Finite Group Databasebeta

← #29646007

Subgroups — #29646007

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3C2×#16839812C211yesmaximal, characteristic, complemented
4#21444187C212yesmaximal, complemented
5#21444185C212yesmaximal, complemented
6#21444173C212yesmaximal, complemented
7#21444169C212yesmaximal, complemented
8#21444137C211yesmaximal, characteristic, complemented
9#21444135C211yesmaximal, characteristic, complemented
10#21444135C211yesmaximal, characteristic, complemented
11C61×#1459C211yesmaximal, characteristic, complemented
12#16840292—21no—
13#16840292—21no—
14#16840292—21no—
15#16840292—21no—
16#16840292—21no—
17#16840292—21no—
18#16840292—21no—
19#16840292—21no—
20C2×#14519772C2211yescharacteristic
21C2×#14519770C2211yescharacteristic
22C2×#14519767C2211yescharacteristic
23C2×#14519763C2211yescharacteristic
24C2×#14519761C411yescharacteristic
25C2×#14519758C411yescharacteristic
26C2×#14519754C411yescharacteristic
27C2×#14519749C411yescharacteristic
28C2×C4×Dic122C411yescharacteristic
29C2×C4×C22⋊D61C411yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C411yescharacteristic
32C2×#14519734C411yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839816—21no—
35#16839816—21no—
36#16839816C2212yes—
37#16839816C2212yes—
38#16839812—21no—
39#16839812—21no—
40#16839812C2212yes—
41#16839812C2212yes—
42C2×#14519706—21no—
43C2×#14519706—21no—
44C2×C22⋊#92418C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519687—21no—
47C2×C8×Dic61—21no—
48#16839488C2212yes—
49#16839487C2212yes—
50#16839487C2212yes—
51#16839486C2212yes—
52#16839485C2212yes—
53#16839485C2212yes—
54C2×C4×D4×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#324C2212yes—
58C61×#323C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×#92418—21no—
66C22×#92418—21no—
67#14519772—21no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519770—21no—
72#14519770—21no—
73#14519770—21no—
74#14519770—21no—
75#14519767—21no—
76#14519767—21no—
77#14519767—21no—
78#14519767—21no—
79#14519763—21no—
80#14519763—21no—
81#14519763—21no—
82#14519763—21no—
83#14519761—21no—
84#14519761—21no—
85#14519761—21no—
86#14519761—21no—
87#14519758—21no—
88#14519758—21no—
89#14519758—21no—
90#14519758—21no—
91#14519754—21no—
92#14519754—21no—
93#14519754—21no—
94#14519754—21no—
95#14519749—21no—
96#14519749—21no—
97#14519749—21no—
98#14519749—21no—
99C4×Dic122—21no—
100C4×Dic122—21no—
101C4×Dic122—21no—
102C4×Dic122—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111#14519736—21no—
112#14519736—21no—
113#14519736—21no—
114#14519736—21no—
115#14519734—21no—
116#14519734—21no—
117#14519734—21no—
118#14519734—21no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2311yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2311yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519706—22no—
150#14519706—22no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154C22⋊#92418—21no—
155C22⋊#92418C2312yes—
156C22⋊#92418C2312yes—
157#14519687—22no—
158#14519687—22no—
159C8×Dic61—22no—
160C8×Dic61—22no—
161C22×D4×C61C2×C411yescharacteristic
162C23×C4×C61C2×C411yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61—21no—
165C22×C8×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169C4×D4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61C2×C411yescharacteristic
172C2×C22⋊C4×C61C2311yescharacteristic
173C2×C42×C61C2×C411yescharacteristic
174C22⋊C8×C61—21no—
175C22⋊C8×C61—21no—
176C22⋊C8×C61C2312yes—
177C22⋊C8×C61C2312yes—
178C24×C61C22×C411yescharacteristic
179C24×C61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—42no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—42no—
208C22×Dic61C22⋊C411yescharacteristic
209C22×Dic61C22⋊C411yescharacteristic
210C22×Dic61C22⋊C411yescharacteristic
211C22×Dic61C22⋊C411yescharacteristic
212C22×Dic61C22⋊C411yescharacteristic
213C22×Dic61C22⋊C411yescharacteristic
214C22×Dic61C22⋊C411yescharacteristic
215C22×Dic61C22⋊C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—42no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—42no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61—42no—
232C2×C8×C61—42no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—42no—
296C2×#92418—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61C2×C22⋊C411yescharacteristic
305C23×C61C2×C22⋊C411yescharacteristic
306C23×C61#13112yes—
307C23×C61#13112yes—
308C23×C61C23×C411yescharacteristic
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—41no—
313C22×D61—41no—
314D4×C61—42no—
315D4×C61—42no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C22⋊D61—42no—
336C22⋊D61—42no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C4×D61—42no—
369C4×D61—42no—
370Dic122—42no—
371Dic122—42no—
372C8×C61—42no—
373C8×C61—42no—
374#92418—42no—
375#92418—42no—
376#17382—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61#40812yes—
391C22×C61#40812yes—
392C22×C61C22×C22⋊C411yescharacteristic
393C22×C61C2×#13111yescharacteristic
394C22×C61C2×#13111yescharacteristic
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—81no—
399C2×D61—81no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61#41012yes—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61#41312yes—
