Finite Group Databasebeta

← #30613509

Subgroups — #30613509

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462665C211yesmaximal, characteristic, complemented
2#21462559C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461441C211yesmaximal, characteristic, complemented
7#21461426C211yesmaximal, characteristic, complemented
8#21461421C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461383C211yesmaximal, characteristic, complemented
12#21461160C211yesmaximal, characteristic, complemented
13#21461154C211yesmaximal, characteristic, complemented
14#21461042C211yesmaximal, characteristic, complemented
15#21454632C211yesmaximal, characteristic
16C2×D61⋊M16—21no—
17Q8×#92420C2211yescharacteristic, complemented
18Q8×#92420C2211yescharacteristic, complemented
19#16840797—21no—
20#16840797—21no—
21#16840797C2211yescharacteristic, complemented
22#16840797C2211yescharacteristic, complemented
23#16840796C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840792—21no—
26#16840792—21no—
27#16840790C2211yescharacteristic
28#16840790C2211yescharacteristic
29#16840783—21no—
30#16840783C2211yescharacteristic
31#16840765C2211yescharacteristic
32#16840734—21no—
33C4×#11758217—21no—
34C4×#11758217C2211yescharacteristic
35C4×#11758217C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519802C411yescharacteristic
53#41×Dic61C2211yescharacteristic
54C2×#14519739C2211yescharacteristic
55#16839871C411yescharacteristic
56#16839871C411yescharacteristic
57#16839865C411yescharacteristic
58#16839865C411yescharacteristic
59#16839847C2211yescharacteristic
60#16839847C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839842C2211yescharacteristic
63#16839802C411yescharacteristic
64#16839768C411yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#417C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69D61⋊M16—44no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×#11758217—21no—
73C2×#11758217—21no—
74C2×#11758217D411yescharacteristic
75C2×#11758217D411yescharacteristic
76C2×D61⋊C8—21no—
77C2×D61⋊C8—21no—
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C22×D244C2×C411yescharacteristic
103C22×C4×D61—21no—
104#14519802—24no—
105C2×#11758201C2×C411yescharacteristic
106C2×#11758201C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108C2×#11758199C2×C411yescharacteristic
109C2×#11758194C2×C411yescharacteristic
110Q8×Dic61C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112D4×Dic61—21no—
113D4×Dic61—21no—
114D4×Dic61C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739—21no—
117#14519739—21no—
118#14519739C2×C411yescharacteristic
119#14519739C2×C411yescharacteristic
120#14519739C2311yescharacteristic
121#14519739C2311yescharacteristic
122#14519736—21no—
123#14519736C2×C411yescharacteristic
124C2×#11758198—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61C2311yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519710C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519708C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519699C2×C411yescharacteristic
134#14519699C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136#14519687C2×C411yescharacteristic
137C8×Dic61C2311yescharacteristic
138C8×Dic61C2311yescharacteristic
139C2×#41×C61C2×C411yescharacteristic
140C2×M16×C61C2×C411yescharacteristic
141C2×C4⋊C4×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145#102×C61C2×C411yescharacteristic
146C23×D61—21no—
147#41×C61—22no—
148#41×C61—41no—
149C2×Q8×C61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61#4111yescharacteristic
159C2×D244—22no—
160C2×D244—21no—
161C2×D244—41no—
162C2×D244C22×C411yescharacteristic
163C2×D244C22×C411yescharacteristic
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170#11758217—22no—
171#11758217—41no—
172#11758217—42no—
173#11758217—42no—
174#11758217—42no—
