Finite Group Databasebeta

← #17199668

Subgroups — #17199668

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×#11763453C211yesmaximal, characteristic
2#14531952C211yesmaximal, characteristic, complemented
3#14531936C211yesmaximal, characteristic, complemented
4#14531927C211yesmaximal, characteristic, complemented
5#14531923C211yesmaximal, characteristic, complemented
6#14531893C211yesmaximal, characteristic, complemented
7#14531832C211yesmaximal, characteristic, complemented
8#14531825C211yesmaximal, characteristic, complemented
9#14531782C211yesmaximal, characteristic, complemented
10#14531763C211yesmaximal, characteristic, complemented
11#14531722C211yesmaximal, characteristic, complemented
12#14531721C211yesmaximal, characteristic, complemented
13#14531635C211yesmaximal, characteristic, complemented
14#14531629C211yesmaximal, characteristic, complemented
15#14531610C211yesmaximal, characteristic, complemented
16D4×C22⋊Dic17C211yesmaximal, characteristic, complemented
17#14531593C211yesmaximal, characteristic, complemented
18#14531575C211yesmaximal, characteristic, complemented
19#14531550C211yesmaximal, characteristic, complemented
20#14531537C211yesmaximal, characteristic, complemented
21#14531486C211yesmaximal, characteristic, complemented
22#14531458C211yesmaximal, characteristic, complemented
23#14531442C211yesmaximal, characteristic, complemented
24#14531439C211yesmaximal, characteristic, complemented
25#14531424C211yesmaximal, characteristic, complemented
26#14531380C211yesmaximal, characteristic, complemented
27#14531371C211yesmaximal, characteristic, complemented
28#14531294C211yesmaximal, characteristic, complemented
29#14531224C211yesmaximal, characteristic, complemented
30C2×#11762703C211yesmaximal, characteristic, complemented
31C17×#2308C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33#11763453C4116yescomplemented
34C2×#10587622C2211yescharacteristic
35C2×#10587621C2211yescharacteristic
36C2×#10587621C2211yescharacteristic
37C2×#10587610C2211yescharacteristic
38C2×#10587625C2211yescharacteristic
39C2×#10587625C2211yescharacteristic
40C2×#10587624C2211yescharacteristic
41C2×#10587639C2211yescharacteristic
42C2×#10587639C2211yescharacteristic
43C2×D4×Dic17C2211yescharacteristic
44C2×D4×Dic17C2211yescharacteristic
45C2×D4×Dic17C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic
47C2×C4×C22⋊D17C2211yescharacteristic, complemented
48C2×C4×C22⋊D17C2211yescharacteristic, complemented
49C2×#10587567C2211yescharacteristic, complemented
50C2×#10587567C2211yescharacteristic, complemented
51C2×#10587563C2211yescharacteristic, complemented
52C2×#10587563C2211yescharacteristic, complemented
53C22×#63225C2211yescharacteristic, complemented
54C22×C22⋊Dic17C2211yescharacteristic
55C22×C22⋊Dic17C2211yescharacteristic
56C22×C22⋊Dic17C2211yescharacteristic
57C22×C22⋊Dic17C2211yescharacteristic
58C22×C4×Dic17C2211yescharacteristic, complemented
59#11762713C2211yescharacteristic, complemented
60#11762713C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762712C2211yescharacteristic
64#11762712C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic, complemented
68#11762709C2211yescharacteristic, complemented
69#11762709C2211yescharacteristic, complemented
70#11762709C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762706C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic
82#11762703C2211yescharacteristic
83#11762703C2211yescharacteristic, complemented
84#11762703C2211yescharacteristic, complemented
85#11762703C2211yescharacteristic, complemented
86#11762703C2211yescharacteristic, complemented
87#11762703C2211yescharacteristic, complemented
88#11762703C2211yescharacteristic, complemented
89#11762703C2211yescharacteristic, complemented
90#11762703C2211yescharacteristic, complemented
91#11762701C2211yescharacteristic, complemented
92#11762701C2211yescharacteristic, complemented
