Finite Group Databasebeta

← #29461023

Subgroups — #29461023

Order 15104.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837936C211yesmaximal, characteristic
2#21435336C214yesmaximal, complemented
3#21435326C212yesmaximal, complemented
4#21435317C212yesmaximal, complemented
5#21435275C214yesmaximal, complemented
6#21435264C214yesmaximal, complemented
7#21434649C212yesmaximal, complemented
8#21434485C212yesmaximal, complemented
9#21434044C212yesmaximal, complemented
10#21434036C212yesmaximal
11#21433897C212yesmaximal, complemented
12#21433889C212yesmaximal, complemented
13#21432729C211yesmaximal, characteristic, complemented
14C2×C59×#533C211yesmaximal, characteristic, complemented
15#16837936—21no—
16#16837936—21no—
17#16837936—21no—
18#16837936—21no—
19#16837936C2212yes—
20#16837936C2212yes—
21#16837936C2212yes—
22#16837936C2212yes—
23C2×#14273721—21no—
24C2×#14273719C2211yescharacteristic
25C2×#14273715C2211yescharacteristic
26C2×#14273710—21no—
27C2×#14273706C2211yescharacteristic
28C2×#14273701C2211yescharacteristic
29C2×C4×Dic118C2211yescharacteristic
30C2×C4×D236C2211yescharacteristic
31C2×C4×C22⋊D59—21no—
32C2×#14273684—21no—
33#16837808C2214yescomplemented
34#16837808C2214yescomplemented
35#16837801C2218yescomplemented
36#16837764C2214yescomplemented
37#16837764C2214yescomplemented
38#16837759C2218yescomplemented
39#16837743C2218yescomplemented
40#16837737C2214yescomplemented
41#16837732C2214yescomplemented
42#16837726C2218yes—
43#16837720C2214yes—
44#16837715C2214yes—
45#16837706C2218yescomplemented
46#16837699C2218yescomplemented
47#16837694C2214yescomplemented
48#16837689C2214yescomplemented
49#16837684C2214yescomplemented
50#16837679C2214yescomplemented
51#16837459C2212yescomplemented
52#16837459C2212yescomplemented
53#16837455C2212yescomplemented
54#16837455C2212yescomplemented
55#16837445C2214yes—
56#16837445C2214yes—
57#16837426C2212yes—
58#16837410C2214yes—
59#16837406C2214yes—
60#16837366C2212yes—
61C4×#11745664C2212yes—
62C59×#533—21no—
63C59×#533—21no—
64C59×#533—21no—
65C59×#533—21no—
66C59×#533C2212yes—
67C59×#533C2212yes—
68C59×#533C2212yescomplemented
69C59×#533C2212yescomplemented
70C2×C4⋊Q8×C59C2211yescharacteristic, complemented
71C2×C4⋊Q8×C59C2211yescharacteristic, complemented
72C2×#125×C59C2212yescomplemented
73C2×C22⋊Q8×C59—21no—
74C2×C22⋊Q8×C59—21no—
75C2×C4×Q8×C59—21no—
76C2×C4×Q8×C59—21no—
77C2×#117×C59C2212yes—
78C22×C42×C59C2211yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C4×D59—21no—
83C2×#11745664C2314yes—
84#14273721—22no—
85#14273721—22no—
86#14273721—22no—
87#14273721—22no—
88#14273719—21no—
89#14273719—21no—
90#14273719C2312yes—
91#14273719C2312yes—
92#14273715—21no—
93#14273715—21no—
94#14273715C2312yes—
95#14273715C2312yes—
96#14273710—22no—
97#14273710—22no—
98#14273710—22no—
99#14273710—22no—
100#14273706—21no—
101#14273706—21no—
102#14273706C2312yes—
103#14273706C2312yes—
104#14273701—21no—
105#14273701—21no—
106#14273701C2312yes—
107#14273701C2312yes—
108C4×Dic118—21no—
109C4×Dic118—21no—
110C4×Dic118C2312yes—
111C4×Dic118C2312yes—
