Finite Group Databasebeta

← #30620512

Subgroups — #30620512

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462621C211yesmaximal, characteristic, complemented
2#21462278C211yesmaximal, characteristic, complemented
3#21461984C211yesmaximal, characteristic, complemented
4#21461984C211yesmaximal, characteristic, complemented
5#21461983C211yesmaximal, characteristic, complemented
6#21461957C211yesmaximal, characteristic, complemented
7#21461956C211yesmaximal, characteristic, complemented
8#21461954C211yesmaximal, characteristic, complemented
9#21461694C211yesmaximal, characteristic, complemented
10#21461693C211yesmaximal, characteristic, complemented
11#21461691C211yesmaximal, characteristic, complemented
12#21461583C211yesmaximal, characteristic, complemented
13#21461582C211yesmaximal, characteristic, complemented
14C4×#14519841C211yesmaximal, characteristic, complemented
15#21459415C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840811—21no—
20#16840767C2211yescharacteristic
21#16840767C2211yescharacteristic
22#16840766C2211yescharacteristic
23C2×#14519842C2211yescharacteristic
24C2×#14519842C2211yescharacteristic
25C2×#14519842C2211yescharacteristic
26C2×#14519842C2211yescharacteristic
27C2×#14519841C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29C2×#14519841C2211yescharacteristic
30C2×#14519841C2211yescharacteristic
31C2×#14519841C2211yescharacteristic
32C2×#14519841C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36C4×#11758213C2211yescharacteristic
37C4×#11758213C2211yescharacteristic
38(C2×#6923)⋊Q8—21no—
39#16840713—21no—
40#16840711—21no—
41#16840711—21no—
42C4×C4⋊#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45#16840698C2211yescharacteristic
46#16840698C2211yescharacteristic
47C42×#6923C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52#16840495C411yescharacteristic, complemented
53#16840495C411yescharacteristic, complemented
54#16840490C411yescharacteristic, complemented
55#16840485C411yescharacteristic, complemented
56#16840481C411yescharacteristic, complemented
57#16840481C411yescharacteristic, complemented
58#16840462—21no—
59#16840457—21no—
60#16840457—21no—
61#16840432C411yescharacteristic, complemented
62#16840420—21no—
63#16840311C2211yescharacteristic
64#16840311C2211yescharacteristic
65#16840310C2211yescharacteristic
66#16840291—21no—
67#16840289—21no—
68#16840289—21no—
69C4×#11758226C2211yescharacteristic
70C4×#11758224—21no—
71C4×#11758224C2211yescharacteristic
72C4×#11758224C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#559C411yescharacteristic, complemented
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923C2311yescharacteristic
85C2×C4×#6923C2311yescharacteristic
86C2×C4×#6923C2311yescharacteristic
87C2×C4×#6923C2311yescharacteristic
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91#14519844—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94#14519842—22no—
95#14519842—22no—
96#14519842—41no—
97#14519842—41no—
98#14519841—22no—
99#14519841—22no—
100#14519841—22no—
101#14519841—22no—
102#14519841—41no—
103#14519841—41no—
104#14519841—41no—
105#14519841—41no—
106#14519832—21no—
107#14519832—21no—
108#14519832—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C4×#92420—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×#11758226C2311yescharacteristic
120C2×#11758224—21no—
121C2×#11758224C2311yescharacteristic
122C2×#11758224C2311yescharacteristic
123C2×Q8×D61D411yescharacteristic
124#14519777C2×C411yescharacteristic
125#14519775C2×C411yescharacteristic
126#14519775C2×C411yescharacteristic
127#14519773C2×C411yescharacteristic
128#14519773C2×C411yescharacteristic
