Finite Group Databasebeta

← #29647078

Subgroups — #29647078

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459445C211yesmaximal, characteristic
2#21454941C211yesmaximal, characteristic, complemented
3#21454458C211yesmaximal, characteristic, complemented
4#21444289C211yesmaximal, characteristic, complemented
5#21444286C211yesmaximal, characteristic, complemented
6#21444268C211yesmaximal, characteristic, complemented
7#21444257C211yesmaximal, characteristic, complemented
8#21444253C211yesmaximal, characteristic, complemented
9#21444252C211yesmaximal, characteristic, complemented
10#21444234C211yesmaximal, characteristic, complemented
11#21444217C211yesmaximal, characteristic, complemented
12#21444216C211yesmaximal, characteristic, complemented
13#21444205C211yesmaximal, characteristic, complemented
14#21444200C211yesmaximal, characteristic, complemented
15C61×#1477C211yesmaximal, characteristic, complemented
16Q8×Dic122C411yescharacteristic
17#16840477—21no—
18#16840477C411yescharacteristic
19#16840475—21no—
20#16840475—21no—
21#16840475C411yescharacteristic
22#16840475C411yescharacteristic
23#16840434C411yescharacteristic
24#16840433—21no—
25#16840433C411yescharacteristic
26#16840431C411yescharacteristic
27#16840431C411yescharacteristic
28#16840312—21no—
29#16840312C2211yescharacteristic
30#16840309—21no—
31#16840309—21no—
32#16840309C2211yescharacteristic
33#16840309C2211yescharacteristic
34C4×#11758226C2211yescharacteristic
35C4×#11758226C2211yescharacteristic
36C4×#11758222—21no—
37C4×#11758222C2211yescharacteristic
38#16839891—21no—
39#16839833—21no—
40#16839832—21no—
41C8×C22⋊D61—21no—
42#16839822—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic
45#16839818C2211yescharacteristic
46#16839815C2211yescharacteristic
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic
50#16839787—21no—
51#16839784C2211yescharacteristic
52C4⋊C8×D61C2211yescharacteristic
53#16839727—21no—
54C4×#11758189C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56Q8⋊#92418C2211yescharacteristic
57Q8⋊#92418C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60#16839491C2211yescharacteristic
61#16839491C2211yescharacteristic
62D4⋊#92418C2211yescharacteristic
63D4⋊#92418C2211yescharacteristic
64#16839489C2211yescharacteristic
65#16839489C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C2×C4⋊C8×C61C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758226C2×C411yescharacteristic
77C2×#11758222—21no—
78C2×#11758222—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222D411yescharacteristic
82C2×#11758189—21no—
83C2×#11758189—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519777—21no—
87#14519777C2×C411yescharacteristic
88#14519776—21no—
89#14519776—21no—
90#14519776C2×C411yescharacteristic
91#14519776C2×C411yescharacteristic
92#14519774—21no—
93#14519774C2×C411yescharacteristic
94#14519773—21no—
95#14519773—21no—
96#14519773C2×C411yescharacteristic
97#14519773C2×C411yescharacteristic
98#14519765—21no—
99#14519765—21no—
100#14519765—21no—
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519763—21no—
105#14519763—21no—
106#14519763—21no—
107#14519752—21no—
108#14519752—21no—
109#14519752C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111#14519751—21no—
112#14519751—21no—
113#14519751—21no—
114#14519751—21no—
115#14519751—21no—
116#14519751C2×C411yescharacteristic
117#14519751C2×C411yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123#14519750—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic
127#14519748C2×C411yescharacteristic
128Q8×Dic61C2×C411yescharacteristic
129Q8×Dic61C2×C411yescharacteristic
130C4×Dic122—21no—
131C4×Dic122C2×C411yescharacteristic
132C4×Dic122D411yescharacteristic
133C4×D244—21no—
134C4×D244—21no—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244C2×C411yescharacteristic
138C4×D244D411yescharacteristic
139C4×D244C2311yescharacteristic
