Finite Group Databasebeta

← #29646646

Subgroups — #29646646

Order 15616.

1010 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
1#21459112C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3C2×#16839813C211yesmaximal, characteristic, complemented
4#21444290C212yesmaximal, complemented
5#21444286C212yesmaximal, complemented
6#21444283C212yesmaximal, complemented
7#21444281C212yesmaximal, complemented
8#21444202C211yesmaximal, characteristic, complemented
9#21444201C211yesmaximal, characteristic, complemented
10#21444199C211yesmaximal, characteristic, complemented
11C61×#1476C211yesmaximal, characteristic, complemented
12#16840316C411yescharacteristic
13#16840316C2211yescharacteristic
14#16840315C411yescharacteristic
15#16840309C411yescharacteristic
16#16840309C2211yescharacteristic
17#16840308C411yescharacteristic
18#16840299C411yescharacteristic
19#16840299C2211yescharacteristic
20#16840294C411yescharacteristic
21#16840294C2211yescharacteristic
22#16840292—21no—
23#16840292—21no—
24#16840290—21no—
25#16840290—21no—
26#16840274C411yescharacteristic
27#16840271—21no—
28#16840271—21no—
29#16840269C411yescharacteristic
30C4×#11758222—21no—
31C4×#11758222—21no—
32C4×#11758222C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839818C2212yes—
35#16839816—21no—
36#16839815C2211yescharacteristic
37#16839813—21no—
38#16839813—21no—
39#16839813—21no—
40#16839813C2212yes—
41#16839813C2212yes—
42#16839784C2212yes—
43C2×#14519706—21no—
44#16839724—21no—
45C2×#14519689—21no—
46C4×#11758189—21no—
47C2×C4×#92418C2211yescharacteristic
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C2×#11758189—22no—
66C22×#92418—21no—
67#14519776C2×C411yescharacteristic
68#14519776C2×C411yescharacteristic
69#14519775C2×C411yescharacteristic
70#14519773C2×C411yescharacteristic
71#14519772—21no—
72#14519772—21no—
73#14519770—21no—
74#14519770—21no—
75#14519768C2×C411yescharacteristic
76#14519768C2×C411yescharacteristic
77#14519767—21no—
78#14519767—21no—
79#14519766C2×C411yescharacteristic
80#14519764C2×C411yescharacteristic
81#14519763—21no—
82#14519763—21no—
83#14519762—21no—
84#14519762—21no—
85#14519761—21no—
86#14519759—21no—
87#14519759—21no—
88#14519758—21no—
89#14519757C2×C411yescharacteristic
90#14519757C2×C411yescharacteristic
91#14519755—21no—
92#14519755—21no—
93#14519754—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519752C2×C411yescharacteristic
99#14519750—21no—
100#14519750—21no—
101#14519749—21no—
102#14519749—21no—
103#14519748C2×C411yescharacteristic
104#14519748C2×C411yescharacteristic
105#14519747—21no—
106#14519745—21no—
107C4×Dic122—21no—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic
112C4×Dic122C2311yescharacteristic
113C4×D244—21no—
114C4×D244—21no—
115C4×D244—21no—
116C4×D244—21no—
117C4×D244C2×C411yescharacteristic
118C4×D244C2311yescharacteristic
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129#14519736—21no—
130#14519736—21no—
131#14519736C2×C411yescharacteristic
132#14519734—21no—
133#14519734—21no—
134#14519734—21no—
135#14519734—21no—
136#14519734—21no—
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61C2311yescharacteristic
148C42×D61C2311yescharacteristic
149C4⋊#92418C2312yes—
150#14519706—22no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154#14519689—22no—
155#14519689—22no—
156#14519689—22no—
157#14519687—22no—
158C4×#92418—21no—
159C4×#92418—21no—
160C4×#92418C2312yes—
161C2×#41×C61C2×C411yescharacteristic
162C22×C8×C61—21no—
163C4×Q8×C61C2×C411yescharacteristic
164C4×Q8×C61C2311yescharacteristic
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61C2×C411yescharacteristic
168C4×D4×C61C2311yescharacteristic
169#117×C61—21no—
170#117×C61C2×C411yescharacteristic
171C2×C42×C61—21no—
172C2×C42×C61C2311yescharacteristic
173C4⋊C8×C61C2312yes—
174C22⋊C8×C61—21no—
175C4×C8×C61—21no—
176C4×C8×C61—21no—
177C4×C8×C61C2312yes—
178C23×D61C22⋊C411yescharacteristic