112C4×D236—21no—
113C4×D236—21no—
114C4×D236C2312yes—
115C4×D236C2312yes—
116C4×C22⋊D59—22no—
117C4×C22⋊D59—22no—
118C4×C22⋊D59—22no—
119C4×C22⋊D59—22no—
120#14273684—22no—
121#14273684—22no—
122#14273684—22no—
123#14273684—22no—
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×C22⋊Dic59—21no—
131C2×(C2×D59)⋊C4—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×C4×Dic59—21no—
136#14273660C2318yes—
137#14273660C2318yes—
138#14273658C2318yes—
139#14273658C2318yes—
140C4⋊(C59⋊C8)C2314yes—
141C4⋊(C59⋊C8)C2314yes—
142#14273650C2318yes—
143#14273650C2318yes—
144#14273647C2318yes—
145#14273647C2318yes—
146C22⋊(C59⋊C8)C2314yes—
147C22⋊(C59⋊C8)C2314yes—
148#14273638C2314yes—
149C4×C59⋊C8C2314yes—
150C22×Q8×C59—21no—
151C22×Q8×C59—21no—
152C23×C4×C59D411yescharacteristic
153C23×C4×C59D411yescharacteristic
154C23×C4×C59C2311yescharacteristic
155C4⋊Q8×C59—21no—
156C4⋊Q8×C59—21no—
157C4⋊Q8×C59—21no—
158C4⋊Q8×C59—21no—
159C4⋊Q8×C59C2312yes—
160C4⋊Q8×C59C2312yes—
161C4⋊Q8×C59C2312yes—
162C4⋊Q8×C59C2312yes—
163#125×C59—22no—
164#125×C59—22no—
165#125×C59C2314yes—
166#125×C59C2314yes—
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59—22no—
169C22⋊Q8×C59—22no—
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59—22no—
172C22⋊Q8×C59—22no—
173C22⋊Q8×C59—22no—
174C22⋊Q8×C59—22no—
175C4×Q8×C59—22no—
176C4×Q8×C59—22no—
177C4×Q8×C59—22no—
178C4×Q8×C59—22no—
179C4×Q8×C59—22no—
180C4×Q8×C59—22no—
181C4×Q8×C59—22no—
182C4×Q8×C59—22no—
183#117×C59—22no—
184#117×C59—22no—
185#117×C59C2314yes—
186#117×C59C2314yes—
187C2×C4⋊C4×C59—22no—
188C2×C4⋊C4×C59—22no—
189C2×C4⋊C4×C59—21no—
190C2×C4⋊C4×C59—21no—
191C2×C4⋊C4×C59C2312yes—
192C2×C4⋊C4×C59C2312yes—
193C2×C22⋊C4×C59—22no—
194C2×C42×C59—22no—
195C2×C42×C59D411yescharacteristic
196C2×C42×C59D411yescharacteristic
197C2×C42×C59D411yescharacteristic
198C2×C42×C59D411yescharacteristic
199C2×C42×C59D411yescharacteristic
200C2×C42×C59D411yescharacteristic
201C2×C42×C59C2311yescharacteristic
202C2×C42×C59C2311yescharacteristic
203C2×C42×C59C2311yescharacteristic
204C2×C42×C59C2311yescharacteristic
205C2×C42×C59C2311yescharacteristic
206C2×C42×C59C2311yescharacteristic
207C24×C59C2×D411yescharacteristic
208C23×D59—21no—
209C2×Q8×C59—22no—
210C2×Q8×C59—22no—
211C2×Q8×C59—22no—
212C2×Q8×C59—22no—
213C2×Q8×C59—44no—
214C2×Q8×C59—44no—
215C22×C4×C59—24no—
216C22×C4×C59—22no—
217C22×C4×C59—22no—
218C22×C4×C59—42no—
219C22×C4×C59—42no—
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59C2×D411yescharacteristic
234C22×C4×C59C2×D411yescharacteristic
235C22×C4×C59C2411yescharacteristic
236C22×C4×C59C2411yescharacteristic
237C22×C4×C59C2411yescharacteristic
238C2×C22⋊D59—22no—
239C2×C22⋊D59—22no—
240C2×C22⋊D59—44no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C2×D236—24no—
245C2×D236—21no—
246C2×D236C2412yes—
247C2×C4×D59—22no—
248C2×C4×D59—22no—
249C2×C4×D59—44no—
250C2×Dic118—24no—
251C2×Dic118—21no—
252C2×Dic118C2412yes—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—24no—
256C4⋊C4×C59—24no—
257C4⋊C4×C59—22no—
258C4⋊C4×C59—22no—
259C4⋊C4×C59—22no—
