Finite Group Databasebeta

← #30612717

Subgroups — #30612717

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462708C211yesmaximal, characteristic, complemented
2#21462667C211yesmaximal, characteristic, complemented
3#21461441C211yesmaximal, characteristic, complemented
4#21461440C211yesmaximal, characteristic, complemented
5#21461421C211yesmaximal, characteristic, complemented
6#21461420C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8#21461415C211yesmaximal, characteristic, complemented
9#21461399C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461159C211yesmaximal, characteristic, complemented
13#21461139C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455818C211yesmaximal, characteristic
16#16840797C2211yescharacteristic, complemented
17#16840797C2211yescharacteristic, complemented
18#16840793—21no—
19#16840793—21no—
20#16840790C2211yescharacteristic
21#16840790C2211yescharacteristic
22#16840789—21no—
23#16840789—21no—
24D4×#92420C2211yescharacteristic
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic, complemented
27D4×#92420C2211yescharacteristic, complemented
28#16840784C2211yescharacteristic
29#16840781C2211yescharacteristic
30#16840780C2211yescharacteristic
31#16840735—21no—
32#16840735—21no—
33C2×#14519834—21no—
34D61⋊(C22⋊C8)—21no—
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic
41#16840610C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic, complemented
45D4⋊#92420C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840310C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840074C411yescharacteristic
55#16840074C411yescharacteristic
56#16840043C411yescharacteristic
57#16840042C411yescharacteristic
58#16839954C411yescharacteristic
59#16839894C411yescharacteristic
60#16839894C411yescharacteristic
61D8×Dic61C2211yescharacteristic
62D8×Dic61C2211yescharacteristic
63#16839842C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#459C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75C22×#92420—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86#14519834D411yescharacteristic
87#14519834D411yescharacteristic
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94#14519832—21no—
95#14519832—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×D4×D61C2×C411yescharacteristic
103C22×C4×D61—21no—
104C2×#11758199C2×C411yescharacteristic
105C2×#11758199C2×C411yescharacteristic
106#14519777C2×C411yescharacteristic
107#14519764—21no—
108#14519748—21no—
109#14519748C2×C411yescharacteristic
110#14519748C2×C411yescharacteristic
111C4×D244C2×C411yescharacteristic
112D4×Dic61—21no—
113D4×Dic61C2311yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739C2311yescharacteristic
117C4×C22⋊D61—21no—
118#14519737—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C22⋊C4×D61—21no—
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519699C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519698C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×D8×C61C2×C411yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139#127×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157#11758224—81no—
158#11758224—81no—
159D4×D61—22no—
160D4×D61—22no—
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—81no—
166C2×C4×D61—81no—
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61#4111yescharacteristic
170C2×Dic122—21no—
171#11758217—81no—
172#11758217—81no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—81no—
180C2×#92420—81no—
181C2×#92420—81no—
182C2×#92420—81no—
183C2×#92420C2×D411yescharacteristic
184C2×#92420C2×D411yescharacteristic
185C2×#92420C2×D411yescharacteristic
186C2×#92420C2×D411yescharacteristic
187#11758213—42no—
188D61⋊C8—81no—
189D61⋊C8—81no—
190D8×C61—22no—
191D8×C61—22no—
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C22×C411yescharacteristic
194C4⋊C4×C61C22×C411yescharacteristic
195C22⋊C4×C61—21no—
196C42×C61C22×C411yescharacteristic
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199C22⋊Dic61—21no—
200C22⋊Dic61—21no—
201C22⋊Dic61—21no—
202#11758199—22no—
203#11758199—22no—
204#11758198—21no—
205#11758198—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209C4⋊Dic61C22×C411yescharacteristic
210#11758196—21no—
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61#4111yescharacteristic
213C4×Dic61C2411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C2×#92418C22×C411yescharacteristic
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C22×D61—21no—
220C22×D61—24no—
221C22×D61—81no—
222C22×D61—81no—
223C22×D61C4×D411yescharacteristic
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—81no—
230D4×C61—81no—
231D4×C61#13112yes—
232C2×C4×C61—21no—
233C2×C4×C61—81no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C22⋊D61—24no—
238C22⋊D61—81no—
239C22⋊D61—81no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251C2×Dic61C2×#4111yescharacteristic
252D244—21no—
253D244#13112yes—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—81no—
262C4×D61—81no—
263Dic122—81no—
264#92420—22no—
265#92420—21no—
266#92420—21no—
267#92420—21no—
268#92420—21no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274C8×C61—21no—
275C8×C61—21no—
276#92418—21no—
277#92418—21no—
278#17922—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61C2×C4×D411yescharacteristic
289C2×D61—21no—
290C2×D61—22no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—84no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—41no—
299C4×C61C2×#13111yescharacteristic
