Finite Group Databasebeta

← C2×#14542496 #17942382

Subgroups — C2×#14542496 #17942382

Order 4352.

7302 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542496C2132yesmaximal, direct product factor
2C2×#11763531C212yesmaximal, complemented
3C2×#11763526C212yesmaximal, complemented
4C2×#11763522C212yesmaximal, complemented
5C2×#11763521C212yesmaximal, complemented
6C2×#11763510C212yesmaximal, complemented
7C2×#11763508C212yesmaximal, complemented
8C2×#11763492C212yesmaximal, complemented
9C2×#11763491C212yesmaximal, complemented
10C2×#11763438C211yesmaximal, characteristic, complemented
11C2×#11763399C211yesmaximal, characteristic, complemented
12C2×#11763396C211yesmaximal, characteristic, complemented
13C2×#11763392C212yesmaximal, complemented
14C2×#11763386C211yesmaximal, characteristic, complemented
15C2×#11763343C211yesmaximal, characteristic, complemented
16C2×#11763336C212yesmaximal, complemented
17C2×#11763317C212yesmaximal, complemented
18C2×#11763288C212yesmaximal, complemented
19C22×#10587558C211yesmaximal, characteristic, complemented
20C2×C17×#529C211yesmaximal, characteristic, complemented
21C22×#63254C2212yes—
22C23×C4×D17C2211yescharacteristic
23#11763531C22132yescomplemented
24#11763526C22132yescomplemented
25#11763522C22132yescomplemented
26#11763521C22132yescomplemented
27#11763510C22132yescomplemented
28#11763508C22132yescomplemented
29#11763492C22132yescomplemented
30#11763491C22132yescomplemented
31#11763438C22116yescomplemented
32#11763399C22116yescomplemented
33#11763396C22116yescomplemented
34#11763392C22132yescomplemented
35#11763386C22116yescomplemented
36C2×#10587574C2212yescomplemented
37C2×#10587630C2212yescomplemented
38#11763343C22116yescomplemented
39#11763336C22132yescomplemented
40C2×#10587584C2212yes—
41C2×#10587584C2212yes—
42C2×#10587584C2212yes—
43C2×#10587584C2212yescomplemented
44C2×#10587562C2212yes—
45C2×#10587562C2212yescomplemented
46C2×#10587565C2212yescomplemented
47C2×#10587556C2211yescharacteristic, complemented
48C2×#10587575C2212yescomplemented
49C2×#10587575C2212yescomplemented
50C2×#10587575C2212yescomplemented
51C2×#10587633C2212yes—
52C2×#10587561C2212yes—
53C2×#10587561C2211yescharacteristic, complemented
54C2×#10587571C2212yes—
55C2×#10587571C2212yes—
56C2×#10587571C2212yescomplemented
57#11763317C22132yescomplemented
58C2×#10587580C2212yes—
59C2×#10587580C2212yes—
60C2×#10587572C2212yes—
61C2×#10587615C2212yes—
62C2×#10587615C2212yes—
63C2×#10587610C2211yescharacteristic
64C2×#10587582C2212yes—
65C2×#10587582C2212yes—
66C2×#10587582C2212yescomplemented
67C2×#10587564C2212yes—
68C2×#10587564C2212yescomplemented
69C2×#10587581C2212yes—
70C2×#10587616C2211yescharacteristic
71C2×#10587616C2212yes—
72C2×#10587570C2212yes—
73C2×#10587570C2212yes—
74C2×#10587570C2212yes—
75C2×#10587570C2212yescomplemented
76C2×#10587625C2212yes—
77C2×#10587625C2212yes—
78C2×#10587625C2212yescomplemented
79C2×#10587568C2212yes—
80C2×#10587623C2212yes—
81#11763288C22132yescomplemented
82C2×C4×Dic34C2212yescomplemented
83C2×C4×Dic34C2211yescharacteristic, complemented
84C2×#10587573C2212yescomplemented
85C2×#10587573C2212yescomplemented
86C2×C4×D68C2211yescharacteristic, complemented
87C2×D4×Dic17C2212yes—
88C2×#10587579C2212yes—
89C2×#10587579C2212yes—
90C2×C4×C22⋊D17C2212yes—
91C2×C4×C22⋊D17C2212yescomplemented
92C2×#10587567C2212yes—
93C2×#10587567C2212yes—
94C2×#10587567C2212yes—
95C2×#10587567C2212yescomplemented
96C2×#10587567C2212yescomplemented
97C2×#10587578C2212yescomplemented
98C2×#10587558C2212yes—
99C2×#10587558C2212yes—
100C2×#10587558C2212yes—
101C2×#10587558C2212yes—
102C2×#10587558C22116yescomplemented
103C2×#10587558C2212yescomplemented