93#11762697C2211yescharacteristic
94#11762697C2211yescharacteristic
95#11762697C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic, complemented
98#11762697C2211yescharacteristic, complemented
99#11762697C2211yescharacteristic, complemented
100#11762697C2211yescharacteristic, complemented
101#11762697C2211yescharacteristic, complemented
102#11762697C2211yescharacteristic, complemented
103#11762697C2211yescharacteristic, complemented
104#11762697C2211yescharacteristic, complemented
105#11762696C2211yescharacteristic, complemented
106#11762696C2211yescharacteristic, complemented
107#11762694C2211yescharacteristic, complemented
108#11762694C2211yescharacteristic, complemented
109#11762692C2211yescharacteristic, complemented
110#11762692C2211yescharacteristic, complemented
111#11762691C2211yescharacteristic, complemented
112#11762691C2211yescharacteristic, complemented
113#11762691C2211yescharacteristic, complemented
114#11762691C2211yescharacteristic, complemented
115#11762689C2211yescharacteristic
116#11762689C2211yescharacteristic
117#11762689C2211yescharacteristic
118#11762689C2211yescharacteristic
119#11762688C2211yescharacteristic, complemented
120#11762688C2211yescharacteristic, complemented
121#11762686C2211yescharacteristic, complemented
122#11762686C2211yescharacteristic, complemented
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic, complemented
126#11762685C2211yescharacteristic, complemented
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762682C2211yescharacteristic, complemented
130#11762682C2211yescharacteristic, complemented
131#11762682C2211yescharacteristic, complemented
132#11762682C2211yescharacteristic, complemented
133#11762681C2211yescharacteristic, complemented
134#11762681C2211yescharacteristic, complemented
135#11762681C2211yescharacteristic, complemented
136#11762681C2211yescharacteristic, complemented
137#11762676C2211yescharacteristic, complemented
138#11762671C2211yescharacteristic, complemented
139#11762670C2211yescharacteristic, complemented
140#11762670C2211yescharacteristic, complemented
141#11762669C2211yescharacteristic
142#11762668C2211yescharacteristic, complemented
143#11762668C2211yescharacteristic, complemented
144#11762667C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic, complemented
148#11762665C2211yescharacteristic
149#11762665C2211yescharacteristic
150#11762660C2211yescharacteristic, complemented
151#11762660C2211yescharacteristic, complemented
152#11762660C2211yescharacteristic, complemented
153C22⋊C4×Dic17C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic, complemented
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×C22⋊Dic17C2211yescharacteristic
162C4×C22⋊Dic17C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762654C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C23×D4×C17C2211yescharacteristic
174C22×C22⋊C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#386C2211yescharacteristic
177C17×#386C2211yescharacteristic
178C17×#386C2211yescharacteristic
179C17×#386C2211yescharacteristic
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#381C2211yescharacteristic
185C17×#381C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C17×#379C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C25×C17C2311yescharacteristic
190C22×D4×C17—42no—
191C22×D4×C17—42no—
192C22×D4×C17C2×C418yescomplemented
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C2×#63254—42no—
216C2×#63254—42no—
217C2×#63254C2×C418yescomplemented
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C2×C22⋊C4×C17—42no—
223C2×C22⋊C4×C17—42no—
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
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
240#10587639C2×C418yescomplemented
241#10587639C2×C418yescomplemented
242C2×C22⋊Dic17—42no—
243C2×C22⋊Dic17—42no—
244C2×C22⋊Dic17C2×C418yescomplemented
245C2×C22⋊Dic17C2×C418yescomplemented
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
