Finite Group Databasebeta

← #30611916

Subgroups — #30611916

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic, complemented
2#21462517C211yesmaximal, characteristic, complemented
3#21461351C211yesmaximal, characteristic, complemented
4#21461350C211yesmaximal, characteristic, complemented
5#21461347C211yesmaximal, characteristic, complemented
6#21461346C211yesmaximal, characteristic, complemented
7#21461343C211yesmaximal, characteristic, complemented
8#21461342C211yesmaximal, characteristic, complemented
9#21461331C211yesmaximal, characteristic, complemented
10#21461327C211yesmaximal, characteristic, complemented
11#21461326C211yesmaximal, characteristic, complemented
12#21461326C211yesmaximal, characteristic, complemented
13#21461317C211yesmaximal, characteristic, complemented
14C2×#16840620C211yesmaximal, characteristic, complemented
15#21459591C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic, complemented
23#16840785C2211yescharacteristic, complemented
24#16840782C2211yescharacteristic, complemented
25#16840782C2211yescharacteristic, complemented
26#16840780C2211yescharacteristic, complemented
27#16840779C2211yescharacteristic, complemented
28#16840779C2211yescharacteristic, complemented
29#16840767C2211yescharacteristic, complemented
30#16840765C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic, complemented
32C2×#14519844C2211yescharacteristic, complemented
33C2×#14519844C2211yescharacteristic, complemented
34#16840735—21no—
35#16840726—21no—
36#16840621C2211yescharacteristic, complemented
37#16840621C2211yescharacteristic, complemented
38#16840621C2211yescharacteristic, complemented
39#16840621C2211yescharacteristic, complemented
40#16840620C2211yescharacteristic, complemented
41#16840620C2211yescharacteristic, complemented
42#16840620C2211yescharacteristic, complemented
43#16840620C2211yescharacteristic, complemented
44#16840620C2211yescharacteristic, complemented
45#16840620C2211yescharacteristic, complemented
46#16840620C2211yescharacteristic, complemented
47#16840620C2211yescharacteristic, complemented
48#16840620C2211yescharacteristic, complemented
49#16840620C2211yescharacteristic, complemented
50#16840620C2211yescharacteristic, complemented
51#16840620C2211yescharacteristic, complemented
52C2×#14519822—21no—
53#16840433C411yescharacteristic
54#16840432C411yescharacteristic
55#16840430—21no—
56D4×D244C411yescharacteristic
57#16840396C411yescharacteristic
58#16840396C411yescharacteristic
59D4×C22⋊D61—21no—
60D4×C22⋊D61C411yescharacteristic
61D4×C22⋊D61C411yescharacteristic
62#16840394—21no—
63#16840394—21no—
64#16840328—21no—
65#16840327—21no—
66#16840327—21no—
67#16840309C2211yescharacteristic
68#16840307C2211yescharacteristic
69#16840307C2211yescharacteristic
70C2×#14519773C2211yescharacteristic
71C2×#14519773C2211yescharacteristic
72#127×D61C2211yescharacteristic
73C4×#11758224C2211yescharacteristic
74D42×C61C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—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—
102#14519832—21no—
103#14519832—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107#14519822—44no—
108#14519822—44no—
109C2×#11758222—21no—
110C2×#11758222—21no—
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224D411yescharacteristic
115C22×D244C2×C411yescharacteristic
116C22×D244C2×C411yescharacteristic
117C22×C22⋊D61—21no—
118C22×C22⋊D61—21no—
119C22×C22⋊D61—21no—
120C22×C22⋊D61—21no—
121C22×C22⋊D61—21no—
122C22×C22⋊D61—21no—
123C2×D4×D61—21no—
124C2×D4×D61—21no—
125C2×D4×D61—21no—
