Finite Group Databasebeta

← #30611798

Subgroups — #30611798

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462735C211yesmaximal, characteristic, complemented
2#21462517C211yesmaximal, characteristic, complemented
3#21461343C211yesmaximal, characteristic, complemented
4#21461342C211yesmaximal, characteristic, complemented
5#21461339C211yesmaximal, characteristic, complemented
6#21461338C211yesmaximal, characteristic, complemented
7#21461337C211yesmaximal, characteristic, complemented
8#21461326C211yesmaximal, characteristic, complemented
9#21461323C211yesmaximal, characteristic, complemented
10#21461322C211yesmaximal, characteristic, complemented
11#21461321C211yesmaximal, characteristic, complemented
12#21461317C211yesmaximal, characteristic, complemented
13#21461316C211yesmaximal, characteristic, complemented
14C2×#16840620C211yesmaximal, characteristic, complemented
15#21459687C211yesmaximal, characteristic
16#16840811—21no—
17#16840789—21no—
18#16840789—21no—
19D4×#92420—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic, complemented
23#16840782C2211yescharacteristic, complemented
24#16840780C2211yescharacteristic, complemented
25#16840780C2211yescharacteristic, complemented
26#16840779C2211yescharacteristic
27#16840779C2211yescharacteristic, complemented
28#16840779C2211yescharacteristic, complemented
29#16840765C2211yescharacteristic
30C2×#14519844C2211yescharacteristic
31C2×#14519844C2211yescharacteristic
32C2×#14519844C2211yescharacteristic, complemented
33D61⋊(C4⋊C8)C2211yescharacteristic, complemented
34#16840735—21no—
35#16840726—21no—
36#16840622C2211yescharacteristic, complemented
37#16840622C2211yescharacteristic, complemented
38#16840622C2211yescharacteristic, complemented
39#16840622C2211yescharacteristic, complemented
40#16840621C2211yescharacteristic, complemented
41#16840621C2211yescharacteristic, complemented
42#16840621C2211yescharacteristic, complemented
43#16840621C2211yescharacteristic, complemented
44#16840620C2211yescharacteristic
45#16840620C2211yescharacteristic
46#16840620C2211yescharacteristic
47#16840620C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840496—21no—
53#16840495C411yescharacteristic
54#16840494C411yescharacteristic
55#16840431C411yescharacteristic
56#16840430—21no—
57#16840430C411yescharacteristic
58#16840408C411yescharacteristic
59#16840406C411yescharacteristic
60#16840403C411yescharacteristic
61#16840402—21no—
62#16840399—21no—
63#16840364—21no—
64#16840362—21no—
65#16840327—21no—
66#16840314C2211yescharacteristic
67#16840311C2211yescharacteristic
68#16840309C2211yescharacteristic
69#16840308C2211yescharacteristic
70#16840307C2211yescharacteristic
71C2×#14519773C2211yescharacteristic
72#16840235—21no—
73C4×#11758224C2211yescharacteristic
74C61×#546C411yescharacteristic
75C2×#11758217—21no—
76C2×D61⋊C8—21no—
77C22×#92420—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844C2311yescharacteristic
84#14519844C2311yescharacteristic
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100#14519832—21no—
101#14519832—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758226C2×C411yescharacteristic
108C2×#11758222—21no—
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224—21no—
111C2×#11758224C2×C411yescharacteristic
112C2×#11758224D411yescharacteristic
113C22×D244C2×C411yescharacteristic
114C22×C22⋊D61—21no—
115C22×C22⋊D61—21no—
116#14519776C2311yescharacteristic
117#14519775C2311yescharacteristic
118#14519773—21no—
119#14519773—21no—
120#14519773—21no—
121#14519773—21no—
122#14519773C2×C411yescharacteristic
123#14519773C2×C411yescharacteristic
124#14519773C2311yescharacteristic
125#14519773C2311yescharacteristic
126#14519767—21no—
127#14519766C2×C411yescharacteristic
128#14519765C2×C411yescharacteristic
129#14519764C2×C411yescharacteristic
130#14519763—21no—
131#14519763—21no—
132#14519763—21no—
133#14519763—21no—
134#14519762—21no—
135#14519762—21no—
136#14519761—21no—
137#14519760—21no—
138#14519759—21no—
139#14519759—21no—
