Finite Group Databasebeta

← #29647055

Subgroups — #29647055

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459434C211yesmaximal, characteristic
2#21454463C211yesmaximal, characteristic, complemented
3#21444291C211yesmaximal, characteristic, complemented
4#21444282C211yesmaximal, characteristic, complemented
5#21444277C211yesmaximal, characteristic, complemented
6#21444265C211yesmaximal, characteristic, complemented
7#21444251C211yesmaximal, characteristic, complemented
8#21444247C211yesmaximal, characteristic, complemented
9#21444230C211yesmaximal, characteristic, complemented
10#21444225C211yesmaximal, characteristic, complemented
11#21444221C211yesmaximal, characteristic, complemented
12#21444213C211yesmaximal, characteristic, complemented
13#21444204C211yesmaximal, characteristic, complemented
14C2×#16839492C211yesmaximal, characteristic, complemented
15C61×#2990C211yesmaximal, characteristic, complemented
16#16840490C411yescharacteristic
17#16840485C411yescharacteristic
18#16840480—21no—
19#16840452C411yescharacteristic
20#16840452C411yescharacteristic
21#16840445—21no—
22#16840445—21no—
23D4×Dic122C411yescharacteristic
24#16840421C411yescharacteristic
25#16840421C411yescharacteristic
26#16840416C411yescharacteristic
27#16840411—21no—
28#16840319C2211yescharacteristic
29#16840316—21no—
30#16840296C2211yescharacteristic
31#16840296C2211yescharacteristic
32#16840292—21no—
33#16840292—21no—
34C4×#11758222C2211yescharacteristic
35C4×#11758224—21no—
36C2×C4×Dic122C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38#16839823—21no—
39#16839823—21no—
40#16839815C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839789—21no—
45#16839729—21no—
46C4×#11758194C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839492C2211yescharacteristic
51#16839492C2211yescharacteristic
52#16839492C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839492C2211yescharacteristic
58#16839492C2211yescharacteristic
59#16839492C2211yescharacteristic
60#16839489C2211yescharacteristic
61#16839489C2211yescharacteristic
62#16839489C2211yescharacteristic
63#16839489C2211yescharacteristic
64C4×#41×C61C2211yescharacteristic
65C61×#446—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic
70C61×#432C2211yescharacteristic
71C61×#431C2211yescharacteristic
72C61×#423C2211yescharacteristic
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758224—21no—
77C22×Dic122C2×C411yescharacteristic
78C22×Dic122C2×C411yescharacteristic
79C2×#11758194—21no—
80C22×#92418—21no—
81#14519777C2×C411yescharacteristic
82#14519777C2×C411yescharacteristic
83#14519776—21no—
84#14519775—21no—
85#14519772—21no—
86#14519772—21no—
87#14519771—21no—
88#14519771—21no—
89#14519770—21no—
90#14519770—21no—
91#14519769—21no—
92#14519769C2×C411yescharacteristic
93#14519769C2×C411yescharacteristic
94#14519767—21no—
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519765C2×C411yescharacteristic
99#14519765C2×C411yescharacteristic
100#14519763—21no—
101#14519763—21no—
102#14519761—21no—
103#14519761—21no—
104#14519760—21no—
105#14519760—21no—
106#14519758—21no—
107#14519758—21no—
108#14519757—21no—
109#14519756—21no—
110#14519756C2×C411yescharacteristic
111#14519756C2×C411yescharacteristic
112#14519756C2×C411yescharacteristic
113#14519756C2×C411yescharacteristic
114#14519755—21no—
115#14519755—21no—
116#14519754—21no—
117#14519754—21no—
118#14519753—21no—
119#14519751C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519749—21no—
122#14519749—21no—
123C4×Dic122—21no—
124C4×Dic122—21no—
125C4×Dic122—21no—
126C4×Dic122—21no—
127C4×Dic122—21no—
128C4×Dic122C2×C411yescharacteristic
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122C2×C411yescharacteristic
132C4×Dic122C2×C411yescharacteristic
133C4×Dic122C2311yescharacteristic
