Finite Group Databasebeta

← #17241861

Subgroups — #17241861

Order 4352.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763432C211yesmaximal, characteristic, complemented
2C2×#11763395C211yesmaximal, characteristic, complemented
3#14537111C211yesmaximal, characteristic, complemented
4#14537084C211yesmaximal, characteristic, complemented
5#14535697C211yesmaximal, characteristic, complemented
6#14535608C211yesmaximal, characteristic, complemented
7#14535600C211yesmaximal, characteristic, complemented
8#14535557C211yesmaximal, characteristic, complemented
9#14535377C211yesmaximal, characteristic, complemented
10#14535357C211yesmaximal, characteristic, complemented
11#14535265C211yesmaximal, characteristic, complemented
12#14535221C211yesmaximal, characteristic, complemented
13#14535195C211yesmaximal, characteristic, complemented
14#14535170C211yesmaximal, characteristic, complemented
15#14535167C211yesmaximal, characteristic, complemented
16#14535089C211yesmaximal, characteristic, complemented
17#14535065C211yesmaximal, characteristic, complemented
18#14535009C211yesmaximal, characteristic, complemented
19#14534989C211yesmaximal, characteristic, complemented
20#14534941C211yesmaximal, characteristic, complemented
21#14534915C211yesmaximal, characteristic, complemented
22#14534467C211yesmaximal, characteristic, complemented
23#14534417C211yesmaximal, characteristic, complemented
24#14534392C211yesmaximal, characteristic, complemented
25#14534377C211yesmaximal, characteristic, complemented
26#14534266C211yesmaximal, characteristic, complemented
27#14533936C211yesmaximal, characteristic, complemented
28#14532215C211yesmaximal, characteristic, complemented
29#14532162C211yesmaximal, characteristic, complemented
30#14531222C211yesmaximal, characteristic, complemented
31C17×#2696C211yesmaximal, characteristic, complemented
32#11763432—28no—
33#11763395—28no—
34C2×#10587574C2211yescharacteristic, complemented
35C2×#10587584C2211yescharacteristic
36C2×#10587584C2211yescharacteristic
37C2×#10587584C2211yescharacteristic, complemented
38C2×#10587565C2211yescharacteristic
39C2×#10587633C2211yescharacteristic
40C2×#10587622C2211yescharacteristic
41C2×#10587571C2211yescharacteristic
42C2×#10587571C2211yescharacteristic
43C2×#10587571C2211yescharacteristic
44C2×#10587571C2211yescharacteristic, complemented
45C2×#10587580C2211yescharacteristic
46C2×#10587569C2211yescharacteristic
47C2×#10587569C2211yescharacteristic, complemented
48C2×#10587583C2211yescharacteristic
49C2×#10587583C2211yescharacteristic
50C2×#10587583C2211yescharacteristic, complemented
51C2×#10587610C2211yescharacteristic, complemented
52C2×#10587616C2211yescharacteristic
53C2×#10587616C2211yescharacteristic
54C2×#10587570C2211yescharacteristic
55C2×#10587570C2211yescharacteristic
56C2×#10587624C2211yescharacteristic
57C2×#10587568C2211yescharacteristic
58C2×#10587623C2211yescharacteristic
59C2×#10587623C2211yescharacteristic
60C2×Q8×Dic17C2211yescharacteristic, complemented
61C2×#10587579C2211yescharacteristic
62C2×C4×C22⋊D17C2211yescharacteristic
63C2×#10587612C2211yescharacteristic, complemented
64C2×#10587578C2211yescharacteristic
65C2×C22⋊C4×D17C2211yescharacteristic
66C2×C42×D17C2211yescharacteristic, complemented
67#11762749C2211yescharacteristic, complemented
68#11762745C2211yescharacteristic
69#11762744C2211yescharacteristic
70#11762741C2211yescharacteristic, complemented
71#11762741C2211yescharacteristic, complemented
72#11762738C2211yescharacteristic
73#11762738C2211yescharacteristic
74#11762738C2211yescharacteristic, complemented
75#11762738C2211yescharacteristic, complemented
76#11762736C2211yescharacteristic
77#11762736C2211yescharacteristic