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
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273#10587625C2×C418yescomplemented
274#10587625C2×C418yescomplemented
275#10587624C2×C418yescomplemented
276#10587622C2×C418yescomplemented
277#10587621C2×C418yescomplemented
278#10587621C2×C418yescomplemented
279D4×Dic17—42no—
280D4×Dic17—42no—
281D4×Dic17C2×C418yescomplemented
282C4×C22⋊D17—42no—
283C4×C22⋊D17—42no—
284C4×C22⋊D17C2×C418yescomplemented
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295#10587610C2×C418yescomplemented
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×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×C4×Dic17—42no—
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
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332#10587567—42no—
333#10587567—42no—
334#10587563—42no—
335#10587563—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—22no—
377C24×C17—22no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17—41no—
383C24×C17—41no—
384C24×C17—41no—
385C24×C17—41no—
386C24×C17—41no—
387C24×C17—41no—
388C24×C17C22×C414yes—
389C24×C17C22×C414yes—
390C24×C17C2411yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C24×C17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C2×D4×C17—22no—
397C2×D4×C17—22no—
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—416no—
405C2×D4×C17C22×C414yes—
406C2×D4×C17C22×C414yes—
407C2×D4×C17C22×C414yes—
408C2×D4×C17C22×C414yes—
409C22×C4×C17—22no—
410C22×C4×C17—22no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17—41no—
423C22×C4×C17C22×C414yes—
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17C22×C414yes—
445C2×C22⋊D17C22×C414yes—
446C2×C22⋊D17C22×C414yes—
447C2×C22⋊D17C22×C414yes—
448C2×C22⋊D17C22×C414yes—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—22no—
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×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17C22×C414yes—
470C22×Dic17C22×C414yes—
471C22×Dic17C22×C414yes—
472C22×Dic17C22×C414yes—
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488#63254—416no—
489C2×C4×D17—22no—
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×D17—41no—
497C2×C4×D17C22×C414yes—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C2×Dic34C22×C414yes—
501C22⋊C4×C17—22no—
502C22⋊C4×C17—22no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
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⋊Dic17—22no—
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—22no—
522C22⋊Dic17—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⋊Dic17C22×C414yes—
534C22⋊Dic17C22×C414yes—
535C22⋊Dic17C22×C414yes—
536C22⋊Dic17C22×C414yes—
537C22⋊Dic17C22×C414yes—
538C22⋊Dic17C22×C414yes—
539C22⋊Dic17C22×C414yes—
540C22⋊Dic17C22×C414yes—
541C22⋊Dic17C22×C414yes—
542C22⋊Dic17C22×C414yes—
543C22⋊Dic17C22×C414yes—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227C22×C414yes—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17C22×C414yes—
554#63225—22no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225C22×C414yes—
569#63225C22×C414yes—
570#63225C22×C414yes—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
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—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—28no—
618C23×C17—44no—
619C23×C17—44no—
620C23×C17—44no—
621C23×C17—44no—
622C23×C17—44no—
623C23×C17—82no—
624C23×C17—82no—
625C23×C17—82no—
626C23×C17—82no—
627C23×C17—82no—
628C23×C17—82no—
629C23×C17—82no—
630C23×C17—82no—
631C23×C17C23×C412yes—
632C23×C17C23×C412yes—
633C23×C17C23×C412yes—
634C23×C17C23×C412yes—
635C23×C17C23×C412yes—
636C23×C17H(5,𝔽2)12yes—
637C23×C17H(5,𝔽2)12yes—
638C23×C17C2511yescharacteristic
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17C23×C412yes—
646D4×C17—28no—
647D4×C17—28no—
648D4×C17—44no—
649D4×C17—44no—
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—44no—
679C2×C4×C17—44no—
