Finite Group Databasebeta

← #30552347

Subgroups — #30552347

Order 15616.

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×#16840296C211yesmaximal, characteristic
2#21457059C214yesmaximal, complemented
3#21457049C212yesmaximal, complemented
4#21457040C212yesmaximal, complemented
5#21456998C214yesmaximal, complemented
6#21456987C214yesmaximal, complemented
7#21456372C212yesmaximal, complemented
8#21456208C212yesmaximal, complemented
9#21455767C212yesmaximal, complemented
10#21455759C212yesmaximal
11#21455620C212yesmaximal, complemented
12#21455612C212yesmaximal, complemented
13#21454452C211yesmaximal, characteristic, complemented
14C2×C61×#533C211yesmaximal, characteristic, complemented
15#16840296—21no—
16#16840296—21no—
17#16840296—21no—
18#16840296—21no—
19#16840296C2212yes—
20#16840296C2212yes—
21#16840296C2212yes—
22#16840296C2212yes—
23C2×#14519771—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519765C2211yescharacteristic
26C2×#14519760—21no—
27C2×#14519756C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29C2×C4×Dic122C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519734—21no—
33#16840168C2214yescomplemented
34#16840168C2214yescomplemented
35#16840161C2218yescomplemented
36#16840124C2214yescomplemented
37#16840124C2214yescomplemented
38#16840119C2218yescomplemented
39#16840103C2218yescomplemented
40#16840097C2214yescomplemented
41#16840092C2214yescomplemented
42#16840086C2218yes—
43#16840080C2214yes—
44#16840075C2214yes—
45#16840066C2218yescomplemented
46#16840059C2218yescomplemented
47#16840054C2214yescomplemented
48#16840049C2214yescomplemented
49#16840044C2214yescomplemented
50#16840039C2214yescomplemented
51#16839819C2212yescomplemented
52#16839819C2212yescomplemented
53#16839815C2212yescomplemented
54#16839815C2212yescomplemented
55#16839805C2214yes—
56#16839805C2214yes—
57#16839786C2212yes—
58#16839770C2214yes—
59#16839766C2214yes—
60#16839726C2212yes—
61C4×#11758194C2212yes—
62C61×#533—21no—
63C61×#533—21no—
64C61×#533—21no—
65C61×#533—21no—
66C61×#533C2212yes—
67C61×#533C2212yes—
68C61×#533C2212yescomplemented
69C61×#533C2212yescomplemented
70C2×C4⋊Q8×C61C2211yescharacteristic, complemented
71C2×C4⋊Q8×C61C2211yescharacteristic, complemented
72C2×#125×C61C2212yescomplemented
73C2×C22⋊Q8×C61—21no—
74C2×C22⋊Q8×C61—21no—
75C2×C4×Q8×C61—21no—
76C2×C4×Q8×C61—21no—
77C2×#117×C61C2212yes—
78C22×C42×C61C2211yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C4×D61—21no—
83C2×#11758194C2314yes—
84#14519771—22no—
85#14519771—22no—
86#14519771—22no—
87#14519771—22no—
88#14519769—21no—
89#14519769—21no—
90#14519769C2312yes—
91#14519769C2312yes—
92#14519765—21no—
93#14519765—21no—
94#14519765C2312yes—
95#14519765C2312yes—
96#14519760—22no—
97#14519760—22no—
98#14519760—22no—
99#14519760—22no—
100#14519756—21no—
101#14519756—21no—
102#14519756C2312yes—
103#14519756C2312yes—
104#14519751—21no—
105#14519751—21no—
106#14519751C2312yes—
107#14519751C2312yes—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122C2312yes—
111C4×Dic122C2312yes—
112C4×D244—21no—
113C4×D244—21no—
114C4×D244C2312yes—
115C4×D244C2312yes—
116C4×C22⋊D61—22no—
117C4×C22⋊D61—22no—
118C4×C22⋊D61—22no—
119C4×C22⋊D61—22no—
120#14519734—22no—
121#14519734—22no—
122#14519734—22no—
123#14519734—22no—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×C22⋊Dic61—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×C4×Dic61—21no—
136#14519710C2318yes—
137#14519710C2318yes—
138#14519708C2318yes—
139#14519708C2318yes—
140C4⋊#92418C2314yes—
141C4⋊#92418C2314yes—
142#14519700C2318yes—
143#14519700C2318yes—
144#14519697C2318yes—
145#14519697C2318yes—
146C22⋊#92418C2314yes—
147C22⋊#92418C2314yes—
148#14519688C2314yes—
149C4×#92418C2314yes—
150C22×Q8×C61—21no—
151C22×Q8×C61—21no—
152C23×C4×C61D411yescharacteristic
153C23×C4×C61D411yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C4⋊Q8×C61—21no—
156C4⋊Q8×C61—21no—
