Finite Group Databasebeta

← #30610644

Subgroups — #30610644

Order 15616.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462740C211yesmaximal, characteristic, complemented
2#21462623C211yesmaximal, characteristic, complemented
3#21461183C212yesmaximal, complemented
4#21461177C212yesmaximal, complemented
5#21461173C212yesmaximal, complemented
6#21461169C212yesmaximal, complemented
7#21461123C211yesmaximal, characteristic, complemented
8#21461116C211yesmaximal, characteristic, complemented
9#21461112C211yesmaximal, characteristic, complemented
10C2×#16840612C211yesmaximal, characteristic, complemented
11#21459253C211yesmaximal, characteristic
12#16840812—21no—
13#16840811—21no—
14#16840796—21no—
15#16840791—22no—
16#16840790—21no—
17#16840789—22no—
18#16840784C2212yes—
19#16840780C2212yes—
20#16840778C2211yescharacteristic
21#16840778C2211yescharacteristic
22#16840766C2212yes—
23C2×C4⋊#92420C2211yescharacteristic
24C4×D61⋊C8C2212yes—
25C2×C4×#92420C2211yescharacteristic
26#16840612C2212yes—
27#16840612C2212yes—
28#16840612C2211yescharacteristic
29#16840612C2211yescharacteristic
30#16840612C2212yes—
31#16840612C2212yes—
32#16840612C2212yes—
33#16840610C2211yescharacteristic
34#16840610C2211yescharacteristic
35#16840610C2212yes—
36#16840386—21no—
37#16840386C412yes—
38#16840375—21no—
39#16840375C412yes—
40#16840361—22no—
41#16840343C411yescharacteristic
42#16840338C411yescharacteristic
43#16840338C411yescharacteristic
44#16840317—21no—
45#16840317C2212yes—
46#16840298—22no—
47#16840297—21no—
48#16840297C2212yes—
49#16840230C2211yescharacteristic
50#16840230C2211yescharacteristic
51C2×#14519742C2211yescharacteristic
52C61×#544C411yescharacteristic
53C2×#11758213—22no—
54C2×D61⋊C8—22no—
55C22×#92420—21no—
56C22×#92420—21no—
57#14519844—22no—
58C4⋊#92420—21no—
59C4⋊#92420—22no—
60C4⋊#92420—21no—
61C4⋊#92420C2312yes—
62C4⋊#92420C2311yescharacteristic
63C4⋊#92420C2311yescharacteristic
64#14519834—22no—
65#14519834—22no—
66C22⋊#92420—21no—
67C22⋊#92420—21no—
68#14519832—22no—
69C4×#92420—21no—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C22×Dic122C2×C411yescharacteristic
78#14519777—21no—
79#14519777C2×C412yes—
80#14519772—22no—
81#14519772—22no—
82#14519772—22no—
83#14519772—22no—
84#14519768—22no—
85#14519768—22no—
86#14519768—22no—
87#14519766—22no—
88#14519765—21no—
89#14519765C2×C412yes—
90#14519762—22no—
91#14519762—22no—
92#14519761—22no—
93#14519761—22no—
94#14519757—21no—
95#14519757—21no—
96#14519757—21no—
97#14519757C2×C412yes—
98#14519757C2×C412yes—
99#14519757C2×C412yes—
100#14519753—22no—
101#14519753—22no—
102#14519752—21no—
103#14519752C2×C412yes—
104#14519751—22no—
105Q8×Dic61—22no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C412yes—
109#14519742C2×C411yescharacteristic
110#14519742D411yescharacteristic
111#14519742D411yescharacteristic
112#14519742C2312yes—
113#14519742C2311yescharacteristic
114#14519739—22no—
115#14519739C2×C411yescharacteristic
116#14519739D411yescharacteristic
117#14519739D411yescharacteristic
118#14519739C2311yescharacteristic
119#14519737—21no—
120#14519737—21no—
121#14519737D412yes—
122#14519737D412yes—
123#14519735—22no—
124#14519735—22no—
125#14519734—21no—
126#14519734C2×C412yes—
127C2×#11758196—21no—
128C2×C4×Dic61—21no—
129C2×C4×Dic61C2311yescharacteristic
130C42×D61—21no—
131C42×D61C2312yes—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2×C412yes—
134#125×C61—21no—
135#125×C61C2×C412yes—
136C22⋊Q8×C61—22no—
137#117×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×Q8×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61C22×C411yescharacteristic
143C2×C22⋊D61—21no—
144C2×C22⋊D61C22⋊C412yes—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148#11758222—24no—
149#11758222—24no—
150C2×D244—22no—
151C2×D244C22⋊C411yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61C22×C412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×Dic122—24no—
160C2×Dic122—21no—
