Finite Group Databasebeta

← #17242187

Subgroups — #17242187

Order 4352.

2210 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537068C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14536644C211yesmaximal, characteristic, complemented
4#14536445C211yesmaximal, characteristic, complemented
5#14536416C211yesmaximal, characteristic, complemented
6#14536404C211yesmaximal, characteristic, complemented
7#14536401C211yesmaximal, characteristic, complemented
8#14536110C211yesmaximal, characteristic, complemented
9#14536066C211yesmaximal, characteristic, complemented
10#14536005C211yesmaximal, characteristic, complemented
11#14535902C211yesmaximal, characteristic, complemented
12#14535777C211yesmaximal, characteristic, complemented
13#14535577C211yesmaximal, characteristic, complemented
14#14535433C211yesmaximal, characteristic, complemented
15#14535419C211yesmaximal, characteristic, complemented
16#14535339C211yesmaximal, characteristic, complemented
17#14535222C211yesmaximal, characteristic, complemented
18#14535080C211yesmaximal, characteristic, complemented
19#14534499C211yesmaximal, characteristic, complemented
20#14534498C211yesmaximal, characteristic, complemented
21#14533163C211yesmaximal, characteristic, complemented
22#14533116C211yesmaximal, characteristic, complemented
23#14533029C211yesmaximal, characteristic, complemented
24#14532337C211yesmaximal, characteristic, complemented
25#14532324C211yesmaximal, characteristic, complemented
26#14532259C211yesmaximal, characteristic, complemented
27#14532246C211yesmaximal, characteristic, complemented
28#14531447C211yesmaximal, characteristic, complemented
29#14531444C211yesmaximal, characteristic, complemented
30C2×#11762685C211yesmaximal, characteristic, complemented
31C17×#2472C211yesmaximal, characteristic, complemented
32C23×C22⋊D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587565C2211yescharacteristic, complemented
35C2×#10587572C2211yescharacteristic
36C2×#10587569C2211yescharacteristic, complemented
37C2×#10587621C2211yescharacteristic
38C2×#10587632C2211yescharacteristic, complemented
39C2×#10587632C2211yescharacteristic, complemented
40C2×#10587570C2211yescharacteristic, complemented
41C2×#10587570C2211yescharacteristic, complemented
42C2×#10587625C2211yescharacteristic
43C2×#10587625C2211yescharacteristic, complemented
44C2×#10587568C2211yescharacteristic
45C2×#10587639C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C22×C22⋊Dic17C2211yescharacteristic
50C22×#63227C2211yescharacteristic
51C17⋊#401C2211yescharacteristic, complemented
52#11762750C2211yescharacteristic, complemented
53#11762750C2211yescharacteristic, complemented
54#11762750C2211yescharacteristic, complemented
55#11762749C2211yescharacteristic, complemented
56#11762748C2211yescharacteristic, complemented
57#11762748C2211yescharacteristic, complemented
58#11762745C2211yescharacteristic, complemented
59#11762743C2211yescharacteristic, complemented
60#11762741C2211yescharacteristic, complemented
61#11762738C2211yescharacteristic, complemented
62#11762737C2211yescharacteristic, complemented
63#11762737C2211yescharacteristic, complemented
64#11762737C2211yescharacteristic, complemented
65#11762735C2211yescharacteristic, complemented
66#11762734C2211yescharacteristic, complemented
67#11762734C2211yescharacteristic, complemented
68#11762734C2211yescharacteristic, complemented
69#11762732C2211yescharacteristic, complemented
70#11762732C2211yescharacteristic, complemented
71#11762732C2211yescharacteristic, complemented
72#11762725C2211yescharacteristic
73#11762725C2211yescharacteristic
74#11762725C2211yescharacteristic
75#11762725C2211yescharacteristic
76#11762725C2211yescharacteristic, complemented
77#11762725C2211yescharacteristic, complemented
78#11762724C2211yescharacteristic
79#11762724C2211yescharacteristic
80#11762724C2211yescharacteristic
81#11762724C2211yescharacteristic
