107#11762691C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762688C2211yescharacteristic
112#11762688C2211yescharacteristic
113#11762688C2211yescharacteristic, complemented
114#11762687C2211yescharacteristic, complemented
115#11762687C2211yescharacteristic, complemented
116#11762687C2211yescharacteristic, complemented
117#11762687C2211yescharacteristic, complemented
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic, complemented
131#11762685C2211yescharacteristic, complemented
132#11762685C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762683C2211yescharacteristic, complemented
135#11762682C2211yescharacteristic, complemented
136#11762680C2211yescharacteristic, complemented
137#11762680C2211yescharacteristic, complemented
138#11762680C2211yescharacteristic, complemented
139#11762676C2211yescharacteristic, complemented
140#11762671C2211yescharacteristic, complemented
141#11762671C2211yescharacteristic, complemented
142#11762670C2211yescharacteristic
143#11762670C2211yescharacteristic
144#11762669C2211yescharacteristic, complemented
145#11762669C2211yescharacteristic, complemented
146#11762668C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic
148#11762666C2211yescharacteristic, complemented
149#11762666C2211yescharacteristic, complemented
150#11762665C2211yescharacteristic
151#11762665C2211yescharacteristic
152#11762664C2211yescharacteristic
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic
157C4×#63227C2211yescharacteristic, complemented
158C4×#63227C2211yescharacteristic, complemented
159C4×#63227C2211yescharacteristic, complemented
160C4×#63227C2211yescharacteristic, complemented
161C4×C22⋊Dic17C2211yescharacteristic, complemented
162C4×C22⋊Dic17C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic, complemented
164#11762656C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762655C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#117C2211yescharacteristic, complemented
174C22×C22⋊C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#385C2211yescharacteristic, complemented
181C17×#385C2211yescharacteristic, complemented
182C17×#381C2211yescharacteristic, complemented
183C17×#380C2211yescharacteristic, complemented
184C17×#379C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C25×C17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17—42no—
195C22×C22⋊D17—42no—
196C22×C22⋊D17C2×C418yescomplemented
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C2×#63252—42no—
206C2×#63252—42no—
207C2×#63252C2×C418yescomplemented
208C22×D68C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C17×#117—42no—
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17—42no—
228C2×C22⋊C4×C17C2×C418yescomplemented
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×C42×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247#10587639C2×C418yescomplemented
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
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
263#10587616C2×C418yescomplemented
264#10587615C2×C418yescomplemented
265C4×C22⋊D17—42no—
266C4×C22⋊D17—42no—
267C4×C22⋊D17—42no—
268C4×C22⋊D17C2×C418yescomplemented
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
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
319#10587579—42no—
320#10587578—42no—
321C4⋊C4×D17—42no—
322#10587571C2×C418yescomplemented
323#10587570C2×C418yescomplemented
324#10587570C2×C418yescomplemented
325#10587569C2×C418yescomplemented
326#10587568C2×C418yescomplemented
327#10587567C2×C418yescomplemented
328C22⋊C4×D17—42no—
329C22⋊C4×D17—42no—
330C22⋊C4×D17—42no—
331C22⋊C4×D17C2×C418yescomplemented
332#10587564C2×C418yescomplemented
333C4×D68—42no—
334C4×D68—42no—
335C42×D17—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
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—41no—
377C24×C17—41no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C23×D17—22no—
387C23×D17—22no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17—41no—
391C23×D17—41no—
392C23×D17C22×C414yes—