140C4×D244C2311yescharacteristic
141#14519739—21no—
142#14519739—21no—
143#14519739C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61C2×C411yescharacteristic
150C4×C22⋊D61C2×C411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153#14519736—21no—
154#14519736D411yescharacteristic
155#14519735—21no—
156#14519735—21no—
157#14519735C2×C411yescharacteristic
158#14519735C2×C411yescharacteristic
159#14519734—21no—
160#14519734—21no—
161#14519734D411yescharacteristic
162#14519734D411yescharacteristic
163C42×D61—21no—
164C42×D61—21no—
165C42×D61C2311yescharacteristic
166C42×D61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418C2311yescharacteristic
169C4⋊#92418C2311yescharacteristic
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519688—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418C2311yescharacteristic
184C4×#92418C2311yescharacteristic
185C8×Dic61—21no—
186C8×Dic61—21no—
187C2×#41×C61C2×C411yescharacteristic
188C22×C8×C61—21no—
189C4×Q8×C61C2×C411yescharacteristic
190C4×Q8×C61C2311yescharacteristic
191C4×D4×C61—21no—
192C4×D4×C61—21no—
193C4×D4×C61C2×C411yescharacteristic
194C4×D4×C61C2311yescharacteristic
195#117×C61—21no—
196#117×C61C2×C411yescharacteristic
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C4⋊C8×C61—21no—
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206#41×C61—22no—
207#41×C61—41no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61C22⋊C411yescharacteristic
226C2×C22⋊D61C22⋊C411yescharacteristic
227#11758226—22no—
228#11758226—22no—
229#11758226—41no—
230#11758226—41no—
231#11758222—42no—
232#11758222—44no—
233#11758222—81no—
234#11758222—81no—
235#11758222—81no—
236#11758222—81no—
237#11758222—81no—
238#11758222—81no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244C22⋊C411yescharacteristic
246C2×D244C22×C411yescharacteristic
247C2×D244C22×C411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×Dic122—21no—
261C2×Dic122—21no—
262C2×Dic122—21no—
263C2×Dic122C22⋊C411yescharacteristic
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—81no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C22×C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C42×C61—21no—
277C42×C61—21no—
278C42×C61—21no—
279C42×C61C22×C411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2411yescharacteristic
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61C22⋊C411yescharacteristic
286C22⋊Dic61C22⋊C411yescharacteristic
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C22⋊C411yescharacteristic
305C4⋊Dic61C22⋊C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308#11758196—21no—
309#11758196—21no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328#11758189—42no—
329#11758189—81no—
330C8×D61—42no—
331C8×D61—81no—
332C23×C61—21no—
333C23×C61C2×C22⋊C411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61C2×C22⋊C411yescharacteristic
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—21no—
339Q8×C61#13112yes—
340D4×C61—21no—
341D4×C61—21no—
342D4×C61—42no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—41no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
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—22no—
362C22⋊D61—41no—
363C22⋊D61—42no—
364C22⋊D61—42no—
365C22⋊D61—81no—
366C22⋊D61—81no—
367C22⋊D61—81no—
368C22⋊D61—81no—
369C22⋊D61—81no—
370C22⋊D61—81no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379D244—21no—
380D244—21no—
381D244—21no—
382D244—21no—
383D244—41no—
384D244—42no—
385D244—42no—
386D244—42no—
387D244—81no—
388D244—81no—
389D244—81no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—21no—
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—22no—
399C4×D61—41no—
400C4×D61—42no—
401C4×D61—42no—
402C4×D61—42no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—42no—
408Dic122—22no—
409Dic122—81no—
410Dic122—81no—
411Dic122—81no—