126C2×D4×D61—21no—
127C2×D4×D61—21no—
128C2×D4×D61C2×C411yescharacteristic
129C2×D4×D61C2×C411yescharacteristic
130#14519776C2311yescharacteristic
131#14519774C2×C411yescharacteristic
132#14519773—21no—
133#14519773—21no—
134#14519773—21no—
135#14519773—21no—
136#14519773—21no—
137#14519773—21no—
138#14519773C2×C411yescharacteristic
139#14519773C2×C411yescharacteristic
140#14519773C2×C411yescharacteristic
141#14519773C2×C411yescharacteristic
142#14519773C2311yescharacteristic
143#14519773C2311yescharacteristic
144#14519773C2311yescharacteristic
145#14519763—21no—
146#14519763—21no—
147#14519763—21no—
148#14519752—21no—
149#14519752C2×C411yescharacteristic
150#14519751—21no—
151#14519751C2×C411yescharacteristic
152#14519751C2×C411yescharacteristic
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519750—21no—
157#14519750—21no—
158#14519749—21no—
159#14519749—21no—
160#14519749—21no—
161#14519749—21no—
162#14519749—21no—
163#14519749—21no—
164#14519748—21no—
165#14519748C2×C411yescharacteristic
166#14519747—21no—
167#14519747—21no—
168#14519747—21no—
169#14519747—21no—
170#14519746—21no—
171#14519746—21no—
172#14519745—21no—
173#14519745—21no—
174#14519745—21no—
175#14519745—21no—
176C4×Dic122C2×C411yescharacteristic
177#14519742D411yescharacteristic
178C4×D244C2×C411yescharacteristic
179D4×Dic61C2×C411yescharacteristic
180D4×Dic61C2×C411yescharacteristic
181D4×Dic61D411yescharacteristic
182#14519739C2×C411yescharacteristic
183#14519739C2×C411yescharacteristic
184C4×C22⋊D61—21no—
185C4×C22⋊D61C2×C411yescharacteristic
186C4×C22⋊D61C2×C411yescharacteristic
187#14519737—21no—
188#14519737—21no—
189#14519737D411yescharacteristic
190#14519737D411yescharacteristic
191#14519735D411yescharacteristic
192#14519733D411yescharacteristic
193#14519733D411yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C2×C4×Dic61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C22×D4×C61—21no—
198C22×D4×C61C2×C411yescharacteristic
199C22×D4×C61C2×C411yescharacteristic
200#127×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic
204#120×C61—21no—
205#120×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207C4×D4×C61C2×C411yescharacteristic
208C24×C61—21no—
209C24×C61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—44no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C22×C411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61—21no—
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—42no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—44no—
253C2×C22⋊D61—42no—
254C2×C22⋊D61—42no—
255C2×C22⋊D61—81no—
256C2×C22⋊D61—81no—
257C2×C22⋊D61—81no—
258C2×C22⋊D61—81no—
259C2×C22⋊D61C22⋊C411yescharacteristic
260C2×C22⋊D61C22⋊C411yescharacteristic
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61C2×D411yescharacteristic
264C22×Dic61C2×D411yescharacteristic
265C22×Dic61C2×D411yescharacteristic
266C22×Dic61C2×D411yescharacteristic
267#11758224—22no—
268#11758224—22no—
269#11758224—44no—
270#11758224—42no—
271#11758224—42no—
272#11758224—42no—
273#11758224—42no—
274D4×D61—42no—
275D4×D61—42no—
276D4×D61—44no—
277D4×D61—44no—
278D4×D61—44no—
279D4×D61—81no—
280D4×D61—81no—
281D4×D61—81no—
282D4×D61—81no—
283#11758222—44no—
284#11758222—42no—
285#11758222—42no—
286C2×D244—21no—
287C2×D244—21no—
288C2×D244—21no—
289C2×D244—21no—
290C2×D244—21no—
291C2×D244—81no—
292C2×D244—81no—
293C2×D244C22×C411yescharacteristic
294C2×D244C22×C411yescharacteristic
295C2×D244C22×C411yescharacteristic
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61C22×C411yescharacteristic