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C22×C4×C17—22no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17C22×C414yes—
407C22×C4×C17C22×C414yes—
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C2×C22⋊D17—22no—
421C2×C22⋊D17—22no—
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—416no—
435C2×C22⋊D17C22×C414yes—
436C2×C22⋊D17C22×C414yes—
437C2×C22⋊D17C22×C414yes—
438C2×C22⋊D17C22×C414yes—
439C2×C22⋊D17C22×C414yes—
440C2×C22⋊D17C22×C414yes—
441C2×C22⋊D17C22×C414yes—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17C22×C414yes—
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458#63252—416no—
459C2×D68—22no—
460C2×D68—22no—
461C2×D68—41no—
462C2×D68—41no—
463C2×D68C22×C414yes—
464C2×D68C22×C414yes—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
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×D17C22×C414yes—
496C2×C4×D17C22×C414yes—
497C2×C4×D17C22×C414yes—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C2×Dic34C22×C414yes—
501C4⋊C4×C17—22no—
502C4⋊C4×C17—41no—
503C4⋊C4×C17—41no—
504C4⋊C4×C17—41no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—22no—
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×C17C22×C414yes—
516C22⋊C4×C17C22×C414yes—
517C22⋊C4×C17C22×C414yes—
518C22⋊C4×C17C22×C414yes—
519C42×C17—22no—
520C42×C17—41no—
521C42×C17—41no—
522C42×C17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17—41no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17C22×C414yes—
536C22⋊Dic17C22×C414yes—
537C22⋊Dic17C22×C414yes—
538#63227—22no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
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#63227—41no—
554#63227C22×C414yes—
555#63227C22×C414yes—
556#63227C22×C414yes—
557#63227C22×C414yes—
558#63227C22×C414yes—
559C4⋊Dic17—41no—
560C4⋊Dic17—41no—
561C4⋊Dic17—41no—
562C4⋊Dic17—41no—
563C4⋊Dic17C22×C414yes—
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—
574#63225C22×C414yes—
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—44no—
608C23×C17—44no—
609C23×C17—44no—
610C23×C17—82no—
611C23×C17—82no—
612C23×C17—82no—
613C23×C17—82no—
614C23×C17C23×C412yes—
615C23×C17C23×C412yes—
616C23×C17C23×C412yes—
617C23×C17C2511yescharacteristic
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
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—28no—
635C22×D17—44no—
636C22×D17—44no—
637C22×D17—82no—
638C22×D17—82no—
639C22×D17—82no—
640C22×D17—82no—
641C22×D17C23×C412yes—
642C22×D17C23×C412yes—
643C22×D17C23×C412yes—
644C22×D17H(5,𝔽2)12yes—
645C22×D17H(5,𝔽2)12yes—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
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—44no—
678C2×C4×C17—44no—
679C2×C4×C17—82no—
680C2×C4×C17—82no—
681C2×C4×C17C23×C412yes—
682C2×C4×C17C23×C412yes—
683C2×C4×C17C23×C412yes—
684C2×C4×C17C23×C412yes—
685C2×C4×C17H(5,𝔽2)12yes—
686C22⋊D17—28no—
687C22⋊D17—28no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—44no—
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×Dic17C23×C412yes—
729C2×Dic17C23×C412yes—
730C2×Dic17C23×C412yes—
731C2×Dic17C23×C412yes—
732C2×Dic17C23×C412yes—
733D68—28no—
734D68—44no—
735C4×D17—28no—
736C4×D17—44no—
737C4×D17—44no—
738C4×D17—44no—
739C4×D17—44no—
740C4×D17—82no—
741C4×D17—82no—
742C4×D17—82no—
743C4×D17—82no—
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#2342D1711yescharacteristic, complemented
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#2321—171no—
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—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—88no—
800C22×C17C24×C411yescharacteristic
801C22×C17C2×H(5,𝔽2)11yescharacteristic
802C22×C17C2×H(5,𝔽2)11yescharacteristic
803C22×C17C2×H(5,𝔽2)11yescharacteristic
804C22×C17#58511yescharacteristic
805C22×C17#58511yescharacteristic
806C22×C17#58511yescharacteristic
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—22no—
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—22no—
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—88no—
828C2×D17#51814yes—
829C4×C17—22no—
830C4×C17—22no—