140#14519758—21no—
141#14519756C2×C411yescharacteristic
142#14519754—21no—
143#14519752—21no—
144#14519752C2×C411yescharacteristic
145#14519751—21no—
146#14519751C2×C411yescharacteristic
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519750—21no—
151#14519750—21no—
152#14519749—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519749—21no—
157#14519748—21no—
158#14519748C2×C411yescharacteristic
159#14519747—21no—
160#14519746—21no—
161#14519745—21no—
162Q8×Dic61C2×C411yescharacteristic
163C4×Dic122C2×C411yescharacteristic
164#14519742—21no—
165#14519742C2×C411yescharacteristic
166#14519742D411yescharacteristic
167C4×D244C2×C411yescharacteristic
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61D411yescharacteristic
170#14519739C2×C411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61C2×C411yescharacteristic
177C4×C22⋊D61C2×C411yescharacteristic
178#14519737—21no—
179#14519737—21no—
180#14519737—21no—
181#14519737—21no—
182#14519737—21no—
183#14519737D411yescharacteristic
184#14519737D411yescharacteristic
185#14519735D411yescharacteristic
186#14519733—21no—
187#14519733D411yescharacteristic
188#14519733D411yescharacteristic
189C2×C22⋊Dic61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61—21no—
206C24×C61—21no—
207C23×D61—21no—
208#41×C61—81no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—81no—
214C2×D4×C61C22⋊C411yescharacteristic
215C2×D4×C61C22×C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—42no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61—81no—
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245#11758226—81no—
246#11758224—22no—
247#11758224—22no—
248#11758224—81no—
249#11758224—81no—
250#11758224—81no—
251#11758222—81no—
252#11758222—81no—
253#11758222—81no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—81no—
258C2×D244C22×C411yescharacteristic
259C2×D244C22×C411yescharacteristic
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122C22⋊C411yescharacteristic
269C2×Dic122C22×C411yescharacteristic
270#11758217—42no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—42no—
280C2×#92420—81no—
281C2×#92420—81no—
282D61⋊C8—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61C22⋊C411yescharacteristic
292C22⋊C4×C61C22⋊C411yescharacteristic
293C42×C61C22×C411yescharacteristic
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311C4⋊Dic61—21no—
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C22×C411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2411yescharacteristic
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—42no—
337C23×C61—81no—
338C23×C61—81no—
339C23×C61C2×C22⋊C411yescharacteristic
340C23×C61C2×C22⋊C411yescharacteristic
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—42no—
344C22×D61—81no—
345C22×D61—81no—
346C22×D61C2×C22⋊C411yescharacteristic
347Q8×C61—41no—
348D4×C61—22no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—81no—
352D4×C61—81no—
353D4×C61—81no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—81no—
359C2×C4×C61—81no—
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C23×C411yescharacteristic
365C22⋊D61—22no—
366C22⋊D61—22no—
367C22⋊D61—41no—
368C22⋊D61—41no—
369C22⋊D61—41no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—41no—
375C22⋊D61—42no—
376C22⋊D61—42no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C22⋊D61—81no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—81no—
392C2×Dic61—81no—
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61#13512yes—
399C2×Dic61#13512yes—
400C2×Dic61C22×D411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402D244—41no—
403D244—41no—
404D244—81no—
405D244—81no—
406D244—81no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—41no—
412C4×D61—81no—
413C4×D61—81no—
414C4×D61—81no—
415C4×D61—81no—
416Dic122—22no—
417Dic122—41no—
418Dic122—41no—
419Dic122—41no—
420#92420—41no—
421#92420—41no—
422#92420—41no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17724—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—162no—
