Finite Group Databasebeta

← #30611919

Subgroups — #30611919

Order 15616.

1104 conjugacy classes of subgroups.

The subgroup lattice has 946 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#21461349C211yesmaximal, characteristic, complemented
6#21461348C211yesmaximal, characteristic, complemented
7#21461343C211yesmaximal, characteristic, complemented
8#21461342C211yesmaximal, characteristic, complemented
9#21461335C211yesmaximal, characteristic, complemented
10#21461334C211yesmaximal, characteristic, complemented
11#21461331C211yesmaximal, characteristic, complemented
12#21461328C211yesmaximal, characteristic, complemented
13#21461317C211yesmaximal, characteristic, complemented
14C2×#16840621C211yesmaximal, characteristic, complemented
15#21459598C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic
23#16840785C2211yescharacteristic
24#16840782C2211yescharacteristic
25#16840782C2211yescharacteristic
26#16840780C2211yescharacteristic
27#16840779C2211yescharacteristic
28#16840779C2211yescharacteristic
29#16840767C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34#16840735—21no—
35#16840726—21no—
36#16840621C2211yescharacteristic
37#16840621C2211yescharacteristic
38#16840621C2211yescharacteristic
39#16840621C2211yescharacteristic
40#16840621C2211yescharacteristic
41#16840621C2211yescharacteristic
42#16840621C2211yescharacteristic
43#16840621C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52C2×#14519824—21no—
53D4×Dic122C411yescharacteristic
54#16840427C411yescharacteristic
55#16840425—21no—
56#16840416C411yescharacteristic
57#16840413C411yescharacteristic
58#16840413C411yescharacteristic
59#16840412C411yescharacteristic
60#16840412C411yescharacteristic
61#16840411—21no—
62#16840410—21no—
63#16840410—21no—
64#16840335—21no—
65#16840334—21no—
66#16840334—21no—
67#16840309C2211yescharacteristic
68#16840307C2211yescharacteristic
69#16840307C2211yescharacteristic
70C2×#14519776C2211yescharacteristic
71C2×#14519776C2211yescharacteristic
72C4⋊Q8×D61C2211yescharacteristic
73C4×#11758224C2211yescharacteristic
74C61×#547C411yescharacteristic
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#14519824—44no—
108#14519824—44no—
109C2×#11758222—21no—
110C2×#11758222—21no—
111C2×#11758222—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—21no—
115C2×#11758224—21no—
116C2×#11758224—21no—
117C2×#11758224D411yescharacteristic
118C22×Dic122—21no—
119C22×Dic122—21no—
120C22×Dic122—21no—
121C2×Q8×D61—21no—
122C2×Q8×D61—21no—
123#14519777C2×C411yescharacteristic
124#14519776—21no—
125#14519776—21no—
126#14519776—21no—
127#14519776—21no—
128#14519776—21no—
129#14519776C2×C411yescharacteristic
130#14519776C2×C411yescharacteristic
131#14519776C2×C411yescharacteristic
132#14519776C2×C411yescharacteristic
133#14519776C2311yescharacteristic
134#14519776C2311yescharacteristic
135#14519776C2311yescharacteristic
136#14519775—21no—
137#14519773C2311yescharacteristic
138#14519763—21no—
139#14519763—21no—
140#14519763—21no—
141#14519762—21no—
142#14519762—21no—
143#14519761—21no—
144#14519761—21no—
145#14519760—21no—
146#14519760—21no—
147#14519759—21no—
148#14519759—21no—
149#14519758—21no—
150#14519758—21no—
151#14519757—21no—
152#14519756—21no—
153#14519755—21no—
154#14519755—21no—
155#14519755—21no—
156#14519755—21no—
157#14519754—21no—
158#14519754—21no—
159#14519754—21no—
160#14519754—21no—
161#14519753—21no—
162#14519752C2×C411yescharacteristic
163#14519751C2×C411yescharacteristic
164#14519751C2×C411yescharacteristic
165#14519750—21no—
166#14519749—21no—
167#14519749—21no—
168#14519748C2×C411yescharacteristic
169C4×Dic122C2×C411yescharacteristic
170#14519742D411yescharacteristic