831C4×C17—22no—
832C4×C17—22no—
833C4×C17—22no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841Dic17—22no—
842Dic17—22no—
843Dic17—22no—
844Dic17—22no—
845Dic17—22no—
846Dic17—41no—
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×#120—171no—
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×D4—171no—
874C2×#117—171no—
875C2×#117C2×D1711yescharacteristic, complemented
876C22×C4⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C22⋊C4—171no—
879C22×C22⋊C4—171no—
880C22×C22⋊C4—171no—
881C22×C22⋊C4C2×D1711yescharacteristic
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#390—171no—
895#390—171no—
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
929#388C2×D1711yescharacteristic
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#386—171no—
960#386—171no—
961#386—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385C2×D1711yescharacteristic, complemented
969#385C2×D1711yescharacteristic, complemented
970#383—171no—
971#381—171no—
972#381—171no—
973#381—171no—
974#381—171no—
975#381C2×D1711yescharacteristic, complemented
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#380—171no—
981#380—171no—
982#380C2×D1711yescharacteristic, complemented
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⋊C4C2×D1711yescharacteristic, complemented
1003C4×C22⋊C4C2×D1711yescharacteristic, complemented
1004C4×C22⋊C4C2×D1711yescharacteristic, complemented
1005#376—171no—
1006#376—171no—
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×C17—42no—
1011C2×C17—42no—
1012C2×C17—42no—
1013C2×C17C2×#51811yescharacteristic
1014C2×C17#342811yescharacteristic
1015C2×C17C4×H(5,𝔽2)11yescharacteristic
1016C2×C17#353411yescharacteristic
1017C2×C17#354211yescharacteristic
1018C2×C17#354511yescharacteristic
1019C2×C17#356011yescharacteristic
1020D17—24no—
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—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—682no—
1040C22×D4—682no—
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×C4C22×D1711yescharacteristic
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#120—178no—
1066C4×D4—178no—
1067C4×D4—178no—
1068C4×D4—682no—
1069C4×D4—682no—
1070C4×D4—682no—
1071C4×D4—682no—
1072C4×D4—682no—
1073C4×D4—682no—
1074#117—42no—
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—682no—
1093C2×C4⋊C4C22×D1711yescharacteristic
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C4⋊C4C22×D1711yescharacteristic
1096C2×C4⋊C4C22×D1711yescharacteristic
1097C2×C22⋊C4—42no—
1098C2×C22⋊C4—171no—
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—178no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
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—171no—
1135C2×C22⋊C4—682no—
1136C2×C22⋊C4—682no—
1137C2×C22⋊C4—682no—
1138C2×C22⋊C4C4×D1718yescomplemented
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—682no—
1167C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1204#95C22×D1711yescharacteristic
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211C17#3449211yescharacteristic, complemented, Sylow
1212C24—41no—
1213C24—41no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—171no—
1219C24—171no—
1220C24—171no—
1221C24—174no—
1222C24—342no—
1223C24—342no—
1224C24—681no—
1225C24—681no—
1226C24—681no—
1227C24—681no—
1228C24C2×C4×D1714yes—
1229C24C23×D1711yescharacteristic
1230C24C23×D1711yescharacteristic
1231C24C23×D1711yescharacteristic
1232#41—6816no—
1233C2×Q8—174no—
1234C2×Q8—681no—
1235C2×Q8—681no—
1236C2×D4—174no—
1237C2×D4—174no—
1238C2×D4—174no—
1239C2×D4—174no—
1240C2×D4—174no—
1241C2×D4—174no—
1242C2×D4—174no—
1243C2×D4—174no—
1244C2×D4—174no—
1245C2×D4—342no—
1246C2×D4—342no—
1247C2×D4—342no—
1248C2×D4—342no—
1249C2×D4—342no—
1250C2×D4—342no—
1251C2×D4—681no—
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—681no—
1261C2×D4—681no—
1262C2×D4—681no—
1263C2×D4—6816no—
1264C22×C4—22no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—174no—
1280C22×C4—174no—
1281C22×C4—174no—
1282C22×C4—174no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—171no—