179#41×C61—22no—
180#41×C61—22no—
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198#11758222—22no—
199#11758222—22no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22×C411yescharacteristic
219C2×C4×D61C22×C411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122C22×C411yescharacteristic
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—42no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2411yescharacteristic
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—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
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×Dic61—21no—
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22×C411yescharacteristic
285C4×Dic61C22×C411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418—42no—
293#11758189—44no—
294C23×C61—21no—
295C23×C61C2×C22⋊C411yescharacteristic
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302Q8×C61—21no—
303Q8×C61—21no—
304D4×C61—21no—
305D4×C61—21no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61#13112yes—
319C2×C4×C61#13112yes—
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C2×Dic61—22no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340D244—21no—
341D244—21no—
342D244—42no—
343D244—42no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361Dic122—21no—
362Dic122—21no—
363Dic122—42no—
364Dic122—42no—
365C8×C61—42no—
366C8×C61—42no—
367#92418—42no—
368#92418—42no—
369#17477—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61#40812yes—
376C22×C61C22×C22⋊C411yescharacteristic
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—44no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61#40812yes—
393C4×C61#42112yes—
394C4×C61C2×#13111yescharacteristic
395C4×C61C2×#13111yescharacteristic
396C4×C61#57512yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—21no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406#3444—611no—
407#2920—611no—
408C2×#431—611no—
409#1497—612no—
410#1496—612no—
411#1495—612no—
412#1495—612no—
413#1476—611no—
414#1476—611no—
415#1476—611no—
416#1476D6111yescharacteristic, complemented
417C2×C61—22no—
418C2×C61—81no—
419C2×C61C2×#40811yescharacteristic
420C2×C61#289611yescharacteristic
421C2×C61C2×#42111yescharacteristic
422D61—41no—
423D61—41no—
424D61—81no—
425#533—611no—
426#533—611no—
427#533—611no—
428#532—611no—
429#532—611no—
430#532—611no—
431#529—611no—
432#529—611no—
433#529—611no—
434#529—611no—
435#529—1221no—
436#529—1221no—
437#529—1221no—
438#529—1221no—
439#525—611no—
440#525—611no—
441#525—1221no—
442#525—1221no—
443C4×#41—611no—
444C4×#41—1221no—
445C4×#41—1221no—
446C4×#41C2×D6111yescharacteristic
447C22×C42—611no—
448#432—612no—
449#432—1221no—
450#431—612no—
451#431—612no—
452#431—611no—
453#431—1221no—
454#431—1221no—
455#431—1221no—
456#431C2×D6111yescharacteristic
457#423—612no—
458C2×C4⋊C8—1221no—
459#407—1221no—
460C2×C22⋊C8—1221no—
461C4×M16—1221no—
462C2×C4×C8—611no—
463C2×C4×C8C2×D6111yescharacteristic
464Q8⋊C8—612no—
465Q8⋊C8—612no—
466Q8⋊C8—612no—
467Q8⋊C8C2×D6112yescomplemented
468D4⋊C8—612no—
469D4⋊C8—612no—
470D4⋊C8—612no—
471D4⋊C8C2×D6112yescomplemented
472C61#1747711yescharacteristic, complemented, Sylow
473C2×#41—611no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41C4×D6111yescharacteristic
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C2×M16—1222no—
481C22×C8—21no—
482C22×C8—1221no—
483C4⋊Q8—611no—
484C4⋊Q8—611no—
485C4⋊Q8—611no—
486#127—611no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#125—611no—
492#125—611no—
493#125—1221no—
494#125—1221no—
495#124—611no—
496#124—611no—
497#124—1221no—
498#124—1221no—
499#123—1221no—
500#123—1221no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504#123—1221no—
505C22⋊Q8—611no—
506C22⋊Q8—611no—
507C22⋊Q8—611no—
508C22⋊Q8—611no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513#121—611no—
514#121—611no—
515#121—611no—
516#121—611no—