418C2×#529—611no—
419C2×#432—611no—
420C2×#431—611no—
421#1473—612no—
422#1473—612no—
423#1470—612no—
424#1469—612no—
425#1459—611no—
426#1459—611no—
427#1459—611no—
428#1459D6111yescharacteristic, complemented
429C2×C61—21no—
430C2×C61—21no—
431C2×C61—22no—
432C2×C61—22no—
433C2×C61—81no—
434C2×C61C2×#40811yescharacteristic
435C2×C61C2×#41011yescharacteristic
436C2×C61C2×#41311yescharacteristic
437D61—81no—
438#529—1221no—
439#529—1221no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#529—1221no—
444#529—1221no—
445#529—1221no—
446C2×#126—611no—
447C2×#126—611no—
448C2×#125—611no—
449C2×#124—611no—
450C2×#123—611no—
451C2×#123—611no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×C4×Q8—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4C2×D6111yescharacteristic
458C2×#117—611no—
459C2×#117—611no—
460C22×C42—611no—
461#432—612no—
462#432—612no—
463#432—1221no—
464#432—1221no—
465#431—612no—
466#431—612no—
467#431—1221no—
468#431—1221no—
469C2×C4⋊C8—1221no—
470C2×C4⋊C8—1221no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8C2×D6111yescharacteristic
474C2×C22⋊C8C2×D6111yescharacteristic
475C2×#97—1221no—
476C2×C4×C8—1221no—
477#324—612no—
478#324—612no—
479#324—612no—
480#324C2×D6112yes—
481#323—612no—
482#323—612no—
483#323—612no—
484#323C2×D6112yes—
485C61#1738211yescharacteristic, complemented, Sylow
486C22×Q8—611no—
487C22×D4—611no—
488C22×D4—611no—
489C22×D4C4×D6111yescharacteristic
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4C4×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—1221no—
498C22×C8—1221no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#126—1221no—
504#126—1221no—
505#126—1221no—
506#126—1221no—
507#125—1221no—
508#125—1221no—
509#125—1221no—
510#125—1221no—
511#124—1221no—
512#124—1221no—
513#124—1221no—
514#124—1221no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519#123—1221no—
520#123—1221no—
521#123—1221no—
522#123—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527#121—1221no—
528#121—1221no—
529#121—1221no—
530#121—1221no—
531C4×Q8—1221no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8—1221no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4C4×D6111yescharacteristic
574C2×C22⋊C4C22×D6111yescharacteristic
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42C4×D6111yescharacteristic
589C4⋊C8—1222no—
590C4⋊C8—1222no—
591C4⋊C8—1222no—
592C4⋊C8—1222no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—612no—
596C22⋊C8—612no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8C22×D6112yes—
600C22⋊C8C22×D6112yes—
601#97—1222no—
602#97—1222no—
603C4×C8—1222no—
604C4×C8—1222no—
605C24—611no—
606C24C2×C4×D6111yescharacteristic
607C24C2×C4×D6111yescharacteristic
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—2442no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—2442no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—1222no—
661C2×C8—1222no—
662C2×C8—2442no—
663C2×C8—2442no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C42—21no—
705C42—21no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—1221no—
723C42—1221no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—1221no—
732C23—1221no—
733C23—1221no—
734C23—2441no—
735C23—2441no—
736C23C22⋊C4×D6111yescharacteristic
737C23C22⋊C4×D6111yescharacteristic
738C23#1451978312yes—
739C23#1451978512yes—
740C23C22×C4×D6111yescharacteristic
741Q8—2442no—
742Q8—2442no—
743D4—42no—
744D4—42no—
745D4—2442no—
746D4—2442no—
747D4—2442no—
748D4—2442no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—2442no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4C22⋊C4×D6111yescharacteristic
796C2×C4C22⋊C4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C8—42no—
800C8—42no—
801C8—2442no—
802C8—2442no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—42no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—81no—
815C22—81no—
816C22—4881no—
817C22—4881no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22#1683972712yes—
822C22#1683972712yes—
823C22C2×C22⋊C4×D6111yescharacteristic
824C22C2×#1451978311yescharacteristic
825C22C2×#1451978511yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—612no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—1221no—
839C4—1221no—
840C4—2441no—
841C4—2441no—
842C4—2441no—
843C4#1683973412yes—
844C2—21no—
845C2—21no—
846C2—22no—
847C2—22no—
848C2—81no—
849C2—4881no—
850C2C2×#1683972711yescharacteristic
851C2C2×#1683973411yescharacteristic
852C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1459C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1459D61
hypocenterC61#17382
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. C2×#16839812C2semidirect
4. #21444187C2semidirect
5. #21444185C2semidirect
6. #21444173C2semidirect
7. #21444169C2semidirect
8. #21444137C2semidirect
9. #21444135C2semidirect
10. #21444135C2semidirect
11. C61×#1459C2semidirect
428. #1459D61semidirect
485. C61#17382semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
C2×#168398162
C2×#168398122
#214441872
#214441852
#214441732
#214441692
#214441372
#214441352
C61×#14592
#1738261