129#14519772—21no—
130#14519772—21no—
131#14519770—21no—
132#14519770—21no—
133#14519770—21no—
134#14519770—21no—
135#14519769—21no—
136#14519767—21no—
137#14519767—21no—
138#14519765C2×C411yescharacteristic
139#14519765C2×C411yescharacteristic
140#14519764C2×C411yescharacteristic
141#14519764C2×C411yescharacteristic
142#14519763—21no—
143#14519763—21no—
144#14519760—21no—
145#14519760—21no—
146#14519759—21no—
147#14519759—21no—
148#14519754—21no—
149#14519754—21no—
150#14519753—21no—
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519749—21no—
156#14519749—21no—
157#14519748—21no—
158#14519748—21no—
159#14519748—21no—
160Q8×Dic61C2×C411yescharacteristic
161Q8×Dic61D411yescharacteristic
162C4×Dic122—21no—
163C4×Dic122C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165C4×Dic122C2×C411yescharacteristic
166C4×Dic122C2×C411yescharacteristic
167C4×Dic122C2×C411yescharacteristic
168#14519742C2×C411yescharacteristic
169#14519742C2×C411yescharacteristic
170#14519742D411yescharacteristic
171#14519742D411yescharacteristic
172#14519742D411yescharacteristic
173C4×D244—21no—
174C4×D244C2×C411yescharacteristic
175D4×Dic61—21no—
176D4×Dic61—21no—
177D4×Dic61C2×C411yescharacteristic
178D4×Dic61C2×C411yescharacteristic
179#14519739—21no—
180#14519739C2×C411yescharacteristic
181C4×C22⋊D61—21no—
182C4×C22⋊D61—21no—
183C4×C22⋊D61—21no—
184C4×C22⋊D61—21no—
185#14519737—21no—
186#14519737—21no—
187#14519737—21no—
188#14519737—21no—
189#14519737—21no—
190#14519737—21no—
191#14519735—21no—
192#14519735—21no—
193#14519735C2311yescharacteristic
194#14519733—21no—
195#14519733—21no—
196#14519733—21no—
197#14519733—21no—
198C4⋊C4×D61D411yescharacteristic
199C4⋊C4×D61D411yescharacteristic
200C4⋊C4×D61D411yescharacteristic
201C2×C4×Dic61—21no—
202C2×C4×Dic61—21no—
203C42×D61—21no—
204C42×D61C2311yescharacteristic
205C42×D61C2311yescharacteristic
206C42×D61C2311yescharacteristic
207#127×C61C2×C411yescharacteristic
208#124×C61—21no—
209#124×C61C2×C411yescharacteristic
210#124×C61C2×C411yescharacteristic
211#123×C61—21no—
212#123×C61—21no—
213C4×Q8×C61C2×C411yescharacteristic
214C4×Q8×C61C2×C411yescharacteristic
215C4×D4×C61—21no—
216C4×D4×C61C2×C411yescharacteristic
217C4×D4×C61C2×C411yescharacteristic
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C2×Q8×C61C22⋊C411yescharacteristic
223C2×Q8×C61C22×C411yescharacteristic
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61C22×C411yescharacteristic
227C2×D4×C61C22×C411yescharacteristic
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240#11758226—21no—
241#11758226—21no—
242#11758226—21no—
243#11758226—21no—
244Q8×D61—42no—
245#11758224—21no—
246#11758224—21no—
247#11758224—21no—
248#11758224—21no—
249#11758224—21no—
250#11758224—21no—
251#11758224—21no—
252#11758224—21no—
253#11758224—44no—
254C2×D244—21no—
255C2×D244C22×C411yescharacteristic
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×Dic122C22⋊C411yescharacteristic
267C2×Dic122C22⋊C411yescharacteristic
268C2×Dic122C22⋊C411yescharacteristic
269C2×Dic122C22×C411yescharacteristic
270C2×Dic122C22×C411yescharacteristic
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C4⋊#6923—42no—
276C4⋊#6923—42no—
277C4⋊#6923—42no—
278C4×#6923—21no—
279C4×#6923—21no—
280C4×#6923—21no—
281C4×#6923—21no—
282C4×#6923—21no—
283C4×#6923—21no—
284C4×#6923—21no—
285C4×#6923—42no—
286C4×#6923—42no—
287C4×#6923#4112yescomplemented
288#11758213—21no—
289#11758213—21no—
290#11758213—21no—
291#11758213—21no—
292#11758213—21no—
293#11758213—21no—
294#11758213—21no—
295#11758213#4112yescomplemented
296C4⋊C4×C61—21no—
297C4⋊C4×C61C22⋊C411yescharacteristic