104C2×#10587558C2212yescomplemented
105C2×#10587563C2212yes—
106C2×#10587563C2212yescomplemented
107C2×#10587563C2212yescomplemented
108C22×#63225C2211yescharacteristic
109C22×#63225C2211yescharacteristic
110C22×#63225C2212yescomplemented
111C2×C4⋊C4×D17C2212yescomplemented
112C22×#63227C2211yescharacteristic
113C22×#63227C2211yescharacteristic
114C22×C4×Dic17C2211yescharacteristic
115C17×#529C22116yescomplemented
116C2×C17×#126C2212yescomplemented
117C2×C17×#125C2211yescharacteristic, complemented
118C2×C17×#124C2211yescharacteristic, complemented
119C2×C17×#123C2212yes—
120C2×C17×C22⋊Q8C2211yescharacteristic
121C2×C17×#121C2211yescharacteristic
122C2×C4×Q8×C17C2211yescharacteristic, complemented
123C2×C4×D4×C17C2212yes—
124C2×C4×D4×C17C2211yescharacteristic, complemented
125C2×C17×#117C2212yescomplemented
126C22×C42×C17C2211yescharacteristic
127C24×D17C2311yescharacteristic
128C22×Q8×C17C2311yescharacteristic
129C22×D4×C17C2312yes—
130C22×D4×C17C2311yescharacteristic
131C23×C4×C17C2311yescharacteristic
132C23×C4×C17C2311yescharacteristic
133C23×C4×C17C2311yescharacteristic
134C23×C4×C17C2312yes—
135C22×C22⋊D17C2312yes—
136C22×C22⋊D17C2312yes—
137C22×C22⋊D17C2312yes—
138C22×C22⋊D17C2312yes—
139C22×C22⋊D17C2312yes—
140C23×Dic17C2312yes—
141C23×Dic17C2311yescharacteristic
142C23×Dic17C2311yescharacteristic
143C23×Dic17C2312yes—
144C23×Dic17C2311yescharacteristic
145C2×#63254—216no—
146C2×#63254C23116yes—
147C22×D68C2312yes—
148C22×D68C2312yes—
149C22×D68C2311yescharacteristic
150C22×C4×D17—28no—
151C22×C4×D17C2312yes—
152C22×C4×D17C2312yes—
153C22×C4×D17C2312yes—
154C22×C4×D17C2318yes—
155C22×C4×D17C2312yes—
156C22×C4×D17C2312yes—
157C22×Dic34C2312yes—
158C22×Dic34C2312yes—
159C22×Dic34C2311yescharacteristic
160C17×#126C23116yescomplemented
161C17×#125C2318yescomplemented
162C17×#124C2318yescomplemented
163C17×#123C23116yes—
164C17×C22⋊Q8C2318yes—
165C17×#121C2318yes—
166C4×Q8×C17C2318yescomplemented
167C4×D4×C17C23116yes—
168C4×D4×C17C2318yescomplemented
169C17×#117C23116yescomplemented
170C2×C4⋊C4×C17C2312yes—
171C2×C4⋊C4×C17C2312yes—
172C2×C4⋊C4×C17C2312yes—
173C2×C4⋊C4×C17C2311yescharacteristic
174C2×C4⋊C4×C17C2311yescharacteristic
175C2×C4⋊C4×C17C2312yes—
176C2×C22⋊C4×C17C2312yes—
177C2×C22⋊C4×C17C2312yes—
178C2×C22⋊C4×C17C2312yes—
179C2×C22⋊C4×C17C2312yes—
180C2×C22⋊C4×C17C2312yes—
181C2×C42×C17C2311yescharacteristic
182C2×C42×C17C2311yescharacteristic
183C2×C42×C17C2311yescharacteristic
184C2×C42×C17C2311yescharacteristic
185C2×C42×C17C2318yes—
186C2×C42×C17C2312yes—
187C2×C22⋊Dic17C2312yes—
188C2×C22⋊Dic17C2312yes—
189C2×C22⋊Dic17C2312yes—
190#10587633C23116yes—
191#10587630C23116yescomplemented
192#10587625C23116yes—
193#10587625C23116yes—
194#10587625C23116yescomplemented
195#10587623C23116yes—
196D4×Dic17C23116yes—
197#10587616C23116yes—
198#10587616C2318yes—
199#10587615C23116yes—
200#10587615C23116yes—
201C4×C22⋊D17C23116yes—
202C4×C22⋊D17C23116yescomplemented
203C2×#63227C2312yes—
204C2×#63227C2312yes—
205C2×#63227C2312yes—
206C2×#63227C2312yes—
207C2×#63227C2318yes—
208C2×#63227C2318yes—
209C2×#63227C2312yes—
210C2×#63227C2312yes—
211C2×#63227C2312yes—
212C2×#63227C2312yes—
213C2×#63227C2312yes—
214C2×#63227C2312yes—
215C2×#63227C2312yes—
216C2×#63227C2312yes—
217C2×#63227C2312yes—
218C2×#63227C2312yes—
219C2×C4⋊Dic17C2312yes—
220C2×C4⋊Dic17C2312yes—
221C2×C4⋊Dic17C2311yescharacteristic
222C2×C4⋊Dic17C2311yescharacteristic
223#10587610C2318yes—
224C2×#63225C2312yes—
225C2×#63225C2312yes—
226C2×#63225C2312yes—
227C2×#63225C2312yes—
228C2×#63225C2312yes—
229C2×#63225C2318yes—
230C2×#63225C2318yes—
231C2×#63225C2312yes—
232C2×#63225C2312yes—
233C2×#63225C2312yes—