82#11762724C2211yescharacteristic, complemented
83#11762724C2211yescharacteristic, complemented
84#11762723C2211yescharacteristic, complemented
85#11762720C2211yescharacteristic, complemented
86#11762718C2211yescharacteristic
87#11762718C2211yescharacteristic
88#11762718C2211yescharacteristic
89#11762718C2211yescharacteristic
90#11762717C2211yescharacteristic
91#11762717C2211yescharacteristic
92#11762717C2211yescharacteristic
93#11762717C2211yescharacteristic
94#11762717C2211yescharacteristic, complemented
95#11762716C2211yescharacteristic, complemented
96#11762711C2211yescharacteristic, complemented
97#11762711C2211yescharacteristic, complemented
98#11762709C2211yescharacteristic, complemented
99#11762709C2211yescharacteristic, complemented
100#11762709C2211yescharacteristic, complemented
101#11762706C2211yescharacteristic, complemented
102#11762703C2211yescharacteristic, complemented
103#11762703C2211yescharacteristic, complemented
104#11762703C2211yescharacteristic, complemented
105#11762702C2211yescharacteristic, complemented
106#11762702C2211yescharacteristic, complemented
107#11762702C2211yescharacteristic, complemented
108#11762701C2211yescharacteristic, complemented
109#11762701C2211yescharacteristic, complemented
110#11762701C2211yescharacteristic, complemented
111#11762701C2211yescharacteristic, complemented
112#11762700C2211yescharacteristic, complemented
113#11762700C2211yescharacteristic, complemented
114#11762699C2211yescharacteristic, complemented
115#11762699C2211yescharacteristic, complemented
116#11762698C2211yescharacteristic, complemented
117#11762698C2211yescharacteristic, complemented
118#11762697C2211yescharacteristic, complemented
119#11762694C2211yescharacteristic, complemented
120#11762694C2211yescharacteristic, complemented
121#11762693C2211yescharacteristic, complemented
122#11762693C2211yescharacteristic, complemented
123#11762693C2211yescharacteristic, complemented
124#11762689C2211yescharacteristic, complemented
125#11762688C2211yescharacteristic
126#11762687C2211yescharacteristic, complemented
127#11762687C2211yescharacteristic, complemented
128#11762687C2211yescharacteristic, complemented
129#11762687C2211yescharacteristic, complemented
130#11762686C2211yescharacteristic
131#11762686C2211yescharacteristic, complemented
132#11762686C2211yescharacteristic, complemented
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762685C2211yescharacteristic
139#11762685C2211yescharacteristic
140#11762685C2211yescharacteristic
141#11762685C2211yescharacteristic, complemented
142#11762685C2211yescharacteristic, complemented
143#11762685C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic, complemented
145#11762684C2211yescharacteristic
146#11762684C2211yescharacteristic, complemented
147#11762682C2211yescharacteristic
148#11762681C2211yescharacteristic
149#11762681C2211yescharacteristic
150#11762680C2211yescharacteristic, complemented
151#11762680C2211yescharacteristic, complemented
152#11762680C2211yescharacteristic, complemented
153#11762680C2211yescharacteristic, complemented
154#11762677C2211yescharacteristic, complemented
155#11762674C2211yescharacteristic, complemented
156#11762670C2211yescharacteristic
157#11762670C2211yescharacteristic
158#11762670C2211yescharacteristic, complemented
159#11762669C2211yescharacteristic
160#11762668C2211yescharacteristic, complemented
161#11762668C2211yescharacteristic, complemented
162#11762668C2211yescharacteristic, complemented
163#11762667C2211yescharacteristic
164#11762666C2211yescharacteristic, complemented
165#11762666C2211yescharacteristic, complemented
166#11762665C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169C22⋊C4×Dic17C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C2×C17×#124C2211yescharacteristic, complemented
173C2×C17×C22⋊Q8C2211yescharacteristic
174C2×C17×#120C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#397C2211yescharacteristic, complemented