134C4×Dic122C2311yescharacteristic
135C4×Dic122C2311yescharacteristic
136#14519742—21no—
137C4×D244C2×C411yescharacteristic
138C4×D244C2311yescharacteristic
139D4×Dic61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144#14519737—21no—
145#14519737—21no—
146#14519736—21no—
147#14519736C2×C411yescharacteristic
148#14519735—21no—
149#14519734—21no—
150#14519734—21no—
151#14519734—21no—
152#14519733—21no—
153#14519733—21no—
154C2×C4⋊Dic61C2×C411yescharacteristic
155C2×C4⋊Dic61C2×C411yescharacteristic
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×C4×Dic61—21no—
159C2×C4×Dic61—21no—
160C42×D61—21no—
161C4⋊#92418—21no—
162C4⋊#92418—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168C22⋊#92418—21no—
169#14519688—21no—
170C4×#92418—21no—
171C4×#92418C2311yescharacteristic
172C4×#92418C2311yescharacteristic
173C4×#92418C2311yescharacteristic
174C4×#92418C2311yescharacteristic
175C2×#41×C61D411yescharacteristic
176C2×M16×C61—21no—
177C22×C8×C61—21no—
178C22×C8×C61—21no—
179C4×Q8×C61C2×C411yescharacteristic
180C4×Q8×C61D411yescharacteristic
181C4×D4×C61C2×C411yescharacteristic
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61C2×C411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187#117×C61D411yescharacteristic
188#117×C61D411yescharacteristic
189#117×C61D411yescharacteristic
190C2×C42×C61C2311yescharacteristic
191C2×C42×C61C2311yescharacteristic
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61—21no—
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C4⋊C8×C61C2311yescharacteristic
197C4⋊C8×C61C2311yescharacteristic
198C4⋊C8×C61C2311yescharacteristic
199C4⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61—21no—
203#97×C61—21no—
204#97×C61—21no—
205C4×C8×C61—21no—
206#41×C61—42no—
207C2×Q8×C61C22⋊C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227#11758224—44no—
228#11758222—22no—
229#11758222—41no—
230C2×D244C22×C411yescharacteristic
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—41no—
240C2×Dic122—41no—
241C2×Dic122C22×C411yescharacteristic
242C2×Dic122C22×C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244M16×C61—81no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—81no—
250C2×C8×C61—81no—
251C4⋊C4×C61C22⋊C411yescharacteristic
252C4⋊C4×C61C22⋊C411yescharacteristic
253C4⋊C4×C61C22⋊C411yescharacteristic
254C4⋊C4×C61C22⋊C411yescharacteristic
255C4⋊C4×C61C22⋊C411yescharacteristic
256C4⋊C4×C61C22⋊C411yescharacteristic
257C22⋊C4×C61C22⋊C411yescharacteristic
258C22⋊C4×C61C22⋊C411yescharacteristic
259C22⋊C4×C61C22⋊C411yescharacteristic
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C22⋊C4×C61C22⋊C411yescharacteristic
263C42×C61C22×C411yescharacteristic
264C42×C61C22×C411yescharacteristic
265C42×C61C22×C411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2411yescharacteristic
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320#11758194—42no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—42no—
326C23×C61C2×C22⋊C411yescharacteristic
327C23×C61C2×C22⋊C411yescharacteristic
328C23×C61C2×C22⋊C411yescharacteristic
329C22×D61—21no—
330Q8×C61—41no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—41no—
334C2×C4×C61—22no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—42no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375D244—21no—
376D244—21no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—41no—
380C4×D61—41no—
381Dic122—21no—
382Dic122—21no—
383Dic122—21no—
384Dic122—21no—
385Dic122—21no—
386Dic122—42no—
387Dic122—42no—
388Dic122—42no—
389Dic122#13112yes—
390C8×C61—41no—
391C8×C61—41no—
392C8×C61—41no—
393C8×C61—41no—
394#92418—41no—
395#92418—41no—
396#92418—41no—
397#92418—41no—
398#17524—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61#42112yes—
408C22×C61C22×C22⋊C411yescharacteristic
