Finite Group Databasebeta

← #29665342

Subgroups — #29665342

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456964C211yesmaximal, characteristic
2#21455625C211yesmaximal, characteristic
3#462×D61C211yesmaximal, characteristic
4#21454898C211yesmaximal, characteristic
5#21445252C211yesmaximal, characteristic, complemented
6#21445251C211yesmaximal, characteristic, complemented
7#21445250C211yesmaximal, characteristic, complemented
8#21445249C211yesmaximal, characteristic, complemented
9#21445204C211yesmaximal, characteristic, complemented
10#21445203C211yesmaximal, characteristic, complemented
11#21445198C211yesmaximal, characteristic, complemented
12#21444588C211yesmaximal, characteristic
13#21444489C211yesmaximal, characteristic
14#21444473C211yesmaximal, characteristic
15C61×#1672C211yesmaximal, characteristic, complemented
16C2×Q16×D61—21no—
17#16840317C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×Q8×D61C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840094—21no—
24#16840094—21no—
25#16840068—21no—
26#16840067—21no—
27#16840054C2211yescharacteristic
28#16840048C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840046—21no—
31#16840046—21no—
32#16839973C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839971—21no—
35#16839970—21no—
36#16839969C2211yescharacteristic
37Q8×#92418C2211yescharacteristic
38C8×Dic122—21no—
39C8×Dic122C2211yescharacteristic
40#16839886—21no—
41#16839886C2211yescharacteristic
42#16839814—21no—
43#16839814C2211yescharacteristic
44#16839813—21no—
45#16839813C2211yescharacteristic
46#16839803—21no—
47#16839784C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49#16839769—21no—
50#103×D61—21no—
51#16839513C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839508C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61D411yescharacteristic
69C2×Dic244—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72Q16×D61—44no—
73C2×#11758189—21no—
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519775—21no—
80#14519768—21no—
81#14519757—21no—
82#14519753—21no—
83Q8×Dic61—21no—
84Q8×Dic61D411yescharacteristic
85C4×Dic122—21no—
86C4×Dic122C2311yescharacteristic
87#14519742—21no—
88#14519742—21no—
89#14519742D411yescharacteristic
90#14519735—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61D411yescharacteristic
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100#14519708—21no—
101#14519708—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706D411yescharacteristic
111#14519706D411yescharacteristic
112#14519702—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519701—21no—
117#14519701—21no—
118#14519700—21no—
119#14519700—21no—
120#14519700—21no—
121#14519700—21no—
122#14519689—21no—
123#14519689D411yescharacteristic
124#14519689D411yescharacteristic
125C4×#92418—21no—
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
129C8×Dic61—21no—
130C2×Q16×C61—21no—
131C4⋊Q8×C61C2311yescharacteristic
132C4⋊Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134#107×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#103×C61—21no—
143C4×C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148Q8×D61—22no—
149Q8×D61—42no—
150Q8×D61—42no—
151Q8×D61SD1614yes—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—41no—
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×Dic122C2×D411yescharacteristic
163Q16×C61—42no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C2×D411yescharacteristic
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177#11758202—42no—
178#11758202—42no—
179#11758198—41no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—41no—
186C4⋊Dic61C2×D411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—41no—
191#11758196—41no—
192#11758196—41no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—41no—
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61#4111yescharacteristic
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205Dic244—42no—
206#11758189—42no—
207C8×D61—42no—
208C22×D61#12111yescharacteristic
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213Q8×C61C2×SD1612yes—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61#12111yescharacteristic
226C2×Dic61#12111yescharacteristic
227C2×Dic61#12111yescharacteristic
228C4×D61—24no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—41no—
232C4×D61—81no—
233C4×D61—82no—
234C4×D61C2×SD1612yes—
235C4×D61#13512yes—
236Dic122—21no—
237Dic122—24no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—41no—
242Dic122—82no—
243Dic122C2×SD1612yes—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#19402—611nomaximal, Sylow
255C22×C61C2×#12111yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61#46512yes—
259C4×C61—22no—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—81no—
263C4×C61—81no—
264C4×C61C22×SD1611yescharacteristic
265C4×C61C2×#13511yescharacteristic