177C17×#394C2211yescharacteristic, complemented
178C17×#394C2211yescharacteristic, complemented
179C17×#393C2211yescharacteristic, complemented
180C17×#390C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#388C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#379C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C25×C17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17—24no—
196C22×C22⋊D17—42no—
197C22×C22⋊D17—42no—
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C22×D68C2311yescharacteristic
213C22×D68C2311yescharacteristic
214C22×C4×D17—42no—
215C22×C4×D17—42no—
216C22×C4×D17—42no—
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C17×#124—42no—
223C17×C22⋊Q8—42no—
224C17×#120—42no—
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17—42no—
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248#10587639—42no—
249C2×C22⋊Dic17—42no—
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
267#10587632—42no—
268#10587632—42no—
269#10587625—42no—
270#10587625—42no—
271#10587623—24no—
272#10587621—42no—
273D4×Dic17—42no—
274C4×C22⋊D17—42no—
275C2×#63227—42no—
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323#10587572—42no—
324#10587570—42no—
325#10587570—42no—
326#10587569—42no—
327#10587568—24no—
328#10587565—42no—
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17—22no—
370C24×C17—22no—
371C24×C17—22no—
372C24×C17—41no—
373C24×C17—41no—
374C24×C17—41no—
375C24×C17—41no—
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C24×C17C2411yescharacteristic
380C23×D17—22no—
381C23×D17—22no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17#4114yes—
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C23×D17C2411yescharacteristic
390C2×Q8×C17—22no—
391C2×Q8×C17—41no—
392C2×Q8×C17—41no—
393C2×D4×C17—22no—
394C2×D4×C17—22no—
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—
402C22×C4×C17—22no—
403C22×C4×C17—22no—
404C22×C4×C17—22no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
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
419C2×C22⋊D17—22no—
420C2×C22⋊D17—22no—
421C2×C22⋊D17—22no—
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—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—416no—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—22no—
455C22×Dic17—22no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C2×D68—22no—
476C2×D68—22no—
477C2×D68—41no—
478C2×D68—41no—
479C2×D68—41no—
480C2×D68—41no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
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—416no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C4⋊C4×C17—41no—
498C4⋊C4×C17—41no—
499C4⋊C4×C17—41no—
500C22⋊C4×C17—22no—
501C22⋊C4×C17—22no—
502C22⋊C4×C17—22no—
503C22⋊C4×C17—22no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—41no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17—41no—
510C22⋊C4×C17—41no—
511C22⋊C4×C17—41no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C42×C17—41no—
518C42×C17—41no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—22no—
522C22⋊Dic17—22no—
523C22⋊Dic17—22no—
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⋊Dic17—41no—
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
540#63227—22no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560C4⋊Dic17—22no—
561C4⋊Dic17—41no—
562C4⋊Dic17—41no—
563C4⋊Dic17—41no—
564C4⋊Dic17—41no—
565C4⋊Dic17—41no—
566C4⋊Dic17—41no—
567#63225—22no—
568#63225—22no—
569#63225—22no—
570#63225—41no—
571#63225—41no—
572#63225—41no—
573#63225—41no—
574#63225—41no—
575#63225—41no—
576#63225—41no—
577#63225—41no—
578#63225—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583#36758—171nomaximal, Sylow
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×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—44no—
610C23×C17—44no—
611C23×C17—44no—
612C23×C17—82no—
613C23×C17—82no—
614C23×C17—82no—
615C23×C17—82no—
616C23×C17C2×#4112yes—
