Finite Group Databasebeta

← #30612702

Subgroups — #30612702

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462735C211yesmaximal, characteristic, complemented
2#21462708C211yesmaximal, characteristic, complemented
3#21461449C211yesmaximal, characteristic, complemented
4#21461440C211yesmaximal, characteristic, complemented
5#21461429C211yesmaximal, characteristic, complemented
6#21461420C211yesmaximal, characteristic, complemented
7#21461415C211yesmaximal, characteristic, complemented
8#21461410C211yesmaximal, characteristic, complemented
9#21461402C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461151C211yesmaximal, characteristic, complemented
13#21461125C211yesmaximal, characteristic, complemented
14#21461041C211yesmaximal, characteristic, complemented
15#21455876C211yesmaximal, characteristic
16#16840811C2211yescharacteristic
17#16840811C2211yescharacteristic
18#16840797C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840793—21no—
21#16840793—21no—
22#16840789—21no—
23#16840789—21no—
24D4×#92420C2211yescharacteristic
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840784C2211yescharacteristic
29#16840781C2211yescharacteristic
30#16840780C2211yescharacteristic
31#16840779—21no—
32C2×#14519844—21no—
33D61⋊(C4⋊C8)C2211yescharacteristic
34#16840735—21no—
35#16840735—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840310C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840084C411yescharacteristic
55#16840084C411yescharacteristic
56#16840058C411yescharacteristic
57#16840052C411yescharacteristic
58#16839959C411yescharacteristic
59#16839904C411yescharacteristic
60#16839904C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839853C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64D8×Dic61C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#459C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C2×D61⋊C8—21no—
70C22×#92420—21no—
71C22×#92420—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77#14519844D411yescharacteristic
78#14519844D411yescharacteristic
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
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—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×#11758224C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105#14519777C2×C411yescharacteristic
106#14519764—21no—
107#14519748—21no—
108#14519748C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110C4×Dic122C2×C411yescharacteristic
111#14519742C2311yescharacteristic
112D4×Dic61—21no—
113D4×Dic61C2311yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116C4×C22⋊D61—21no—
117#14519737—21no—
118#14519735C2×C411yescharacteristic
119#14519733—21no—
120C2×C4×Dic61—21no—
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519702C2×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
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157#11758224—22no—
158#11758224—22no—
159#11758224—81no—
160#11758224—81no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×Dic122—21no—
165C2×Dic122C22×C411yescharacteristic
166#11758217—81no—
167#11758217—81no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—81no—
175C2×#92420—81no—
176C2×#92420—81no—
177C2×#92420—81no—
178C2×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182D61⋊C8—81no—
183D8×C61—22no—
184D8×C61—22no—
185C2×C8×C61C22×C411yescharacteristic
186C2×C8×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C22⋊C4×C61—21no—
189C42×C61C22×C411yescharacteristic
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195#11758200—22no—
196#11758200—22no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C22×C411yescharacteristic
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202#11758196—21no—
203#11758196—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61#4111yescharacteristic
209C4×Dic61C2411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C22×D61C4×D411yescharacteristic
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—81no—
222D4×C61—81no—
223D4×C61#13112yes—
224C2×C4×C61—21no—
225C2×C4×C61—81no—
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C22⋊D61—24no—
230C22⋊D61—81no—
231C22⋊D61—81no—
232C2×Dic61—24no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61C4×D411yescharacteristic
244C2×Dic61C22×D411yescharacteristic
245C2×Dic61C2×#4111yescharacteristic
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—41no—
251Dic122—21no—
252Dic122—81no—
253Dic122#13112yes—
254#92420—21no—
255#92420—21no—
256#92420—21no—
257#92420—21no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264C8×C61—21no—
265C8×C61—21no—
266#92418—21no—
267#92418—21no—
268#17920—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61C2×C4×D411yescharacteristic
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61C2×#13111yescharacteristic
286C4×C61C2×#13111yescharacteristic