266C4×C61#57811yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—21no—
269Dic61—22no—
270Dic61—21no—
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274Dic61#46512yes—
275#3229—611no—
276#3078—611no—
277C2×#462—611no—
278#2982—611no—
279#1680—611no—
280#1680—611no—
281#1680—611no—
282#1680—611no—
283#1672—611no—
284#1672—611no—
285#1672—611no—
286#1672D6111yescharacteristic, complemented
287#1570—611no—
288#1546—611no—
289#1542—611no—
290C2×C61#304411yescharacteristic
291C2×C61C2×#46511yescharacteristic
292C2×C61#306911yescharacteristic
293D61—22no—
294C22×Q16—1221no—
295#533—611no—
296C2×C4⋊Q8—611no—
297C2×C4×Q8—611no—
298#498—611no—
299#498C2×D6111yescharacteristic
300#487—611no—
301#487—611no—
302#483—1221no—
303#483—1221no—
304#479—1221no—
305#479—1221no—
306#477—611no—
307#477C2×D6111yescharacteristic
308#475—611no—
309#475—611no—
310#475—1221no—
311#475—1221no—
312#462—611no—
313#462—611no—
314#462—611no—
315#462—1221no—
316#462—1221no—
317#462C2×D6111yescharacteristic
318C8×Q8—611no—
319C8×Q8—611no—
320C8×Q8—611no—
321C8×Q8—1221no—
322C8×Q8—1221no—
323C8×Q8C2×D6111yescharacteristic
324#431—611no—
325#431—611no—
326#431—1221no—
327#431—1221no—
328#428—1221no—
329#423—611no—
330C2×C4⋊C8—611no—
331#419—1221no—
332C2×#103—1221no—
333#334—611no—
334#334—611no—
335#334—611no—
336#334C2×D6111yescharacteristic
337#333—611no—
338#333C2×D6111yescharacteristic
339#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332C2×D6111yescharacteristic
345C61#1940211yescharacteristic, complemented, Sylow
346C22×Q8—611no—
347C22×Q8—1221no—
348C2×Q16—21no—
349C2×Q16—1221no—
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16—2444no—
353C2×M16—1221no—
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—1221no—
358C4⋊Q8—1221no—
359C4⋊Q8—1221no—
360C4⋊Q8C22×D6111yescharacteristic
361C4⋊Q8C22×D6111yescharacteristic
362#125—1221no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8—1221no—
372C4×Q8C22×D6111yescharacteristic
373#117—1221no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C42—611no—
379C2×C42—1221no—
380#107—21no—
381#107—1221no—
382#106—21no—
383#106—21no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388C4⋊C8—21no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402#103—21no—
403#103—21no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C4×C8—21no—
418C4×C8—611no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—614no—
427C2×Q8—611no—
428C2×Q8—1221no—
429C2×Q8—1222no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—2441no—
433C2×Q8—2442no—
434C2×Q8—2442no—
435C2×Q8D4×D6111yescharacteristic
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—2441no—
442Q16—42no—
443Q16—2442no—
444Q16—2442no—
445Q16—2442no—
446M16—2442no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—2442no—
456C2×C8D4×D6111yescharacteristic
457C2×C8D4×D6111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C4⋊C4—2441no—
476C4⋊C4D4×D6111yescharacteristic
477C22⋊C4—2441no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—2441no—
486C42C23×D6111yescharacteristic
487C23—611no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—612no—
493Q8—1224no—
494Q8—1221no—
495Q8—4882no—
496Q8—2441no—
497Q8—2441no—
498Q8—2441no—
499Q8—2441no—
500Q8SD16×D6112yes—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—611no—
506C2×C4—612no—
507C2×C4—612no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—1224no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—4881no—
516C2×C4—4882no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×D4×D6111yescharacteristic
522C2×C4#41×D6111yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C22—612no—
534C22—1221no—
535C22—1221no—
536C22#121×D6111yescharacteristic
537C4—22no—
538C4—21no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—612no—
543C4—1222no—
544C4—1221no—
545C4—1221no—
546C4—4881no—
547C4—4881no—
548C4—2441no—
549C4C2×SD16×D6111yescharacteristic
550C4#135×D6111yescharacteristic
551C4#1684057511yescharacteristic
552C4#1684057811yescharacteristic
553C2—1222no—
554C2#2145534411yescharacteristic
555C2#465×D6111yescharacteristic
556C2#2145555111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1672C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1672D61
hypocenterC61#19402
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #21445252C2semidirect
6. #21445251C2semidirect
7. #21445250C2semidirect
8. #21445249C2semidirect
9. #21445204C2semidirect
10. #21445203C2semidirect
11. #21445198C2semidirect
15. C61×#1672C2semidirect
286. #1672D61semidirect
345. C61#19402semidirect

Maximal subgroups

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

subgroupindex
#214569642
#214556252
#462×D612
#214548982
#214452522
#214452512
#214452502
#214452492
#214452042
#214452032
#214451982
#214445882
#214444892
#214444732
C61×#16722
#1940261