Finite Group Databasebeta

← #30612720

Subgroups — #30612720

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#21462709C211yesmaximal, characteristic, complemented
2#21462669C211yesmaximal, characteristic, complemented
3#21461441C211yesmaximal, characteristic, complemented
4#21461439C211yesmaximal, characteristic, complemented
5#21461421C211yesmaximal, characteristic, complemented
6#21461419C211yesmaximal, characteristic, complemented
7#21461417C211yesmaximal, characteristic, complemented
8#21461416C211yesmaximal, characteristic, complemented
9#21461400C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461160C211yesmaximal, characteristic, complemented
13#21461138C211yesmaximal, characteristic, complemented
14#21461036C211yesmaximal, characteristic, complemented
15#21455816C211yesmaximal, characteristic
16#16840797C2211yescharacteristic, complemented
17#16840796C2211yescharacteristic, complemented
18#16840794—21no—
19#16840791—21no—
20#16840790—21no—
21#16840790—21no—
22#16840790C2211yescharacteristic
23#16840790C2211yescharacteristic
24#16840790C2211yescharacteristic
25#16840790C2211yescharacteristic
26#16840790C2211yescharacteristic, complemented
27D4×#92420C2211yescharacteristic, complemented
28#16840783C2211yescharacteristic
29#16840778C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840736—21no—
32#16840735—21no—
33D61⋊(C22⋊C8)—21no—
34D61⋊(C22⋊C8)—21no—
35C4×#11758217C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic
41#16840610C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840307C2211yescharacteristic
53C2×#14519739C2211yescharacteristic
54#16840075C411yescharacteristic
55#16840041C411yescharacteristic
56#16840041C411yescharacteristic
57#16839956C411yescharacteristic
58#16839956C411yescharacteristic
59#16839898C411yescharacteristic
60#16839895C411yescharacteristic
61#16839844C2211yescharacteristic
62#16839844C2211yescharacteristic
63#16839842C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#480C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74C2×D61⋊C8—21no—
75C22×#92420—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420D411yescharacteristic
93C22⋊#92420D411yescharacteristic
94#14519832—21no—
95#14519832—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C22×D244C2×C411yescharacteristic
103C22×C4×D61—21no—
104C2×D488C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106C2×#11758199C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108#14519776C2×C411yescharacteristic
109#14519773C2×C411yescharacteristic
110#14519763—21no—
111#14519751C2×C411yescharacteristic
112#14519749—21no—
113D4×Dic61C2311yescharacteristic
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic
117#14519739C2×C411yescharacteristic
118#14519739C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519737—21no—
122C2×#11758198—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#121×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61#4111yescharacteristic
155#11758224—81no—
156#11758224—81no—
157C2×D244—21no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244C22×C411yescharacteristic
161C2×D244C22×C411yescharacteristic
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×Dic122—21no—
171#11758217—42no—
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×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184#11758213—81no—
185D61⋊C8—81no—
186D61⋊C8—81no—
187D61⋊C8—81no—
188D61⋊C8—81no—
189D61⋊C8—81no—
190C2×C8×C61C22×C411yescharacteristic
191C2×C8×C61C22×C411yescharacteristic
192C4⋊C4×C61—21no—
193C4⋊C4×C61C22×C411yescharacteristic
194C4⋊C4×C61C22×C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C22⋊C4×C61—21no—
197C22⋊Dic61—21no—
198#11758199—22no—
199#11758199—22no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206C4⋊Dic61C22×C411yescharacteristic
207#11758196—21no—
208C4×Dic61C22×C411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61#4111yescharacteristic
211C4×Dic61C2411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214D488—22no—
215D488—22no—
216C23×C61—21no—
217C23×C61C4×D411yescharacteristic
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—24no—
221C22×D61—21no—
222C22×D61—81no—
223C22×D61—81no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—81no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—81no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C22⋊D61—81no—
236C22⋊D61—81no—
237C22⋊D61—81no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C4×D411yescharacteristic
246C2×Dic61C22×D411yescharacteristic
247C2×Dic61C2×#4111yescharacteristic
248D244—24no—
249D244—21no—
250D244—21no—
251D244—21no—
252D244—21no—
253D244#13112yes—
254D244#13112yes—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
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—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—84no—
296C4×C61—21no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61C2×#13111yescharacteristic
301C4×C61C2×#13111yescharacteristic
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
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—41no—
324C2×C61—81no—
325C2×C61#292911yescharacteristic
326C2×C61#294811yescharacteristic
327C2×C61#295611yescharacteristic
328D61—42no—
329D61—42no—
330D61—81no—
331#532—611no—
332C2×C4×D4—611no—
333#480—611no—
334#480#692311yescharacteristic
335#474—611no—
336#474—611no—
337#459—611no—
338#459—611no—
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×D8—611no—
389C2×D8—611no—
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#127—611no—
401#124—1221no—
402#121—611no—
403#121—1221no—
404#121C2×#692311yescharacteristic
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4—1221no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417#107—611no—
418#107—611no—
419#107C2×#692311yescharacteristic
420#107C2×#692311yescharacteristic
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—611no—
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—1221no—
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⋊C8C2×#692311yescharacteristic
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—611no—
466C2×D4—611no—
467C2×D4—611no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4C22×#692311yescharacteristic
475C22×C4—21no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4C22×#692311yescharacteristic
487D8—1222no—
488D8—1222no—
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—21no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4C22×#692311yescharacteristic
518C4⋊C4C22×#692311yescharacteristic
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—
531C42—611no—
532C23—21no—
533C23—1224no—
534C23—1221no—
535C23—1221no—
536C23—1221no—
537C23—4881no—
538C23—4881no—
539C23D4×#692311yescharacteristic
540Q8—4881no—
541D4—21no—
542D4—21no—
543D4—81no—
544D4—612no—
545D4—612no—
546D4—1224no—
547D4—1221no—
548D4—1221no—
549D4—1221no—
550D4—1221no—
551D4—4881no—
552D4—4881no—
553D4—4881no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—81no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—4881no—
568C2×C4—4881no—
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×C4—2441no—
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—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—1222no—
601C22—1222no—
602C22—4884no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22C2×D4×#692311yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—611no—
616C4—611no—
617C4—1221no—
618C4—1221no—
619C4—1221no—
620C4—2441no—
621C4D61⋊#13111yescharacteristic
622C4D61⋊#13111yescharacteristic
623C2—41no—
624C2—81no—
625C2—4881no—
626C2—2442no—
627C2—2442no—
628C2#2146253611yescharacteristic
629C2#2146257811yescharacteristic
630C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#480C4
socleC22×C61C2×C4×D4
prime radical#21455816C2
cosocleC4×Dic61C24
hypercenter#480#6923
hypocenterC61#17922
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #21462709C2semidirect
2. #21462669C2semidirect
3. #21461441C2semidirect
4. #21461439C2semidirect
5. #21461421C2semidirect
6. #21461419C2semidirect
7. #21461417C2semidirect
8. #21461416C2semidirect
9. #21461400C2semidirect
10. #21461399C2semidirect
11. #21461390C2semidirect
12. #21461160C2semidirect
13. #21461138C2semidirect
14. #21461036C2semidirect
16. #16840797C22semidirect
17. #16840796C22semidirect
26. #16840790C22semidirect
27. D4×#92420C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
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
#214627092
#214626692
#214614412
#214614392
#214614212
#214614192
#214614172
#214614162
#214614002
#214613992
#214613902
#214611602
#214611382
#214610362
#214558162
#1792261