78#11762735C2211yescharacteristic
79#11762734C2211yescharacteristic, complemented
80#11762734C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic
82#11762732C2211yescharacteristic
83#11762732C2211yescharacteristic, complemented
84#11762731C2211yescharacteristic
85#11762730C2211yescharacteristic, complemented
86#11762729C2211yescharacteristic, complemented
87#11762728C2211yescharacteristic, complemented
88#11762727C2211yescharacteristic
89#11762727C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic
92#11762725C2211yescharacteristic
93#11762725C2211yescharacteristic, complemented
94#11762724C2211yescharacteristic
95#11762724C2211yescharacteristic
96#11762724C2211yescharacteristic
97#11762724C2211yescharacteristic
98#11762723C2211yescharacteristic
99#11762723C2211yescharacteristic
100#11762722C2211yescharacteristic
101#11762722C2211yescharacteristic
102#11762721C2211yescharacteristic
103#11762721C2211yescharacteristic, complemented
104#11762720C2211yescharacteristic
105#11762717C2211yescharacteristic
106#11762717C2211yescharacteristic
107#11762717C2211yescharacteristic
108#11762717C2211yescharacteristic, complemented
109#11762715C2211yescharacteristic, complemented
110#11762714C2211yescharacteristic, complemented
111#11762713C2211yescharacteristic, complemented
112#11762713C2211yescharacteristic, complemented
113#11762712C2211yescharacteristic
114#11762712C2211yescharacteristic, complemented
115#11762709C2211yescharacteristic
116#11762709C2211yescharacteristic
117#11762709C2211yescharacteristic
118#11762709C2211yescharacteristic
119#11762706C2211yescharacteristic, complemented
120#11762706C2211yescharacteristic, complemented
121#11762706C2211yescharacteristic, complemented
122#11762705C2211yescharacteristic, complemented
123#11762704C2211yescharacteristic, complemented
124#11762703C2211yescharacteristic
125#11762703C2211yescharacteristic
126#11762702C2211yescharacteristic
127#11762702C2211yescharacteristic
128#11762702C2211yescharacteristic
129#11762702C2211yescharacteristic, complemented
130#11762702C2211yescharacteristic, complemented
131#11762702C2211yescharacteristic, complemented
132#11762701C2211yescharacteristic
133#11762701C2211yescharacteristic
134#11762701C2211yescharacteristic
135#11762701C2211yescharacteristic
136#11762700C2211yescharacteristic
137#11762700C2211yescharacteristic
138#11762698C2211yescharacteristic
139#11762697C2211yescharacteristic
140#11762697C2211yescharacteristic, complemented
141#11762697C2211yescharacteristic, complemented
142#11762697C2211yescharacteristic, complemented
143#11762696C2211yescharacteristic, complemented
144#11762696C2211yescharacteristic, complemented
145#11762695C2211yescharacteristic, complemented
146#11762694C2211yescharacteristic, complemented
147#11762694C2211yescharacteristic, complemented
148#11762688C2211yescharacteristic
149#11762687C2211yescharacteristic
150#11762687C2211yescharacteristic
151#11762687C2211yescharacteristic
152#11762685C2211yescharacteristic
153#11762685C2211yescharacteristic
154#11762685C2211yescharacteristic
155#11762685C2211yescharacteristic, complemented
156#11762685C2211yescharacteristic, complemented
157#11762685C2211yescharacteristic, complemented
158#11762683C2211yescharacteristic
159#11762683C2211yescharacteristic, complemented
160#11762682C2211yescharacteristic, complemented
161#11762682C2211yescharacteristic, complemented
162#11762680C2211yescharacteristic, complemented
163#11762674C2211yescharacteristic, complemented
164#11762671C2211yescharacteristic
165#11762671C2211yescharacteristic
166#11762668C2211yescharacteristic, complemented
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762660C2211yescharacteristic, complemented