175#11758217—42no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184C2×#92420C2×D411yescharacteristic
185C2×#92420C2×D411yescharacteristic
186#11758213—42no—
187#11758213—42no—
188D61⋊C8—42no—
189D61⋊C8—42no—
190M16×C61—41no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C4⋊C4×C61—21no—
194C4⋊C4×C61C22×C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199#11758201—22no—
200#11758201M1614yescomplemented
201#11758199—22no—
202#11758199—22no—
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206#11758198—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C22×C411yescharacteristic
210C4⋊Dic61C22×C411yescharacteristic
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61#4111yescharacteristic
217C4×Dic61C2411yescharacteristic
218#11758194—22no—
219C2×#92418C22×C411yescharacteristic
220C2×#92418C22×C411yescharacteristic
221C23×C61—21no—
222C23×C61C4×D411yescharacteristic
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—81no—
228Q8×C61—21no—
229Q8×C61C2×M1612yescomplemented
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—42no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C23×C411yescharacteristic
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—81no—
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C4×D411yescharacteristic
252C2×Dic61C22×D411yescharacteristic
253C2×Dic61C2×#4111yescharacteristic
254D244—21no—
255D244—21no—
256D244—21no—
257D244—42no—
258D244C2×M1612yes—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265#92420—22no—
266#92420—21no—
267#92420—21no—
268#92420—21no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274#92420AGL(1,ℤ/8)12yescomplemented
275C8×C61—21no—
276C8×C61—21no—
277#92418—21no—
278#92418C2×M1612yescomplemented
279#18048—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61C2×C4×D411yescharacteristic
287C2×D61—22no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—84no—
294C4×C61—21no—
295C4×C61—22no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61C22×M1611yescharacteristic
299C4×C61#56811yescharacteristic
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—41no—
304Dic61—41no—
305Dic61C2×AGL(1,ℤ/8)11yescharacteristic
306Dic61#57511yescharacteristic
307#2971—611no—
308C4×AGL(1,ℤ/8)—611no—
309D4×M16—611no—
310#1594—611no—
311#1589—611no—
312#1588—611no—
313#1586—611no—
314#1583—611no—
315#1581—611no—
316SD16⋊C8—611no—
317C8×SD16—611no—
318#1569—611no—
319#1490—611no—
320#1489—611no—
321#1455—611no—
322C2×C61—41no—
323C2×C61—81no—
324C2×C61D4×M1611yescharacteristic
325C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
326C2×C61#295611yescharacteristic
327D61—42no—
328D61—81no—
329C2×AGL(1,ℤ/8)—611no—
330C22×M16—1221no—
331C4×#41—611no—
332C2×C4×D4—611no—
333C8×Q8—611no—
334C8×Q8—611no—
335#442—611no—
336#442—611no—
337#440—611no—
338#440—611no—
339C4×SD16—611no—
340C4×SD16—611no—
341C4×D8—611no—
342C4×D8—611no—
343#436—611no—
344#436—611no—
345#436—611no—
346#436—611no—
347#436—1221no—
348#436—1221no—
349#435—1221no—
350#435—1221no—
351C8×D4—611no—
352C8×D4—611no—
353#432—611no—
354#432—1221no—
355#428—611no—
356#423—611no—
357#418—611no—
358#417#692311yescharacteristic
359#407—1221no—
360C4×M16—611no—
361C4×M16—611no—
362C4×M16—611no—
363C4×M16—1221no—
364#335—611no—
365#335—611no—
366#334—611no—
367#334—611no—
368Q8⋊C8—611no—
369Q8⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376#322—611no—
377#322—611no—
378#322—611no—
379C82—611no—
380C61#1804811yescharacteristic, complemented, Sylow
381C2×#41C2×#692311yescharacteristic
382C22×D4—611no—
383C23×C4—1221no—
384AGL(1,ℤ/8)—1224no—
385C2×SD16—611no—
386C2×SD16—611no—
387C2×D8—611no—
388C2×D8—611no—
389C2×M16—611no—
390C2×M16—611no—
391C2×M16—611no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16—1221no—
395C2×M16—1221no—
396C2×M16—1221no—
397C2×M16—1221no—
398C2×M16—2444no—
399C2×M16C2×#692311yescharacteristic