617C23×C17H(5,𝔽2)12yes—
618C23×C17H(5,𝔽2)12yes—
619C23×C17C2511yescharacteristic
620C22×D17—28no—
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—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17—44no—
645C22×D17—44no—
646C22×D17C2×#4112yes—
647C22×D17C2×#4112yes—
648Q8×C17—82no—
649D4×C17—44no—
650D4×C17—82no—
651D4×C17—82no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—44no—
685C2×C4×C17—82no—
686C2×C4×C17H(5,𝔽2)12yes—
687C22⋊D17—44no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—82no—
693C22⋊D17—82no—
694C22⋊D17—82no—
695C22⋊D17—82no—
696C22⋊D17—82no—
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—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—44no—
736C2×Dic17—44no—
737C2×Dic17—82no—
738C2×Dic17—82no—
739C2×Dic17H(5,𝔽2)12yes—
740D68—82no—
741D68—82no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—44no—
745C4×D17—44no—
746C4×D17—82no—
747#2848—171no—
748#2847—171no—
749#2797—171no—
750#2781—171no—
751#2779—171no—
752#2778—171no—
753#2778—171no—
754#2756—171no—
755#2753—171no—
756#2749—171no—
757#2741—171no—
758#2730—171no—
759#2714—171no—
760#2703—171no—
761#2702—171no—
762#2696—171no—
763#2688—171no—
764#2676—171no—
765#2613—171no—
766#2613—171no—
767#2493—171no—
768#2488—171no—
769#2480—171no—
770#2472D1711yescharacteristic, complemented
771#2425—171no—
772#2424—171no—
773#2419—171no—
774#2418—171no—
775#2321—171no—
776#2321—171no—
777C2×#386—171no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
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—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—88no—
806C22×C17#53814yes—
807C22×C17C22×#4111yescharacteristic
808C22×C17C2×H(5,𝔽2)11yescharacteristic
809C22×C17C2×H(5,𝔽2)11yescharacteristic
810C22×C17C2×H(5,𝔽2)11yescharacteristic
811C22×C17C2×H(5,𝔽2)11yescharacteristic
812C22×C17#58511yescharacteristic
813C22×C17#58511yescharacteristic
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—22no—
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—416no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C2×D17—41no—
832C2×D17—41no—
833C2×D17—41no—
834C2×D17—41no—
835C2×D17—41no—
836C4×C17—22no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17—41no—
845C4×C17—41no—
846C4×C17—41no—
847Dic17—22no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856Dic17—41no—
857Dic17—41no—
858Dic17—41no—
859Dic17—41no—
860C23×D4—171no—
861C24×C4—171no—
862C2×#126—171no—
863C2×#124C2×D1711yescharacteristic, complemented
864C2×#123—171no—
865C2×#123—171no—
866C2×#123—171no—
867C2×C22⋊Q8—171no—
868C2×C22⋊Q8—171no—
869C2×C22⋊Q8C2×D1711yescharacteristic
870C2×#121—171no—
871C2×#121—171no—
872C2×#121—171no—
873C2×#121—171no—
874C2×#120—171no—
875C2×#120—171no—
876C2×#120—171no—
877C2×#120C2×D1711yescharacteristic
878C2×C4×D4—171no—
879C2×C4×D4—171no—
880C22×C22⋊C4—171no—
881C22×C22⋊C4—171no—
882C22×C22⋊C4C2×D1711yescharacteristic
883#401—171no—
884#400—171no—
885#400—171no—
886#400—171no—
887#400—171no—
888#400—171no—
889#400—171no—
890#399—171no—
891#398—171no—
892#398—171no—
893#397—171no—
894#397—171no—
895#397—171no—
896#397—171no—
897#397—171no—
898#397—171no—
899#397—171no—
900#397—171no—
901#397C2×D1711yescharacteristic, complemented
902#396—171no—
903#396—171no—
904#396—171no—
905#394—171no—
906#394—171no—
907#394—171no—
908#394—171no—
909#394—171no—
910#394—171no—
911#394—171no—
912#394—171no—
913#394—171no—
914#394—171no—
915#394—171no—
916#394—171no—
917#394—171no—
918#394C2×D1711yescharacteristic, complemented
919#394C2×D1711yescharacteristic, complemented
920#393—171no—
921#393C2×D1711yescharacteristic, complemented
922#392—171no—
923#392—171no—
924#392—171no—
925#392—171no—
926#392—171no—
927#392—171no—
928#392—171no—
929#392—171no—
930#392—171no—
931#391—171no—
932#390—171no—
933#390—171no—
934#390—171no—
935#390—171no—
936#390—171no—
937#390C2×D1711yescharacteristic, complemented