171#11762656C2211yescharacteristic
172#11762656C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic
175C2×C17×C22⋊Q8C2211yescharacteristic, complemented
176C17×#400C2211yescharacteristic, complemented
177C17×#397C2211yescharacteristic
178C17×#394C2211yescharacteristic
179C17×#393C2211yescharacteristic
180C17×#393C2211yescharacteristic, complemented
181C17×#392C2211yescharacteristic
182C17×#390C2211yescharacteristic
183C17×#388C2211yescharacteristic, complemented
184C17×#387C2211yescharacteristic, complemented
185C17×#386C2211yescharacteristic
186C17×#386C2211yescharacteristic, complemented
187C17×#386C2211yescharacteristic, complemented
188C17×#380C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×Dic34C2311yescharacteristic
211C22×Dic34C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×#123—24no—
214C17×C22⋊Q8—24no—
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250#10587633—24no—
251Q8×Dic17—24no—
252#10587624—24no—
253#10587623—24no—
254#10587623—42no—
255#10587622—42no—
256#10587616—24no—
257#10587616—24no—
258C4×C22⋊D17—24no—
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
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
286#10587612—24no—
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297#10587610—42no—
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×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
321#10587584—24no—
322#10587584—24no—
323#10587584—24no—
324#10587583—24no—
325#10587583—24no—
326#10587583—24no—
327#10587580—24no—
328#10587579D418yescomplemented
329#10587578—42no—
330#10587574—24no—
331#10587571—24no—
332#10587571—24no—
333#10587571—24no—
334#10587571—24no—
335#10587570—24no—
336#10587570—42no—
337#10587569—24no—
338#10587569—24no—
339#10587568—24no—
340C22⋊C4×D17—24no—
341#10587565—24no—
342C42×D17—42no—
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
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
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C24×C17C2411yescharacteristic
382C23×D17—22no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17C2411yescharacteristic
390C23×D17C2411yescharacteristic
391C23×D17C2411yescharacteristic
392C2×Q8×C17—22no—
393C2×Q8×C17—41no—
394C2×Q8×C17—41no—
395C2×D4×C17—22no—
396C2×D4×C17—41no—
397C2×D4×C17—41no—
398C2×D4×C17—41no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C22×C4×C17—22no—
405C22×C4×C17—22no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
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
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
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—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C2×D68—22no—
457C2×D68—41no—
458C2×D68—41no—
459C2×D68—41no—
460C2×D68—41no—
461C2×D68C2×D414yes—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17C2×D414yes—
476C2×C4×D17C2×D414yes—
477C2×Dic34—22no—
478C2×Dic34—22no—
479C2×Dic34—22no—
480C2×Dic34—41no—
481C2×Dic34—41no—
482C2×Dic34—41no—
483C2×Dic34—41no—
484C2×Dic34—41no—
485C2×Dic34—41no—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—22no—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—41no—
490C4⋊C4×C17C2×D414yes—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—22no—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—22no—
495C22⋊C4×C17—22no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C42×C17—41no—
505C22⋊Dic17—22no—
506C22⋊Dic17—22no—
507C22⋊Dic17—22no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227C2×D414yes—
547#63227C2×D414yes—
548C4⋊Dic17—22no—
549C4⋊Dic17—22no—
550C4⋊Dic17—22no—
551C4⋊Dic17—22no—
552C4⋊Dic17—22no—
553C4⋊Dic17—22no—
554C4⋊Dic17—22no—
555C4⋊Dic17—22no—
556C4⋊Dic17—41no—
557C4⋊Dic17—41no—