260C4⋊C4×C59—22no—
261C4⋊C4×C59—22no—
262C4⋊C4×C59—22no—
263C4⋊C4×C59C2414yes—
264C4⋊C4×C59C2414yes—
265C22⋊C4×C59—24no—
266C22⋊C4×C59—24no—
267C42×C59—24no—
268C42×C59—24no—
269C42×C59C2×D411yescharacteristic
270C42×C59C2×D411yescharacteristic
271C42×C59C2×D411yescharacteristic
272C42×C59C2×D411yescharacteristic
273C42×C59C2×D411yescharacteristic
274C42×C59C2×D411yescharacteristic
275C42×C59C2×D411yescharacteristic
276C42×C59C2×D411yescharacteristic
277C42×C59C2×D411yescharacteristic
278C42×C59C2×D411yescharacteristic
279C42×C59C2×D411yescharacteristic
280C42×C59C2×D411yescharacteristic
281C42×C59C2411yescharacteristic
282C42×C59C2411yescharacteristic
283C42×C59C2411yescharacteristic
284C42×C59C2411yescharacteristic
285C22⋊Dic59—22no—
286C22⋊Dic59—22no—
287(C2×D59)⋊C4—22no—
288(C2×D59)⋊C4—22no—
289(C2×D59)⋊C4—22no—
290(C2×D59)⋊C4—22no—
291(C2×D59)⋊C4—22no—
292(C2×D59)⋊C4—22no—
293(C2×D59)⋊C4—22no—
294(C2×D59)⋊C4—22no—
295C4⋊Dic59—21no—
296C4⋊Dic59—21no—
297C4⋊Dic59C2412yes—
298C4⋊Dic59C2412yes—
299Dic59⋊C4—22no—
300Dic59⋊C4—22no—
301Dic59⋊C4—22no—
302Dic59⋊C4—22no—
303Dic59⋊C4—22no—
304Dic59⋊C4—22no—
305Dic59⋊C4—22no—
306Dic59⋊C4—22no—
307C4×Dic59—22no—
308C4×Dic59—22no—
309#11745664—28no—
310C2×C59⋊C8C2418yes—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—41no—
314C23×C59C22×D411yescharacteristic
315C23×C59C22×D411yescharacteristic
316C23×C59C22×D411yescharacteristic
317C22×D59—22no—
318C22×D59—42no—
319C22×D59—42no—
320C22×D59—42no—
321Q8×C59—44no—
322Q8×C59—44no—
323Q8×C59—44no—
324Q8×C59—44no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—24no—
336C2×C4×C59—24no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—44no—
345C2×C4×C59—44no—
346C2×C4×C59C22×D411yescharacteristic
347C2×C4×C59C22×D411yescharacteristic
348C2×C4×C59C22×D411yescharacteristic
349C2×C4×C59C22×D411yescharacteristic
350C2×C4×C59C22×D411yescharacteristic
351C2×C4×C59C22×D411yescharacteristic
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59C22×D411yescharacteristic
357C2×C4×C592−1+414yes—
358C2×C4×C59C2511yescharacteristic
359C22⋊D59—44no—
360C22⋊D59—44no—
361C2×Dic59—22no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—42no—
365C2×Dic59—42no—
366C2×Dic59—42no—
367D236—24no—
368D236—42no—
369C4×D59—44no—
370C4×D59—44no—
371Dic118—24no—
372Dic118—42no—
373C59⋊C8—28no—
374#60866—591nomaximal, Sylow
375C22×C59—21no—
376C22×C59—21no—
377C22×C59—21no—
378C22×C59—21no—
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—21no—
382C22×C59—44no—
383C22×C59#53612yes—
384C22×C59#57512yes—
385C22×C59C23×D411yescharacteristic
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—84no—
390C4×C59—21no—
391C4×C59—21no—
392C4×C59—21no—
393C4×C59—21no—
394C4×C59—21no—
395C4×C59—21no—
396C4×C59—21no—
397C4×C59—21no—
398C4×C59—21no—
399C4×C59—44no—
400C4×C59—44no—
401C4×C59#53612yes—
402C4×C59#57512yes—
403C4×C59C2×2−1+412yes—
404Dic59—42no—
405Dic59—42no—
406Dic59—42no—
407C2×#533D5911yescharacteristic, complemented
408C2×#529—591no—
409#3240—594no—
410#3239—592no—
411#3238—592no—
412#3233—594no—