234C2×#63225C2312yes—
235C2×#63225C2312yes—
236C2×#63225C2312yes—
237C2×#63225C2312yes—
238C2×#63225C2312yes—
239C2×#63225C2312yes—
240C2×#63225C23116yescomplemented
241C2×C4×Dic17C2312yes—
242C2×C4×Dic17C2312yes—
243C2×C4×Dic17C2318yes—
244C2×C4×Dic17C2312yes—
245C2×C4×Dic17C2312yes—
246C2×C4×Dic17C2312yes—
247C2×C4×Dic17C2312yes—
248C2×C4×Dic17C2312yes—
249#10587584C23116yes—
250#10587584C23116yes—
251#10587584C23116yes—
252#10587584C23116yescomplemented
253#10587582C23116yes—
254#10587582C23116yes—
255#10587582C23116yescomplemented
256#10587581C23116yes—
257#10587580C23116yes—
258#10587580C23116yes—
259#10587579C23116yes—
260#10587579C23116yes—
261#10587578C23116yescomplemented
262C4⋊C4×D17C23116yescomplemented
263#10587575C23116yescomplemented
264#10587575C23116yescomplemented
265#10587575C23116yescomplemented
266#10587574C23116yescomplemented
267#10587573C23116yescomplemented
268#10587573C23116yescomplemented
269#10587572C23116yes—
270#10587571C23116yes—
271#10587571C23116yes—
272#10587571C23116yescomplemented
273#10587570C23116yes—
274#10587570C23116yes—
275#10587570C23116yes—
276#10587570C23116yescomplemented
277#10587568C23116yes—
278#10587567C23116yes—
279#10587567C23116yes—
280#10587567C23116yes—
281#10587567C23116yescomplemented
282#10587567C23116yescomplemented
283#10587565C23116yescomplemented
284#10587564C23116yes—
285#10587564C23116yescomplemented
286#10587563C23116yes—
287#10587563C23116yescomplemented
288#10587563C23116yescomplemented
289#10587562C23116yes—
290#10587562C23116yescomplemented
291#10587561C23116yes—
292#10587561C2318yescomplemented
293C4×D68C2318yescomplemented
294#10587558C23116yes—
295#10587558C23116yes—
296#10587558C23116yes—
297#10587558C23116yes—
298#10587558C23116yescomplemented
299#10587558C23116yescomplemented
300#10587556C2318yescomplemented
301C4×Dic34C23116yescomplemented
302C4×Dic34C2318yescomplemented
303C24×C17C2412yes—
304C24×C17C2411yescharacteristic
305C23×D17—24no—
306C23×D17—42no—
307C23×D17—42no—
308C23×D17C2412yes—
309C23×D17C2412yes—
310C23×D17C2414yes—
311C2×Q8×C17—42no—
312C2×Q8×C17C2414yes—
313C2×D4×C17—28no—
314C2×D4×C17—42no—
315C2×D4×C17C2418yes—
316C2×D4×C17C2414yes—
317C22×C4×C17—24no—
318C22×C4×C17—42no—
319C22×C4×C17—42no—
320C22×C4×C17—44no—
321C22×C4×C17C2414yes—
322C22×C4×C17C2412yes—
323C22×C4×C17C2411yescharacteristic
324C22×C4×C17C2412yes—
325C22×C4×C17C2411yescharacteristic
326C22×C4×C17C2411yescharacteristic
327C22×C4×C17C2411yescharacteristic
328C22×C4×C17C2412yes—
329C22×C4×C17C2411yescharacteristic
330C22×C4×C17C2411yescharacteristic
331C22×C4×C17C2414yes—
332C22×C4×C17C2414yes—
333C22×C4×C17C2418yes—
334C2×C22⋊D17—28no—
335C2×C22⋊D17—28no—
336C2×C22⋊D17—44no—
337C2×C22⋊D17—44no—
338C2×C22⋊D17—44no—
339C2×C22⋊D17C2418yes—
340C2×C22⋊D17C2418yes—
341C2×C22⋊D17C2418yes—
342C2×C22⋊D17C2418yes—
343C2×C22⋊D17C2418yes—
344C22×Dic17—28no—
345C22×Dic17—42no—
346C22×Dic17—42no—
347C22×Dic17—44no—
348C22×Dic17#4118yes—
349C22×Dic17C2412yes—
350C22×Dic17C2412yes—
351C22×Dic17C2412yes—
352C22×Dic17C2412yes—
353C22×Dic17C2412yes—
354C22×Dic17C2418yes—
355C22×Dic17C2418yes—
356C22×Dic17C2414yes—
357C22×Dic17C2414yes—
358C22×Dic17C2412yes—
359C22×Dic17C2414yes—
360#63254—264no—
361C2×D68—42no—
362C2×D68—44no—
363C2×D68—44no—
364C2×D68C2414yes—
365C2×D68C2418yes—
366C2×D68C2418yes—
367C2×C4×D17—28no—
368C2×C4×D17—28no—
369C2×C4×D17—232no—
370C2×C4×D17—28no—
371C2×C4×D17—44no—
372C2×C4×D17—44no—
373C2×C4×D17C2418yes—
374C2×C4×D17C2418yes—
375C2×C4×D17C2418yes—
376C2×C4×D17C2418yes—
377C2×C4×D17C2418yes—
378C2×Dic34—28no—
379C2×Dic34—42no—
380C2×Dic34—44no—
381C2×Dic34C2418yes—
382C2×Dic34C2414yes—
383C2×Dic34C2418yes—