938#389—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#388C2×D1711yescharacteristic, complemented
958#387—171no—
959#387—171no—
960#387—171no—
961#387—171no—
962#387—171no—
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#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386C2×D1711yescharacteristic
985#386C2×D1711yescharacteristic
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#383—171no—
996#382—171no—
997#381—171no—
998#381—171no—
999#381—171no—
1000#380—171no—
1001#380—171no—
1002#380—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#379—171no—
1008#379—171no—
1009#379—171no—
1010#379C2×D1711yescharacteristic
1011C4×C22⋊C4—171no—
1012C4×C22⋊C4C2×D1711yescharacteristic
1013C2×#95—171no—
1014C2×#95—171no—
1015C2×C17—24no—
1016C2×C17—81no—
1017C2×C17—81no—
1018C2×C17—81no—
1019C2×C17C2×#53811yescharacteristic
1020C2×C17#350511yescharacteristic
1021C2×C17#350511yescharacteristic
1022C2×C17#353211yescharacteristic
1023C2×C17#353311yescharacteristic
1024C2×C17#354211yescharacteristic
1025C2×C17#354211yescharacteristic
1026D17—42no—
1027D17—42no—
1028D17—81no—
1029C25—171no—
1030C25C22×D1711yescharacteristic
1031C22×Q8C22×D1711yescharacteristic
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—344no—
1045C22×D4—682no—
1046C22×D4—682no—
1047C22×D4C22×D1711yescharacteristic
1048C22×D4C22×D1711yescharacteristic
1049C22×D4C22×D1711yescharacteristic
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—171no—
1059C23×C4—682no—
1060C23×C4—682no—
1061C23×C4—682no—
1062C23×C4C22×D1711yescharacteristic
1063C23×C4C22×D1711yescharacteristic
1064#126—682no—
1065#124—42no—
1066#123—682no—
1067#123—682no—
1068#123—682no—
1069C22⋊Q8—42no—
1070C22⋊Q8—682no—
1071C22⋊Q8—682no—
1072#121—682no—
1073#121—682no—
1074#121—682no—
1075#121—682no—
1076#120—42no—
1077#120—344no—
1078#120—344no—
1079#120—682no—
1080C4×D4—682no—
1081C4×D4—682no—
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—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4C22×D1711yescharacteristic
1102C2×C4⋊C4C22×D1711yescharacteristic
1103C2×C4⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4—42no—
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—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—682no—
1147C2×C22⋊C4—682no—
1148C2×C22⋊C4C22×D1711yescharacteristic
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4C22×D1711yescharacteristic
1154C2×C22⋊C4C22×D1711yescharacteristic
1155C2×C22⋊C4C22×D1711yescharacteristic
1156C2×C22⋊C4C22×D1711yescharacteristic
1157C2×C22⋊C4C22×D1711yescharacteristic
1158C2×C22⋊C4C22×D1711yescharacteristic
1159C2×C22⋊C4C22×D1711yescharacteristic
1160C2×C22⋊C4C22×D1711yescharacteristic
1161C2×C22⋊C4C22×D1711yescharacteristic
1162C2×C22⋊C4C22×D1711yescharacteristic
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C42—171no—
1166C2×C42—171no—
1167C2×C42—171no—
1168C2×C42—171no—
1169C2×C42C22×D1711yescharacteristic
1170C2×C42C22×D1711yescharacteristic
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211C17#3675811yescharacteristic, complemented, Sylow
1212C24—22no—
1213C24—22no—
1214C24—22no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—41no—
1219C24—171no—
1220C24—171no—
1221C24—174no—
1222C24—171no—
1223C24—342no—
1224C24—342no—
1225C24—681no—
1226C24—681no—
1227C24—681no—
1228C24—681no—
1229C24C23×D1711yescharacteristic
1230C24C23×D1711yescharacteristic
1231C24C23×D1711yescharacteristic
1232C24C23×D1711yescharacteristic
1233C2×Q8—22no—
1234C2×Q8—41no—
1235C2×Q8—41no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—342no—
1246C2×D4—342no—
1247C2×D4—342no—
1248C2×D4—342no—
1249C2×D4—342no—
1250C2×D4—342no—
1251C2×D4—342no—
1252C2×D4—342no—
1253C2×D4—342no—
1254C2×D4—342no—
1255C2×D4—342no—
1256C2×D4—342no—
1257C2×D4—681no—
1258C2×D4—681no—
1259C2×D4—681no—
1260C2×D4—681no—
1261C2×D4—681no—
1262C2×D4—681no—
1263C2×D4—681no—
1264C2×D4—681no—
1265C2×D4—681no—
1266C2×D4—681no—
1267C2×D4—681no—
1268C2×D4—681no—