1287C22×C4—171no—
1288C22×C4—171no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—342no—
1292C22×C4—342no—
1293C22×C4—342no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—681no—
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×C4C2×C4×D1714yes—
1324C22×C4C2×C4×D1714yes—
1325C22×C4C23×D1711yescharacteristic
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—22no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—174no—
1342C4⋊C4—174no—
1343C4⋊C4—174no—
1344C4⋊C4—174no—
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—174no—
1368C22⋊C4—174no—
1369C22⋊C4—174no—
1370C22⋊C4—174no—
1371C22⋊C4—174no—
1372C22⋊C4—174no—
1373C22⋊C4—174no—
1374C22⋊C4—174no—
1375C22⋊C4—342no—
1376C22⋊C4—342no—
1377C22⋊C4—342no—
1378C22⋊C4—342no—
1379C22⋊C4—342no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
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⋊C4C2×C4×D1714yes—
1404C22⋊C4C2×C4×D1714yes—
1405C22⋊C4C2×C4×D1714yes—
1406C22⋊C4C2×C4×D1714yes—
1407C42—22no—
1408C42—41no—
1409C42—41no—
1410C42—41no—
1411C42—174no—
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—44no—
1443C23—44no—
1444C23—44no—
1445C23—82no—
1446C23—82no—
1447C23—82no—
1448C23—82no—
1449C23—172no—
1450C23—172no—
1451C23—172no—
1452C23—172no—
1453C23—172no—
1454C23—348no—
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—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—684no—
1472C23—684no—
1473C23—1362no—
1474C23—1362no—
1475C23—1362no—
1476C23—1362no—
1477C23C22×C4×D1712yes—
1478C23C22×C4×D1712yes—
1479C23C22×C4×D1712yes—
1480C23C24×D1711yescharacteristic
1481Q8—684no—
1482D4—348no—
1483D4—348no—
1484D4—348no—
1485D4—684no—
1486D4—684no—
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—21no—
1522C2×C4—44no—
1523C2×C4—44no—
1524C2×C4—82no—
1525C2×C4—82no—
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—684no—
1567C2×C4—684no—
1568C2×C4—684no—
1569C2×C4—684no—
1570C2×C4—684no—
1571C2×C4—1362no—
1572C2×C4—1362no—
1573C2×C4—1362no—
1574C2×C4—1362no—
1575C2×C4—1362no—
1576C2×C4—1362no—
1577C2×C4C22×C4×D1712yes—
1578C2×C4C22×C4×D1712yes—
1579C2×C4C22×C4×D1712yes—
1580C2×C4C22×C4×D1712yes—
1581C2×C4#1058769112yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—88no—
1604C22—174no—
1605C22—342no—
1606C22—342no—
1607C22—342no—
1608C22—342no—
1609C22—342no—
1610C22—342no—
1611C22—342no—
1612C22—342no—
1613C22—342no—
1614C22—342no—
1615C22—342no—
1616C22—342no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22—1368no—
1626C22C23×C4×D1711yescharacteristic
1627C22H(5,𝔽2)×D1711yescharacteristic
1628C22H(5,𝔽2)×D1711yescharacteristic
1629C22C2×#1058769111yescharacteristic
1630C22#1176364511yescharacteristic
1631C22#1176364511yescharacteristic
1632C22#1176364511yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—22no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—342no—
1646C4—342no—
1647C4—342no—
1648C4—342no—
1649C4—342no—
1650C4—681no—
1651C4—681no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C2—42no—
1659C2—42no—
1660C2—42no—
1661C2—344no—
1662C2—682no—
1663C2—682no—
1664C2D17×#51811yescharacteristic
1665C2#1454198511yescharacteristic
1666C2C4×#1058769111yescharacteristic
1667C2#1454296611yescharacteristic
1668C2#1454309811yescharacteristic
1669C2#1454313711yescharacteristic
1670C2#1454333111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2342C2
socle, cosocleC23×C17C25
prime radicalC2×#11763449C2
hypercenter#2342D17
hypocenterC17#34492
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #14531951C2semidirect
3. #14531940C2semidirect
4. #14531928C2semidirect
5. #14531923C2semidirect
6. #14531892C2semidirect
7. #14531835C2semidirect
8. #14531822C2semidirect
9. #14531779C2semidirect
10. #14531762C2semidirect
11. #14531721C2semidirect
12. #14531719C2semidirect
13. #14531632C2semidirect
14. #14531615C2semidirect
15. C22⋊C4×C22⋊D17C2semidirect
16. #14531592C2semidirect
17. #14531574C2semidirect
18. #14531546C2semidirect
19. #14531534C2semidirect
20. #14531481C2semidirect