384C4⋊C4×C17C2414yes—
385C4⋊C4×C17C2418yes—
386C4⋊C4×C17C2418yes—
387C4⋊C4×C17C2418yes—
388C4⋊C4×C17C2418yes—
389C4⋊C4×C17C2414yes—
390C22⋊C4×C17C2418yes—
391C22⋊C4×C17C2418yes—
392C22⋊C4×C17C2418yes—
393C22⋊C4×C17C2418yes—
394C22⋊C4×C17C2418yes—
395C42×C17C2414yes—
396C42×C17C2414yes—
397C42×C17C2418yes—
398C42×C17C2414yes—
399C42×C17C2414yes—
400C22⋊Dic17C2418yes—
401C22⋊Dic17C2418yes—
402C22⋊Dic17C2418yes—
403#63227C2418yes—
404#63227C2418yes—
405#63227C2418yes—
406#63227C2418yes—
407#63227C2418yes—
408#63227C2418yes—
409#63227C2418yes—
410#63227C2418yes—
411#63227C2418yes—
412#63227C2418yes—
413#63227C2418yes—
414#63227C2418yes—
415#63227C2418yes—
416#63227C2418yes—
417C4⋊Dic17C2414yes—
418C4⋊Dic17C2418yes—
419C4⋊Dic17C2414yes—
420C4⋊Dic17C2418yes—
421#63225C2418yes—
422#63225C2418yes—
423#63225C2418yes—
424#63225C2418yes—
425#63225C2418yes—
426#63225C2418yes—
427#63225C2418yes—
428#63225C2418yes—
429#63225C2418yes—
430#63225C2418yes—
431#63225C2418yes—
432#63225C2418yes—
433#63225C2418yes—
434#63225C2418yes—
435C4×Dic17C2418yes—
436C4×Dic17C2418yes—
437C4×Dic17C2418yes—
438C4×Dic17C2418yes—
439C4×Dic17C2418yes—
440C4×Dic17C2418yes—
441C4×Dic17C2418yes—
442C2×#3493—171nomaximal, Sylow
443C23×C17—22no—
444C23×C17—22no—
445C23×C17—24no—
446C23×C17—24no—
447C23×C17—24no—
448C23×C17C2×#4114yes—
449C23×C17C2514yes—
450C23×C17C2512yes—
451C23×C17C2511yescharacteristic
452C22×D17—28no—
453C22×D17—24no—
454C22×D17—24no—
455C22×D17—24no—
456C22×D17—24no—
457C22×D17—24no—
458C22×D17—24no—
459C22×D17—44no—
460C22×D17—44no—
461C22×D17—416no—
462C22×D17C2514yes—
463C22×D17C2514yes—
464Q8×C17—44no—
465D4×C17—216no—
466D4×C17—44no—
467C2×C4×C17—24no—
468C2×C4×C17—28no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—24no—
473C2×C4×C17—22no—
474C2×C4×C17—24no—
475C2×C4×C17—22no—
476C2×C4×C17—22no—
477C2×C4×C17—44no—
478C2×C4×C17—44no—
479C2×C4×C17—48no—
480C2×C4×C17C2512yes—
481C2×C4×C17C2512yes—
482C2×C4×C17C2512yes—
483C2×C4×C17C2512yes—
484C2×C4×C17C2512yes—
485C2×C4×C17C2512yes—
486C2×C4×C17C2514yes—
487C2×C4×C17C2514yes—
488C2×C4×C17C2514yes—
489C22⋊D17—216no—
490C22⋊D17—216no—
491C22⋊D17—48no—
492C22⋊D17—48no—
493C22⋊D17—48no—
494C2×Dic17—24no—
495C2×Dic17—24no—
496C2×Dic17—24no—
497C2×Dic17—24no—
498C2×Dic17—24no—
499C2×Dic17—216no—
500C2×Dic17—44no—
501C2×Dic17—44no—
502C2×Dic17—48no—
503C2×Dic17C2×#4118yes—
504C2×Dic17C2×#41116yes—
505C2×Dic17C2514yes—
506C2×Dic17C2514yes—
507C2×Dic17C2514yes—
508C2×Dic17C2514yes—
509C2×Dic17C2514yes—
510C2×Dic17C2514yes—
511D68—44no—
512D68—48no—
513D68—48no—
514C4×D17—216no—
515C4×D17—216no—
516C4×D17—216no—
517C4×D17—48no—
518C4×D17—48no—
519Dic34—216no—
520Dic34—44no—
521Dic34—48no—
522#3493—1732no—
523C2×#556—172no—
524C2×#556—172no—
525C2×#555—172no—
526C2×#555—172no—
527C2×#553—172no—
528C2×#553—172no—
529C2×#552—172no—
530C2×#552—172no—
531C2×#544—171no—
532C2×#538—171no—
533C2×#538—171no—
534C2×#538—172no—
535C2×#537—171no—
536C2×#529—171no—
537C2×#529—172no—
538C2×#529D1711yescharacteristic, complemented
539C2×#525—172no—
540C2×#520—172no—
541C22×#117—171no—
542C22×C17—22no—
543C22×C17—22no—
544C22×C17—28no—
545C22×C17—24no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—48no—
549C22×C17C22×#4114yes—
550C22×C17C22×#4112yes—
551C22×C17#58512yes—
552C22×C17#58512yes—
553C22×C17C2611yescharacteristic
554C2×D17—24no—
555C2×D17—24no—
556C2×D17—24no—
557C2×D17—24no—
558C2×D17—24no—
559C2×D17—24no—
560C2×D17—416no—
561C2×D17—48no—
562C2×D17—48no—
563C4×C17—24no—
564C4×C17—22no—
565C4×C17—22no—
566C4×C17—22no—
567C4×C17—24no—
568C4×C17—22no—
569C4×C17—24no—
570C4×C17—22no—
571C4×C17—22no—
572Dic17—24no—
573Dic17—24no—
574Dic17—24no—