441C22×C61#41612yes—
442C22×C61C22×C22⋊C411yescharacteristic
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—162no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—41no—
465Dic61—41no—
466Dic61#41612yes—
467Dic61C2×#13511yescharacteristic
468Dic61C2×#13511yescharacteristic
469Dic61#57611yescharacteristic
470Dic61#57711yescharacteristic
471#3508—611no—
472#2988—611no—
473#2925—611no—
474#1553—611no—
475#1553—611no—
476#1551—611no—
477#1551—611no—
478#1550—611no—
479#1545—611no—
480#1543—611no—
481#1543—611no—
482#1542—611no—
483#1540—611no—
484#1540—611no—
485C2×#331—611no—
486C2×C61—22no—
487C2×C61—41no—
488C2×C61—81no—
489C2×C61—81no—
490C2×C61#288811yescharacteristic
491C2×C61C2×#41611yescharacteristic
492C2×C61#289711yescharacteristic
493D61—41no—
494D61—81no—
495D61—81no—
496#559—611no—
497#559—611no—
498#559—1221no—
499#550—611no—
500#550—611no—
501#550—1221no—
502#546—611no—
503#546—611no—
504#546—611no—
505#546—1221no—
506#546—1221no—
507#546#692311yescharacteristic
508#540—1221no—
509#540—1221no—
510#535—1221no—
511#533—611no—
512#532—611no—
513#532—611no—
514#532—611no—
515#532—611no—
516C2×#127—611no—
517#518—1221no—
518C4×#41—611no—
519C8×Q8—1221no—
520C8×D4—1221no—
521C8×D4—1221no—
522C8×D4—1221no—
523#433—1221no—
524#433—1221no—
525#432—611no—
526#432—611no—
527#431—611no—
528#431—611no—
529#431—611no—
530#431—611no—
531#431—611no—
532#423—611no—
533C2×C4⋊C8—611no—
534C2×C4⋊C8—611no—
535C2×C4⋊C8—611no—
536C2×C4⋊C8—611no—
537#408—1221no—
538#405—1221no—
539#333—611no—
540#333—611no—
541#333—611no—
542#333—611no—
543#332—611no—
544#332—611no—
545#332—611no—
546#332—611no—
547#331—611no—
548#331—611no—
549#331—611no—
550#331—611no—
551#331—611no—
552#331—611no—
553#331—611no—
554#331—611no—
555C61#1772411yescharacteristic, complemented, Sylow
556C2×#41—611no—
557C2×#41—611no—
558C2×#41—611no—
559C2×#41—611no—
560C2×#41—1221no—
561C2×#41—1221no—
562C2×#41C2×#692311yescharacteristic
563C22×D4—611no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4C2×#692311yescharacteristic
567C2×M16—1221no—
568C22×C8—1221no—
569C22×C8—1221no—
570C22×C8—1221no—
571C22×C8—1221no—
572C4⋊Q8—611no—
573C4⋊Q8—611no—
574#127—611no—
575#127—611no—
576#127—611no—
577#127—611no—
578#127—1221no—
579#127—1221no—
580#127—1221no—
581#127—1221no—
582#125—1221no—
583#124—611no—
584#124—611no—
585#124—611no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124C2×#692311yescharacteristic
591#123—21no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599C22⋊Q8—611no—
600C22⋊Q8—1221no—
601C22⋊Q8C2×#692311yescharacteristic
602#121—21no—
603#121—611no—
604#121—611no—
605#121—611no—
606#121—1221no—
607#121—1221no—
608#121—1221no—
609#121—1221no—
610#121—1221no—
611#121—1221no—
612#121—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121C2×#692311yescharacteristic
620#120—21no—
621#120—1221no—
622#120—1221no—
623#120—1221no—
624C4×Q8—611no—
625C4×Q8—611no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×Q8—1221no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4C2×#692311yescharacteristic
648C4×D4C2×#692311yescharacteristic
649#117—611no—
650#117—611no—
651#117—611no—
652#117—1221no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C42—611no—
658C2×C42—611no—
659C2×C42—611no—
660C4⋊C8—611no—
661C4⋊C8—611no—
662C4⋊C8—611no—
663C4⋊C8—611no—
664C4⋊C8—611no—
665C4⋊C8—611no—
666C4⋊C8—611no—
667C4⋊C8—611no—
668C4⋊C8—1221no—
669C4⋊C8—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C4⋊C8—1221no—
673C22⋊C8—1221no—
674C22⋊C8—1221no—
675C22⋊C8—1221no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680#97—1221no—
681#97—1221no—
682C4×C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685C4×C8—1221no—
686C4×C8—1221no—
687C24—21no—
688C24—1221no—
689#41—81no—
690#41—1222no—
691#41—1222no—
692#41—4881no—
693#41—4881no—
694#41—4881no—
695#41—4881no—
696#41—4881no—
697#41—4881no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—611no—
701C2×Q8—1221no—