558#63225—22no—
559#63225—22no—
560#63225—22no—
561#63225—22no—
562#63225—22no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570#63225—41no—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—22no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17C2×D414yes—
581#36745—171nomaximal, Sylow
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
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×C17C2511yescharacteristic
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—44no—
624C22×D17—82no—
625C22×D17—82no—
626C22×D17—82no—
627C22×D17—82no—
628C22×D17—82no—
629C22×D17—82no—
630C22×D17C22×D412yes—
631C22×D17C22×D412yes—
632Q8×C17—44no—
633D4×C17—82no—
634D4×C17—82no—
635D4×C17—82no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
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—44no—
670C2×C4×C17—82no—
671C2×C4×C17C22×D412yes—
672C2×C4×C17C22×D412yes—
673C2×C4×C17C22×D412yes—
674C22⋊D17—44no—
675C22⋊D17—82no—
676C22⋊D17—82no—
677C22⋊D17—82no—
678C22⋊D17—82no—
679C22⋊D17—82no—
680C22⋊D17—82no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
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×Dic17C22×D412yes—
718C2×Dic17C22×D412yes—
719C2×Dic17H(5,𝔽2)12yes—
720D68—44no—
721D68—82no—
722C4×D17—44no—
723C4×D17—44no—
724C4×D17—44no—
725C4×D17—44no—
726C4×D17—82no—
727Dic34—82no—
728Dic34—82no—
729Dic34—82no—
730C2×#542—171no—
731C2×#538—171no—
732#2854—171no—
733#2850—171no—
734#2723—171no—
735#2716—171no—
736#2715—171no—
737#2712—171no—
738#2700—171no—
739#2698—171no—
740#2696D1711yescharacteristic, complemented
741#2691—171no—
742#2688—171no—
743#2686—171no—
744#2685—171no—
745#2684—171no—
746#2676—171no—
747#2674—171no—
748#2670—171no—
749#2668—171no—
750#2663—171no—
751#2661—171no—
752#2610—171no—
753#2604—171no—
754#2602—171no—
755#2601—171no—
756#2592—171no—
757#2561—171no—
758#2415—171no—
759#2411—171no—
760#2290—171no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17C23×D411yescharacteristic
783C22×C17C2×H(5,𝔽2)11yescharacteristic
784C22×C17#58511yescharacteristic
785C22×C17#58511yescharacteristic
786C22×C17#58511yescharacteristic
787C22×C17#58511yescharacteristic
788C22×C17#58511yescharacteristic
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—88no—
811C4×C17—22no—
812C4×C17—22no—
813C4×C17—22no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821C4×C17—41no—
822C4×C17—41no—
823Dic17—22no—
824Dic17—22no—
825Dic17—22no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836#542—348no—
837#538—348no—
838C2×C4⋊Q8—171no—
839C2×#126—171no—
840C2×#126—171no—
841C2×#126—171no—
842C2×#126—171no—
843C2×#124—171no—
844C2×#124—171no—
845C2×#124—171no—
846C2×#124—171no—
847C2×#124—171no—
848C2×#124—171no—
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—171no—
852C2×#123C2×D1711yescharacteristic
853C2×C22⋊Q8—171no—
854C2×C22⋊Q8—171no—
855C2×C22⋊Q8—171no—
856C2×C22⋊Q8—171no—
857C2×C22⋊Q8C2×D1711yescharacteristic, complemented
858C2×#121—171no—
859C2×#121—171no—
860C2×#121—171no—
861C2×#121—171no—
862C2×#121—171no—
863C2×#120—171no—
864C2×#120—171no—
865C2×#120—171no—
866C2×C4×Q8—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×#117—171no—
870C2×#117—171no—
871C22×C22⋊C4—171no—
872C22×C42—171no—
873#400—171no—
874#400C2×D1711yescharacteristic, complemented
875#399—171no—
876#399—171no—
877#398—171no—
878#398—171no—
879#397—171no—
880#397—171no—
881#397—171no—
882#397—171no—
883#397—171no—
884#397—171no—
885#397—171no—
886#397—171no—
887#397—171no—
888#397C2×D1711yescharacteristic
889#396—171no—
890#396—171no—
891#396—171no—
892#396—171no—
893#395—171no—
894#395—171no—
895#395—171no—
896#394—171no—
897#394—171no—
898#394—171no—
899#394—171no—
900#394—171no—
901#394—171no—