575Dic17—24no—
576Dic17—24no—
577Dic17C22×#4118yes—
578C22×#41—172no—
579C24×C4—171no—
580#556—1732no—
581#556—1732no—
582#555—1732no—
583#555—1732no—
584#553—1732no—
585#553—1732no—
586#552—1732no—
587#552—1732no—
588#544—1716no—
589#538—1716no—
590#538—1716no—
591#538—1732no—
592#537—1716no—
593C2×C4⋊Q8—172no—
594C2×C4⋊Q8—172no—
595#529—1732no—
596#529—1716no—
597#529C2×D17116yescomplemented
598C2×#126—172no—
599C2×#126—172no—
600C2×#126—172no—
601C2×#126—172no—
602C2×#126—172no—
603C2×#126—172no—
604C2×#126—172no—
605C2×#126C2×D1712yescomplemented
606C2×#125—172no—
607C2×#125—172no—
608C2×#125—172no—
609C2×#125—171no—
610C2×#125C2×D1711yescharacteristic, complemented
611C2×#124—172no—
612C2×#124—172no—
613C2×#124—172no—
614C2×#124—172no—
615C2×#124—171no—
616C2×#124—172no—
617C2×#124C2×D1711yescharacteristic, complemented
618#525—1732no—
619C2×#123—172no—
620C2×#123—172no—
621C2×#123—172no—
622C2×#123—172no—
623C2×#123—172no—
624C2×#123C2×D1712yes—
625C2×C22⋊Q8—171no—
626C2×C22⋊Q8—172no—
627C2×C22⋊Q8—172no—
628C2×C22⋊Q8—172no—
629C2×C22⋊Q8—172no—
630C2×C22⋊Q8—172no—
631C2×C22⋊Q8C2×D1711yescharacteristic
632C2×#121—172no—
633C2×#121—172no—
634C2×#121—172no—
635C2×#121—171no—
636C2×#121—172no—
637C2×#121—172no—
638C2×#121—172no—
639C2×#121—172no—
640C2×#121—172no—
641C2×#121—172no—
642C2×#121C2×D1711yescharacteristic
643C2×#120—172no—
644C2×#120—172no—
645#520—1732no—
646C2×C4×Q8—172no—
647C2×C4×Q8—172no—
648C2×C4×Q8—172no—
649C2×C4×Q8—171no—
650C2×C4×Q8C2×D1711yescharacteristic, complemented
651C2×C4×D4—172no—
652C2×C4×D4—172no—
653C2×C4×D4—172no—
654C2×C4×D4—172no—
655C2×C4×D4—172no—
656C2×C4×D4—172no—
657C2×C4×D4—172no—
658C2×C4×D4—172no—
659C2×C4×D4—172no—
660C2×C4×D4—172no—
661C2×C4×D4—171no—
662C2×C4×D4C2×D1712yes—
663C2×C4×D4C2×D1711yescharacteristic, complemented
664C2×#117—172no—
665C2×#117—172no—
666C2×#117—172no—
667C2×#117—172no—
668C2×#117—172no—
669C2×#117—172no—
670C2×#117—172no—
671C2×#117—172no—
672C2×#117—1716no—
673C2×#117—172no—
674C2×#117—172no—
675C2×#117C2×D1712yescomplemented
676C22×C4⋊C4—171no—
677C22×C4⋊C4—171no—
678C22×C4⋊C4—172no—
679C22×C4⋊C4—172no—
680C22×C22⋊C4—171no—
681C22×C22⋊C4—171no—
682C22×C42—171no—
683C22×C42C2×D1711yescharacteristic
684C2×C17—24no—
685C2×C17—44no—
686C2×C17#349314yescomplemented
687C2×C17C23×#4111yescharacteristic
688C2×C17C2×#58511yescharacteristic
689C2×C17C2×#58511yescharacteristic
690D17—44no—
691D17—44no—
692C25—171no—
693C2×#41—1716no—
694C2×#41—3416no—
695C22×Q8—172no—
696C22×Q8—171no—
697C22×Q8—172no—
698C22×Q8C22×D1711yescharacteristic
699C22×D4—172no—
700C22×D4—172no—
701C22×D4—172no—
702C22×D4—172no—
703C22×D4—172no—
704C22×D4—172no—
705C22×D4—172no—
706C22×D4—171no—
707C22×D4C22×D1712yes—
708C22×D4C22×D1711yescharacteristic
709C23×C4—171no—
710C23×C4—172no—
711C23×C4—171no—
712C23×C4—171no—
713C23×C4—172no—
714C23×C4—172no—
715C23×C4—172no—
716C23×C4—172no—
717C23×C4—178no—
718C23×C4—172no—
719C23×C4—172no—
720C23×C4—348no—
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1712yes—
725C4⋊Q8—1716no—
726C4⋊Q8—1716no—
727#126—1716no—
728#126—1716no—
729#126—1716no—
730#126—1716no—
731#126—1716no—
732#126—1716no—
733#126—1716no—
734#126C22×D17116yescomplemented
735#125—1716no—
736#125—1716no—
737#125—1716no—
738#125—178no—
739#125C22×D1718yescomplemented
740#124—1716no—
741#124—1716no—
742#124—1716no—
743#124—1716no—
744#124—178no—
745#124—1716no—
746#124C22×D1718yescomplemented
747#123—1716no—
748#123—1716no—
749#123—1716no—
750#123—1716no—
751#123—1716no—
752#123C22×D17116yes—
753C22⋊Q8—178no—
754C22⋊Q8—1716no—
755C22⋊Q8—1716no—
756C22⋊Q8—1716no—
757C22⋊Q8—1716no—
758C22⋊Q8—1716no—
759C22⋊Q8C22×D1718yes—
760#121—1716no—