300C2×C4×D61C2×D411yescharacteristic
301C2×C4×D61C2×D411yescharacteristic
302C2×Dic122—21no—
303C2×Dic122C22⋊C411yescharacteristic
304#11758217—42no—
305#11758217—81no—
306C2×#92420—21no—
307C2×#92420—21no—
308C2×#92420—21no—
309C2×#92420—21no—
310C2×#92420—21no—
311C2×#92420—21no—
312C2×#92420—21no—
313C2×#92420—21no—
314C2×#92420—42no—
315C2×#92420—81no—
316#11758213—81no—
317C4⋊C4×C61C22⋊C411yescharacteristic
318C4⋊C4×C61C22×C411yescharacteristic
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61C22⋊C411yescharacteristic
323C22⋊C4×C61C22⋊C411yescharacteristic
324C42×C61C22×C411yescharacteristic
325C22⋊Dic61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61—21no—
328C22⋊Dic61C22⋊C411yescharacteristic
329C22⋊Dic61C22⋊C411yescharacteristic
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198C22⋊C411yescharacteristic
337#11758198C22⋊C411yescharacteristic
338C4⋊Dic61C22⋊C411yescharacteristic
339C4⋊Dic61C22×C411yescharacteristic
340#11758196—21no—
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344#11758196C22⋊C411yescharacteristic
345C4×Dic61C22×C411yescharacteristic
346C4×Dic61C22×C411yescharacteristic
347C4×Dic61C2×D411yescharacteristic
348C4×Dic61C2×D411yescharacteristic
349C4×Dic61C2×D411yescharacteristic
350C4×Dic61C2×D411yescharacteristic
351C4×Dic61C2×D411yescharacteristic
352C4×Dic61C2×D411yescharacteristic
353C4×Dic61C2411yescharacteristic
354C23×C61—21no—
355C23×C61—21no—
356C23×C61—21no—
357C23×C61—42no—
358C23×C61—42no—
359C23×C61—81no—
360C23×C61—81no—
361C23×C61—81no—
362C23×C61—81no—
363C23×C61C2×C22⋊C411yescharacteristic
364C23×C61C2×C22⋊C411yescharacteristic
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—42no—
369C22×D61—42no—
370C22×D61—42no—
371C22×D61—42no—
372C22×D61—81no—
373C22×D61—81no—
374C22×D61—81no—
375C22×D61—81no—
376C22×D61—81no—
377C22×D61—81no—
378C22×D61—81no—
379C22×D61—81no—
380C22×D61C2×C22⋊C411yescharacteristic
381D4×C61—22no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—41no—
385D4×C61—42no—
386D4×C61—42no—
387D4×C61—42no—
388D4×C61—81no—
389D4×C61—81no—
390D4×C61—81no—
391C2×C4×C61—21no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—42no—
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C2×C22⋊C411yescharacteristic
399C2×C4×C61C23×C411yescharacteristic
400C22⋊D61—22no—
401C22⋊D61—22no—
402C22⋊D61—42no—
403C22⋊D61—42no—
404C22⋊D61—42no—
405C22⋊D61—42no—
406C22⋊D61—42no—
407C22⋊D61—41no—
408C22⋊D61—41no—
409C22⋊D61—41no—
410C22⋊D61—41no—
411C22⋊D61—41no—
412C22⋊D61—41no—
413C22⋊D61—41no—
414C22⋊D61—41no—
415C22⋊D61—41no—
416C22⋊D61—41no—
417C22⋊D61—41no—
418C22⋊D61—41no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—81no—
422C22⋊D61—81no—
423C22⋊D61—81no—
424C22⋊D61—81no—
425C22⋊D61—81no—
426C22⋊D61—81no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—21no—
434C2×Dic61—42no—
435C2×Dic61—42no—
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439C2×Dic61C2×C22⋊C411yescharacteristic
440C2×Dic61C2×C22⋊C411yescharacteristic
441C2×Dic61AGL(1,ℤ/8)12yes—
442C2×Dic61AGL(1,ℤ/8)12yes—
443C2×Dic61C22×D411yescharacteristic
444C2×Dic61C22×D411yescharacteristic
445D244—41no—
446D244—41no—
447D244—41no—
448D244—42no—
449D244—42no—
450D244—81no—
451D244—81no—
452D244—81no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—41no—
458C4×D61—42no—
459C4×D61—42no—
460C4×D61—42no—
461Dic122—22no—
462Dic122—41no—
463Dic122—41no—
464#92420—41no—
465#92420—41no—
466#92420—41no—
467#92420—41no—