902#394—171no—
903#394—171no—
904#394—171no—
905#394—171no—
906#394—171no—
907#394—171no—
908#394C2×D1711yescharacteristic
909#393—171no—
910#393—171no—
911#393—171no—
912#393—171no—
913#393—171no—
914#393C2×D1711yescharacteristic
915#393C2×D1711yescharacteristic, complemented
916#392—171no—
917#392—171no—
918#392—171no—
919#392—171no—
920#392C2×D1711yescharacteristic
921#391—171no—
922#391—171no—
923#391—171no—
924#391—171no—
925#390—171no—
926#390—171no—
927#390—171no—
928#390—171no—
929#390—171no—
930#390—171no—
931#390C2×D1711yescharacteristic
932#389—171no—
933#389—171no—
934#389—171no—
935#389—171no—
936#389—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388C2×D1711yescharacteristic, complemented
957#387—171no—
958#387—171no—
959#387—171no—
960#387—171no—
961#387—171no—
962#387C2×D1711yescharacteristic, complemented
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386C2×D1711yescharacteristic
974#386C2×D1711yescharacteristic, complemented
975#386C2×D1711yescharacteristic, complemented
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385—171no—
981#382—171no—
982#381—171no—
983#381—171no—
984#380—171no—
985#380C2×D1711yescharacteristic, complemented
986#379—171no—
987#379—171no—
988#379—171no—
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992#376—171no—
993C2×C17—81no—
994C2×C17—81no—
995C2×C17—81no—
996C2×C17#344911yescharacteristic
997C2×C17#349611yescharacteristic
998C2×C17#350011yescharacteristic
999C2×C17#353311yescharacteristic
1000C2×C17#354011yescharacteristic
1001C2×C17#356611yescharacteristic
1002C2×C17#356811yescharacteristic
1003D17—42no—
1004D17—42no—
1005D17—81no—
1006C25—171no—
1007C22×Q8—171no—
1008C22×Q8—171no—
1009C22×Q8—171no—
1010C22×Q8C22×D1711yescharacteristic
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—171no—
1017C22×D4—171no—
1018C22×D4—171no—
1019C22×D4—171no—
1020C22×D4C22×D1711yescharacteristic
1021C22×D4C22×D1711yescharacteristic
1022C22×D4C22×D1711yescharacteristic
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—171no—
1028C23×C4C22×D1711yescharacteristic
1029C23×C4C22×D1711yescharacteristic
1030C4⋊Q8—344no—
1031#126—344no—
1032#126—344no—
1033#126—344no—
1034#126—344no—
1035#124—344no—
1036#124—344no—
1037#124—344no—
1038#124—344no—
1039#124—344no—
1040#124—682no—
1041#123—24no—
1042#123—344no—
1043#123—344no—
1044#123—344no—
1045C22⋊Q8—24no—
1046C22⋊Q8—344no—
1047C22⋊Q8—344no—
1048C22⋊Q8—344no—
1049C22⋊Q8—682no—
1050#121—344no—
1051#121—344no—
1052#121—344no—
1053#121—344no—
1054#121—682no—
1055#120—344no—
1056#120—344no—
1057#120—682no—
1058C4×Q8—344no—
1059C4×D4—178no—
1060C4×D4—344no—
1061#117—344no—
1062#117—682no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1087C2×C4⋊C4C22×D1711yescharacteristic
1088C2×C4⋊C4C22×D1711yescharacteristic
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
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—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—344no—
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
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×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—682no—
1159C2×C42C22×D1711yescharacteristic
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
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#95C22×D1711yescharacteristic
1187#95C22×D1711yescharacteristic
1188#95C22×D1711yescharacteristic
1189#95C22×D1711yescharacteristic
1190#95C22×D1711yescharacteristic
1191#95C22×D1711yescharacteristic
1192#95C22×D1711yescharacteristic
1193#95C22×D1711yescharacteristic
1194#95C22×D1711yescharacteristic
1195#95C22×D1711yescharacteristic
1196C17#3674511yescharacteristic, complemented, Sylow
1197C24—171no—
1198C24—171no—
1199C24—171no—