680C2×C4×C17—82no—
681C2×C4×C17—82no—
682C2×C4×C17—82no—
683C2×C4×C17C23×C412yes—
684C2×C4×C17C23×C412yes—
685C22⋊D17—28no—
686C22⋊D17—44no—
687C22⋊D17—44no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C2×Dic17—28no—
691C2×Dic17—21no—
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—21no—
728C2×Dic17—44no—
729C2×Dic17—44no—
730C2×Dic17—44no—
731C2×Dic17—44no—
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×Dic17C23×C412yes—
742C2×Dic17H(5,𝔽2)12yes—
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#2321—171no—
771#2319—171no—
772#2312—171no—
773#2311—171no—
774#2308D1711yescharacteristic, complemented
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—22no—
794C22×C17—22no—
795C22×C17—22no—
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—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—88no—
813C22×C17—88no—
814C22×C17#51814yes—
815C22×C17C24×C411yescharacteristic
816C22×C17C2×H(5,𝔽2)11yescharacteristic
817C22×C17C2×H(5,𝔽2)11yescharacteristic
818C22×C17C2×H(5,𝔽2)11yescharacteristic
819C22×C17#58511yescharacteristic
820C22×C17#58511yescharacteristic
821C22×C17#58511yescharacteristic
822C2×D17—22no—
823C2×D17—22no—
824C2×D17—22no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C4×C17—22no—
830C4×C17—22no—
831C4×C17—41no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839Dic17—22no—
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×D4C2×D1711yescharacteristic
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×#117—171no—
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#388—171no—
927#388—171no—
928#388—171no—
929#388—171no—
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#386C2×D1711yescharacteristic
955#386C2×D1711yescharacteristic
956#386C2×D1711yescharacteristic
957#386C2×D1711yescharacteristic
958#386C2×D1711yescharacteristic
959#386C2×D1711yescharacteristic
960#386C2×D1711yescharacteristic
961#386C2×D1711yescharacteristic
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#385—171no—
970#383—171no—
971#381—171no—
972#381—171no—
973#381—171no—
974#381C2×D1711yescharacteristic
975#381C2×D1711yescharacteristic
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#379C2×D1711yescharacteristic
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⋊C4—171no—
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×C17—42no—
1015C2×C17C2×#51811yescharacteristic
1016C2×C17#342811yescharacteristic
1017C2×C17C4×H(5,𝔽2)11yescharacteristic
1018C2×C17#353411yescharacteristic
1019C2×C17#354211yescharacteristic
1020C2×C17#354511yescharacteristic
1021C2×C17#356011yescharacteristic
1022D17—42no—
1023C25C22×D1711yescharacteristic
1024C25C22×D1711yescharacteristic
1025C2×#41—178no—
1026C2×#41—682no—
1027C2×#41—682no—
1028C22×Q8—171no—
1029C22×D4—42no—
1030C22×D4—42no—
1031C22×D4—171no—
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4C4×D1718yescomplemented
1037C22×D4C22×D1711yescharacteristic
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×C4C22×D1711yescharacteristic
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—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—171no—
1094C2×C4⋊C4—171no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—682no—
1097C2×C22⋊C4—42no—
1098C2×C22⋊C4—42no—
1099C2×C22⋊C4—178no—
1100C2×C22⋊C4—178no—
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—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⋊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—171no—
1168C2×C42—171no—
1169C2×C42—171no—
1170C2×C42—682no—
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—22no—
1213C24—22no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—41no—
1219C24—41no—
1220C24—41no—
1221C24—41no—
1222C24—41no—
1223C24—41no—
1224C24—171no—
1225C24C2×C4×D1714yes—
1226C24C2×C4×D1714yes—
1227C24C23×D1711yescharacteristic
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—22no—
1239C2×D4—22no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—416no—