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61C2×#13111yescharacteristic
423C4×C61#56811yescharacteristic
424C4×C61#57711yescharacteristic
425C4×C61#57811yescharacteristic
426Dic61—22no—
427Dic61—41no—
428Dic61—41no—
429Dic61—41no—
430Dic61—41no—
431Dic61—41no—
432Dic61—41no—
433#3482—611no—
434#2990D6111yescharacteristic, complemented
435#2922—611no—
436#1497—611no—
437#1495—611no—
438#1494—611no—
439#1491—611no—
440#1488—611no—
441#1487—611no—
442#1483—611no—
443#1482—611no—
444#1481—611no—
445#1479—611no—
446#1477—611no—
447C2×Q8⋊C8—611no—
448C2×C61—22no—
449C2×C61—41no—
450C2×C61—41no—
451C2×C61#288011yescharacteristic
452C2×C61#289811yescharacteristic
453C2×C61C2×#42111yescharacteristic
454D61—81no—
455#557—611no—
456#556—611no—
457#556—1221no—
458#552—611no—
459#552—611no—
460#552—1221no—
461#552—1221no—
462D4×Q8—611no—
463#548—611no—
464#548—611no—
465#547—611no—
466#547—1221no—
467#533—611no—
468#533—1221no—
469#529—611no—
470#529—611no—
471#529—1221no—
472#529—1221no—
473C4×#41—611no—
474C4×#41—1221no—
475C4×#41C2×D6111yescharacteristic
476C2×C4×Q8—611no—
477C2×C4×Q8—611no—
478#446—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482#433—1221no—
483#433—1221no—
484#432C2×D6111yescharacteristic
485#432C2×D6111yescharacteristic
486#431—611no—
487#431—611no—
488#431—611no—
489#431—611no—
490#431C2×D6111yescharacteristic
491#424—1221no—
492#423C2×D6111yescharacteristic
493C2×C4⋊C8C2×D6111yescharacteristic
494C2×C4⋊C8C2×D6111yescharacteristic
495#408—1221no—
496C4×M16—611no—
497C2×C4×C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510D4⋊C8—611no—
511D4⋊C8—611no—
512D4⋊C8—611no—
513D4⋊C8—611no—
514C61#1752411yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—1221no—
517C2×#41D24411yescharacteristic
518C22×Q8—611no—
519C22×Q8—611no—
520C2×M16—21no—
521C2×M16—1221no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—1221no—
528C4⋊Q8—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#125—611no—
536#125—611no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#124—611no—
543#124—611no—
544#124—1221no—
545#124—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563#121—611no—
564#121—611no—
565#121—1221no—
566#121—1221no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8C4×D6111yescharacteristic
582C4×Q8C22⋊D6111yescharacteristic
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4C4×D6111yescharacteristic
593C4×D4C4×D6111yescharacteristic
594C4×D4C4×D6111yescharacteristic
595C4×D4C22⋊D6111yescharacteristic
596C4×D4C22⋊D6111yescharacteristic
597C4×D4C22⋊D6111yescharacteristic
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117D24411yescharacteristic
607#117D24411yescharacteristic
608#117D24411yescharacteristic
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42C22×D6111yescharacteristic
617C2×C42C22×D6111yescharacteristic
618C2×C42C22×D6111yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—1221no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8C22×D6111yescharacteristic
627C4⋊C8C22×D6111yescharacteristic
628C4⋊C8C22×D6111yescharacteristic
629C4⋊C8C22×D6111yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637#97—21no—
638#97—21no—
639#97—1221no—
640C4×C8—21no—
641C4×C8—611no—
642C4×C8—611no—
643C4×C8—611no—
644C4×C8—611no—
645C4×C8—1221no—
646#41—42no—
647#41—1222no—
648#41—2441no—
649#41—2444no—
650C2×Q8—611no—
651C2×Q8—611no—
652C2×Q8—611no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8—1221no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8—2441no—
659C2×Q8—2441no—
660C2×Q8#1175819811yescharacteristic
661C2×D4—611no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4#1175819811yescharacteristic
666C2×D4#1175819811yescharacteristic
667C2×D4#1175819811yescharacteristic
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4C2×C4×D6111yescharacteristic