517#121—1221no—
518#121—1221no—
519#121—1221no—
520#121—1221no—
521#120—1221no—
522#120—1221no—
523C4×Q8—611no—
524C4×Q8—611no—
525C4×Q8—1221no—
526C4×Q8—1221no—
527C4×Q8—1221no—
528C4×Q8—1221no—
529C4×Q8C4×D6111yescharacteristic
530C4×Q8C22×D6111yescharacteristic
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—611no—
534C4×D4—611no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4C4×D6111yescharacteristic
550C4×D4C22×D6111yescharacteristic
551#117—21no—
552#117—611no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117C4×D6111yescharacteristic
561C2×C42—21no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—1221no—
574C2×C42C22×D6111yescharacteristic
575C4⋊C8—612no—
576C4⋊C8—1222no—
577C4⋊C8—1222no—
578C4⋊C8—1222no—
579C4⋊C8C22×D6112yes—
580C22⋊C8—21no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1221no—
585#97—1222no—
586C4×C8—21no—
587C4×C8—21no—
588C4×C8—612no—
589C4×C8—1221no—
590C4×C8—1221no—
591C4×C8C22×D6112yes—
592C24—611no—
593#41—22no—
594#41—22no—
595#41—1222no—
596#41—1222no—
597#41—2444no—
598#41—2444no—
599C2×Q8—611no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8C2×C4×D6111yescharacteristic
603C2×D4—21no—
604C2×D4—611no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4C2×C4×D6111yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641M16—2444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—42no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—2442no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—611no—
651C4⋊C4—611no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4C2×C4×D6111yescharacteristic
667C4⋊C4C2×C4×D6111yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42C2×C4×D6111yescharacteristic
705C42D4×D6111yescharacteristic
706C42D4×D6111yescharacteristic
707C42C23×D6111yescharacteristic
708C23—21no—
709C23—611no—
710C23—611no—
711C23—1222no—
712C23—1221no—
713C23—2441no—
714C23—2441no—
715C23C22⋊C4×D6111yescharacteristic
716Q8—21no—
717Q8—21no—
718Q8—1221no—
719Q8—1221no—
720Q8—2442no—
721Q8—2442no—
722D4—21no—
723D4—21no—
724D4—42no—
725D4—1221no—
726D4—1221no—
727D4—2442no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732D4—2442no—
733D4—2442no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C22⋊C4×D6111yescharacteristic
773C2×C4C22⋊C4×D6111yescharacteristic
774C2×C4#1451978312yes—
775C2×C4#1451978512yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C8—42no—
780C8—42no—
781C8—2442no—
782C8—2442no—
783C22—21no—
784C22—21no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—2444no—
795C22—2441no—
796C22—2441no—
797C22—2441no—
798C22#1683972712yes—
799C22C2×C22⋊C4×D6111yescharacteristic
800C4—21no—
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—2441no—
812C4—2441no—
813C4—2441no—
814C4#1683972712yes—
815C4#1683977712yes—
816C4C2×#1451978311yescharacteristic
817C4C2×#1451978511yescharacteristic
818C4#1684055912yes—
819C2—22no—
820C2—81no—
821C2—4881no—
822C2—2441no—
823C2—2441no—
824C2C2×#1683972711yescharacteristic
825C2#2145433411yescharacteristic
826C2C2×#1683977711yescharacteristic
subgroupG/H
centerC42D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1476C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC42×C61C24
hypercenter#1476D61
hypocenterC61#17477
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. C2×#16839813C2semidirect
4. #21444290C2semidirect
5. #21444286C2semidirect
6. #21444283C2semidirect
7. #21444281C2semidirect
8. #21444202C2semidirect
9. #21444201C2semidirect
10. #21444199C2semidirect
11. C61×#1476C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
416. #1476D61semidirect
467. Q8⋊C8C2×D61semidirect
471. D4⋊C8C2×D61semidirect
472. C61#17477semidirect

Maximal subgroups

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

subgroupindex
#214591122
#214544472
C2×#168398132
#214442902
#214442862
#214442832
#214442812
#214442022
#214442012
#214441992
C61×#14762
#1747761