287Dic61—22no—
288Dic61—21no—
289Dic61—21no—
290Dic61—41no—
291Dic61—41no—
292Dic61—41no—
293Dic61#57611yescharacteristic
294Dic61#57711yescharacteristic
295#3106—611no—
296#2988—611no—
297#2981—611no—
298#1588—611no—
299#1586—611no—
300#1583—611no—
301#1581—611no—
302#1580—611no—
303SD16⋊C8—611no—
304C8×SD16—611no—
305C8×D8—611no—
306#1573—611no—
307#1488—611no—
308#1480—611no—
309#1454—611no—
310C2×C61—42no—
311C2×C61—81no—
312C2×C61—81no—
313C2×C61#292911yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61#295711yescharacteristic
316D61—41no—
317#532—611no—
318C4×#41—611no—
319#482—611no—
320#482—611no—
321#477—611no—
322#476—611no—
323#460—611no—
324#459#692311yescharacteristic
325#449—611no—
326#449—611no—
327C8×Q8—611no—
328C8×Q8—611no—
329C4×SD16—611no—
330C4×SD16—611no—
331C4×D8—611no—
332C4×D8—611no—
333#436—611no—
334#436—611no—
335#435—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4—1221no—
343#432—611no—
344#431—611no—
345#431—611no—
346#431—611no—
347#431—1221no—
348C2×C4⋊C8—611no—
349C2×C4⋊C8—1221no—
350#408—1221no—
351#408—1221no—
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364#322—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C61#1792011yescharacteristic, complemented, Sylow
369C2×#41—611no—
370C2×#41—1221no—
371C2×SD16—611no—
372C2×SD16—611no—
373C2×D8C2×#692311yescharacteristic
374C2×D8C2×#692311yescharacteristic
375C2×M16—1221no—
376C2×M16—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383#127C2×#692311yescharacteristic
384#124—1221no—
385#121—611no—
386#121—611no—
387#121—1221no—
388C4×Q8—611no—
389C4×Q8—611no—
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4C2×#692311yescharacteristic
397#117—611no—
398#117—1221no—
399C2×C42—611no—
400C2×C42—1221no—
401#107—611no—
402#107—611no—
403#106—611no—
404#106—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C2×#692311yescharacteristic
417#103—611no—
418#103—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102C2×#692311yescharacteristic
424#102C2×#692311yescharacteristic
425C22⋊C8—611no—
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437#97—1221no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—1221no—
445C4×C8—1221no—
446#41—1222no—
447#41—1222no—
448#41—4881no—
449#41—4881no—
450C2×Q8—611no—
451C2×Q8—1221no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4C22×#692311yescharacteristic
458C2×D4C22×#692311yescharacteristic
459C2×D4C22×#692311yescharacteristic
460C22×C4—21no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468SD16—1222no—
469SD16—1222no—
470D8—22no—
471D8—22no—
472M16—4881no—
473M16—4881no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8C22×#692311yescharacteristic
492C2×C8C22×#692311yescharacteristic
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C22×#692311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—1221no—
511C42—1221no—
512C42—1221no—
513C42C22×#692311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—611no—
518Q8—612no—
519Q8—1221no—
520Q8—4881no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—81no—
528D4—1224no—
529D4—4881no—
530D4—4881no—
531D4#1451986412yes—
532C2×C4—21no—
533C2×C4—81no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1224no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4D4×#692311yescharacteristic
554C2×C4D4×#692311yescharacteristic
555C2×C4C23×#692311yescharacteristic
556C8—21no—
557C8—21no—
558C8—1221no—
559C8—1221no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—2441no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—1221no—
580C22—1221no—
581C22—1221no—
582C22C2×D4×#692311yescharacteristic
583C4—21no—
584C4—21no—
585C4—41no—
586C4—611no—
587C4—611no—
588C4—1221no—
589C4—1222no—
590C4—1221no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4C2×#1451986411yescharacteristic
595C4D61⋊#13111yescharacteristic
596C2—42no—
597C2—81no—
598C2—81no—
599C2—2441no—
600C2#2146253311yescharacteristic
601C2#2146257611yescharacteristic
602C2#2146259511yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#21455876C2
cosocleC4×Dic61C24
hypercenter#459#6923
hypocenterC61#17920
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. #21462735C2semidirect
2. #21462708C2semidirect
3. #21461449C2semidirect
4. #21461440C2semidirect
5. #21461429C2semidirect
6. #21461420C2semidirect
7. #21461415C2semidirect
8. #21461410C2semidirect
9. #21461402C2semidirect
10. D8×#92420C2semidirect
11. #21461393C2semidirect
12. #21461151C2semidirect
13. #21461125C2semidirect
14. #21461041C2semidirect
368. C61#17920semidirect

Maximal subgroups

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

subgroupindex
#214627352
#214627082
#214614492
#214614402
#214614292
#214614202
#214614152
#214614102
#214614022
D8×#924202
#214613932
#214611512
#214611252
#214610412
#214558762
#1792061