413#3232—594no—
414#3166—592no—
415#3140—592no—
416#3095—592no—
417#3094—592no—
418#3078—592no—
419#3077—592no—
420#2920—591no—
421C2×C59—22no—
422C2×C59—22no—
423C2×C59—41no—
424C2×C59C2×#53611yescharacteristic
425C2×C59C2×#57511yescharacteristic
426C2×C59C2×#57511yescharacteristic
427D59—82no—
428#533—21no—
429#533—21no—
430#533—21no—
431#533—21no—
432#533C2×D5912yes—
433#533C2×D5912yes—
434#533C2×D5912yescomplemented
435#533C2×D5912yescomplemented
436C2×C4⋊Q8C2×D5911yescharacteristic, complemented
437C2×C4⋊Q8C2×D5911yescharacteristic, complemented
438#529—592no—
439#529—592no—
440#529—592no—
441#529—592no—
442#529—1181no—
443#529—1181no—
444#529—1181no—
445#529—1181no—
446C2×#126—1181no—
447C2×#125—591no—
448C2×#125C2×D5912yescomplemented
449C2×#124—591no—
450C2×#123—1181no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8—591no—
454C2×#121—591no—
455C2×C4×Q8—21no—
456C2×C4×Q8—21no—
457C2×C4×Q8—591no—
458C2×C4×D4—591no—
459C2×C4×D4—1181no—
460C2×#117—1181no—
461C2×#117C2×D5912yes—
462C22×C42C2×D5911yescharacteristic
463#501—594no—
464#501—594no—
465#499—598no—
466#489—594no—
467#489—594no—
468#488—598no—
469#485—598no—
470#484—594no—
471#483—594no—
472#482—598no—
473#481—594no—
474#480—594no—
475#479—598no—
476#478—598no—
477#477—594no—
478#476—594no—
479#475—594no—
480#474—594no—
481#432—592no—
482#432—592no—
483#431—592no—
484#431—592no—
485#428—594no—
486#428—594no—
487#423—592no—
488#419—594no—
489#418—594no—
490#407—592no—
491C4×M16—592no—
492C59#6086611yescharacteristic, complemented, Sylow
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—591no—
496C22×D4—591no—
497C22×D4—1181no—
498C23×C4—1181no—
499C23×C4C22⋊D5911yescharacteristic
500C23×C4C22⋊D5911yescharacteristic
501C23×C4C22×D5911yescharacteristic
502C2×M16—594no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507C4⋊Q8C22×D5912yes—
508C4⋊Q8C22×D5912yes—
509C4⋊Q8C22×D5912yes—
510C4⋊Q8C22×D5912yes—
511#126—1182no—
512#126—1182no—
513#126—1182no—
514#126—1182no—
515#125—22no—
516#125—22no—
517#125—592no—
518#125—592no—
519#125—1181no—
520#125—1181no—
521#125C22×D5914yes—
522#125C22×D5914yes—
523#124—592no—
524#124—592no—
525#124—1181no—
526#124—1181no—
527#123—1182no—
528#123—1182no—
529#123—1182no—
530#123—1182no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—592no—
540C22⋊Q8—592no—
541C22⋊Q8—1181no—
542C22⋊Q8—1181no—
543#121—592no—
544#121—592no—
545#121—1181no—
546#121—1181no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—592no—
556C4×Q8—592no—
557C4×Q8—1181no—
558C4×Q8—1181no—
559C4×D4—592no—
560C4×D4—592no—
561C4×D4—1182no—
562C4×D4—1182no—
563C4×D4—1182no—
564C4×D4—1182no—
565C4×D4—1181no—
566C4×D4—1181no—
567#117—22no—
568#117—22no—
569#117—1182no—
570#117—1182no—
571#117—1182no—
572#117—1182no—
573#117C22×D5914yes—
574#117C22×D5914yes—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—591no—
580C2×C4⋊C4—591no—
581C2×C4⋊C4—1181no—
582C2×C4⋊C4—1181no—
583C2×C4⋊C4—1181no—
584C2×C4⋊C4—1181no—
585C2×C4⋊C4C22×D5912yes—
586C2×C4⋊C4C22×D5912yes—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—1181no—