1245C2×D4—174no—
1246C2×D4—174no—
1247C2×D4—174no—
1248C2×D4—174no—
1249C2×D4—174no—
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×D4C2×C4×D1714yes—
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—41no—
1274C22×C4—41no—
1275C22×C4—41no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—174no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—171no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—171no—
1287C22×C4—174no—
1288C22×C4—174no—
1289C22×C4—174no—
1290C22×C4—174no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
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×C4C2×C4×D1714yes—
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—174no—
1338C4⋊C4—174no—
1339C4⋊C4—174no—
1340C4⋊C4—174no—
1341C4⋊C4—342no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4—681no—
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—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—174no—
1374C22⋊C4—174no—
1375C22⋊C4—174no—
1376C22⋊C4—174no—
1377C22⋊C4—174no—
1378C22⋊C4—174no—
1379C22⋊C4—174no—
1380C22⋊C4—174no—
1381C22⋊C4—174no—
1382C22⋊C4—174no—
1383C22⋊C4—174no—
1384C22⋊C4—174no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—342no—
1389C22⋊C4—342no—
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⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C42—174no—
1408C42—342no—
1409C42—342no—
1410C42—681no—
1411C42—681no—
1412C42—681no—
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—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—28no—
1453C23—44no—
1454C23—44no—
1455C23—44no—
1456C23—44no—
1457C23—44no—
1458C23—82no—
1459C23—82no—
1460C23—82no—
1461C23—82no—
1462C23—82no—
1463C23—82no—
1464C23—82no—
1465C23—82no—
1466C23—172no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23C22×C4×D1712yes—
1474C23C22×C4×D1712yes—
1475C23C22×C4×D1712yes—
1476C23C22×C4×D1712yes—
1477C23C22×C4×D1712yes—
1478C23#1058769112yes—
1479C23#1058769112yes—
1480C23C24×D1711yescharacteristic
1481Q8—684no—
1482D4—28no—
1483D4—28no—
1484D4—44no—
1485D4—44no—
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—44no—
1520C2×C4—44no—
1521C2×C4—82no—
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—172no—
1532C2×C4—348no—
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—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—684no—
1571C2×C4—684no—
1572C2×C4—684no—
1573C2×C4—684no—
1574C2×C4—684no—
1575C2×C4—1362no—
1576C2×C4—1362no—
1577C2×C4—1362no—
1578C2×C4—1362no—
1579C2×C4—1362no—
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—22no—
1598C22—22no—
1599C22—22no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—88no—
1617C22—88no—
1618C22—342no—
1619C22—342no—
1620C22—342no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22#1176328214yes—
1626C22C23×C4×D1711yescharacteristic
1627C22H(5,𝔽2)×D1711yescharacteristic
1628C22C2×#1058769111yescharacteristic
1629C22C2×#1058769111yescharacteristic
1630C22#1176364411yescharacteristic
1631C22#1176364411yescharacteristic
1632C22#1176364411yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—342no—
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—42no—
1663C2—682no—
1664C2C2×#1176328211yescharacteristic
1665C2#1454198211yescharacteristic
1666C2#1454198811yescharacteristic
1667C2#1454297111yescharacteristic
1668C2#1454309511yescharacteristic
1669C2#1454313311yescharacteristic
1670C2#1454332611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2308C2
socle, cosocleC23×C17C25
prime radicalC2×#11763453C2
hypercenter#2308D17
hypocenterC17#34492
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. #14531952C2semidirect
3. #14531936C2semidirect
4. #14531927C2semidirect
5. #14531923C2semidirect
6. #14531893C2semidirect
7. #14531832C2semidirect
8. #14531825C2semidirect
9. #14531782C2semidirect
10. #14531763C2semidirect
11. #14531722C2semidirect
12. #14531721C2semidirect
13. #14531635C2semidirect