298C4⋊C4×C61C22⋊C411yescharacteristic
299C4⋊C4×C61C22⋊C411yescharacteristic
300C4⋊C4×C61C22×C411yescharacteristic
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C42×C61—21no—
308C42×C61C22×C411yescharacteristic
309C42×C61C22×C411yescharacteristic
310C42×C61C22×C411yescharacteristic
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61C22⋊C411yescharacteristic
328C4⋊Dic61C22⋊C411yescharacteristic
329C4⋊Dic61C22⋊C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196C22⋊C411yescharacteristic
340#11758196C22⋊C411yescharacteristic
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344#11758196C22⋊C411yescharacteristic
345C4×Dic61—21no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61C22×C411yescharacteristic
352C4×Dic61C22×C411yescharacteristic
353C4×Dic61C22×C411yescharacteristic
354C4×Dic61C2×D411yescharacteristic
355C4×Dic61C2×D411yescharacteristic
356C4×Dic61C2×D411yescharacteristic
357C4×Dic61C2×D411yescharacteristic
358C4×Dic61C2×D411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C23×C61—21no—
361C23×C61—21no—
362C22×D61—21no—
363C22×D61C22×D411yescharacteristic
364C2×#6923—22no—
365C2×#6923—22no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376Q8×C61—21no—
377Q8×C61—21no—
378Q8×C61—41no—
379D4×C61—21no—
380D4×C61—21no—
381D4×C61—21no—
382D4×C61—21no—
383D4×C61—42no—
384D4×C61—81no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—81no—
388C2×C4×C61—81no—
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C23×C411yescharacteristic
396C22⋊D61—42no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—42no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—42no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—42no—
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C22×D411yescharacteristic
420D244—21no—
421D244—21no—
422D244—41no—
423D244—41no—
424C4×D61—22no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—42no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—81no—
434C4×D61C2×#4111yescharacteristic
435C4×D61C2×#4111yescharacteristic
436C4×D61H(5,𝔽2)11yescharacteristic
437C4×D612−1+411yescharacteristic
438Dic122—22no—
439Dic122—22no—
440Dic122—21no—
441Dic122—21no—
442Dic122—21no—
443Dic122—21no—
444Dic122—41no—
445#92420—22no—
446#92420—41no—
447#92420—41no—
448#92420—41no—
449#22551—611nomaximal, Sylow
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61C22×C22⋊C411yescharacteristic
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61#54811yescharacteristic
463C2×D61#55011yescharacteristic
464#6923—42no—
465#6923—42no—
466#6923—81no—
467#6923—81no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—41no—
475C4×C61—41no—
476C4×C61C4×#4111yescharacteristic
477C4×C61#52011yescharacteristic
478Dic61—21no—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—21no—
483Dic61—41no—
484Dic61—41no—
485Dic61—41no—
486Dic61#42112yes—
487Dic61#54811yescharacteristic
488Dic61#55011yescharacteristic
489#3480—611no—
490Q8×M16—611no—
491#2295—611no—
492#1980—611no—
493#1980—611no—
494#1980—611no—
495#1963—611no—
496#1963—611no—
497#1962—611no—
498#1806—611no—
499#1806—611no—
500#1806—611no—
501#1759—611no—
502#1759—611no—
503C4×#104—611no—
504C2×C61—81no—
505C2×C61—81no—
506C2×C61#234111yescharacteristic
507C2×C61C2×#42111yescharacteristic
508C2×C61#290111yescharacteristic
509D61—21no—
510D61—21no—
511D61—81no—
512#559—611no—
513#559—611no—
514#559#692311yescharacteristic, complemented
515#557—611no—
516#556—611no—
517#556—611no—
518#556—611no—
519#553—1221no—
520#553—1221no—
521#553—1221no—
522#550—611no—
523#548—1221no—
524#532—611no—
525#532—611no—
526#532—611no—
527#529—1221no—
528#529—1221no—
