Finite Group Databasebeta

← #30622110

Subgroups — #30622110

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462615C211yesmaximal, characteristic, complemented
2#21462466C211yesmaximal, characteristic
3#21462007C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461928C211yesmaximal, characteristic, complemented
6#21461927C211yesmaximal, characteristic, complemented
7#21461887C211yesmaximal, characteristic, complemented
8#21461884C211yesmaximal, characteristic, complemented
9#21461788C211yesmaximal, characteristic
10#21461786C211yesmaximal, characteristic
11#21461608C211yesmaximal, characteristic, complemented
12#21461598C211yesmaximal, characteristic
13#21461594C211yesmaximal, characteristic
14#21461582C211yesmaximal, characteristic
15#21455600C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18#16840813—21no—
19#16840813—21no—
20#16840812—21no—
21#16840811—21no—
22C2×#14519848C2211yescharacteristic
23C2×#14519847C2211yescharacteristic
24#16840769C2211yescharacteristic
25#16840769C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840768—21no—
29#16840768—21no—
30#16840767C2211yescharacteristic
31#16840765—21no—
32C2×#14519844—21no—
33D61⋊(C4⋊C8)C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36#16840727C2211yescharacteristic
37#16840727C2211yescharacteristic
38C4×#11758213C2211yescharacteristic
39C2×#14519831C2211yescharacteristic
40C2×C8×#6923C2211yescharacteristic
41#16840698C2211yescharacteristic
42#16840638C2211yescharacteristic
43#16840638C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840317C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840068C411yescharacteristic, complemented
55#16840068C411yescharacteristic, complemented
56#16840060C411yescharacteristic, complemented
57#16840060C411yescharacteristic, complemented
58#16840058C411yescharacteristic, complemented
59#16840052C411yescharacteristic, complemented
60#16840044C411yescharacteristic, complemented
61#16839799C2211yescharacteristic
62#16839799C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#16839755C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#474C411yescharacteristic, complemented
67#14519864—22no—
68#14519864—22no—
69#14519864—41no—
70#14519864—41no—
71C2×#11758213C2311yescharacteristic
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C22×#92420—21no—
80C22×#92420—21no—
81C2×C4×#6923C2311yescharacteristic
82C2×C4×#6923C2311yescharacteristic
83#14519848—41no—
84#14519847—41no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91#14519844D411yescharacteristic
92#14519844D411yescharacteristic
93C4⋊#92420—21no—
94C4⋊#92420—21no—
95C4⋊#92420—21no—
96C4⋊#92420—21no—
97C4⋊#92420D411yescharacteristic
98C4⋊#92420D411yescharacteristic
99#14519841—22no—
100#14519841Q814yescomplemented
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104#14519831—41no—
105C4×#92420—21no—
106C4×#92420—21no—
107C4×#92420—21no—
108C8×#6923—41no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111C2×#11758224C2311yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519777C2×C411yescharacteristic
115#14519768C2×C411yescharacteristic
116#14519768C2×C411yescharacteristic
117#14519757—21no—
118#14519753—21no—
119Q8×Dic61—21no—
120C4×Dic122C2×C411yescharacteristic
121#14519742—21no—
122#14519742C2×C411yescharacteristic
123D4×Dic61C2×C411yescharacteristic
124C4×C22⋊D61—21no—
125#14519737—21no—
126#14519735C2311yescharacteristic
127#14519735C2311yescharacteristic
128#14519735C2311yescharacteristic
129#14519733—21no—
130C2×C4×Dic61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic
133#14519711C2×C411yescharacteristic
134#14519708C2×C411yescharacteristic
135#14519708C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138C4⋊#92418C2×C411yescharacteristic
139#14519706C2×C411yescharacteristic
140#14519706C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519702C2×C411yescharacteristic
143#14519700C2×C411yescharacteristic
144#14519700C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519698C2×C411yescharacteristic
147C4⋊Q8×C61C2×C411yescharacteristic
148C4×D4×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic
150#107×C61C2×C411yescharacteristic
151C4⋊C8×C61C2×C411yescharacteristic
152#102×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154C22×#6923—21no—
155C22×#6923—21no—
156C2×Q8×C61—21no—
157C2×D4×C61C22×C411yescharacteristic