161C2×Dic122C22⋊C411yescharacteristic
162C2×Dic122C22×C412yes—
163C2×Dic122C22×C411yescharacteristic
164C2×#92420—21no—
165C2×#92420—22no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—22no—
170C2×#92420—42no—
171C2×#92420—81no—
172#11758213—82no—
173D61⋊C8—44no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61C22⋊C411yescharacteristic
179C4⋊C4×C61C22⋊C411yescharacteristic
180C4⋊C4×C61C22×C412yes—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61C22⋊C412yes—
185C42×C61—21no—
186C42×C61C22×C412yes—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—21no—
193#11758198—22no—
194#11758198—21no—
195#11758198C22⋊C412yes—
196#11758198C22⋊C412yes—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202#11758196—22no—
203#11758196—21no—
204#11758196—22no—
205#11758196—21no—
206#11758196C22⋊C412yes—
207#11758196C22⋊C412yes—
208C4×Dic61—21no—
209C4×Dic61—22no—
210C4×Dic61—21no—
211C4×Dic61—22no—
212C4×Dic61C22×C411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D412yes—
217C4×Dic61C2411yescharacteristic
218C23×C61C2×C22⋊C411yescharacteristic
219C22×D61—21no—
220C22×D61C2×C22⋊C412yes—
221Q8×C61—82no—
222C2×C4×C61—22no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—81no—
226C2×C4×C61C2×C22⋊C412yes—
227C2×C4×C61C2×C22⋊C412yes—
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61#13114yes—
230C2×C4×C61C23×C411yescharacteristic
231C22⋊D61—24no—
232C22⋊D61—42no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—41no—
238C2×Dic61—42no—
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C22×D411yescharacteristic
243C2×Dic61C22×D411yescharacteristic
244D244—22no—
245D244—22no—
246D244—82no—
247C4×D61—24no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—81no—
255Dic122—22no—
256Dic122—24no—
257Dic122—22no—
258Dic122—42no—
259#92420—22no—
260#92420—42no—
261#92420—41no—
262#92420—41no—
263#92420—42no—
264#92420—41no—
265#17484—611nomaximal, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61#40812yes—
269C22×C61C22×C22⋊C411yescharacteristic
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—42no—
281C4×C61#40812yes—
282C4×C61C2×#13112yes—
283Dic61—22no—
284Dic61—21no—
285Dic61—21no—
286Dic61—21no—
287Dic61—42no—
288Dic61—41no—
289Dic61#57711yescharacteristic
290Dic61#57811yescharacteristic
291#3461—611no—
292#2989—611no—
293C8×#41—611no—
294#1497—612no—
295#1495—612no—
296#1494—612no—
297#1493—612no—
298#1479—611no—
299#1477—611no—
300#1476—611no—
301C2×Q8⋊C8—611no—
302C2×C61—22no—
303C2×C61C2×#40811yescharacteristic
304C2×C61#289811yescharacteristic
305C2×C61#290111yescharacteristic
306D61—42no—
307D61—81no—
308#544#692311yescharacteristic
309#542—612no—
310#542—1221no—
311#541—612no—
312#541—1221no—
313#539—1222no—
314#537—611no—
315#536—611no—
316#536—611no—
317#533—612no—
318#533—1221no—
319#529—612no—
320#529—1222no—
321#529—1221no—
322C4×#41—611no—
323C4×#41—611no—
324C2×C4×Q8—611no—
325#446—1221no—
326C8×Q8—1221no—
327#436—1221no—
328#435—1222no—
329C8×D4—1222no—
330C8×D4—1221no—
331#432—612no—
332#431—611no—
333#431—612no—
334#431—611no—
335#423—612no—
336C2×C4⋊C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—612no—
339Q8⋊C8—612no—
340Q8⋊C8—612no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—612no—
344Q8⋊C8—612no—
345Q8⋊C8—612no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—612no—
349C61#1748411yescharacteristic, complemented, Sylow
350C2×#41—611no—
351C2×#41—611no—
352C22×Q8—611no—
353C2×M16—1222no—
354C22×C8—1221no—
355C22×C8—1221no—
356C22×C8—1222no—
357C4⋊Q8—21no—
358C4⋊Q8—612no—
359C4⋊Q8—1221no—
360C4⋊Q8C2×#692312yes—
361#126—1222no—
362#126—1222no—
363#126—1222no—
364#126—1222no—
365#125—21no—
366#125—1222no—
367#125—1222no—
368#125—1222no—
369#125C2×#692312yes—
370#124—612no—
371#124—1221no—
372#124—1222no—
373#123—1222no—
374#123—1222no—
375#123—1222no—
376#123—1222no—
377C22⋊Q8—22no—
378C22⋊Q8—612no—
379C22⋊Q8—612no—
380C22⋊Q8—612no—
381C22⋊Q8—1221no—
382C22⋊Q8—1222no—
383C22⋊Q8—1222no—