702C2×Q8C22×#692311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—81no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—4881no—
727C2×D4—4881no—
728C2×D4—4881no—
729C2×D4—2442no—
730C2×D4—2442no—
731C2×D4C22⋊#692311yescharacteristic
732C2×D4C22×#692311yescharacteristic
733C2×D4C22×#692311yescharacteristic
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4C22×#692311yescharacteristic
750C22×C4C22×#692311yescharacteristic
751M16—2442no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—4881no—
761C2×C8—4881no—
762C2×C8—4881no—
763C2×C8—2442no—
764C4⋊C4—21no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—611no—
770C4⋊C4—611no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4C22⋊#692311yescharacteristic
778C4⋊C4C22×#692311yescharacteristic
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4C22⋊#692311yescharacteristic
802C22⋊C4C22⋊#692311yescharacteristic
803C42—611no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—611no—
810C42—611no—
811C42—611no—
812C42—1221no—
813C42—1221no—
814C42C22×#692311yescharacteristic
815C23—21no—
816C23—21no—
817C23—42no—
818C23—81no—
819C23—81no—
820C23—611no—
821C23—1221no—
822C23—1221no—
823C23—4881no—
824C23—4881no—
825C23—2442no—
826C23C2×C22⋊#692311yescharacteristic
827C23C2×C22⋊#692311yescharacteristic
828Q8—41no—
829Q8—1222no—
830Q8—2441no—
831Q8—2441no—
832Q8—2441no—
833D4—22no—
834D4—41no—
835D4—41no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—1222no—
840D4—1222no—
841D4—4881no—
842D4—4881no—
843D4—4881no—
844D4—4881no—
845D4—4881no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—2441no—
851D4—2441no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2442no—
861D4—2442no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—4881no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4881no—
895C2×C4—2441no—
896C2×C4C2×C22⋊#692311yescharacteristic
897C2×C4C2×C22⋊#692311yescharacteristic
898C2×C4C2×C22⋊#692311yescharacteristic
899C2×C4C2×C22⋊#692311yescharacteristic
900C2×C4C23×#692311yescharacteristic
901C8—2441no—
902C8—2441no—
903C8—2441no—
904C8—2441no—
905C8—2441no—
906C8—2441no—
907C8—2441no—
908C8—2441no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—162no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—9762no—
925C22—2441no—
926C22—2441no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22#1684075212yes—
932C22C22×C22⋊#692311yescharacteristic
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—41no—
939C4—41no—
940C4—611no—
941C4—611no—
942C4—612no—
943C4—611no—
944C4—611no—
945C4—1221no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—2441no—
950C4—2441no—
951C2—22no—
952C2—41no—
953C2—81no—
954C2—81no—
955C2—4881no—
956C2—4881no—
957C2—2441no—
958C2#2146242911yescharacteristic
959C2C2×#1684075211yescharacteristic
960C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459687C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17724
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462735C2semidirect
2. #21462517C2semidirect
3. #21461343C2semidirect
4. #21461342C2semidirect
5. #21461339C2semidirect
6. #21461338C2semidirect
7. #21461337C2semidirect
8. #21461326C2semidirect
9. #21461323C2semidirect
10. #21461322C2semidirect
11. #21461321C2semidirect
12. #21461317C2semidirect
13. #21461316C2semidirect
14. C2×#16840620C2semidirect
22. #16840785C22semidirect
23. #16840782C22semidirect
24. #16840780C22semidirect
25. #16840780C22semidirect
27. #16840779C22semidirect
28. #16840779C22semidirect
32. C2×#14519844C22semidirect
33. D61⋊(C4⋊C8)C22semidirect
36. #16840622C22semidirect
37. #16840622C22semidirect
38. #16840622C22semidirect
39. #16840622C22semidirect
40. #16840621C22semidirect
41. #16840621C22semidirect
42. #16840621C22semidirect
43. #16840621C22semidirect
555. C61#17724semidirect

Maximal subgroups

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

subgroupindex
#214627352
#214625172
#214613432
#214613422
#214613392
#214613382
#214613372
#214613262
#214613232
#214613222
#214613212
#214613172
#214613162
C2×#168406202
#214596872
#1772461