1269C2×D4—681no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—6816no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—171no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
1305C22×C4—342no—
1306C22×C4—342no—
1307C22×C4—342no—
1308C22×C4—342no—
1309C22×C4—342no—
1310C22×C4—342no—
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—6816no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—342no—
1344C4⋊C4—342no—
1345C4⋊C4—342no—
1346C4⋊C4—342no—
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—
1357C4⋊C4—681no—
1358C4⋊C4—681no—
1359C4⋊C4—681no—
1360C4⋊C4—681no—
1361C4⋊C4—681no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—342no—
1380C22⋊C4—342no—
1381C22⋊C4—342no—
1382C22⋊C4—342no—
1383C22⋊C4—342no—
1384C22⋊C4—342no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—342no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C22⋊C4—681no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C42—41no—
1421C42—41no—
1422C42—681no—
1423C42—681no—
1424C42—681no—
1425C42—681no—
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—44no—
1452C23—44no—
1453C23—44no—
1454C23—82no—
1455C23—82no—
1456C23—82no—
1457C23—82no—
1458C23—172no—
1459C23—172no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—348no—
1473C23—341no—
1474C23—341no—
1475C23—341no—
1476C23—341no—
1477C23—341no—
1478C23—341no—
1479C23—341no—
1480C23—684no—
1481C23—684no—
1482C23—684no—
1483C23—684no—
1484C23—684no—
1485C23—684no—
1486C23#1058769112yes—
1487C23#41×D1712yes—
1488C23#1058769612yes—
1489C23C24×D1711yescharacteristic
1490Q8—82no—
1491D4—44no—
1492D4—82no—
1493D4—82no—
1494D4—684no—
1495D4—684no—
1496D4—684no—
1497D4—684no—
1498D4—684no—
1499D4—1362no—
1500D4—1362no—
1501D4—1362no—
1502D4—1362no—
1503D4—1362no—
1504D4—1362no—
1505D4—1362no—
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—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—44no—
1539C2×C4—82no—
1540C2×C4—172no—
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—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—684no—
1580C2×C4—684no—
1581C2×C4—684no—
1582C2×C4—684no—
1583C2×C4—684no—
1584C2×C4—684no—
1585C2×C4—1362no—
1586C2×C4—1362no—
1587C2×C4—1362no—
1588C2×C4#1058769112yes—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—88no—
1617C22—342no—
1618C22—342no—
1619C22—342no—
1620C22—342no—
1621C22—342no—
1622C22—342no—
1623C22—6816no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22—681no—
1631C22—681no—
1632C22—681no—
1633C22—681no—
1634C22—681no—
1635C22—681no—
1636C22—681no—
1637C22—681no—
1638C22—681no—
1639C22#1176339314yes—
1640C22C2×#41×D1711yescharacteristic
1641C22H(5,𝔽2)×D1711yescharacteristic
1642C22C2×#1058769111yescharacteristic
1643C22C2×#1058769111yescharacteristic
1644C22C2×#1058769611yescharacteristic
1645C22#1176364411yescharacteristic
1646C22#1176364511yescharacteristic
1647C4—22no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—342no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C4—681no—
1663C4—681no—
1664C4—681no—
1665C4—681no—
1666C4—681no—
1667C4—681no—
1668C4—681no—
1669C4—681no—
1670C4—681no—
1671C2—24no—
1672C2—81no—
1673C2—81no—
1674C2—81no—
1675C2—682no—
1676C2—682no—
1677C2—1361no—
1678C2C2×#1176339311yescharacteristic
1679C2#1454261211yescharacteristic
1680C2#1454262211yescharacteristic
1681C2#1454293411yescharacteristic
1682C2#1454294311yescharacteristic
1683C2#1454308611yescharacteristic
1684C2#1454309311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2472C2
hypercenter#2472D17
hypocenterC17#36758
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2472

Complements

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

NH ≅ G/Ntype
1. #14537068C2semidirect
2. #14537065C2semidirect
3. #14536644C2semidirect
4. #14536445C2semidirect
5. #14536416C2semidirect
6. #14536404C2semidirect
7. #14536401C2semidirect
8. #14536110C2semidirect
9. #14536066C2semidirect
10. #14536005C2semidirect
11. #14535902C2semidirect