171C4×D244C2×C411yescharacteristic
172D4×Dic61C2×C411yescharacteristic
173D4×Dic61C2×C411yescharacteristic
174D4×Dic61D411yescharacteristic
175#14519739C2×C411yescharacteristic
176#14519739C2×C411yescharacteristic
177C4×C22⋊D61—21no—
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737—21no—
181#14519737—21no—
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519735D411yescharacteristic
185#14519733D411yescharacteristic
186#14519733D411yescharacteristic
187C2×C4⋊Dic61C2×C411yescharacteristic
188C2×C4⋊Dic61C2×C411yescharacteristic
189C2×#11758196—21no—
190C2×#11758196—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61C2×C411yescharacteristic
193C4⋊C4×D61C2×C411yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C2×C4×Dic61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C2×#41×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic
199#123×C61—21no—
200#123×C61—21no—
201C22⋊Q8×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×C4⋊C4×C61C2×C411yescharacteristic
208#41×C61—44no—
209C2×Q8×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22⋊C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234Q8×D61—44no—
235Q8×D61—42no—
236Q8×D61—42no—
237#11758224—22no—
238#11758224—22no—
239#11758224—42no—
240#11758224—42no—
241#11758224—44no—
242#11758224—44no—
243#11758224—44no—
244#11758224—42no—
245#11758224—42no—
246#11758222—42no—
247#11758222—42no—
248#11758222—44no—
249#11758222—44no—
250C2×D244—21no—
251C2×D244C22×C411yescharacteristic
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61C22×C411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×Dic122—21no—
261C2×Dic122—21no—
262C2×Dic122—21no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—44no—
269C2×Dic122—42no—
270C2×Dic122—42no—
271C2×Dic122—42no—
272C2×Dic122—42no—
273C2×Dic122C22⋊C411yescharacteristic
274#11758217—42no—
275#11758217—81no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—42no—
285C2×#92420—81no—
286#11758213—81no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C22⋊C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61C22⋊C411yescharacteristic
298C22⋊C4×C61C22⋊C411yescharacteristic
299C42×C61C22×C411yescharacteristic
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61C22⋊C411yescharacteristic
304C22⋊Dic61C22⋊C411yescharacteristic
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319C4⋊Dic61C22×C411yescharacteristic
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C22×C411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C4×Dic61C2411yescharacteristic
342C23×C61—21no—
343C23×C61C2×C22⋊C411yescharacteristic
344C23×C61C2×C22⋊C411yescharacteristic
345C22×D61—21no—
346C22×D61C2×C22⋊C411yescharacteristic
347Q8×C61—42no—
348D4×C61—22no—
349D4×C61—41no—
350D4×C61—42no—
351D4×C61—42no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
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—42no—
368C22⋊D61—42no—
369C22⋊D61—42no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—42no—
384C2×Dic61—42no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61AGL(1,ℤ/8)12yes—
393C2×Dic61AGL(1,ℤ/8)12yes—
394C2×Dic61C22×D411yescharacteristic
395C2×Dic61C22×D411yescharacteristic
396D244—41no—
397D244—42no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—41no—
403C4×D61—42no—
404C4×D61—42no—
405C4×D61—42no—
406C4×D61—42no—
407C4×D61—42no—
408Dic122—22no—
409Dic122—42no—
410Dic122—42no—
411Dic122—42no—
412Dic122—41no—
413Dic122—41no—
414Dic122—41no—
415Dic122—41no—
416Dic122—41no—
417Dic122—41no—
418Dic122—42no—
419Dic122—42no—
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#17759—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#41812yes—