761#121—1716no—
762#121—1716no—
763#121—178no—
764#121—1716no—
765#121—1716no—
766#121—1716no—
767#121—1716no—
768#121—1716no—
769#121—1716no—
770#121C22×D1718yes—
771#120—1716no—
772#120—1716no—
773C4×Q8—1716no—
774C4×Q8—1716no—
775C4×Q8—1716no—
776C4×Q8—178no—
777C4×Q8C22×D1718yescomplemented
778C4×D4—1716no—
779C4×D4—1716no—
780C4×D4—1716no—
781C4×D4—1716no—
782C4×D4—1716no—
783C4×D4—1716no—
784C4×D4—1716no—
785C4×D4—1716no—
786C4×D4—1716no—
787C4×D4—1716no—
788C4×D4—178no—
789C4×D4C22×D17116yes—
790C4×D4C22×D1718yescomplemented
791#117—1716no—
792#117—1716no—
793#117—1716no—
794#117—1716no—
795#117—1716no—
796#117—1716no—
797#117—1716no—
798#117—1716no—
799#117—1716no—
800#117—1716no—
801#117C22×D17116yescomplemented
802C2×C4⋊C4—172no—
803C2×C4⋊C4—172no—
804C2×C4⋊C4—172no—
805C2×C4⋊C4—178no—
806C2×C4⋊C4—172no—
807C2×C4⋊C4—172no—
808C2×C4⋊C4—178no—
809C2×C4⋊C4—172no—
810C2×C4⋊C4—172no—
811C2×C4⋊C4—172no—
812C2×C4⋊C4—1716no—
813C2×C4⋊C4—172no—
814C2×C4⋊C4—172no—
815C2×C4⋊C4—172no—
816C2×C4⋊C4—172no—
817C2×C4⋊C4—172no—
818C2×C4⋊C4—172no—
819C2×C4⋊C4—172no—
820C2×C4⋊C4—171no—
821C2×C4⋊C4—172no—
822C2×C4⋊C4—171no—
823C2×C4⋊C4—1716no—
824C2×C4⋊C4C22×D1712yes—
825C2×C4⋊C4C22×D1712yes—
826C2×C4⋊C4C22×D1712yes—
827C2×C4⋊C4C22×D1712yes—
828C2×C4⋊C4C22×D1711yescharacteristic
829C2×C4⋊C4C22×D1711yescharacteristic
830C2×C22⋊C4—172no—
831C2×C22⋊C4—172no—
832C2×C22⋊C4—172no—
833C2×C22⋊C4—172no—
834C2×C22⋊C4—172no—
835C2×C22⋊C4—172no—
836C2×C22⋊C4—172no—
837C2×C22⋊C4—178no—
838C2×C22⋊C4—178no—
839C2×C22⋊C4—172no—
840C2×C22⋊C4—172no—
841C2×C22⋊C4—172no—
842C2×C22⋊C4—172no—
843C2×C22⋊C4—172no—
844C2×C22⋊C4—172no—
845C2×C22⋊C4—172no—
846C2×C22⋊C4—172no—
847C2×C22⋊C4—172no—
848C2×C22⋊C4—172no—
849C2×C22⋊C4C22×D1712yes—
850C2×C22⋊C4C22×D1712yes—
851C2×C22⋊C4C22×D1712yes—
852C2×C22⋊C4C22×D1712yes—
853C2×C22⋊C4C22×D1712yes—
854C2×C42—172no—
855C2×C42—172no—
856C2×C42—172no—
857C2×C42—172no—
858C2×C42—172no—
859C2×C42—178no—
860C2×C42—172no—
861C2×C42—172no—
862C2×C42C22×D1711yescharacteristic
863C2×C42C22×D1711yescharacteristic
864C2×C42C22×D1711yescharacteristic
865C2×C42C22×D1711yescharacteristic
866C2×C42C22×D1718yes—
867C2×C42C22×D1712yes—
868C17C2×#349311yescharacteristic, complemented, Sylow
869C24—172no—
870C24—172no—
871C24—174no—
872C24—344no—
873C24—682no—
874C24—682no—
875C24C23×D1712yes—
876C24C23×D1711yescharacteristic
877#41—3464no—
878C2×Q8—42no—
879C2×Q8—178no—
880C2×Q8—174no—
881C2×Q8—178no—
882C2×Q8—348no—
883C2×Q8—682no—
884C2×Q8—684no—
885C2×Q8C23×D1714yes—
886C2×D4—28no—
887C2×D4—42no—
888C2×D4—178no—
889C2×D4—178no—
890C2×D4—178no—
891C2×D4—178no—
892C2×D4—178no—
893C2×D4—178no—
894C2×D4—178no—
895C2×D4—174no—
896C2×D4—348no—
897C2×D4—348no—
898C2×D4—684no—
899C2×D4—682no—
900C2×D4—684no—
901C2×D4—684no—
902C2×D4—684no—
903C2×D4—684no—
904C2×D4C23×D1718yes—
905C2×D4C23×D1714yes—
906C22×C4—24no—
907C22×C4—42no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—178no—
911C22×C4—174no—
912C22×C4—172no—
913C22×C4—178no—
914C22×C4—172no—
915C22×C4—172no—
916C22×C4—172no—
917C22×C4—172no—
918C22×C4—172no—
919C22×C4—174no—
920C22×C4—174no—
921C22×C4—178no—
922C22×C4—178no—
923C22×C4—178no—
924C22×C4—178no—
925C22×C4—178no—
926C22×C4—178no—
927C22×C4—348no—
928C22×C4—348no—
929C22×C4—3432no—
930C22×C4—348no—
931C22×C4—348no—
932C22×C4—684no—
933C22×C4—684no—
934C22×C4—682no—
935C22×C4—684no—
936C22×C4—682no—
937C22×C4C23×D1714yes—
938C22×C4C23×D1711yescharacteristic
939C22×C4C23×D1711yescharacteristic
940C22×C4C23×D1711yescharacteristic
941C22×C4C23×D1712yes—
942C22×C4C23×D1712yes—
943C22×C4C23×D1712yes—
944C22×C4C23×D1711yescharacteristic
945C22×C4C23×D1711yescharacteristic