676C22×C4C2×C4×D6111yescharacteristic
677C22×C4C2×C4×D6111yescharacteristic
678C22×C4C2×D24411yescharacteristic
679C22×C4C2×D24411yescharacteristic
680C22×C4C2×D24411yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684M16—81no—
685M16—2442no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—81no—
691C2×C8—81no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—2442no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4#1175819811yescharacteristic
723C4⋊C4#1175819811yescharacteristic
724C4⋊C4#1175819811yescharacteristic
725C4⋊C4#1175819811yescharacteristic
726C4⋊C4#1175819811yescharacteristic
727C4⋊C4#1175819811yescharacteristic
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4#1175819811yescharacteristic
742C22⋊C4#1175819811yescharacteristic
743C22⋊C4#1175819811yescharacteristic
744C22⋊C4#1175819811yescharacteristic
745C22⋊C4#1175819811yescharacteristic
746C22⋊C4#1175819811yescharacteristic
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42—1221no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42C2×C4×D6111yescharacteristic
757C42C2×C4×D6111yescharacteristic
758C42C2×C4×D6111yescharacteristic
759C42C2×D24411yescharacteristic
760C42C2×D24411yescharacteristic
761C42C2×D24411yescharacteristic
762C42C2×C22⋊D6111yescharacteristic
763C42C2×C22⋊D6111yescharacteristic
764C42C2×C22⋊D6111yescharacteristic
765C42C23×D6111yescharacteristic
766C23—1221no—
767C23C2×#1175819811yescharacteristic
768C23C2×#1175819811yescharacteristic
769C23C2×#1175819811yescharacteristic
770Q8—41no—
771Q8—612no—
772Q8—1221no—
773Q8—1221no—
774Q8—1221no—
775Q8—1221no—
776Q8—1221no—
777Q8—2442no—
778Q8—2442no—
779Q8—2442no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—1221no—
784D4—1221no—
785D4—2442no—
786D4—2442no—
787D4—2442no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4C2×#1175819811yescharacteristic
819C2×C4C2×#1175819811yescharacteristic
820C2×C4C2×#1175819811yescharacteristic
821C2×C4C2×#1175819811yescharacteristic
822C2×C4C2×#1175819811yescharacteristic
823C2×C4C2×#1175819811yescharacteristic
824C2×C4C2×#1175819811yescharacteristic
825C2×C4C2×#1175819811yescharacteristic
826C2×C4C2×#1175819811yescharacteristic
827C2×C4C22×C4×D6111yescharacteristic
828C2×C4C22×C22⋊D6111yescharacteristic
829C2×C4C22×D24411yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—2441no—
835C8—2441no—
836C8—2441no—
837C8—2441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22#1683977812yes—
850C22C22×#1175819811yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—1222no—
862C4—2441no—
863C4—2441no—
864C4—2441no—
865C4—2441no—
866C4—2441no—
867C4—2441no—
868C4#131×D6111yescharacteristic
869C4#1684052711yescharacteristic
870C4#1684057311yescharacteristic
871C4#1684057711yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—4881no—
876C2#2145426611yescharacteristic
877C2#2145434911yescharacteristic
878C2C2×#1683977811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2990C2
socleC22×C61C22×C22⋊C4
prime radical#21459434C2
cosocleC42×C61C24
hypercenter#2990D61
hypocenterC61#17524
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #21454463C2semidirect
3. #21444291C2semidirect
4. #21444282C2semidirect
5. #21444277C2semidirect
6. #21444265C2semidirect
7. #21444251C2semidirect
8. #21444247C2semidirect
9. #21444230C2semidirect
10. #21444225C2semidirect
11. #21444221C2semidirect
12. #21444213C2semidirect
13. #21444204C2semidirect
14. C2×#16839492C2semidirect
15. C61×#2990C2semidirect
434. #2990D61semidirect
514. C61#17524semidirect

Maximal subgroups

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

subgroupindex
#214594342
#214544632
#214442912
#214442822
#214442772
#214442652
#214442512
#214442472
#214442302
#214442252
#214442212
#214442132
#214442042
C2×#168394922
C61×#29902
#1752461