Finite Group Databasebeta

← #30612681

Subgroups — #30612681

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×#92420C211yesmaximal, characteristic, complemented
2#21462542C211yesmaximal, characteristic, complemented
3#21461428C211yesmaximal, characteristic, complemented
4#21461426C211yesmaximal, characteristic, complemented
5#21461420C211yesmaximal, characteristic, complemented
6#21461418C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8#21461415C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10SD16⋊#92420C211yesmaximal, characteristic, complemented
11#21461395C211yesmaximal, characteristic, complemented
12#21461154C211yesmaximal, characteristic, complemented
13#21461138C211yesmaximal, characteristic, complemented
14#21461030C211yesmaximal, characteristic, complemented
15#21455872C211yesmaximal, characteristic
16C2×#14519864—21no—
17Q8×#92420C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840795—21no—
22#16840790C2211yescharacteristic
23#16840789—21no—
24D4×#92420—21no—
25D4×#92420—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840778—21no—
30#16840778C2211yescharacteristic
31#16840765C2211yescharacteristic
32#16840735—21no—
33C4×#11758217C2211yescharacteristic
34C2×C4×#92420—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51#16840603C2211yescharacteristic
52#16840307C2211yescharacteristic
53#41×Dic61C2211yescharacteristic
54#16840087C411yescharacteristic
55#16840083C411yescharacteristic
56#16840055C411yescharacteristic
57#16840050C411yescharacteristic
58#16839960C411yescharacteristic
59#16839955C411yescharacteristic
60#16839907C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839847C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#449C411yescharacteristic
67#14519864—44no—
68C2×#11758213—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×D61⋊C8—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75C22×#92420—21no—
76C22×#92420D411yescharacteristic
77C22×#92420D411yescharacteristic
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420D411yescharacteristic
97C4×#92420D411yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758224—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105#14519776C2×C411yescharacteristic
106#14519773C2×C411yescharacteristic
107#14519763—21no—
108#14519751C2×C411yescharacteristic
109#14519749—21no—
110Q8×Dic61C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112D4×Dic61—21no—
113D4×Dic61—21no—
114D4×Dic61C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117#14519739C2311yescharacteristic
118#14519737—21no—
119#14519736—21no—
120#14519736C2×C411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519709C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519706C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519698C2×C411yescharacteristic
135C22⋊#92418C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×#41×C61C2×C411yescharacteristic
139C2×SD16×C61C2×C411yescharacteristic
140C2×D8×C61C2×C411yescharacteristic
141#121×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C22⋊C8×C61C2×C411yescharacteristic
145#41×C61—22no—
146#41×C61—22no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61C22×C411yescharacteristic
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61C22×C411yescharacteristic
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61#4111yescharacteristic
162#11758224—42no—
163#11758224—42no—
164C2×D244C22×C411yescharacteristic
165C2×C4×D61—21no—
166C2×Dic122—21no—
167#11758217—42no—
168#11758217—42no—
169#11758217—42no—
170C2×#92420—22no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—41no—
178C2×#92420—42no—
179C2×#92420—42no—
180C2×#92420—42no—
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184C2×#92420C2×D411yescharacteristic
185#11758213—42no—
186D61⋊C8—42no—
187SD16×C61—22no—
188D8×C61—22no—
189C2×C8×C61C22×C411yescharacteristic
190C2×C8×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197#11758201—22no—
198#11758199—22no—
199#11758198—21no—
200#11758198—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61#4111yescharacteristic
213C4×Dic61C2411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C2×#92418C22×C411yescharacteristic
216C23×C61—21no—
217C23×C61—21no—
218C23×C61C4×D411yescharacteristic
219C22×D61—21no—
220Q8×C61—21no—
221Q8×C61#13112yescomplemented
222D4×C61—24no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—42no—
227D4×C61#13112yescomplemented
228C2×C4×C61—24no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C22⋊D61—42no—
236C22⋊D61—42no—
237C22⋊D61—42no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—22no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—42no—
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C22×D411yescharacteristic
252C2×Dic61C2×#4111yescharacteristic
253D244—21no—
254D244—21no—
255C4×D61—41no—
256C4×D61—41no—
257Dic122—42no—
258#92420—21no—
259#92420—21no—
260#92420—21no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420—41no—
266#92420—41no—
267#92420AGL(1,ℤ/8)12yes—
268C8×C61—21no—
269C8×C61—21no—
270#92418—21no—
271#92418—21no—
272#17917—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—22no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C2×C4×D411yescharacteristic
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C4×C61—21no—
287C4×C61—22no—
288C4×C61—41no—
289C4×C61C2×#13111yescharacteristic
290C4×C61C2×#13111yescharacteristic