438C22×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—41no—
451C4×C61—41no—
452C4×C61—41no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—41no—
458Dic61—41no—
459Dic61—41no—
460Dic61#41812yes—
461Dic61C2×AGL(1,ℤ/8)11yescharacteristic
462Dic61C2×AGL(1,ℤ/8)11yescharacteristic
463Dic61#57711yescharacteristic
464Dic61#57811yescharacteristic
465#3499—611no—
466#2989—611no—
467#2925—611no—
468#1557—611no—
469#1557—611no—
470#1556—611no—
471#1556—611no—
472#1553—611no—
473#1553—611no—
474#1549—611no—
475#1549—611no—
476#1547—611no—
477#1546—611no—
478#1540—611no—
479C2×#332—611no—
480C2×C61—22no—
481C2×C61—41no—
482C2×C61—81no—
483C2×C61#288911yescharacteristic
484C2×C61C2×#41811yescharacteristic
485C2×C61#289811yescharacteristic
486D61—41no—
487D61—81no—
488C2×2−1+4—1221no—
489D4×Q8—611no—
490D4×Q8—611no—
491D4×Q8—1221no—
492#547—611no—
493#547—611no—
494#547—611no—
495#547—611no—
496#547—611no—
497#547—1221no—
498#547—1221no—
499#547—1221no—
500#547#692311yescharacteristic
501#536—1221no—
502#536—1221no—
503#536—1221no—
504#532—611no—
505#532—611no—
506#532—611no—
507C2×C4⋊Q8—611no—
508C2×C4⋊Q8—611no—
509C2×C4⋊Q8—611no—
510C4×#41—611no—
511#446—1221no—
512#436—1221no—
513#435—1221no—
514#435—1221no—
515#433—1221no—
516#433—1221no—
517#432—611no—
518#432—611no—
519#432—611no—
520#432—611no—
521#431—611no—
522#431—611no—
523#431—611no—
524#423—611no—
525#423—611no—
526#423—611no—
527C2×C4⋊C8—611no—
528C2×C4⋊C8—611no—
529#408—1221no—
530#405—1221no—
531#332—611no—
532#332—611no—
533#332—611no—
534#332—611no—
535#332—611no—
536#332—611no—
537#332—611no—
538#332—611no—
539#332—611no—
540#332—611no—
541#332—611no—
542#332—611no—
543#331—611no—
544#331—611no—
545#331—611no—
546#331—611no—
547C61#1775911yescharacteristic, complemented, Sylow
5482−1+4—2444no—
5492−1+4—2444no—
550C2×#41—21no—
551C2×#41—611no—
552C2×#41—1221no—
553C2×#41—1221no—
554C2×#41—1221no—
555C2×#41—1221no—
556C2×#41—1221no—
557C2×#41—1221no—
558C2×#41—1221no—
559C2×#41—1221no—
560C22×Q8—1221no—
561C22×Q8—1221no—
562C22×Q8—1221no—
563C22×Q8—1221no—
564C22×Q8—1221no—
565C2×M16—1221no—
566C2×M16—1221no—
567C2×M16—1221no—
568C22×C8—1221no—
569C22×C8—1221no—
570C4⋊Q8—611no—
571C4⋊Q8—611no—
572C4⋊Q8—611no—
573C4⋊Q8—611no—
574C4⋊Q8—611no—
575C4⋊Q8—611no—
576C4⋊Q8—611no—
577C4⋊Q8—611no—
578C4⋊Q8—1221no—
579C4⋊Q8—1221no—
580C4⋊Q8—1221no—
581C4⋊Q8—1221no—
582C4⋊Q8—1221no—
583C4⋊Q8—1221no—
584C4⋊Q8C2×#692311yescharacteristic
585#127—611no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#123—21no—
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601C22⋊Q8—21no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613#121—611no—
614#121—611no—
615#121—611no—
616#121—611no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121C2×#692311yescharacteristic
621#121C2×#692311yescharacteristic
622C4×Q8—611no—
623C4×Q8—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4C2×#692311yescharacteristic
638C4×D4C2×#692311yescharacteristic
639#117—611no—
640#117—611no—
641#117—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—1221no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4C2×#692311yescharacteristic
650C2×C4⋊C4C2×#692311yescharacteristic
651C2×C42—611no—
652C2×C42—611no—
653C2×C42—611no—
654C4⋊C8—611no—
655C4⋊C8—611no—
656C4⋊C8—611no—
657C4⋊C8—611no—
658C4⋊C8—611no—
659C4⋊C8—611no—
660C4⋊C8—611no—
661C4⋊C8—611no—
662C4⋊C8—1221no—
663C4⋊C8—1221no—
664C4⋊C8—1221no—
665C4⋊C8—1221no—
666C4⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8—1221no—
670C22⋊C8—1221no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8—1221no—
674#97—1221no—
675#97—1221no—
676#97—1221no—
677#97—1221no—
678C4×C8—1221no—
679C4×C8—1221no—