412C8×C61—41no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#17526—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61C22×C22⋊C411yescharacteristic
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—41no—
440C4×C61—22no—
441C4×C61—21no—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—41no—
446C4×C61—41no—
447C4×C61C2×#13111yescharacteristic
448C4×C61#56811yescharacteristic
449C4×C61#57611yescharacteristic
450C4×C61#57711yescharacteristic
451Dic61—21no—
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—41no—
457Dic61—41no—
458Dic61#42112yes—
459#3483—611no—
460#2990—611no—
461#2922—611no—
462#1496—611no—
463#1496—611no—
464#1492—611no—
465#1489—611no—
466#1488—611no—
467#1488—611no—
468#1484—611no—
469#1480—611no—
470#1480—611no—
471#1477—611no—
472#1477D6111yescharacteristic, complemented
473#1476—611no—
474C2×C61—41no—
475C2×C61—81no—
476C2×C61#288011yescharacteristic
477C2×C61#289711yescharacteristic
478C2×C61C2×#42111yescharacteristic
479D61—41no—
480D61—41no—
481D61—81no—
482D61—81no—
483Q82—611no—
484#555—611no—
485#555—611no—
486#555—611no—
487#555—1221no—
488#555—1221no—
489#555—1221no—
490#550—611no—
491#550—611no—
492#550—611no—
493#550—611no—
494#550—1221no—
495#532—611no—
496#532—611no—
497#532—611no—
498#532—1221no—
499#532—1221no—
500#532—1221no—
501C4×#41—611no—
502C4×#41—611no—
503C4×#41—611no—
504C4×#41—1221no—
505C4×#41C2×D6111yescharacteristic
506#446—1221no—
507#435—1221no—
508#435—1221no—
509C8×D4—1221no—
510#433—1221no—
511#433—1221no—
512#432—611no—
513#432—611no—
514#431—611no—
515#431—611no—
516#431—611no—
517#431—611no—
518#431C2×D6111yescharacteristic
519#424—1221no—
520#423—611no—
521C2×C4⋊C8—611no—
522C2×C4⋊C8C2×D6111yescharacteristic
523#408—1221no—
524C4×M16—611no—
525C2×C4×C8—611no—
526Q8⋊C8—611no—
527Q8⋊C8—611no—
528Q8⋊C8C2×D6111yescharacteristic
529Q8⋊C8C2×D6111yescharacteristic
530D4⋊C8—611no—
531D4⋊C8—611no—
532D4⋊C8—611no—
533D4⋊C8—611no—
534D4⋊C8—611no—
535D4⋊C8—611no—
536D4⋊C8—611no—
537D4⋊C8—611no—
538D4⋊C8—611no—
539D4⋊C8—611no—
540D4⋊C8C2×D6111yescharacteristic
541D4⋊C8C2×D6111yescharacteristic
542C61#1752611yescharacteristic, complemented, Sylow
543C2×#41—611no—
544C2×#41—611no—
545C2×#41—611no—
546C2×#41—1221no—
547C2×#41—1221no—
548C2×#41—1221no—
549C2×#41—1221no—
550C2×#41C4×D6111yescharacteristic
551C2×M16—1221no—
552C2×M16—1221no—
553C22×C8—21no—
554C22×C8—1221no—
555C22×C8—1221no—
556C4⋊Q8—611no—
557C4⋊Q8—611no—
558C4⋊Q8—611no—
559C4⋊Q8—1221no—
560C4⋊Q8—1221no—
561C4⋊Q8—1221no—
562#127—611no—
563#127—611no—
564#127—611no—
565#127—1221no—
566#127—1221no—
567#127—1221no—
568#124—1221no—
569#124—1221no—
570#124—1221no—
571#124—1221no—
572#124—1221no—
573#124—1221no—
574#124—1221no—
575#124—1221no—
576#124—1221no—
577#121—611no—
578#121—611no—
579#121—611no—
580#121—611no—
581#121—611no—
582#121—611no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8—1221no—
603C4×Q8C4×D6111yescharacteristic
604C4×Q8C22×D6111yescharacteristic
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4C4×D6111yescharacteristic
628C4×D4C22×D6111yescharacteristic
629#117—21no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638#117—1221no—
639#117—1221no—
640#117C4×D6111yescharacteristic
641C2×C42—21no—
642C2×C42—611no—
643C2×C42—611no—
644C2×C42—1221no—
645C2×C42—1221no—
646C2×C42C22×D6111yescharacteristic
647C4⋊C8—21no—
648C4⋊C8—21no—
649C4⋊C8—611no—
650C4⋊C8—611no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8C22×D6111yescharacteristic
657C4⋊C8C22×D6111yescharacteristic
658C22⋊C8—21no—
659C22⋊C8—1221no—
660C22⋊C8—1221no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C22⋊C8—1221no—
665#97—1221no—
666#97—1221no—
667#97—1221no—
668C4×C8—611no—
669C4×C8—611no—
670C4×C8—1221no—
671C4×C8—1221no—
672C4×C8C22×D6111yescharacteristic
673C4×C8C22×D6111yescharacteristic
674#41—22no—
675#41—41no—
676#41—1222no—
677#41—1222no—
678#41—4881no—
679#41—4881no—