589C2×C22⋊C4—1181no—
590C2×C22⋊C4—1181no—
591C2×C22⋊C4—1181no—
592C2×C22⋊C4—1181no—
593C2×C42—22no—
594C2×C42—1181no—
595C2×C42C22⋊D5911yescharacteristic
596C2×C42C22⋊D5911yescharacteristic
597C2×C42C22⋊D5911yescharacteristic
598C2×C42C22⋊D5911yescharacteristic
599C2×C42C22⋊D5911yescharacteristic
600C2×C42C22⋊D5911yescharacteristic
601C2×C42C22×D5911yescharacteristic
602C2×C42C22×D5911yescharacteristic
603C2×C42C22×D5911yescharacteristic
604C2×C42C22×D5911yescharacteristic
605C2×C42C22×D5911yescharacteristic
606C2×C42C22×D5911yescharacteristic
607#107—598no—
608#107—598no—
609#106—598no—
610#106—598no—
611C4⋊C8—594no—
612C4⋊C8—594no—
613#103—598no—
614#103—598no—
615#102—598no—
616#102—598no—
617C22⋊C8—594no—
618C22⋊C8—594no—
619#97—594no—
620C4×C8—594no—
621C24—1181no—
622C24C2×C22⋊D5911yescharacteristic
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—592no—
630C2×Q8—1181no—
631C2×Q8—1184no—
632C2×D4—592no—
633C2×D4—1182no—
634C2×D4—1182no—
635C2×D4—1181no—
636C2×D4—1184no—
637C2×D4—2364no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—1181no—
644C22×C4—1181no—
645C22×C4—1181no—
646C22×C4—1182no—
647C22×C4—1182no—
648C22×C4—2364no—
649C22×C4C2×C22⋊D5911yescharacteristic
650C22×C4C2×C22⋊D5911yescharacteristic
651C22×C4C2×C22⋊D5911yescharacteristic
652C22×C4C2×C22⋊D5911yescharacteristic
653C22×C4C2×C22⋊D5911yescharacteristic
654C22×C4C2×C22⋊D5911yescharacteristic
655C22×C4C2×C22⋊D5911yescharacteristic
656C22×C4C2×C22⋊D5911yescharacteristic
657C22×C4C2×C22⋊D5911yescharacteristic
658C22×C4C2×C22⋊D5911yescharacteristic
659C22×C4C2×C22⋊D5911yescharacteristic
660C22×C4C2×C22⋊D5911yescharacteristic
661C22×C4C2×C22⋊D5911yescharacteristic
662C22×C4C2×C22⋊D5911yescharacteristic
663C22×C4C2×C22⋊D5911yescharacteristic
664C22×C4C23×D5911yescharacteristic
665C22×C4C23×D5911yescharacteristic
666C22×C4C23×D5911yescharacteristic
667M16—1188no—
668C2×C8—598no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—592no—
680C4⋊C4—592no—
681C4⋊C4—1181no—
682C4⋊C4—1181no—
683C4⋊C4—1182no—
684C4⋊C4—1182no—
685C4⋊C4—1182no—
686C4⋊C4—1182no—
687C4⋊C4—1182no—
688C4⋊C4—1182no—
689C4⋊C4—1182no—
690C4⋊C4—1182no—
691C4⋊C4C23×D5914yes—
692C4⋊C4C23×D5914yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—1182no—
696C22⋊C4—1182no—
697C22⋊C4—1182no—
698C22⋊C4—1182no—
699C22⋊C4—1182no—
700C22⋊C4—1182no—
701C22⋊C4—1182no—
702C22⋊C4—1182no—
703C22⋊C4—1182no—
704C22⋊C4—1182no—
705C42—24no—
706C42—24no—
707C42—1182no—
708C42—1182no—
709C42C2×C22⋊D5911yescharacteristic
710C42C2×C22⋊D5911yescharacteristic
711C42C2×C22⋊D5911yescharacteristic
712C42C2×C22⋊D5911yescharacteristic
713C42C2×C22⋊D5911yescharacteristic
714C42C2×C22⋊D5911yescharacteristic
715C42C2×C22⋊D5911yescharacteristic
716C42C2×C22⋊D5911yescharacteristic
717C42C2×C22⋊D5911yescharacteristic
718C42C2×C22⋊D5911yescharacteristic
719C42C2×C22⋊D5911yescharacteristic
720C42C2×C22⋊D5911yescharacteristic
721C42C23×D5911yescharacteristic
722C42C23×D5911yescharacteristic
723C42C23×D5911yescharacteristic
724C42C23×D5911yescharacteristic
725C23—22no—