157C4⋊Q8×C61—21no—
158C4⋊Q8×C61—21no—
159C4⋊Q8×C61C2312yes—
160C4⋊Q8×C61C2312yes—
161C4⋊Q8×C61C2312yes—
162C4⋊Q8×C61C2312yes—
163#125×C61—22no—
164#125×C61—22no—
165#125×C61C2314yes—
166#125×C61C2314yes—
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61—22no—
172C22⋊Q8×C61—22no—
173C22⋊Q8×C61—22no—
174C22⋊Q8×C61—22no—
175C4×Q8×C61—22no—
176C4×Q8×C61—22no—
177C4×Q8×C61—22no—
178C4×Q8×C61—22no—
179C4×Q8×C61—22no—
180C4×Q8×C61—22no—
181C4×Q8×C61—22no—
182C4×Q8×C61—22no—
183#117×C61—22no—
184#117×C61—22no—
185#117×C61C2314yes—
186#117×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61—22no—
190C2×C4⋊C4×C61—22no—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2312yes—
193C2×C22⋊C4×C61—22no—
194C2×C42×C61—22no—
195C2×C42×C61D411yescharacteristic
196C2×C42×C61D411yescharacteristic
197C2×C42×C61D411yescharacteristic
198C2×C42×C61D411yescharacteristic
199C2×C42×C61D411yescharacteristic
200C2×C42×C61D411yescharacteristic
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C2×C42×C61C2311yescharacteristic
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209C2×Q8×C61—22no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—44no—
214C2×Q8×C61—44no—
215C22×C4×C61—24no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—44no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244C2412yes—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—44no—
250C2×Dic122—24no—
251C2×Dic122—21no—
252C2×Dic122C2412yes—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61C2414yes—
264C4⋊C4×C61C2414yes—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C42×C61—24no—
268C42×C61—24no—
269C42×C61C2×D411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C42×C61C2411yescharacteristic
283C42×C61C2411yescharacteristic
284C42×C61C2411yescharacteristic
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61C2412yes—
298C4⋊Dic61C2412yes—
299#11758196—22no—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309#11758194—28no—
310C2×#92418C2418yes—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—41no—
314C23×C61C22×D411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C22×D61—22no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321Q8×C61—44no—
322Q8×C61—44no—
323Q8×C61—44no—
324Q8×C61—44no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—24no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—44no—
345C2×C4×C61—44no—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C612−1+414yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—44no—
360C22⋊D61—44no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367D244—24no—
368D244—42no—
369C4×D61—44no—
370C4×D61—44no—
371Dic122—24no—
372Dic122—42no—
373#92418—28no—
374#60866—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—44no—
383C22×C61#53612yes—
384C22×C61#57512yes—
385C22×C61C23×D411yescharacteristic
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—84no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—44no—
400C4×C61—44no—
401C4×C61#53612yes—
402C4×C61#57512yes—
403C4×C61C2×2−1+412yes—
404Dic61—42no—
405Dic61—42no—
406Dic61—42no—
407C2×#533D6111yescharacteristic, complemented
408C2×#529—611no—
409#3240—614no—
410#3239—612no—
411#3238—612no—
412#3233—614no—
413#3232—614no—
414#3166—612no—
415#3140—612no—
416#3095—612no—
417#3094—612no—
418#3078—612no—
419#3077—612no—
420#2920—611no—
421C2×C61—22no—
422C2×C61—22no—
423C2×C61—41no—
424C2×C61C2×#53611yescharacteristic
425C2×C61C2×#57511yescharacteristic
426C2×C61C2×#57511yescharacteristic
427D61—82no—
428#533—21no—
429#533—21no—
430#533—21no—
431#533—21no—
432#533C2×D6112yes—
433#533C2×D6112yes—
434#533C2×D6112yescomplemented
435#533C2×D6112yescomplemented
436C2×C4⋊Q8C2×D6111yescharacteristic, complemented
437C2×C4⋊Q8C2×D6111yescharacteristic, complemented
438#529—612no—
439#529—612no—
440#529—612no—
441#529—612no—
442#529—1221no—
443#529—1221no—
444#529—1221no—
445#529—1221no—
446C2×#126—1221no—