529#529—1221no—
530C4×#41—611no—
531C4×#41—611no—
532C4×#41—611no—
533C4×#41—1221no—
534C2×C4×Q8—611no—
535#446—1221no—
536#446—1221no—
537#446—1221no—
538C8×Q8—1221no—
539#423—611no—
540#423—611no—
541#423—611no—
542C2×#104—611no—
543C2×#104—611no—
544C2×#104—611no—
545C2×#104—611no—
546C2×#104—611no—
547C2×#104—611no—
548C2×#104—611no—
549C2×#104—611no—
550C2×#104—611no—
551C2×#104—611no—
552C2×#104—611no—
553C2×#104—611no—
554C4×M16—611no—
555C4×M16—611no—
556C4×M16—611no—
557#391—1221no—
558#389—1221no—
559#387—1221no—
560#387—1221no—
561C4×C4⋊C4—611no—
562C4×C4⋊C4—611no—
563C4×C4⋊C4—611no—
564#376—611no—
565#376—611no—
566C43—611no—
567#339—611no—
568#339—611no—
569#339—611no—
570#339—611no—
571C61#2255111yescharacteristic, complemented, Sylow
572C2×#41—611no—
573C2×#41—611no—
574C2×#41—611no—
575C2×#41—1221no—
576C22×Q8—611no—
577C2×M16—611no—
578C2×M16—611no—
579C2×M16—611no—
580C2×M16—611no—
581C4⋊Q8—611no—
582C4⋊Q8—611no—
583C4⋊Q8—611no—
584#127—611no—
585#127—611no—
586#127C2×#692311yescharacteristic
587#126—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#126—1221no—
592#126—1221no—
593#125—1221no—
594#125—1221no—
595#125—1221no—
596#124—21no—
597#124—611no—
598#124—611no—
599#124—611no—
600#124—611no—
601#124—1221no—
602#124—1221no—
603#124C2×#692311yescharacteristic
604#124C2×#692311yescharacteristic
605#123—21no—
606#123—21no—
607#123—1221no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623C4×Q8—611no—
624C4×Q8—611no—
625C4×Q8—611no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×Q8—611no—
629C4×Q8—611no—
630C4×Q8—611no—
631C4×Q8—611no—
632C4×Q8—611no—
633C4×Q8—611no—
634C4×Q8—611no—
635C4×Q8—1221no—
636C4×Q8C2×#692311yescharacteristic
637C4×Q8C2×#692311yescharacteristic
638C4×D4—21no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4C2×#692311yescharacteristic
658C4×D4C2×#692311yescharacteristic
659#117—611no—
660#117—1221no—
661#117—1221no—
662#117—1221no—
663#117—1221no—
664#117—1221no—
665#117—1221no—
666C2×C4⋊C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C42—611no—
673C2×C42—611no—
674C2×C42—611no—
675C2×C42—611no—
676C2×C42—611no—
677C2×C42—611no—
678C2×C42—611no—
679C2×C42—1221no—
680C2×C42—1221no—
681C2×C42—1221no—
682C2×C42—1221no—
683C2×C42—1221no—
684C4⋊C8—1221no—
685C4⋊C8—1221no—
686C4⋊C8—1221no—
687C4⋊C8—1221no—
688C4⋊C8—1221no—
689C4⋊C8—1221no—
690#104—1222no—
691#104—1222no—
692#104—1222no—
693#104—1222no—
694#104—1222no—
695#104—1222no—
696#104—2441no—
697#104—2441no—
698#104—2441no—
699#104—2441no—
700#104—2441no—
701#104—2441no—
702#97—1221no—
703#97—1221no—
704#97—1221no—
705C4×C8—1221no—
706C4×C8—1221no—
707C4×C8—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712#95—1221no—
713#95—1221no—
714#95—1221no—
715#41—1221no—
716#41—1221no—
717#41—1221no—
718#41—1221no—
719#41—1221no—
720#41—1221no—
721#41—1221no—
722#41—1221no—
723#41—1221no—
724#41—1221no—
725#41—1221no—
726#41—1221no—
727#41—2444no—
728C2×Q8—611no—
729C2×Q8—611no—
730C2×Q8—611no—
731C2×Q8—611no—
732C2×Q8—611no—
733C2×Q8—2442no—
734C2×Q8C22⋊#692311yescharacteristic
735C2×Q8C22×#692311yescharacteristic
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—611no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4C22×#692311yescharacteristic
747C2×D4C22×#692311yescharacteristic
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768M16—612no—
769M16—1221no—
770M16—1221no—
771M16—1221no—
772M16—1221no—
773M16—1221no—
774M16—1221no—
775M16—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C4⋊C4—21no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—611no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—2442no—