300C4×C61C2×#13111yescharacteristic
301Dic61—21no—
302Dic61—21no—
303Dic61—41no—
304Dic61—41no—
305Dic61—41no—
306Dic61#57611yescharacteristic
307Dic61#57611yescharacteristic
308#3100—611no—
309#2981—611no—
310#2972—611no—
311#1586—611no—
312#1586—611no—
313#1581—611no—
314#1581—611no—
315#1580—611no—
316#1580—611no—
317C8×D8—611no—
318C8×D8—611no—
319#1572—611no—
320#1490—611no—
321#1484—611no—
322#1453—611no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61—81no—
326C2×C61#292911yescharacteristic
327C2×C61#294811yescharacteristic
328C2×C61#295611yescharacteristic
329D61—41no—
330D61—42no—
331#532—611no—
332C2×C4×D4—611no—
333#480—611no—
334#480—611no—
335#474—611no—
336#474—611no—
337#459—611no—
338#459#692311yescharacteristic
339#447—611no—
340#447—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344C4×D8—611no—
345#436—611no—
346#436—611no—
347#435—1221no—
348#435—1221no—
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356C8×D4—1221no—
357#432—611no—
358#431—611no—
359#431—611no—
360#431—611no—
361#408—1221no—
362#408—1221no—
363C2×C22⋊C8—1221no—
364C2×C22⋊C8—1221no—
365C4×M16—611no—
366#335—611no—
367#335—611no—
368#334—611no—
369#334—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378#322—611no—
379#322—611no—
380#322—611no—
381C82—611no—
382C61#1792211yescharacteristic, complemented, Sylow
383C2×#41—1221no—
384C22×D4—611no—
385C23×C4—1221no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8C2×#692311yescharacteristic
389C2×D8C2×#692311yescharacteristic
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C4⋊Q8—611no—
400#127C2×#692311yescharacteristic
401#124—1221no—
402#121—611no—
403#121—611no—
404#121—1221no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—611no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4C2×#692311yescharacteristic
414C2×C4⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417#107—611no—
418#107—611no—
419#107—611no—
420#107—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8C2×#692311yescharacteristic
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102C2×#692311yescharacteristic
436#102C2×#692311yescharacteristic
437C22⋊C8—611no—
438C22⋊C8—611no—
439C22⋊C8—611no—
440C22⋊C8—611no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451#97—1221no—
452#97—1221no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—1221no—
460C24—1221no—
461#41—4881no—
462#41—4881no—
463C2×Q8—1221no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—611no—
467C2×D4—1221no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4C22×#692311yescharacteristic
473C2×D4C22×#692311yescharacteristic
474C2×D4C22×#692311yescharacteristic
475C22×C4—21no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—4881no—
486C22×C4—4881no—
487D8—22no—
488D8—22no—
489D8—1222no—
490D8—1222no—
491M16—4881no—
492M16—4881no—
493M16—2442no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8—4881no—
509C2×C8—4881no—
510C2×C8—4881no—
511C2×C8—4881no—
512C2×C8C22×#692311yescharacteristic
513C2×C8C22×#692311yescharacteristic
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C22×#692311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42C22×#692311yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—611no—
536C23—1224no—
537C23—1221no—
538C23—4881no—
539C23—4881no—
540Q8—4881no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—81no—
547D4—81no—
548D4—612no—
549D4—1224no—
550D4—1221no—
551D4—4881no—
552D4—4881no—
553D4#1451986412yes—
554C2×C4—21no—
555C2×C4—81no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—4881no—
567C2×C4—4881no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4D4×#692311yescharacteristic
578C2×C4D4×#692311yescharacteristic
579C2×C4C23×#692311yescharacteristic
580C8—21no—
581C8—21no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1222no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C8—2441no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—1221no—
604C22—1222no—
605C22—1221no—
606C22—1221no—
607C22—4884no—
608C22—2441no—
609C22—2441no—
610C22C2×D4×#692311yescharacteristic
611C4—21no—
612C4—21no—
613C4—41no—
614C4—611no—
615C4—611no—
616C4—1221no—
617C4—1221no—
618C4—2441no—
619C4—2441no—
620C4—2441no—
621C4C2×#1451986411yescharacteristic
622C4D61⋊#13111yescharacteristic
623C2—42no—
624C2—81no—
625C2—81no—
626C2—2441no—
627C2—2442no—
628C2#2146253311yescharacteristic
629C2#2146257811yescharacteristic
630C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#21455818C2
cosocleC4×Dic61C24
hypercenter#459#6923
hypocenterC61#17922
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #21462708C2semidirect
2. #21462667C2semidirect
3. #21461441C2semidirect
4. #21461440C2semidirect
5. #21461421C2semidirect
6. #21461420C2semidirect
7. #21461416C2semidirect
8. #21461415C2semidirect
9. #21461399C2semidirect
10. D8×#92420C2semidirect
11. #21461391C2semidirect
12. #21461159C2semidirect
13. #21461139C2semidirect
14. #21461037C2semidirect
16. #16840797C22semidirect
17. #16840797C22semidirect
26. D4×#92420C22semidirect
27. D4×#92420C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
44. D4⋊#92420C22semidirect
45. D4⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
382. C61#17922semidirect

Maximal subgroups

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

subgroupindex
#214627082
#214626672
#214614412
#214614402
#214614212
#214614202
#214614162
#214614152
#214613992
D8×#924202
#214613912
#214611592
#214611392
#214610372
#214558182
#1792261