447C2×#125—611no—
448C2×#125C2×D6112yescomplemented
449C2×#124—611no—
450C2×#123—1221no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8—611no—
454C2×#121—611no—
455C2×C4×Q8—21no—
456C2×C4×Q8—21no—
457C2×C4×Q8—611no—
458C2×C4×D4—611no—
459C2×C4×D4—1221no—
460C2×#117—1221no—
461C2×#117C2×D6112yes—
462C22×C42C2×D6111yescharacteristic
463#501—614no—
464#501—614no—
465#499—618no—
466#489—614no—
467#489—614no—
468#488—618no—
469#485—618no—
470#484—614no—
471#483—614no—
472#482—618no—
473#481—614no—
474#480—614no—
475#479—618no—
476#478—618no—
477#477—614no—
478#476—614no—
479#475—614no—
480#474—614no—
481#432—612no—
482#432—612no—
483#431—612no—
484#431—612no—
485#428—614no—
486#428—614no—
487#423—612no—
488#419—614no—
489#418—614no—
490#407—612no—
491C4×M16—612no—
492C61#6086611yescharacteristic, complemented, Sylow
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—611no—
496C22×D4—611no—
497C22×D4—1221no—
498C23×C4—1221no—
499C23×C4C22⋊D6111yescharacteristic
500C23×C4C22⋊D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C2×M16—614no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507C4⋊Q8C22×D6112yes—
508C4⋊Q8C22×D6112yes—
509C4⋊Q8C22×D6112yes—
510C4⋊Q8C22×D6112yes—
511#126—1222no—
512#126—1222no—
513#126—1222no—
514#126—1222no—
515#125—22no—
516#125—22no—
517#125—612no—
518#125—612no—
519#125—1221no—
520#125—1221no—
521#125C22×D6114yes—
522#125C22×D6114yes—
523#124—612no—
524#124—612no—
525#124—1221no—
526#124—1221no—
527#123—1222no—
528#123—1222no—
529#123—1222no—
530#123—1222no—
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—612no—
540C22⋊Q8—612no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543#121—612no—
544#121—612no—
545#121—1221no—
546#121—1221no—
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—612no—
556C4×Q8—612no—
557C4×Q8—1221no—
558C4×Q8—1221no—
559C4×D4—612no—
560C4×D4—612no—
561C4×D4—1222no—
562C4×D4—1222no—
563C4×D4—1222no—
564C4×D4—1222no—
565C4×D4—1221no—
566C4×D4—1221no—
567#117—22no—
568#117—22no—
569#117—1222no—
570#117—1222no—
571#117—1222no—
572#117—1222no—
573#117C22×D6114yes—
574#117C22×D6114yes—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4C22×D6112yes—
586C2×C4⋊C4C22×D6112yes—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C42—22no—
594C2×C42—1221no—
595C2×C42C22⋊D6111yescharacteristic
596C2×C42C22⋊D6111yescharacteristic
597C2×C42C22⋊D6111yescharacteristic
598C2×C42C22⋊D6111yescharacteristic
599C2×C42C22⋊D6111yescharacteristic
600C2×C42C22⋊D6111yescharacteristic
601C2×C42C22×D6111yescharacteristic
602C2×C42C22×D6111yescharacteristic
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C2×C42C22×D6111yescharacteristic
606C2×C42C22×D6111yescharacteristic
607#107—618no—
608#107—618no—
609#106—618no—
610#106—618no—
611C4⋊C8—614no—
612C4⋊C8—614no—
613#103—618no—
614#103—618no—
615#102—618no—
616#102—618no—
617C22⋊C8—614no—
618C22⋊C8—614no—
619#97—614no—
620C4×C8—614no—
621C24—1221no—
622C24C2×C22⋊D6111yescharacteristic
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—612no—
630C2×Q8—1221no—
631C2×Q8—1224no—
632C2×D4—612no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—1221no—
636C2×D4—1224no—
637C2×D4—2444no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—2444no—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C2×C22⋊D6111yescharacteristic
656C22×C4C2×C22⋊D6111yescharacteristic
657C22×C4C2×C22⋊D6111yescharacteristic
658C22×C4C2×C22⋊D6111yescharacteristic
659C22×C4C2×C22⋊D6111yescharacteristic
660C22×C4C2×C22⋊D6111yescharacteristic
661C22×C4C2×C22⋊D6111yescharacteristic
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C23×D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666C22×C4C23×D6111yescharacteristic
667M16—1228no—
668C2×C8—618no—
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—612no—
680C4⋊C4—612no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1222no—
688C4⋊C4—1222no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4C23×D6114yes—