158C22×C4×C61—21no—
159C2×C22⋊D61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162#11758224—21no—
163#11758224—21no—
164#11758224C2×Q812yes—
165#11758224#4112yes—
166C2×C4×D61#4111yescharacteristic
167C2×C4×D61#4111yescharacteristic
168C2×C4×D61C2411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122C22×C411yescharacteristic
171#11758217—42no—
172#11758217—42no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—42no—
178C2×#92420—42no—
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C4×#6923—21no—
184C4×#6923—21no—
185C4×#6923—21no—
186C4×#6923C2×Q812yes—
187#11758213—21no—
188#11758213—21no—
189#11758213—21no—
190#11758213—21no—
191#11758213—21no—
192#11758213—21no—
193#11758213—21no—
194#11758213C2×Q812yes—
195D61⋊C8—21no—
196D61⋊C8—21no—
197D61⋊C8—21no—
198D61⋊C8—21no—
199C2×C8×C61C22×C411yescharacteristic
200C2×C8×C61C22×C411yescharacteristic
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C411yescharacteristic
203C4⋊C4×C61C22×C411yescharacteristic
204C4⋊C4×C61C22×C411yescharacteristic
205C22⋊C4×C61—21no—
206C42×C61C22×C411yescharacteristic
207C22⋊Dic61—21no—
208#11758198—21no—
209#11758198—21no—
210#11758198—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216C4⋊Dic61C22×C411yescharacteristic
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C2×#92418C22×C411yescharacteristic
230C2×#92418C22×C411yescharacteristic
231C8×D61—21no—
232C8×D61—21no—
233C8×D61—21no—
234C8×D61—21no—
235C23×C61—21no—
236C22×D61C2×#4111yescharacteristic
237C2×#6923—22no—
238C2×#6923—41no—
239C2×#6923—41no—
240C2×#6923—41no—
241C2×#6923—41no—
242C2×#6923—41no—
243Q8×C61—81no—
244D4×C61—21no—
245D4×C61C4×Q812yes—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—81no—
250C2×C4×C61C4×D411yescharacteristic
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C23×C411yescharacteristic
253C22⋊D61—22no—
254C22⋊D61—22no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—42no—
262C2×Dic61C4×D411yescharacteristic
263C2×Dic61C4×D411yescharacteristic
264C2×Dic61C22×D411yescharacteristic
265C4×D61—41no—
266C4×D61—41no—
267C4×D61C22×Q811yescharacteristic
268C4×D61C2×#4111yescharacteristic
269C4×D61H(5,𝔽2)11yescharacteristic
270C4×D612−1+411yescharacteristic
271Dic122—21no—
272Dic122—42no—
273Dic122C4×Q812yes—
274#92420—21no—
275#92420—21no—
276#92420—21no—
277#92420—21no—
278#92420—22no—
279#92420—41no—
280#92420—41no—
281#92420—41no—
282C8×C61—21no—
283C8×C61—21no—
284#92418—21no—
285#92418—21no—
286#22984—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61C2×C4×D411yescharacteristic
291C2×D61—21no—
292C2×D61—21no—
293C2×D61#55211yescharacteristic
294C2×D61#55411yescharacteristic
295#6923—42no—
296#6923—81no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61C2×C4×Q811yescharacteristic
303C4×C61#52011yescharacteristic
304Dic61—22no—
305Dic61—21no—
306Dic61—21no—
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310Dic61#54611yescharacteristic
311Dic61D4×Q811yescharacteristic
312#3076—611no—
313#2962—611no—
314#2906—611no—
315#1995—611no—
316#1950—611no—
317#1946—611no—
318#1945—611no—
319#1922—611no—
320#1922—611no—
321#1866—611no—
322#1866—611no—
323#1768—611no—
324#1765—611no—
325#1764—611no—
326#1759—611no—
327C2×C61—42no—
328C2×C61#236011yescharacteristic
329C2×C61#295511yescharacteristic
330C2×C61#295711yescharacteristic
331D61—21no—
332D61—21no—
333C2×#131—611no—
334C2×#131—611no—
335#533—611no—
336C4×#41—611no—
337#479—611no—
338#479—611no—
339#478—611no—
340#478—611no—
341#477—611no—
342#476—611no—
343#475—611no—
344#474#692311yescharacteristic, complemented
345#446—1221no—
346#446—1221no—
347#446—1221no—
348C8×Q8—1221no—
349C2×#108—611no—
350C2×#108—611no—
351#427—611no—
352#427—611no—
353#424—611no—
354#424—611no—
355#424—611no—
356#424—611no—
357#424—1221no—
358#424—1221no—
359#423—611no—
360#423—1221no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—1221no—
364C2×#104—611no—
365C2×#104—611no—
366#416—611no—
367#416—611no—
368#405—611no—
369#405—611no—
370C4×M16—611no—
371C2×#97—611no—
372C2×C4×C8—611no—
373#376—611no—
374#341—611no—
375#341—611no—
376#339—611no—
377#339—611no—
378#339—611no—
379#339—611no—
380#339—611no—
381#339—611no—
382#336—611no—
383#336—611no—
384C61#2298411yescharacteristic, complemented, Sylow
385C2×#41—611no—
386#131—1222no—
387#131—1222no—
388#131—2441no—
389#131—2441no—