680#41—4881no—
681#41—4881no—
682#41—4881no—
683#41—4881no—
684#41—2442no—
685#41—2444no—
686#41—2441no—
687#41—2441no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8C2×C4×D6111yescharacteristic
693C2×D4—21no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4C2×C4×D6111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4C2×C4×D6111yescharacteristic
730C22×C4D4×D6111yescharacteristic
731C22×C4D4×D6111yescharacteristic
732M16—4881no—
733M16—2442no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—81no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—4881no—
744C2×C8—2442no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4C2×C4×D6111yescharacteristic
761C4⋊C4C2×C4×D6111yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—611no—
766C22⋊C4—611no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C42—21no—
784C42—21no—
785C42—21no—
786C42—611no—
787C42—611no—
788C42—611no—
789C42—611no—
790C42—611no—
791C42—611no—
792C42—1221no—
793C42—1221no—
794C42—1221no—
795C42—1221no—
796C42C2×C4×D6111yescharacteristic
797C42D4×D6111yescharacteristic
798C42D4×D6111yescharacteristic
799C42C23×D6111yescharacteristic
800C23—21no—
801C23—611no—
802C23—611no—
803C23—1221no—
804C23—1221no—
805C23C22⋊C4×D6111yescharacteristic
806Q8—21no—
807Q8—1222no—
808Q8—4881no—
809Q8—4881no—
810Q8—4881no—
811Q8#1451978312yes—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—1222no—
816D4—1221no—
817D4—1221no—
818D4—1221no—
819D4—1221no—
820D4—4881no—
821D4—4881no—
822D4—4881no—
823D4—4881no—
824D4—4881no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—2441no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2441no—
835D4—2442no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—1222no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—2441no—
866C2×C4—2442no—
867C2×C4—2442no—
868C2×C4—2442no—
869C2×C4—2442no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4C22⋊C4×D6111yescharacteristic
875C2×C4C22⋊C4×D6111yescharacteristic
876C2×C4C22⋊C4×D6111yescharacteristic
877C2×C4C22×C4×D6111yescharacteristic
878C2×C4C2×D4×D6111yescharacteristic
879C2×C4C2×D4×D6111yescharacteristic
880C8—41no—
881C8—41no—
882C8—41no—
883C8—41no—
884C8—2441no—
885C8—2441no—
886C8—2441no—
887C8—2441no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—1221no—
895C22—1221no—
896C22—1221no—
897C22—1221no—
898C22—1221no—
899C22—1221no—
900C22—2441no—
901C22—2441no—
902C22—2441no—
903C22—2441no—
904C22—2441no—
905C22—2441no—
906C22C2×C22⋊C4×D6111yescharacteristic
907C4—21no—
908C4—21no—
909C4—21no—
910C4—21no—
911C4—22no—
912C4—41no—
913C4—41no—
914C4—612no—
915C4—1221no—
916C4—1221no—
917C4—1221no—
918C4—1221no—
919C4—1221no—
920C4—2441no—
921C4—2441no—
922C4C2×#1451978311yescharacteristic
923C4#1684052811yescharacteristic
924C4#1684056611yescharacteristic
925C4#1684057111yescharacteristic
926C2—41no—
927C2—81no—
928C2—4881no—
929C2—4881no—
930C2—2441no—
931C2—2441no—
932C2#2145426511yescharacteristic
933C2#2145434311yescharacteristic
934C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1477C2
socleC22×C61C22×C22⋊C4
prime radical#21459445C2
cosocleC42×C61C24
hypercenter#1477D61
hypocenterC61#17526
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #21454941C2semidirect
3. #21454458C2semidirect
4. #21444289C2semidirect
5. #21444286C2semidirect
6. #21444268C2semidirect
7. #21444257C2semidirect
8. #21444253C2semidirect
9. #21444252C2semidirect
10. #21444234C2semidirect
11. #21444217C2semidirect
12. #21444216C2semidirect
13. #21444205C2semidirect
14. #21444200C2semidirect
15. C61×#1477C2semidirect
472. #1477D61semidirect
542. C61#17526semidirect

Maximal subgroups

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

subgroupindex
#214594452
#214549412
#214544582
#214442892
#214442862
#214442682
#214442572
#214442532
#214442522
#214442342
#214442172
#214442162
#214442052
#214442002
C61×#14772
#1752661