400C22×C8—1221no—
401C22×C8—1221no—
402C4×Q8—611no—
403C4×Q8—611no—
404C4×D4—611no—
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×D4—1221no—
414#117—611no—
415#117—1221no—
416C2×C4⋊C4C2×#692311yescharacteristic
417C2×C22⋊C4—1221no—
418C2×C42—611no—
419C2×C42—1221no—
420#107—611no—
421#107—611no—
422#106—611no—
423#106—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431#103C2×#692311yescharacteristic
432#103C2×#692311yescharacteristic
433#102—611no—
434#102—611no—
435#102—611no—
436#102—611no—
437#102C2×#692311yescharacteristic
438#102C2×#692311yescharacteristic
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—611no—
447#97—611no—
448#97—611no—
449#97—611no—
450#97—1221no—
451#97—1221no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—1221no—
459C4×C8—1221no—
460C24—1221no—
461#41—22no—
462#41—41no—
463C2×Q8C22×#692311yescharacteristic
464C2×D4—21no—
465C2×D4—611no—
466C2×D4—611no—
467C2×D4—1222no—
468C2×D4—1221no—
469C2×D4—2441no—
470C2×D4C22×#692311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4C22×#692311yescharacteristic
484SD16—614no—
485SD16—1222no—
486D8—1222no—
487D8—1222no—
488M16—41no—
489M16—1222no—
490M16—1222no—
491M16—2442no—
492M16—2442no—
493M16—2441no—
494M16—2442no—
495M16—2442no—
496M16—2442no—
497M16—2442no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—2442no—
511C2×C8—2442no—
512C2×C8C22×#692311yescharacteristic
513C2×C8C22×#692311yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C22×#692311yescharacteristic
520C4⋊C4C22×#692311yescharacteristic
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—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C23—21no—
536C23—1221no—
537C23—1221no—
538C23—4881no—
539C23—2442no—
540C23—2442no—
541C23D4×#692311yescharacteristic
542Q8—21no—
543Q8D61⋊M1612yescomplemented
544D4—21no—
545D4—21no—
546D4—42no—
547D4—612no—
548D4—1221no—
549D4—1221no—
550D4—1221no—
551D4—2442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—4881no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4D4×#692311yescharacteristic
578C2×C4C23×#692311yescharacteristic
579C8—21no—
580C8—21no—
581C8—612no—
582C8—612no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1222no—
587C8—1221no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—1222no—
600C22—4884no—
601C22—2441no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22C2×D4×#692311yescharacteristic
607C4—21no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—611no—
612C4—611no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—2441no—
617C4—2441no—
618C4C2×D61⋊M1611yescharacteristic
619C4#1684084011yescharacteristic
620C2—41no—
621C2—81no—
622C2—4881no—
623C2—2442no—
624C2#2146255711yescharacteristic
625C2AGL(1,ℤ/8)×#692311yescharacteristic
626C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519802C4
cosocleC4×Dic61C24
hypercenter#417#6923
hypocenterC61#18048
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #21462665C2semidirect
2. #21462559C2semidirect
3. #21461467C2semidirect
4. #21461450C2semidirect
5. #21461446C2semidirect
6. #21461441C2semidirect
7. #21461426C2semidirect
8. #21461421C2semidirect
9. #21461409C2semidirect
10. #21461403C2semidirect
11. #21461383C2semidirect
12. #21461160C2semidirect
13. #21461154C2semidirect
14. #21461042C2semidirect
17. Q8×#92420C22semidirect
18. Q8×#92420C22semidirect
21. #16840797C22semidirect
22. #16840797C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
200. #11758201M16semidirect
229. Q8×C61C2×M16semidirect
274. #92420AGL(1,ℤ/8)semidirect
278. #92418C2×M16semidirect
380. C61#18048semidirect
543. Q8D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
#214626652
#214625592
#214614672
#214614502
#214614462
#214614412
#214614262
#214614212
#214614092
#214614032
#214613832
#214611602
#214611542
#214610422
#214546322
#1804861