726C23—22no—
727C23—41no—
728C23—1182no—
729C23—2362no—
730C23—2362no—
731C23—2362no—
732C23C22×C22⋊D5911yescharacteristic
733C23C22×C22⋊D5911yescharacteristic
734C23C22×C22⋊D5911yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—44no—
739Q8—1184no—
740Q8—2362no—
741D4—1184no—
742D4—2364no—
743D4—2364no—
744D4—2362no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—1182no—
767C2×C4—1182no—
768C2×C4—1182no—
769C2×C4—2364no—
770C2×C4—2362no—
771C2×C4—2362no—
772C2×C4—2362no—
773C2×C4—2364no—
774C2×C4C22×C22⋊D5911yescharacteristic
775C2×C4C22×C22⋊D5911yescharacteristic
776C2×C4C22×C22⋊D5911yescharacteristic
777C2×C4C22×C22⋊D5911yescharacteristic
778C2×C4C22×C22⋊D5911yescharacteristic
779C2×C4C22×C22⋊D5911yescharacteristic
780C2×C4C22×C22⋊D5911yescharacteristic
781C2×C4C22×C22⋊D5911yescharacteristic
782C2×C4C22×C22⋊D5911yescharacteristic
783C2×C4C22×C22⋊D5911yescharacteristic
784C2×C4C22×C22⋊D5911yescharacteristic
785C2×C4#1427377514yes—
786C2×C4C24×D5911yescharacteristic
787C8—1188no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—4724no—
797C22—2362no—
798C22—2362no—
799C22—2362no—
800C22#1683797612yes—
801C22#1683820012yes—
802C22C23×C22⋊D5911yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—44no—
814C4—2362no—
815C4—2362no—
816C4—2362no—
817C4#1683797612yes—
818C4#1683820012yes—
819C4C2×#1427377512yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—4722no—
824C2C2×#1683797611yescharacteristic
825C2C2×#1683820011yescharacteristic
826C2C2×#1683820011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#533C2
socleC22×C59C23×D4
prime radicalC2×#14273701C22
hypercenterC2×#533D59
hypocenterC59#60866
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #21435336C2semidirect
3. #21435326C2semidirect
4. #21435317C2semidirect
5. #21435275C2semidirect
6. #21435264C2semidirect
7. #21434649C2semidirect
8. #21434485C2semidirect
9. #21434044C2semidirect
11. #21433897C2semidirect
12. #21433889C2semidirect
13. #21432729C2semidirect
14. C2×C59×#533C2semidirect
33. #16837808C22semidirect
34. #16837808C22semidirect
35. #16837801C22semidirect
36. #16837764C22semidirect
37. #16837764C22semidirect
38. #16837759C22semidirect
39. #16837743C22semidirect
40. #16837737C22semidirect
41. #16837732C22semidirect
45. #16837706C22semidirect
46. #16837699C22semidirect
47. #16837694C22semidirect
48. #16837689C22semidirect
49. #16837684C22semidirect
50. #16837679C22semidirect
51. #16837459C22semidirect
52. #16837459C22semidirect
53. #16837455C22semidirect
54. #16837455C22semidirect
68. C59×#533C22semidirect
69. C59×#533C22semidirect
70. C2×C4⋊Q8×C59C22semidirect
71. C2×C4⋊Q8×C59C22semidirect
72. C2×#125×C59C22semidirect
407. C2×#533D59semidirect
434. #533C2×D59semidirect
435. #533C2×D59semidirect
436. C2×C4⋊Q8C2×D59semidirect
437. C2×C4⋊Q8C2×D59semidirect
448. C2×#125C2×D59semidirect
492. C59#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#168379362
#214353362
#214353262
#214353172
#214352752
#214352642
#214346492
#214344852
#214340442
#214340362
#214338972
#214338892
#214327292
C2×C59×#5332
#6086659