390C2×M16—611no—
391C2×M16—611no—
392C2×M16—611no—
393C2×M16—611no—
394C2×M16—1221no—
395C2×M16—1221no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—1221no—
401C22×C8—1221no—
402C4⋊Q8—611no—
403C4⋊Q8C2×#692311yescharacteristic
404#125—611no—
405#125—611no—
406C22⋊Q8—1221no—
407C22⋊Q8—1221no—
408C4×Q8—611no—
409C4×Q8—611no—
410C4×Q8—1221no—
411C4×Q8—1221no—
412C4×D4—611no—
413C4×D4—1221no—
414C4×D4—1221no—
415C4×D4C2×#692311yescharacteristic
416#117—611no—
417#117—611no—
418#117—611no—
419#117—1221no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—1221no—
424#108—2441no—
425#108—2441no—
426#107—611no—
427#107—611no—
428#107C2×#692311yescharacteristic
429#107C2×#692311yescharacteristic
430#106—611no—
431#106—611no—
432#106—611no—
433#106—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8—1221no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8C2×#692311yescharacteristic
452#104—614no—
453#104—1222no—
454#103—611no—
455#103—611no—
456#103—611no—
457#103—611no—
458#102—611no—
459#102—611no—
460#102C2×#692311yescharacteristic
461#102C2×#692311yescharacteristic
462#97—1221no—
463#97—1221no—
464#97—1221no—
465#97—2441no—
466C4×C8—1221no—
467C4×C8—1221no—
468C4×C8—1221no—
469C4×C8—2441no—
470#95—1221no—
471#95—1221no—
472#41—612no—
473#41—612no—
474#41—1221no—
475#41—1221no—
476C2×Q8—21no—
477C2×Q8—611no—
478C2×Q8—1221no—
479C2×D4—1221no—
480C2×D4C22×#692311yescharacteristic
481C22×C4—21no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489M16—612no—
490M16—1221no—
491M16—1221no—
492M16—1221no—
493M16—1221no—
494M16—1221no—
495M16—1221no—
496M16—1221no—
497M16—2442no—
498M16—2442no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—2442no—
518C2×C8—2442no—
519C2×C8C22×#692311yescharacteristic
520C2×C8C22×#692311yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—611no—
523C4⋊C4—611no—
524C4⋊C4—611no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4C22×#692311yescharacteristic
533C4⋊C4C22×#692311yescharacteristic
534C4⋊C4C22×#692311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—612no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42C22×#692311yescharacteristic
553C23—21no—
554C23—611no—
555Q8—81no—
556Q8—612no—
557Q8—1221no—
558Q8—2442no—
559D4—21no—
560D4—1222no—
561D4—1222no—
562D4Q8×#692312yes—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—81no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1221no—
577C2×C4—1222no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2442no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4D4×#692311yescharacteristic
590C2×C4D4×#692311yescharacteristic
591C2×C4C23×#692311yescharacteristic
592C8—21no—
593C8—21no—
594C8—1221no—
595C8—1221no—
596C8—1221no—
597C8—1221no—
598C8—1222no—
599C8—1221no—
600C8—1221no—
601C8—2441no—
602C8—2441no—
603C8—2441no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—611no—
608C22—611no—
609C22—1221no—
610C22—1221no—
611C22C2×D4×#692311yescharacteristic
612C4—21no—
613C4—21no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—611no—
618C4—611no—
619C4—1221no—
620C4—1221no—
621C4—1222no—
622C4—4881no—
623C4—2442no—
624C4—2441no—
625C4—2441no—
626C4—2441no—
627C4C2×Q8×#692311yescharacteristic
628C4#1684083111yescharacteristic
629C2—42no—
630C2—1221no—
631C2—1221no—
632C2#2146234311yescharacteristic
633C2#2146259211yescharacteristic
634C2#2146259511yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#474C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C23
cosocleC2×C4×D61C24
hypercenter#474#6923
hypocenterC61#22984
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #21462615C2semidirect
3. #21462007C2semidirect
4. #21461935C2semidirect
5. #21461928C2semidirect
6. #21461927C2semidirect
7. #21461887C2semidirect
8. #21461884C2semidirect
11. #21461608C2semidirect
54. #16840068C4semidirect
55. #16840068C4semidirect
56. #16840060C4semidirect
57. #16840060C4semidirect
58. #16840058C4semidirect
59. #16840052C4semidirect
60. #16840044C4semidirect
66. C61×#474C4semidirect
100. #14519841Q8semidirect
344. #474#6923semidirect
384. C61#22984semidirect

Maximal subgroups

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

subgroupindex
#214626152
#214624662
#214620072
#214619352
#214619282
#214619272
#214618872
#214618842
#214617882
#214617862
#214616082
#214615982
#214615942
#214615822
#214556002
#2298461