680C4×C8—1221no—
681#41—44no—
682#41—1222no—
683#41—1222no—
684#41—2442no—
685#41—2442no—
686#41—2444no—
687#41—2444no—
688#41—2442no—
689#41—2442no—
690#41—2442no—
691#41—2442no—
692#41—2444no—
693#41—2444no—
694#41—2444no—
695C2×Q8—21no—
696C2×Q8—611no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—1221no—
700C2×Q8—1221no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8—1221no—
705C2×Q8—2442no—
706C2×Q8—2442no—
707C2×Q8—2442no—
708C2×Q8—2442no—
709C2×Q8—2444no—
710C2×Q8—2442no—
711C2×Q8—2442no—
712C2×Q8—2444no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4C22⋊#692311yescharacteristic
725C2×D4C22×#692311yescharacteristic
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4C22×#692311yescharacteristic
746C22×C4C22×#692311yescharacteristic
747M16—4881no—
748M16—4881no—
749M16—2442no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—4881no—
759C2×C8—2442no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—611no—
764C4⋊C4—611no—
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⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4C22⋊#692311yescharacteristic
784C4⋊C4C22×#692311yescharacteristic
785C4⋊C4C22×#692311yescharacteristic
786C4⋊C4C22×#692311yescharacteristic
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4C22⋊#692311yescharacteristic
804C22⋊C4C22⋊#692311yescharacteristic
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—611no—
810C42—611no—
811C42—611no—
812C42—611no—
813C42—611no—
814C42C22×#692311yescharacteristic
815C23—21no—
816C23—611no—
817C23—1221no—
818C23C2×C22⋊#692311yescharacteristic
819C23C2×C22⋊#692311yescharacteristic
820Q8—42no—
821Q8—1222no—
822Q8—2442no—
823Q8—2441no—
824Q8—2441no—
825Q8—2442no—
826Q8—2441no—
827Q8—2441no—
828Q8—2441no—
829Q8—2441no—
830Q8—2442no—
831Q8—2442no—
832Q8—2442no—
833D4—22no—
834D4—41no—
835D4—42no—
836D4—42no—
837D4—1222no—
838D4—1222no—
839D4—2441no—
840D4—2442no—
841D4—2441no—
842D4—2441no—
843D4—2441no—
844D4—2441no—
845D4—2442no—
846D4—2442no—
847D4—2442no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—2441no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4—2442no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4C2×C22⋊#692311yescharacteristic
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C2×C22⋊#692311yescharacteristic
891C2×C4C2×C22⋊#692311yescharacteristic
892C2×C4C23×#692311yescharacteristic
893C8—2441no—
894C8—2441no—
895C8—2441no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C8—2441no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22#1684075412yes—
916C22C22×C22⋊#692311yescharacteristic
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—611no—
926C4—611no—
927C4—612no—
928C4—611no—
929C4—611no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—2441no—
935C4—2441no—
936C4—2441no—
937C2—22no—
938C2—41no—
939C2—81no—
940C2—4881no—
941C2—2441no—
942C2#2146243111yescharacteristic
943C2C2×#1684075411yescharacteristic
944C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459598C2
cosocleC4×Dic61C24
hypercenter#547#6923
hypocenterC61#17759
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462517C2semidirect
3. #21461351C2semidirect
4. #21461350C2semidirect
5. #21461349C2semidirect
6. #21461348C2semidirect
7. #21461343C2semidirect
8. #21461342C2semidirect
9. #21461335C2semidirect
10. #21461334C2semidirect
11. #21461331C2semidirect
12. #21461328C2semidirect
13. #21461317C2semidirect
14. C2×#16840621C2semidirect
547. C61#17759semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214625172
#214613512
#214613502
#214613492
#214613482
#214613432
#214613422
#214613352
#214613342
#214613312
#214613282
#214613172
C2×#168406212
#214595982
#1775961