384C22⋊Q8—1221no—
385C22⋊Q8—1221no—
386#121—612no—
387#121—1221no—
388#121—1222no—
389C4×Q8—611no—
390C4×Q8—611no—
391C4×Q8—612no—
392C4×Q8—612no—
393C4×Q8—611no—
394C4×Q8—611no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8—1222no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—612no—
401C4×D4—612no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—1221no—
405C4×D4—1221no—
406C4×D4—1222no—
407#117—612no—
408#117—1221no—
409#117—1222no—
410#117—1222no—
411#117C2×#692311yescharacteristic
412#117C2×#692311yescharacteristic
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C42—611no—
416C2×C42—612no—
417C2×C42—1221no—
418C2×C42—1221no—
419C4⋊C8—612no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—1221no—
423C4⋊C8—1222no—
424C4⋊C8—1221no—
425C4⋊C8—1222no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1222no—
429C22⋊C8—1222no—
430#97—1222no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—612no—
434C4×C8—1221no—
435C4×C8—1222no—
436C4×C8—1221no—
437#41—1224no—
438#41—1224no—
439C2×Q8—22no—
440C2×Q8—611no—
441C2×Q8—612no—
442C2×Q8—611no—
443C2×Q8—1221no—
444C2×Q8—1224no—
445C2×D4—612no—
446C2×D4—611no—
447C2×D4—611no—
448C2×D4—1222no—
449C2×D4—1221no—
450C22×C4—21no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4C22×#692311yescharacteristic
461M16—4882no—
462C2×C8—1221no—
463C2×C8—1222no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1222no—
468C2×C8—4881no—
469C2×C8—2444no—
470C2×C8—2442no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—612no—
476C4⋊C4—612no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4C22⋊#692311yescharacteristic
487C4⋊C4C22⋊#692311yescharacteristic
488C4⋊C4C22×#692312yes—
489C4⋊C4C22×#692311yescharacteristic
490C4⋊C4C22×#692311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—612no—
493C22⋊C4—612no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4C22⋊#692312yes—
503C42—21no—
504C42—611no—
505C42—611no—
506C42—612no—
507C42—612no—
508C42—611no—
509C42—611no—
510C42—1221no—
511C42—1222no—
512C42—1221no—
513C42—1222no—
514C42C22×#692312yes—
515C23—612no—
516C23—1221no—
517C23C2×C22⋊#692311yescharacteristic
518Q8—82no—
519Q8—1222no—
520Q8—1224no—
521Q8—1222no—
522Q8—2442no—
523D4—1224no—
524D4—1222no—
525D4—1222no—
526D4—4882no—
527D4—2442no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—81no—
532C2×C4—611no—
533C2×C4—611no—
534C2×C4—611no—
535C2×C4—612no—
536C2×C4—611no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1224no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—4881no—
545C2×C4—2442no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4C2×C22⋊#692312yes—
552C2×C4C2×C22⋊#692312yes—
553C2×C4C2×C22⋊#692311yescharacteristic
554C2×C4#1451986514yes—
555C2×C4C23×#692311yescharacteristic
556C8—1222no—
557C8—2441no—
558C8—2442no—
559C8—2441no—
560C8—2442no—
561C8—2441no—
562C22—21no—
563C22—21no—
564C22—1222no—
565C22—1222no—
566C22—1222no—
567C22—2441no—
568C22—2441no—
569C22—2441no—
570C22#1684073712yes—
571C22C22×C22⋊#692311yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—611no—
578C4—611no—
579C4—1222no—
580C4—1221no—
581C4—1221no—
582C4—1221no—
583C4—2441no—
584C4—2442no—
585C4#1684073712yes—
586C4C2×#1451986512yes—
587C2—22no—
588C2—4881no—
589C2—2442no—
590C2C2×#1684073711yescharacteristic
591C2#2146244111yescharacteristic
592C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radical#16840343C4
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #21462740C2semidirect
2. #21462623C2semidirect
3. #21461183C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461169C2semidirect
7. #21461123C2semidirect
8. #21461116C2semidirect
9. #21461112C2semidirect
10. C2×#16840612C2semidirect
349. C61#17484semidirect

Maximal subgroups

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

subgroupindex
#214627402
#214626232
#214611832
#214611772
#214611732
#214611692
#214611232
#214611162
#214611122
C2×#168406122
#214592532
#1748461