Finite Group Databasebeta

← #29663469

Subgroups — #29663469

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457157C211yesmaximal, characteristic
2#21457150C211yesmaximal, characteristic
3#21456401C211yesmaximal, characteristic, complemented
4#21454788C211yesmaximal, characteristic
5#21445336C211yesmaximal, characteristic, complemented
6#21445331C211yesmaximal, characteristic, complemented
7#21445312C211yesmaximal, characteristic, complemented
8#21445307C211yesmaximal, characteristic, complemented
9#21445252C211yesmaximal, characteristic, complemented
10#21445248C211yesmaximal, characteristic, complemented
11#21445245C211yesmaximal, characteristic, complemented
12#21445241C211yesmaximal, characteristic, complemented
13C2×#16839512C211yesmaximal, characteristic, complemented
14#21444520C211yesmaximal, characteristic, complemented
15C61×#1552C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840141C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840070—21no—
23#16840069—21no—
24#16840048C2211yescharacteristic
25#16840044C2211yescharacteristic
26#16840043C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840003—21no—
29#16840001—21no—
30#16840001—21no—
31#16840001—21no—
32#16839993—21no—
33#16839991—21no—
34#16839985—21no—
35#16839984—21no—
36#16839973C2211yescharacteristic
37#16839969C2211yescharacteristic
38#16839968C2211yescharacteristic
39#16839964C2211yescharacteristic
40#16839889C2211yescharacteristic
41#16839886C2211yescharacteristic
42C4×#11758202—21no—
43C4×#11758202—21no—
44#16839839C2211yescharacteristic
45#16839830—21no—
46#16839827C2211yescharacteristic
47#16839825—21no—
48#16839824—21no—
49C2×C4⋊#92418C2211yescharacteristic
50#16839719—21no—
51C2×C4×#92418C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Dic244—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758201—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418D411yescharacteristic
76C22×#92418D411yescharacteristic
77C2×C8×D61—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519771—21no—
81#14519769—21no—
82#14519769D411yescharacteristic
83#14519765D411yescharacteristic
84#14519760—21no—
85#14519756—21no—
86#14519756—21no—
87#14519756D411yescharacteristic
88#14519751D411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122C2311yescharacteristic
92C4×D244C2311yescharacteristic
93C4×C22⋊D61—21no—
94#14519736—21no—
95#14519734—21no—
96#14519711—21no—
97#14519710—21no—
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519708—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519702—21no—
109#14519702—21no—
110#14519701—21no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519700—21no—
115#14519700—21no—
116#14519700—21no—
117#14519699—21no—
118#14519697—21no—
119#14519689—21no—
120#14519689—21no—
121#14519687—21no—
122C4×#92418D411yescharacteristic
123C4×#92418D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×Q8×C61—21no—
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143#97×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122C2×D411yescharacteristic
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—81no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C42×C61—41no—
168C42×C61C2×D411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61#4111yescharacteristic
171C42×C61C2411yescharacteristic
172C22⋊Dic61—21no—
173C22⋊Dic61—41no—
174#11758202—42no—
175#11758202—42no—
176#11758202—81no—
177#11758201—81no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61C2×D411yescharacteristic
187C4⋊Dic61C2×D411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—41no—
193#11758196—41no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196C2×#92418—22no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—41no—
200C2×#92418—81no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205Dic244—81no—
206#11758190—81no—
207#11758189—42no—
208C8×D61—42no—
209C23×C61#12111yescharacteristic
210C22×D61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—42no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234D244—21no—
235D244—21no—
236C4×D61—41no—
237C4×D61—41no—
238Dic122—21no—
239Dic122—21no—
240Dic122—41no—
241Dic122—41no—
242Dic122—41no—
243Dic122—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418#13512yes—
254#19228—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61#47312yes—
258C22×C61C2×#12111yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61C2×#13511yescharacteristic
269C4×C61#57511yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57711yescharacteristic
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—81no—
276Dic61—81no—
277#3248—611no—
278#3248—611no—
279#3170—611no—
280#2966—611no—
281#1694—611no—
282#1693—611no—
283#1690—611no—
284#1689—611no—
285#1680—611no—
286#1680—611no—
287#1679—611no—
288#1679—611no—
289C2×#334—611no—