468#92420—41no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#17758—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—162no—
488C22×C61—162no—
489C22×C61#41812yes—
490C22×C61C22×C22⋊C411yescharacteristic
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—41no—
499C2×D61—41no—
500C2×D61—41no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—162no—
504C2×D61—162no—
505C2×D61—162no—
506C2×D61—162no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—41no—
513Dic61—21no—
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—41no—
518Dic61#41812yes—
519Dic61C2×AGL(1,ℤ/8)11yescharacteristic
520Dic61C2×AGL(1,ℤ/8)11yescharacteristic
521Dic61#57611yescharacteristic
522Dic61#57711yescharacteristic
523#3498—611no—
524#2989—611no—
525#2925—611no—
526#1557—611no—
527#1557—611no—
528#1555—611no—
529#1555—611no—
530#1553—611no—
531#1553—611no—
532#1547—611no—
533#1545—611no—
534#1545—611no—
535#1545—611no—
536#1540—611no—
537C2×#331—611no—
538C2×C61—22no—
539C2×C61—41no—
540C2×C61—81no—
541C2×C61—81no—
542C2×C61—81no—
543C2×C61#288811yescharacteristic
544C2×C61C2×#41811yescharacteristic
545C2×C61#289711yescharacteristic
546D61—41no—
547D61—81no—
548D61—81no—
549D61—81no—
550C2×H(5,𝔽2)—1221no—
551#550—611no—
552#550—611no—
553#550—1221no—
554D42—611no—
555D42—611no—
556D42—611no—
557D42—611no—
558D42—611no—
559D42—1221no—
560D42—1221no—
561D42—1221no—
562D42#692311yescharacteristic
563#535—1221no—
564#535—1221no—
565#535—1221no—
566#532—611no—
567#532—611no—
568#532—611no—
569C2×#127—611no—
570C2×#127—611no—
571C2×#127—611no—
572C4×#41—611no—
573#446—1221no—
574#436—1221no—
575#435—1221no—
576#435—1221no—
577#433—1221no—
578#433—1221no—
579#432—611no—
580#432—611no—
581#432—611no—
582#432—611no—
583#431—611no—
584#431—611no—
585#431—611no—
586#423—611no—
587#423—611no—
588#423—611no—
589C2×C4⋊C8—611no—
590C2×C4⋊C8—611no—
591#408—1221no—
592#405—1221no—
593#332—611no—
594#332—611no—
595#332—611no—
596#332—611no—
597#331—611no—
598#331—611no—
599#331—611no—
600#331—611no—
601#331—611no—
602#331—611no—
603#331—611no—
604#331—611no—
605#331—611no—
606#331—611no—
607#331—611no—
608#331—611no—
609C61#1775811yescharacteristic, complemented, Sylow
610H(5,𝔽2)—2444no—
611H(5,𝔽2)—2444no—
612C2×#41—611no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—1221no—
616C2×#41—1221no—
617C2×#41—1221no—
618C22×D4—21no—
619C22×D4—611no—
620C22×D4—611no—
621C22×D4—611no—
622C22×D4—611no—
623C22×D4—1221no—
624C22×D4—1221no—
625C22×D4—1221no—
626C22×D4—1221no—
627C22×D4—1221no—
628C22×D4—1221no—
629C22×D4—1221no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4—1221no—
633C22×D4—1221no—
634C22×D4C2×#692311yescharacteristic
635C22×D4C2×#692311yescharacteristic
636C2×M16—1221no—
637C2×M16—1221no—
638C2×M16—1221no—
639C22×C8—1221no—
640C22×C8—1221no—
641C4⋊Q8—611no—
642#127—611no—
643#127—611no—
644#127—611no—
645#127—611no—
646#127—611no—
647#127—611no—
648#127—611no—
649#127—611no—
650#127—1221no—
651#127—1221no—
652#127—1221no—
653#127—1221no—
654#127—1221no—
655#127—1221no—
656#127C2×#692311yescharacteristic
657#124—1221no—
658#124—1221no—
659#124—1221no—
660#121—21no—
661#121—611no—
662#121—611no—
663#121—611no—
664#121—611no—
665#121—1221no—
666#121—1221no—
667#121—1221no—
668#121—1221no—
669#121—1221no—
670#121—1221no—
671#121—1221no—
672#121—1221no—
673#121—1221no—
674#121—1221no—
675#121—1221no—
676#121—1221no—
677#121—1221no—
678#121—1221no—
679#121C2×#692311yescharacteristic
680#121C2×#692311yescharacteristic
681#120—21no—
682#120—21no—
683#120—1221no—
684#120—1221no—
685#120—1221no—