291Dic61—21no—
292Dic61—21no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61#44412yes—
297Dic61C2×AGL(1,ℤ/8)11yescharacteristic
298Dic61#57511yescharacteristic
299#3106—611no—
300C8×#41—611no—
301#2931—611no—
302#1583—611no—
303#1583—611no—
304#1581—611no—
305#1581—611no—
306#1580—611no—
307#1580—611no—
308SD16⋊C8—611no—
309SD16⋊C8—611no—
310#1574—611no—
311#1489—611no—
312#1484—611no—
313#1451—611no—
314C2×C61—41no—
315C2×C61—42no—
316C2×C61—81no—
317C2×C61#292911yescharacteristic
318C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C61C2×#44411yescharacteristic
320D61—81no—
321C2×#131—1221no—
322#532—611no—
323C4×#41—611no—
324#482—611no—
325#482—611no—
326#477—611no—
327#476—611no—
328#460—611no—
329#459—611no—
330#449—611no—
331#449#692311yescharacteristic
332C8×Q8—611no—
333C8×Q8—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×D8—611no—
337C4×D8—611no—
338#436—611no—
339#436—611no—
340#436—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—611no—
345C8×D4—1221no—
346C8×D4—1221no—
347C8×D4—1221no—
348#431—611no—
349#431—611no—
350#431—1221no—
351#423—611no—
352#408—1221no—
353C4×M16—611no—
354C2×C4×C8—611no—
355C2×C4×C8—1221no—
356#335—611no—
357#335—611no—
358#334—611no—
359#334—611no—
360Q8⋊C8—611no—
361Q8⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368#322—611no—
369#322—611no—
370#322—611no—
371#322—611no—
372C61#1791711yescharacteristic, complemented, Sylow
373C2×#41—1221no—
374C2×#41C2×#692311yescharacteristic
375C2×SD16—611no—
376C2×SD16C2×#692311yescharacteristic
377C2×D8—611no—
378C2×D8C2×#692311yescharacteristic
379#131—2444no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8—1221no—
390C4⋊Q8—611no—
391#127—611no—
392#124—1221no—
393#121—611no—
394#121—1221no—
395#121C2×#692311yescharacteristic
396C4×Q8—611no—
397C4×Q8—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1221no—
405#117—611no—
406#117—1221no—
407C2×C42—611no—
408C2×C42—1221no—
409#107—611no—
410#107—611no—
411#106—611no—
412#106—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8—611no—
419C4⋊C8—1221no—
420C4⋊C8—1221no—
421C4⋊C8—1221no—
422#103—611no—
423#103C2×#692311yescharacteristic
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429#102C2×#692311yescharacteristic
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8C2×#692311yescharacteristic
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—1221no—
449C4×C8—1221no—
450C4×C8—1221no—
451#41—22no—
452#41—22no—
453#41—2442no—
454#41—2442no—
455C2×Q8—1221no—
456C2×Q8C22×#692311yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—611no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4C22×#692311yescharacteristic
464C2×D4C22×#692311yescharacteristic
465C22×C4—21no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4C22×#692311yescharacteristic
473SD16—22no—
474SD16—1222no—
475D8—22no—
476D8—1222no—
477M16—2442no—
478M16—2442no—
479M16—2442no—
480M16—2442no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—1222no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—2442no—
495C2×C8—2441no—
496C2×C8—2442no—
497C2×C8—2442no—
498C2×C8—2442no—
499C2×C8C22×#692311yescharacteristic
500C2×C8C22×#692311yescharacteristic
501C4⋊C4—611no—
502C4⋊C4—611no—
503C4⋊C4—611no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4C22×#692311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—1221no—
520C42—1221no—
521C42—1221no—
522C23—21no—
523C23—21no—
524C23—1221no—
525C23D4×#692311yescharacteristic
526Q8—21no—
527Q8—2442no—
528Q8#1451986412yescomplemented
529D4—24no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—1221no—
535D4—1221no—
536D4—2442no—
537D4—2442no—
538D4—2442no—
539D4#1451986412yescomplemented
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1222no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2442no—
561C2×C4—2441no—
562C2×C4D4×#692311yescharacteristic
563C2×C4C23×#692311yescharacteristic
564C8—21no—
565C8—21no—
566C8—612no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—1221no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22C2×D4×#692311yescharacteristic
591C4—21no—
592C4—22no—
593C4—41no—
594C4—611no—
595C4—611no—
596C4—612no—
597C4—1221no—
598C4—1221no—
599C4—2441no—
600C4—2441no—
601C4—2441no—
602C4C2×#1451986411yescharacteristic
603C4C2×#1451986411yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—4881no—
608C2#2146253411yescharacteristic
609C2AGL(1,ℤ/8)×#692311yescharacteristic
610C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#21455872C2
cosocleC4×Dic61C24
hypercenter#449#6923
hypocenterC61#17917
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #41×#92420C2semidirect
2. #21462542C2semidirect
3. #21461428C2semidirect
4. #21461426C2semidirect
5. #21461420C2semidirect
6. #21461418C2semidirect
7. #21461416C2semidirect
8. #21461415C2semidirect
9. #21461409C2semidirect
10. SD16⋊#92420C2semidirect
11. #21461395C2semidirect
12. #21461154C2semidirect
13. #21461138C2semidirect
14. #21461030C2semidirect
221. Q8×C61#131semidirect
227. D4×C61#131semidirect
372. C61#17917semidirect
528. Q8#14519864semidirect
539. D4#14519864semidirect

Maximal subgroups

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

subgroupindex
#41×#924202
#214625422
#214614282
#214614262
#214614202
#214614182
#214614162
#214614152
#214614092
SD16⋊#924202
#214613952
#214611542
#214611382
#214610302
#214558722
#1791761