803C4⋊C4—2442no—
804C4⋊C4—2442no—
805C4⋊C4C22⋊#692311yescharacteristic
806C4⋊C4C22⋊#692311yescharacteristic
807C4⋊C4C22⋊#692311yescharacteristic
808C4⋊C4C22×#692311yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C42—21no—
829C42—611no—
830C42—611no—
831C42—611no—
832C42—611no—
833C42—611no—
834C42—611no—
835C42—611no—
836C42—611no—
837C42—611no—
838C42—612no—
839C42—1221no—
840C42—1221no—
841C42—1221no—
842C42—1221no—
843C42—1221no—
844C42—1221no—
845C42—1221no—
846C42—1221no—
847C42—1221no—
848C42—1221no—
849C42—1221no—
850C42—1221no—
851C42—1221no—
852C42—2442no—
853C42—2442no—
854C42C22×#692311yescharacteristic
855C42C22×#692311yescharacteristic
856C42C22×#692311yescharacteristic
857C23—21no—
858C23—21no—
859C23—611no—
860C23—1221no—
861Q8—21no—
862Q8—21no—
863Q8—41no—
864Q8—1222no—
865Q8—1222no—
866Q8—1221no—
867Q8—1221no—
868Q8—1221no—
869Q8—1221no—
870Q8—2441no—
871D4—21no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—42no—
876D4—81no—
877D4—1221no—
878D4—1221no—
879D4—4881no—
880D4—4881no—
881D4—2441no—
882D4—2441no—
883D4—2442no—
884D4—2442no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—611no—
896C2×C4—611no—
897C2×C4—611no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—4881no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2442no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2442no—
924C2×C4—2442no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4C2×C22⋊#692311yescharacteristic
936C2×C4C2×C22⋊#692311yescharacteristic
937C2×C4C2×C22⋊#692311yescharacteristic
938C2×C4C2×C22⋊#692311yescharacteristic
939C2×C4C2×C22⋊#692311yescharacteristic
940C2×C4C2×C22⋊#692311yescharacteristic
941C2×C4C23×#692311yescharacteristic
942C8—1222no—
943C8—2441no—
944C8—2441no—
945C8—2441no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—611no—
953C22—611no—
954C22—1221no—
955C22—1221no—
956C22—2441no—
957C22—2441no—
958C22—2441no—
959C22C22×C22⋊#692311yescharacteristic
960C4—21no—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—21no—
965C4—21no—
966C4—41no—
967C4—41no—
968C4—611no—
969C4—611no—
970C4—612no—
971C4—1221no—
972C4—1221no—
973C4—1221no—
974C4—1221no—
975C4—1221no—
976C4—4881no—
977C4—4881no—
978C4—2442no—
979C4—2442no—
980C4—2441no—
981C4—2441no—
982C4—2441no—
983C4#41×#692311yescharacteristic
984C4#1684083111yescharacteristic
985C2—81no—
986C2—81no—
987C2—1221no—
988C2—1221no—
989C2—4881no—
990C2#2146232411yescharacteristic
991C2D61⋊#42111yescharacteristic
992C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#559C4
socleC22×C61C22×C22⋊C4
prime radical#21459415C2
cosocleC2×C4×D61C24
hypercenter#559#6923
hypocenterC61#22551
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #21462621C2semidirect
2. #21462278C2semidirect
3. #21461984C2semidirect
4. #21461984C2semidirect
5. #21461983C2semidirect
6. #21461957C2semidirect
7. #21461956C2semidirect
8. #21461954C2semidirect
9. #21461694C2semidirect
10. #21461693C2semidirect
11. #21461691C2semidirect
12. #21461583C2semidirect
13. #21461582C2semidirect
14. C4×#14519841C2semidirect
52. #16840495C4semidirect
53. #16840495C4semidirect
54. #16840490C4semidirect
55. #16840485C4semidirect
56. #16840481C4semidirect
57. #16840481C4semidirect
61. #16840432C4semidirect
74. C61×#559C4semidirect
287. C4×#6923#41semidirect
295. #11758213#41semidirect
514. #559#6923semidirect
571. C61#22551semidirect

Maximal subgroups

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

subgroupindex
#214626212
#214622782
#214619842
#214619832
#214619572
#214619562
#214619542
#214616942
#214616932
#214616912
#214615832
#214615822
C4×#145198412
#214594152
#2255161