686#120—1221no—
687#120—1221no—
688#120—1221no—
689#120—1221no—
690#120—1221no—
691#120—1221no—
692#120—1221no—
693C4×Q8—611no—
694C4×Q8—611no—
695C4×D4—611no—
696C4×D4—611no—
697C4×D4—611no—
698C4×D4—611no—
699C4×D4—611no—
700C4×D4—611no—
701C4×D4—611no—
702C4×D4—611no—
703C4×D4—611no—
704C4×D4—611no—
705C4×D4—1221no—
706C4×D4—1221no—
707C4×D4—1221no—
708C4×D4C2×#692311yescharacteristic
709C4×D4C2×#692311yescharacteristic
710#117—611no—
711#117—611no—
712#117—611no—
713C2×C42—611no—
714C2×C42—611no—
715C2×C42—611no—
716C4⋊C8—611no—
717C4⋊C8—611no—
718C4⋊C8—611no—
719C4⋊C8—611no—
720C4⋊C8—611no—
721C4⋊C8—611no—
722C4⋊C8—611no—
723C4⋊C8—611no—
724C4⋊C8—1221no—
725C4⋊C8—1221no—
726C4⋊C8—1221no—
727C4⋊C8—1221no—
728C4⋊C8—1221no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735C22⋊C8—1221no—
736#97—1221no—
737#97—1221no—
738#97—1221no—
739#97—1221no—
740C4×C8—1221no—
741C4×C8—1221no—
742C4×C8—1221no—
743C24—21no—
744C24—21no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749#41—1222no—
750#41—1222no—
751#41—2442no—
752#41—2442no—
753#41—2444no—
754#41—2442no—
755#41—2442no—
756#41—2442no—
757#41—2442no—
758#41—2444no—
759C2×Q8—611no—
760C2×Q8—1221no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—44no—
768C2×D4—81no—
769C2×D4—81no—
770C2×D4—611no—
771C2×D4—611no—
772C2×D4—611no—
773C2×D4—611no—
774C2×D4—611no—
775C2×D4—1221no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—1221no—
779C2×D4—1221no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—1221no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—4881no—
800C2×D4—4881no—
801C2×D4—4881no—
802C2×D4—4881no—
803C2×D4—4881no—
804C2×D4—4881no—
805C2×D4—4881no—
806C2×D4—4881no—
807C2×D4—4881no—
808C2×D4—4881no—
809C2×D4—2442no—
810C2×D4—2442no—
811C2×D4—2442no—
812C2×D4—2442no—
813C2×D4—2442no—
814C2×D4—2442no—
815C2×D4—2444no—
816C2×D4—2444no—
817C2×D4—2444no—
818C2×D4—2444no—
819C2×D4—2444no—
820C2×D4C22⋊#692311yescharacteristic
821C2×D4C22×#692311yescharacteristic
822C2×D4C22×#692311yescharacteristic
823C2×D4C22×#692311yescharacteristic
824C22×C4—21no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4C22×#692311yescharacteristic
838C22×C4C22×#692311yescharacteristic
839M16—4881no—
840M16—4881no—
841M16—2442no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—1221no—
845C2×C8—1221no—
846C2×C8—1221no—
847C2×C8—1221no—
848C2×C8—1221no—
849C2×C8—1221no—
850C2×C8—4881no—
851C2×C8—2442no—
852C4⋊C4—611no—
853C4⋊C4—611no—
854C4⋊C4—611no—
855C4⋊C4—611no—
856C4⋊C4—611no—
857C4⋊C4—611no—
858C4⋊C4—1221no—
859C4⋊C4C22⋊#692311yescharacteristic
860C4⋊C4C22×#692311yescharacteristic
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—611no—
865C22⋊C4—611no—
866C22⋊C4—611no—
867C22⋊C4—611no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4C22⋊#692311yescharacteristic
878C22⋊C4C22⋊#692311yescharacteristic
879C42—611no—
880C42—611no—
881C42—611no—
882C42—611no—
883C42—611no—
884C42—611no—
885C42—611no—
886C42—611no—
887C42—611no—
888C42C22×#692311yescharacteristic
889C23—21no—
890C23—21no—
891C23—21no—
892C23—42no—
893C23—42no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—611no—
899C23—1221no—
900C23—1221no—
901C23—1221no—
902C23—4881no—
903C23—4881no—
904C23—4881no—
905C23—4881no—
906C23—4881no—
907C23—4881no—
908C23—4881no—
909C23—4881no—
910C23—2442no—
911C23—2442no—
912C23—2442no—
913C23—2442no—
914C23C2×C22⋊#692311yescharacteristic
915C23C2×C22⋊#692311yescharacteristic
916Q8—1222no—
917Q8—2441no—
918Q8—2441no—
919D4—22no—
920D4—41no—
921D4—41no—