946C22×C4C23×D1711yescharacteristic
947C22×C4C23×D1714yes—
948C22×C4C23×D1714yes—
949C22×C4C23×D1718yes—
950C4⋊C4—178no—
951C4⋊C4—178no—
952C4⋊C4—178no—
953C4⋊C4—178no—
954C4⋊C4—178no—
955C4⋊C4—178no—
956C4⋊C4—178no—
957C4⋊C4—178no—
958C4⋊C4—178no—
959C4⋊C4—178no—
960C4⋊C4—178no—
961C4⋊C4—178no—
962C4⋊C4—178no—
963C4⋊C4—178no—
964C4⋊C4—178no—
965C4⋊C4—174no—
966C4⋊C4—178no—
967C4⋊C4—174no—
968C4⋊C4C23×D1718yes—
969C4⋊C4C23×D1718yes—
970C4⋊C4C23×D1718yes—
971C4⋊C4C23×D1718yes—
972C4⋊C4C23×D1714yes—
973C4⋊C4C23×D1714yes—
974C22⋊C4—178no—
975C22⋊C4—178no—
976C22⋊C4—178no—
977C22⋊C4—178no—
978C22⋊C4—178no—
979C22⋊C4—178no—
980C22⋊C4—178no—
981C22⋊C4—178no—
982C22⋊C4—178no—
983C22⋊C4—178no—
984C22⋊C4—178no—
985C22⋊C4—178no—
986C22⋊C4—178no—
987C22⋊C4—178no—
988C22⋊C4—178no—
989C22⋊C4—178no—
990C22⋊C4—178no—
991C22⋊C4C23×D1718yes—
992C22⋊C4C23×D1718yes—
993C22⋊C4C23×D1718yes—
994C22⋊C4C23×D1718yes—
995C22⋊C4C23×D1718yes—
996C42—178no—
997C42—178no—
998C42—178no—
999C42—178no—
1000C42—178no—
1001C42—178no—
1002C42—178no—
1003C42C23×D1714yes—
1004C42C23×D1714yes—
1005C42C23×D1714yes—
1006C42C23×D1714yes—
1007C42C23×D1718yes—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—174no—
1014C23—174no—
1015C23—348no—
1016C23—344no—
1017C23—344no—
1018C23—344no—
1019C23—344no—
1020C23—344no—
1021C23—344no—
1022C23—684no—
1023C23—684no—
1024C23—6816no—
1025C23#41×D1714yes—
1026C23C24×D1714yes—
1027C23C24×D1712yes—
1028C23C24×D1711yescharacteristic
1029Q8—44no—
1030Q8—3416no—
1031Q8—684no—
1032Q8—688no—
1033D4—216no—
1034D4—44no—
1035D4—3416no—
1036D4—3416no—
1037D4—688no—
1038D4—684no—
1039D4—688no—
1040D4—688no—
1041D4—688no—
1042D4—688no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—44no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—178no—
1057C2×C4—1716no—
1058C2×C4—174no—
1059C2×C4—174no—
1060C2×C4—174no—
1061C2×C4—174no—
1062C2×C4—174no—
1063C2×C4—174no—
1064C2×C4—3416no—
1065C2×C4—3416no—
1066C2×C4—3416no—
1067C2×C4—3416no—
1068C2×C4—344no—
1069C2×C4—344no—
1070C2×C4—344no—
1071C2×C4—344no—
1072C2×C4—344no—
1073C2×C4—688no—
1074C2×C4—688no—
1075C2×C4—684no—
1076C2×C4—688no—
1077C2×C4—684no—
1078C2×C4C24×D1712yes—
1079C2×C4C24×D1712yes—
1080C2×C4C24×D1712yes—
1081C2×C4C24×D1714yes—
1082C2×C4C24×D1714yes—
1083C2×C4C24×D1714yes—
1084C2×C4C24×D1712yes—
1085C2×C4C24×D1712yes—
1086C2×C4C24×D1712yes—
1087C22—28no—
1088C22—22no—
1089C22—22no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—48no—
1094C22—344no—
1095C22—344no—
1096C22—344no—
1097C22—344no—
1098C22—344no—
1099C22—344no—
1100C22—6816no—
1101C22—688no—
1102C22—688no—
1103C22C2×#41×D1714yes—
1104C22C2×#41×D1712yes—
1105C22#1176364512yes—
1106C22#1176364512yes—
1107C22C25×D1711yescharacteristic
1108C4—22no—
1109C4—22no—
1110C4—24no—
1111C4—22no—
1112C4—22no—
1113C4—24no—
1114C4—22no—
1115C4—22no—
1116C4—24no—
1117C4—178no—
1118C4—344no—
1119C4—344no—
1120C4—344no—
1121C4—344no—
1122C4—344no—
1123C2—24no—
1124C2—44no—
1125C2—684no—
1126C2—684no—
1127C2#1454249614yesdirect product factor
1128C2C22×#41×D1711yescharacteristic
1129C2C2×#1176364511yescharacteristic
1130C2C2×#1176364511yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#529C2
socleC23×C17C25
hypercenterC2×#529D17
hypocenterC17C2×#3493
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #14542496C2direct (N × H)
2. C2×#11763531C2semidirect
3. C2×#11763526C2semidirect
4. C2×#11763522C2semidirect
5. C2×#11763521C2semidirect
6. C2×#11763510C2semidirect
7. C2×#11763508C2semidirect
8. C2×#11763492C2semidirect
9. C2×#11763491C2semidirect
10. C2×#11763438C2semidirect
11. C2×#11763399C2semidirect
12. C2×#11763396C2semidirect
13. C2×#11763392C2semidirect