21. #14531451C2semidirect
22. #14531446C2semidirect
23. #14531442C2semidirect
24. #14531425C2semidirect
25. #14531382C2semidirect
26. #14531373C2semidirect
27. #14531360C2semidirect
28. C4×#10587570C2semidirect
29. #14531221C2semidirect
30. D17×#388C2semidirect
31. C17×#2342C2semidirect
34. #11763449C4semidirect
44. C2×C4×D68C22semidirect
45. C2×C4×D68C22semidirect
46. C2×#10587579C22semidirect
50. C2×C4×C22⋊D17C22semidirect
52. C2×#10587578C22semidirect
53. C2×C4⋊C4×D17C22semidirect
58. C2×C42×D17C22semidirect
59. #11762715C22semidirect
60. #11762715C22semidirect
61. #11762713C22semidirect
62. #11762713C22semidirect
63. #11762710C22semidirect
68. #11762709C22semidirect
69. #11762709C22semidirect
70. #11762709C22semidirect
71. #11762706C22semidirect
72. #11762706C22semidirect
73. #11762705C22semidirect
74. #11762704C22semidirect
77. #11762703C22semidirect
78. #11762703C22semidirect
79. #11762703C22semidirect
84. #11762702C22semidirect
85. #11762702C22semidirect
86. #11762702C22semidirect
87. #11762702C22semidirect
88. #11762701C22semidirect
89. #11762701C22semidirect
90. #11762700C22semidirect
91. #11762700C22semidirect
92. #11762700C22semidirect
93. #11762699C22semidirect
94. #11762698C22semidirect
95. #11762698C22semidirect
98. #11762697C22semidirect
99. #11762697C22semidirect
100. #11762697C22semidirect
101. #11762696C22semidirect
102. #11762696C22semidirect
103. #11762694C22semidirect
104. #11762694C22semidirect
105. #11762693C22semidirect
106. #11762691C22semidirect
107. #11762691C22semidirect
108. #11762690C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
113. #11762688C22semidirect
114. #11762687C22semidirect
115. #11762687C22semidirect
116. #11762687C22semidirect
117. #11762687C22semidirect
130. #11762685C22semidirect
131. #11762685C22semidirect
132. #11762685C22semidirect
133. #11762683C22semidirect
134. #11762683C22semidirect
135. #11762682C22semidirect
136. #11762680C22semidirect
137. #11762680C22semidirect
138. #11762680C22semidirect
139. #11762676C22semidirect
140. #11762671C22semidirect
141. #11762671C22semidirect
144. #11762669C22semidirect
145. #11762669C22semidirect
146. #11762668C22semidirect
148. #11762666C22semidirect
149. #11762666C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
157. C4×#63227C22semidirect
158. C4×#63227C22semidirect
159. C4×#63227C22semidirect
160. C4×#63227C22semidirect
161. C4×C22⋊Dic17C22semidirect
162. C4×C22⋊Dic17C22semidirect
163. C4×C22⋊Dic17C22semidirect
164. #11762656C22semidirect
165. #11762656C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762655C22semidirect
169. #11762654C22semidirect
170. #95×D17C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
173. C2×C17×#117C22semidirect
180. C17×#385C22semidirect
181. C17×#385C22semidirect
182. C17×#381C22semidirect
183. C17×#380C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
196. C22×C22⋊D17C2×C4semidirect
207. C2×#63252C2×C4semidirect
228. C2×C22⋊C4×C17C2×C4semidirect
247. #10587639C2×C4semidirect
263. #10587616C2×C4semidirect
264. #10587615C2×C4semidirect
268. C4×C22⋊D17C2×C4semidirect
322. #10587571C2×C4semidirect
323. #10587570C2×C4semidirect
324. #10587570C2×C4semidirect
325. #10587569C2×C4semidirect
326. #10587568C2×C4semidirect
327. #10587567C2×C4semidirect
331. C22⋊C4×D17C2×C4semidirect
332. #10587564C2×C4semidirect
760. #2342D17semidirect
875. C2×#117C2×D17semidirect
968. #385C2×D17semidirect
969. #385C2×D17semidirect
975. #381C2×D17semidirect
982. #380C2×D17semidirect
1002. C4×C22⋊C4C2×D17semidirect
1003. C4×C22⋊C4C2×D17semidirect
1004. C4×C22⋊C4C2×D17semidirect
1138. C2×C22⋊C4C4×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×#117634492
#145319512
#145319402
#145319282
#145319232
#145318922
#145318352
#145318222
#145317792
#145317622
#145317212
#145317192
#145316322
#145316152
C22⋊C4×C22⋊D172
#145315922
#145315742
#145315462
#145315342
#145314812
#145314512
#145314462
#145314422
#145314252
#145313822
#145313732
#145313602
C4×#105875702
#145312212
D17×#3882
C17×#23422
#3449217