290#1552—611no—
291#1552D6111yescharacteristic, complemented
292C2×C61—22no—
293C2×C61#303511yescharacteristic
294C2×C61#306011yescharacteristic
295C2×C61C2×#47311yescharacteristic
296D61—81no—
297#533—611no—
298#533C2×D6111yescharacteristic
299#529—611no—
300#500—611no—
301#494—611no—
302#487—611no—
303#487—611no—
304#479—1221no—
305#479—1221no—
306#475—611no—
307#475—611no—
308#474—611no—
309#474—611no—
310#467—1221no—
311#467—1221no—
312#467—1221no—
313#467—1221no—
314#465—1221no—
315#465—1221no—
316#464—1221no—
317#464—1221no—
318#462—611no—
319#462—611no—
320#461—611no—
321#461—611no—
322#446—611no—
323C8×Q8—611no—
324C4×Q16—1221no—
325C4×Q16—1221no—
326#436—611no—
327#435—1221no—
328C8×D4—611no—
329C8×D4—1221no—
330#433—1221no—
331#432C2×D6111yescharacteristic
332C2×C4⋊C8—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334#405—1221no—
335C2×C4×C8—611no—
336#334—611no—
337#334—611no—
338#334—611no—
339#334—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332C2×D6111yescharacteristic
345#332C2×D6111yescharacteristic
346#332C2×D6111yescharacteristic
347#332C2×D6111yescharacteristic
348C61#1922811yescharacteristic, complemented, Sylow
349C2×Q16—1221no—
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16—1221no—
353C2×SD16—1221no—
354C2×SD16—1221no—
355C2×M16—1221no—
356C22×C8—21no—
357C22×C8—611no—
358C22×C8—611no—
359C22×C8—1221no—
360C22×C8—1221no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#126—1221no—
366#125—21no—
367#125—611no—
368#125—1221no—
369#124—611no—
370#123—1221no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—611no—
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376#121—611no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—611no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382C4×D4—611no—
383C4×D4—1221no—
384#117—21no—
385#117—1221no—
386#117—1221no—
387C2×C42C22×D6111yescharacteristic
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
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—
414#102—1221no—
415#102—1221no—
416C22⋊C8—21no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419#97—21no—
420#97—1221no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×D4—611no—
432C2×D4—1221no—
433C22×C4—1221no—
434C22×C4#1175822211yescharacteristic
435C22×C4D4×D6111yescharacteristic
436C22×C4D4×D6111yescharacteristic
437Q16—4881no—
438Q16—4881no—
439Q16—2442no—
440Q16—2442no—
441SD16—4881no—
442SD16—4881no—
443M16—2442no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1222no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—4881no—
457C2×C8—2442no—
458C2×C8—2441no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—611no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—2441no—
476C4⋊C4—2441no—
477C22⋊C4—41no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—2441no—
484C42—41no—
485C42—1221no—
486C42—2441no—
487C42#1175822211yescharacteristic
488C42D4×D6111yescharacteristic
489C42D4×D6111yescharacteristic
490C42C23×D6111yescharacteristic
491C23—1221no—
492C23#1451975011yescharacteristic
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—1221no—
498Q8—1221no—
499Q8—2441no—
500Q8—2441no—
501Q8—2441no—
502Q8—2441no—
503D4—1221no—
504D4—1221no—
505D4—2442no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4#1451975011yescharacteristic
521C2×C4#1451975011yescharacteristic
522C2×C4#1451975011yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4C2×D4×D6111yescharacteristic
525C2×C4C2×#1175822211yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—612no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—2441no—
539C22—2441no—
540C22—2441no—
541C22#1684003612yes—
542C22C2×#1451975011yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—4881no—
550C4—4881no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#135×D6111yescharacteristic
555C4#1684055911yescharacteristic
556C4#1684057111yescharacteristic
557C4#1684057211yescharacteristic
558C2—22no—
559C2—4881no—
560C2#2145527211yescharacteristic
561C2#2145548011yescharacteristic
562C2C2×#1684003611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1552D61
hypocenterC61#19228
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
3. #21456401C2semidirect
5. #21445336C2semidirect
6. #21445331C2semidirect
7. #21445312C2semidirect
8. #21445307C2semidirect
9. #21445252C2semidirect
10. #21445248C2semidirect
11. #21445245C2semidirect
12. #21445241C2semidirect
13. C2×#16839512C2semidirect
14. #21444520C2semidirect
15. C61×#1552C2semidirect
291. #1552D61semidirect
348. C61#19228semidirect

Maximal subgroups

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

subgroupindex
#214571572
#214571502
#214564012
#214547882
#214453362
#214453312
#214453122
#214453072
#214452522
#214452482
#214452452
#214452412
C2×#168395122
#214445202
C61×#15522
#1922861