922D4—41no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—81no—
927D4—81no—
928D4—81no—
929D4—1222no—
930D4—1222no—
931D4—4881no—
932D4—4881no—
933D4—4881no—
934D4—4881no—
935D4—4881no—
936D4—4881no—
937D4—4881no—
938D4—4881no—
939D4—4881no—
940D4—2441no—
941D4—2441no—
942D4—2441no—
943D4—2442no—
944D4—2442no—
945D4—2441no—
946D4—2441no—
947D4—2441no—
948D4—2441no—
949D4—2441no—
950D4—2441no—
951D4—2441no—
952D4—2441no—
953D4—2441no—
954D4—2441no—
955D4—2441no—
956D4—2441no—
957D4—2442no—
958D4—2442no—
959D4—2442no—
960D4—2442no—
961D4—2442no—
962D4—2442no—
963D4—2442no—
964C2×C4—21no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—42no—
968C2×C4—612no—
969C2×C4—612no—
970C2×C4—611no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1221no—
987C2×C4—1221no—
988C2×C4—2441no—
989C2×C4—2442no—
990C2×C4—2442no—
991C2×C4—2442no—
992C2×C4—2442no—
993C2×C4—2442no—
994C2×C4C2×C22⋊#692311yescharacteristic
995C2×C4C2×C22⋊#692311yescharacteristic
996C2×C4C2×C22⋊#692311yescharacteristic
997C2×C4C2×C22⋊#692311yescharacteristic
998C2×C4C23×#692311yescharacteristic
999C8—2441no—
1000C8—2441no—
1001C8—2441no—
1002C8—2441no—
1003C8—2441no—
1004C8—2441no—
1005C8—2441no—
1006C8—2441no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—162no—
1022C22—162no—
1023C22—1221no—
1024C22—1221no—
1025C22—1221no—
1026C22—9762no—
1027C22—9762no—
1028C22—9762no—
1029C22—9762no—
1030C22—2441no—
1031C22—2441no—
1032C22—2441no—
1033C22—2441no—
1034C22—2441no—
1035C22—2441no—
1036C22—2441no—
1037C22—2441no—
1038C22—2441no—
1039C22#1684075412yes—
1040C22C22×C22⋊#692311yescharacteristic
1041C4—21no—
1042C4—21no—
1043C4—21no—
1044C4—21no—
1045C4—21no—
1046C4—41no—
1047C4—611no—
1048C4—611no—
1049C4—612no—
1050C4—611no—
1051C4—611no—
1052C4—1221no—
1053C4—1221no—
1054C4—1221no—
1055C4—1221no—
1056C4—2441no—
1057C2—22no—
1058C2—41no—
1059C2—81no—
1060C2—81no—
1061C2—81no—
1062C2—4881no—
1063C2—4881no—
1064C2—4881no—
1065C2—2441no—
1066C2#2146242911yescharacteristic
1067C2C2×#1684075411yescharacteristic
1068C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459591C2
cosocleC4×Dic61C24
hypercenterD42#6923
hypocenterC61#17758
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462517C2semidirect
3. #21461351C2semidirect
4. #21461350C2semidirect
5. #21461347C2semidirect
6. #21461346C2semidirect
7. #21461343C2semidirect
8. #21461342C2semidirect
9. #21461331C2semidirect
10. #21461327C2semidirect
11. #21461326C2semidirect
12. #21461326C2semidirect
13. #21461317C2semidirect
14. C2×#16840620C2semidirect
22. #16840785C22semidirect
23. #16840785C22semidirect
24. #16840782C22semidirect
25. #16840782C22semidirect
26. #16840780C22semidirect
27. #16840779C22semidirect
28. #16840779C22semidirect
29. #16840767C22semidirect
30. #16840765C22semidirect
31. #16840765C22semidirect
32. C2×#14519844C22semidirect
33. C2×#14519844C22semidirect
36. #16840621C22semidirect
37. #16840621C22semidirect
38. #16840621C22semidirect
39. #16840621C22semidirect
40. #16840620C22semidirect
41. #16840620C22semidirect
42. #16840620C22semidirect
43. #16840620C22semidirect
44. #16840620C22semidirect
45. #16840620C22semidirect
46. #16840620C22semidirect
47. #16840620C22semidirect
48. #16840620C22semidirect
49. #16840620C22semidirect
50. #16840620C22semidirect
51. #16840620C22semidirect
609. C61#17758semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214625172
#214613512
#214613502
#214613472
#214613462
#214613432
#214613422
#214613312
#214613272
#214613262
#214613172
C2×#168406202
#214595912
#1775861