1200C24—342no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24—681no—
1205C24—681no—
1206C24—681no—
1207C24C23×D1711yescharacteristic
1208C24C23×D1711yescharacteristic
1209C24C23×D1711yescharacteristic
1210C2×Q8—22no—
1211C2×Q8—41no—
1212C2×Q8—41no—
1213C2×Q8—342no—
1214C2×Q8—342no—
1215C2×Q8—342no—
1216C2×Q8—681no—
1217C2×Q8—681no—
1218C2×Q8—681no—
1219C2×Q8—681no—
1220C2×Q8—681no—
1221C2×Q8—681no—
1222C2×D4—22no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—174no—
1232C2×D4—342no—
1233C2×D4—342no—
1234C2×D4—342no—
1235C2×D4—342no—
1236C2×D4—342no—
1237C2×D4—342no—
1238C2×D4—342no—
1239C2×D4—342no—
1240C2×D4—681no—
1241C2×D4—681no—
1242C2×D4—681no—
1243C2×D4—681no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—681no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4—681no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—174no—
1268C22×C4—174no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—41no—
1308C4⋊C4—342no—
1309C4⋊C4—342no—
1310C4⋊C4—342no—
1311C4⋊C4—342no—
1312C4⋊C4—342no—
1313C4⋊C4—342no—
1314C4⋊C4—342no—
1315C4⋊C4—342no—
1316C4⋊C4—342no—
1317C4⋊C4—342no—
1318C4⋊C4—342no—
1319C4⋊C4—342no—
1320C4⋊C4—342no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4D4×D1714yes—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—174no—
1346C22⋊C4—174no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—342no—
1357C22⋊C4—342no—
1358C22⋊C4—342no—
1359C22⋊C4—342no—
1360C22⋊C4—342no—
1361C22⋊C4—342no—
1362C22⋊C4—342no—
1363C22⋊C4—342no—
1364C22⋊C4—342no—
1365C22⋊C4—342no—
1366C22⋊C4—342no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C42—41no—
1389C42—174no—
1390C42—342no—
1391C42—342no—
1392C42—342no—
1393C42—342no—
1394C42—342no—
1395C42—342no—
1396C42—681no—
1397C42—681no—
1398C42—681no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—172no—
1421C23—172no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23—341no—
1432C23—341no—
1433C23—341no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—341no—
1440C23—341no—
1441C23—684no—
1442C23—1362no—
1443C23—1362no—
1444C23—1362no—
1445C23—1362no—
1446C23—1362no—
1447C23—1362no—
1448C23C24×D1711yescharacteristic
1449Q8—44no—
1450Q8—1362no—
1451Q8—1362no—
1452Q8—1362no—
1453D4—82no—
1454D4—82no—
1455D4—82no—
1456D4—684no—
1457D4—684no—
1458D4—1362no—
1459D4—1362no—
1460D4—1362no—
1461D4—1362no—
1462D4—1362no—
1463D4—1362no—
1464D4—1362no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—44no—
1499C2×C4—82no—
1500C2×C4—172no—
1501C2×C4—172no—
1502C2×C4—172no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—684no—
1540C2×C4—684no—
1541C2×C4—684no—
1542C2×C4—684no—
1543C2×C4—1362no—
1544C2×C4C2×D4×D1712yes—
1545C2×C4C2×D4×D1712yes—
1546C2×C4C2×D4×D1712yes—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—342no—
1569C22—342no—
1570C22—342no—
1571C22—342no—
1572C22—342no—
1573C22—342no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22—681no—
1582C22—681no—
1583C22—681no—
1584C22—681no—
1585C22—681no—
1586C22—681no—
1587C22—681no—
1588C22—681no—
1589C22—1368no—
1590C22C22×D4×D1711yescharacteristic
1591C22H(5,𝔽2)×D1711yescharacteristic
1592C22#1176364411yescharacteristic
1593C22#1176364411yescharacteristic
1594C22#1176364511yescharacteristic
1595C22#1176364511yescharacteristic
1596C22#1176364611yescharacteristic
1597C4—22no—
1598C4—22no—
1599C4—22no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—342no—
1610C4—342no—
1611C4—342no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C4—681no—
1621C4—681no—
1622C2—81no—
1623C2—81no—
1624C2—81no—
1625C2—682no—
1626C2—682no—
1627C2—1361no—
1628C2#1454211511yescharacteristic
1629C2#1454254411yescharacteristic
1630C2#1454257511yescharacteristic