692C4⋊C4C23×D6114yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1222no—
700C22⋊C4—1222no—
701C22⋊C4—1222no—
702C22⋊C4—1222no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C42—24no—
706C42—24no—
707C42—1222no—
708C42—1222no—
709C42C2×C22⋊D6111yescharacteristic
710C42C2×C22⋊D6111yescharacteristic
711C42C2×C22⋊D6111yescharacteristic
712C42C2×C22⋊D6111yescharacteristic
713C42C2×C22⋊D6111yescharacteristic
714C42C2×C22⋊D6111yescharacteristic
715C42C2×C22⋊D6111yescharacteristic
716C42C2×C22⋊D6111yescharacteristic
717C42C2×C22⋊D6111yescharacteristic
718C42C2×C22⋊D6111yescharacteristic
719C42C2×C22⋊D6111yescharacteristic
720C42C2×C22⋊D6111yescharacteristic
721C42C23×D6111yescharacteristic
722C42C23×D6111yescharacteristic
723C42C23×D6111yescharacteristic
724C42C23×D6111yescharacteristic
725C23—22no—
726C23—22no—
727C23—41no—
728C23—1222no—
729C23—2442no—
730C23—2442no—
731C23—2442no—
732C23C22×C22⋊D6111yescharacteristic
733C23C22×C22⋊D6111yescharacteristic
734C23C22×C22⋊D6111yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—44no—
739Q8—1224no—
740Q8—2442no—
741D4—1224no—
742D4—2444no—
743D4—2444no—
744D4—2442no—
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—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—2444no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2444no—
774C2×C4C22×C22⋊D6111yescharacteristic
775C2×C4C22×C22⋊D6111yescharacteristic
776C2×C4C22×C22⋊D6111yescharacteristic
777C2×C4C22×C22⋊D6111yescharacteristic
778C2×C4C22×C22⋊D6111yescharacteristic
779C2×C4C22×C22⋊D6111yescharacteristic
780C2×C4C22×C22⋊D6111yescharacteristic
781C2×C4C22×C22⋊D6111yescharacteristic
782C2×C4C22×C22⋊D6111yescharacteristic
783C2×C4C22×C22⋊D6111yescharacteristic
784C2×C4C22×C22⋊D6111yescharacteristic
785C2×C4#1451982514yes—
786C2×C4C24×D6111yescharacteristic
787C8—1228no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—4884no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22#1684033612yes—
801C22#1684056012yes—
802C22C23×C22⋊D6111yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—44no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C4#1684033612yes—
818C4#1684056012yes—
819C4C2×#1451982512yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—4882no—
824C2C2×#1684033611yescharacteristic
825C2C2×#1684056011yescharacteristic
826C2C2×#1684056011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#533C2
socleC22×C61C23×D4
prime radicalC2×#14519751C22
hypercenterC2×#533D61
hypocenterC61#60866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #21457059C2semidirect
3. #21457049C2semidirect
4. #21457040C2semidirect
5. #21456998C2semidirect
6. #21456987C2semidirect
7. #21456372C2semidirect
8. #21456208C2semidirect
9. #21455767C2semidirect
11. #21455620C2semidirect
12. #21455612C2semidirect
13. #21454452C2semidirect
14. C2×C61×#533C2semidirect
33. #16840168C22semidirect
34. #16840168C22semidirect
35. #16840161C22semidirect
36. #16840124C22semidirect
37. #16840124C22semidirect
38. #16840119C22semidirect
39. #16840103C22semidirect
40. #16840097C22semidirect
41. #16840092C22semidirect
45. #16840066C22semidirect
46. #16840059C22semidirect
47. #16840054C22semidirect
48. #16840049C22semidirect
49. #16840044C22semidirect
50. #16840039C22semidirect
51. #16839819C22semidirect
52. #16839819C22semidirect
53. #16839815C22semidirect
54. #16839815C22semidirect
68. C61×#533C22semidirect
69. C61×#533C22semidirect
70. C2×C4⋊Q8×C61C22semidirect
71. C2×C4⋊Q8×C61C22semidirect
72. C2×#125×C61C22semidirect
407. C2×#533D61semidirect
434. #533C2×D61semidirect
435. #533C2×D61semidirect
436. C2×C4⋊Q8C2×D61semidirect
437. C2×C4⋊Q8C2×D61semidirect
448. C2×#125C2×D61semidirect
492. C61#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
#214570592
#214570492
#214570402
#214569982
#214569872
#214563722
#214562082
#214557672
#214557592
#214556202
#214556122
#214544522
C2×C61×#5332
#6086661