14. #14531629C2semidirect
15. #14531610C2semidirect
16. D4×C22⋊Dic17C2semidirect
17. #14531593C2semidirect
18. #14531575C2semidirect
19. #14531550C2semidirect
20. #14531537C2semidirect
21. #14531486C2semidirect
22. #14531458C2semidirect
23. #14531442C2semidirect
24. #14531439C2semidirect
25. #14531424C2semidirect
26. #14531380C2semidirect
27. #14531371C2semidirect
28. #14531294C2semidirect
29. #14531224C2semidirect
30. C2×#11762703C2semidirect
31. C17×#2308C2semidirect
33. #11763453C4semidirect
47. C2×C4×C22⋊D17C22semidirect
48. C2×C4×C22⋊D17C22semidirect
49. C2×#10587567C22semidirect
50. C2×#10587567C22semidirect
51. C2×#10587563C22semidirect
52. C2×#10587563C22semidirect
53. C22×#63225C22semidirect
58. C22×C4×Dic17C22semidirect
59. #11762713C22semidirect
60. #11762713C22semidirect
61. #11762713C22semidirect
62. #11762713C22semidirect
67. #11762709C22semidirect
68. #11762709C22semidirect
69. #11762709C22semidirect
70. #11762709C22semidirect
71. #11762706C22semidirect
72. #11762706C22semidirect
73. #11762706C22semidirect
74. #11762706C22semidirect
83. #11762703C22semidirect
84. #11762703C22semidirect
85. #11762703C22semidirect
86. #11762703C22semidirect
87. #11762703C22semidirect
88. #11762703C22semidirect
89. #11762703C22semidirect
90. #11762703C22semidirect
91. #11762701C22semidirect
92. #11762701C22semidirect
97. #11762697C22semidirect
98. #11762697C22semidirect
99. #11762697C22semidirect
100. #11762697C22semidirect
101. #11762697C22semidirect
102. #11762697C22semidirect
103. #11762697C22semidirect
104. #11762697C22semidirect
105. #11762696C22semidirect
106. #11762696C22semidirect
107. #11762694C22semidirect
108. #11762694C22semidirect
109. #11762692C22semidirect
110. #11762692C22semidirect
111. #11762691C22semidirect
112. #11762691C22semidirect
113. #11762691C22semidirect
114. #11762691C22semidirect
119. #11762688C22semidirect
120. #11762688C22semidirect
121. #11762686C22semidirect
122. #11762686C22semidirect
125. #11762685C22semidirect
126. #11762685C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
129. #11762682C22semidirect
130. #11762682C22semidirect
131. #11762682C22semidirect
132. #11762682C22semidirect
133. #11762681C22semidirect
134. #11762681C22semidirect
135. #11762681C22semidirect
136. #11762681C22semidirect
137. #11762676C22semidirect
138. #11762671C22semidirect
139. #11762670C22semidirect
140. #11762670C22semidirect
142. #11762668C22semidirect
143. #11762668C22semidirect
144. #11762667C22semidirect
145. #11762667C22semidirect
146. #11762667C22semidirect
147. #11762667C22semidirect
150. #11762660C22semidirect
151. #11762660C22semidirect
152. #11762660C22semidirect
153. C22⋊C4×Dic17C22semidirect
154. C22⋊C4×Dic17C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
162. C4×C22⋊Dic17C22semidirect
163. C4×C22⋊Dic17C22semidirect
164. C4×C22⋊Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762654C22semidirect
169. #11762654C22semidirect
170. C2×#10587502C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
192. C22×D4×C17C2×C4semidirect
217. C2×#63254C2×C4semidirect
240. #10587639C2×C4semidirect
241. #10587639C2×C4semidirect
244. C2×C22⋊Dic17C2×C4semidirect
245. C2×C22⋊Dic17C2×C4semidirect
273. #10587625C2×C4semidirect
274. #10587625C2×C4semidirect
275. #10587624C2×C4semidirect
276. #10587622C2×C4semidirect
277. #10587621C2×C4semidirect
278. #10587621C2×C4semidirect
281. D4×Dic17C2×C4semidirect
284. C4×C22⋊D17C2×C4semidirect
295. #10587610C2×C4semidirect
774. #2308D17semidirect
1036. C22×D4C4×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×#117634532
#145319522
#145319362
#145319272
#145319232
#145318932
#145318322
#145318252
#145317822
#145317632
#145317222
#145317212
#145316352
#145316292
#145316102
D4×C22⋊Dic172
#145315932
#145315752
#145315502
#145315372
#145314862
#145314582
#145314422
#145314392
#145314242
#145313802
#145313712
#145312942
#145312242
C2×#117627032
C17×#23082
#3449217