1631C2#1454294611yescharacteristic
1632C2#1454305511yescharacteristic
1633C2#1454346311yescharacteristic
1634C2#1454347511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2696C2
hypercenter#2696D17
hypocenterC17#36745
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2696

Complements

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

NH ≅ G/Ntype
1. C2×#11763432C2semidirect
2. C2×#11763395C2semidirect
3. #14537111C2semidirect
4. #14537084C2semidirect
5. #14535697C2semidirect
6. #14535608C2semidirect
7. #14535600C2semidirect
8. #14535557C2semidirect
9. #14535377C2semidirect
10. #14535357C2semidirect
11. #14535265C2semidirect
12. #14535221C2semidirect
13. #14535195C2semidirect
14. #14535170C2semidirect
15. #14535167C2semidirect
16. #14535089C2semidirect
17. #14535065C2semidirect
18. #14535009C2semidirect
19. #14534989C2semidirect
20. #14534941C2semidirect
21. #14534915C2semidirect
22. #14534467C2semidirect
23. #14534417C2semidirect
24. #14534392C2semidirect
25. #14534377C2semidirect
26. #14534266C2semidirect
27. #14533936C2semidirect
28. #14532215C2semidirect
29. #14532162C2semidirect
30. #14531222C2semidirect
31. C17×#2696C2semidirect
34. C2×#10587574C22semidirect
37. C2×#10587584C22semidirect
44. C2×#10587571C22semidirect
47. C2×#10587569C22semidirect
50. C2×#10587583C22semidirect
51. C2×#10587610C22semidirect
60. C2×Q8×Dic17C22semidirect
63. C2×#10587612C22semidirect
66. C2×C42×D17C22semidirect
67. #11762749C22semidirect
70. #11762741C22semidirect
71. #11762741C22semidirect
74. #11762738C22semidirect
75. #11762738C22semidirect
79. #11762734C22semidirect
80. #11762734C22semidirect
83. #11762732C22semidirect
85. #11762730C22semidirect
86. #11762729C22semidirect
87. #11762728C22semidirect
93. #11762725C22semidirect
103. #11762721C22semidirect
108. #11762717C22semidirect
109. #11762715C22semidirect
110. #11762714C22semidirect
111. #11762713C22semidirect
112. #11762713C22semidirect
114. #11762712C22semidirect
119. #11762706C22semidirect
120. #11762706C22semidirect
121. #11762706C22semidirect
122. #11762705C22semidirect
123. #11762704C22semidirect
129. #11762702C22semidirect
130. #11762702C22semidirect
131. #11762702C22semidirect
140. #11762697C22semidirect
141. #11762697C22semidirect
142. #11762697C22semidirect
143. #11762696C22semidirect
144. #11762696C22semidirect
145. #11762695C22semidirect
146. #11762694C22semidirect
147. #11762694C22semidirect
155. #11762685C22semidirect
156. #11762685C22semidirect
157. #11762685C22semidirect
159. #11762683C22semidirect
160. #11762682C22semidirect
161. #11762682C22semidirect
162. #11762680C22semidirect
163. #11762674C22semidirect
166. #11762668C22semidirect
170. #11762660C22semidirect
172. #11762656C22semidirect
173. #11762654C22semidirect
175. C2×C17×C22⋊Q8C22semidirect
176. C17×#400C22semidirect
180. C17×#393C22semidirect
183. C17×#388C22semidirect
184. C17×#387C22semidirect
186. C17×#386C22semidirect
187. C17×#386C22semidirect
188. C17×#380C22semidirect
328. #10587579D4semidirect
740. #2696D17semidirect
857. C2×C22⋊Q8C2×D17semidirect
874. #400C2×D17semidirect
915. #393C2×D17semidirect
956. #388C2×D17semidirect
962. #387C2×D17semidirect
974. #386C2×D17semidirect
975. #386C2×D17semidirect
985. #380C2×D17semidirect
1196. C17#36745semidirect

Maximal subgroups

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

subgroupindex
C2×#117634322
C2×#117633952
#145371112
#145370842
#145356972
#145356082
#145356002
#145355572
#145353772
#145353572
#145352652
#145352212
#145351952
#145351702
#145351672
#145350892
#145350652
#145350092
#145349892
#145349412
#145349152
#145344672
#145344172
#145343922
#145343772
#145342662
#145339362
#145322152
#145321622
#145312222
C17×#26962
#3674517