12. #14535777C2semidirect
13. #14535577C2semidirect
14. #14535433C2semidirect
15. #14535419C2semidirect
16. #14535339C2semidirect
17. #14535222C2semidirect
18. #14535080C2semidirect
19. #14534499C2semidirect
20. #14534498C2semidirect
21. #14533163C2semidirect
22. #14533116C2semidirect
23. #14533029C2semidirect
24. #14532337C2semidirect
25. #14532324C2semidirect
26. #14532259C2semidirect
27. #14532246C2semidirect
28. #14531447C2semidirect
29. #14531444C2semidirect
30. C2×#11762685C2semidirect
31. C17×#2472C2semidirect
34. C2×#10587565C22semidirect
36. C2×#10587569C22semidirect
38. C2×#10587632C22semidirect
39. C2×#10587632C22semidirect
40. C2×#10587570C22semidirect
41. C2×#10587570C22semidirect
43. C2×#10587625C22semidirect
51. C17⋊#401C22semidirect
52. #11762750C22semidirect
53. #11762750C22semidirect
54. #11762750C22semidirect
55. #11762749C22semidirect
56. #11762748C22semidirect
57. #11762748C22semidirect
58. #11762745C22semidirect
59. #11762743C22semidirect
60. #11762741C22semidirect
61. #11762738C22semidirect
62. #11762737C22semidirect
63. #11762737C22semidirect
64. #11762737C22semidirect
65. #11762735C22semidirect
66. #11762734C22semidirect
67. #11762734C22semidirect
68. #11762734C22semidirect
69. #11762732C22semidirect
70. #11762732C22semidirect
71. #11762732C22semidirect
76. #11762725C22semidirect
77. #11762725C22semidirect
82. #11762724C22semidirect
83. #11762724C22semidirect
84. #11762723C22semidirect
85. #11762720C22semidirect
94. #11762717C22semidirect
95. #11762716C22semidirect
96. #11762711C22semidirect
97. #11762711C22semidirect
98. #11762709C22semidirect
99. #11762709C22semidirect
100. #11762709C22semidirect
101. #11762706C22semidirect
102. #11762703C22semidirect
103. #11762703C22semidirect
104. #11762703C22semidirect
105. #11762702C22semidirect
106. #11762702C22semidirect
107. #11762702C22semidirect
108. #11762701C22semidirect
109. #11762701C22semidirect
110. #11762701C22semidirect
111. #11762701C22semidirect
112. #11762700C22semidirect
113. #11762700C22semidirect
114. #11762699C22semidirect
115. #11762699C22semidirect
116. #11762698C22semidirect
117. #11762698C22semidirect
118. #11762697C22semidirect
119. #11762694C22semidirect
120. #11762694C22semidirect
121. #11762693C22semidirect
122. #11762693C22semidirect
123. #11762693C22semidirect
124. #11762689C22semidirect
126. #11762687C22semidirect
127. #11762687C22semidirect
128. #11762687C22semidirect
129. #11762687C22semidirect
131. #11762686C22semidirect
132. #11762686C22semidirect
141. #11762685C22semidirect
142. #11762685C22semidirect
143. #11762685C22semidirect
144. #11762685C22semidirect
146. #11762684C22semidirect
150. #11762680C22semidirect
151. #11762680C22semidirect
152. #11762680C22semidirect
153. #11762680C22semidirect
154. #11762677C22semidirect
155. #11762674C22semidirect
158. #11762670C22semidirect
160. #11762668C22semidirect
161. #11762668C22semidirect
162. #11762668C22semidirect
164. #11762666C22semidirect
165. #11762666C22semidirect
172. C2×C17×#124C22semidirect
176. C17×#397C22semidirect
177. C17×#394C22semidirect
178. C17×#394C22semidirect
179. C17×#393C22semidirect
180. C17×#390C22semidirect
181. C17×#388C22semidirect
182. C17×#388C22semidirect
770. #2472D17semidirect
863. C2×#124C2×D17semidirect
901. #397C2×D17semidirect
918. #394C2×D17semidirect
919. #394C2×D17semidirect
921. #393C2×D17semidirect
937. #390C2×D17semidirect
956. #388C2×D17semidirect
957. #388C2×D17semidirect
1211. C17#36758semidirect

Maximal subgroups

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

subgroupindex
#145370682
#145370652
#145366442
#145364452
#145364162
#145364042
#145364012
#145361102
#145360662
#145360052
#145359022
#145357772
#145355772
#145354332
#145354192
#145353392
#145352222
#145350802
#145344992
#145344982
#145331632
#145331162
#145330292
#145323372
#145323242
#145322592
#145322462
#145314472
#145314442
C2×#117626852
C17×#24722
#3675817