14. C2×#11763386C2semidirect
15. C2×#11763343C2semidirect
16. C2×#11763336C2semidirect
17. C2×#11763317C2semidirect
18. C2×#11763288C2semidirect
19. C22×#10587558C2semidirect
20. C2×C17×#529C2semidirect
23. #11763531C22semidirect
24. #11763526C22semidirect
25. #11763522C22semidirect
26. #11763521C22semidirect
27. #11763510C22semidirect
28. #11763508C22semidirect
29. #11763492C22semidirect
30. #11763491C22semidirect
31. #11763438C22semidirect
32. #11763399C22semidirect
33. #11763396C22semidirect
34. #11763392C22semidirect
35. #11763386C22semidirect
36. C2×#10587574C22semidirect
37. C2×#10587630C22semidirect
38. #11763343C22semidirect
39. #11763336C22semidirect
43. C2×#10587584C22semidirect
45. C2×#10587562C22semidirect
46. C2×#10587565C22semidirect
47. C2×#10587556C22semidirect
48. C2×#10587575C22semidirect
49. C2×#10587575C22semidirect
50. C2×#10587575C22semidirect
53. C2×#10587561C22semidirect
56. C2×#10587571C22semidirect
57. #11763317C22semidirect
66. C2×#10587582C22semidirect
68. C2×#10587564C22semidirect
75. C2×#10587570C22semidirect
78. C2×#10587625C22semidirect
81. #11763288C22semidirect
82. C2×C4×Dic34C22semidirect
83. C2×C4×Dic34C22semidirect
84. C2×#10587573C22semidirect
85. C2×#10587573C22semidirect
86. C2×C4×D68C22semidirect
91. C2×C4×C22⋊D17C22semidirect
95. C2×#10587567C22semidirect
96. C2×#10587567C22semidirect
97. C2×#10587578C22semidirect
102. C2×#10587558C22semidirect
103. C2×#10587558C22semidirect
104. C2×#10587558C22semidirect
106. C2×#10587563C22semidirect
107. C2×#10587563C22semidirect
110. C22×#63225C22semidirect
111. C2×C4⋊C4×D17C22semidirect
115. C17×#529C22semidirect
116. C2×C17×#126C22semidirect
117. C2×C17×#125C22semidirect
118. C2×C17×#124C22semidirect
122. C2×C4×Q8×C17C22semidirect
124. C2×C4×D4×C17C22semidirect
125. C2×C17×#117C22semidirect
160. C17×#126C23semidirect
161. C17×#125C23semidirect
162. C17×#124C23semidirect
166. C4×Q8×C17C23semidirect
168. C4×D4×C17C23semidirect
169. C17×#117C23semidirect
191. #10587630C23semidirect
194. #10587625C23semidirect
202. C4×C22⋊D17C23semidirect
240. C2×#63225C23semidirect
252. #10587584C23semidirect
255. #10587582C23semidirect
261. #10587578C23semidirect
262. C4⋊C4×D17C23semidirect
263. #10587575C23semidirect
264. #10587575C23semidirect
265. #10587575C23semidirect
266. #10587574C23semidirect
267. #10587573C23semidirect
268. #10587573C23semidirect
272. #10587571C23semidirect
276. #10587570C23semidirect
281. #10587567C23semidirect
282. #10587567C23semidirect
283. #10587565C23semidirect
285. #10587564C23semidirect
287. #10587563C23semidirect
288. #10587563C23semidirect
290. #10587562C23semidirect
292. #10587561C23semidirect
293. C4×D68C23semidirect
298. #10587558C23semidirect
299. #10587558C23semidirect
300. #10587556C23semidirect
301. C4×Dic34C23semidirect
302. C4×Dic34C23semidirect
538. C2×#529D17semidirect
597. #529C2×D17semidirect
605. C2×#126C2×D17semidirect
610. C2×#125C2×D17semidirect
617. C2×#124C2×D17semidirect
650. C2×C4×Q8C2×D17semidirect
663. C2×C4×D4C2×D17semidirect
675. C2×#117C2×D17semidirect
686. C2×C17#3493semidirect
734. #126C22×D17semidirect
739. #125C22×D17semidirect
746. #124C22×D17semidirect
777. C4×Q8C22×D17semidirect
790. C4×D4C22×D17semidirect
801. #117C22×D17semidirect
868. C17C2×#3493semidirect
1127. C2#14542496direct (N × H)

Maximal subgroups

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

subgroupindex
#145424962
C2×#117635312
C2×#117635262
C2×#117635222
C2×#117635212
C2×#117635102
C2×#117635082
C2×#117634922
C2×#117634912
C2×#117634382
C2×#117633992
C2×#117633962
C2×#117633922
C2×#117633862
C2×#117633432
C2×#117633362
C2×#117633172
C2×#117632882
C22×#105875582
C2×C17×#5292
C2×#349317