Finite Group Databasebeta

← #29836870

Subgroups — #29836870

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458220C211yesmaximal, characteristic, complemented
2#21457505C211yesmaximal, characteristic, complemented
3#21448053C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21448012C211yesmaximal, characteristic, complemented
6#21447916C211yesmaximal, characteristic, complemented
7#21447906C211yesmaximal, characteristic, complemented
8#21447875C211yesmaximal, characteristic, complemented
9#21447743C211yesmaximal, characteristic, complemented
10#21447732C211yesmaximal, characteristic, complemented
11C4×#14519718C211yesmaximal, characteristic, complemented
12#21447638C211yesmaximal, characteristic, complemented
13#21447523C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840465—21no—
19#16840407—21no—
20C2×#14519722C2211yescharacteristic, complemented
21C2×D976C2211yescharacteristic
22C2×#14519718C2211yescharacteristic
23C2×C16×D61C2211yescharacteristic
24C2×C16×D61C2211yescharacteristic, complemented
25#16840146C2211yescharacteristic
26#16840088—21no—
27#16840082—21no—
28#16840059—21no—
29#16840004C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839999C2211yescharacteristic
32#16839999C2211yescharacteristic, complemented
33#16839977—21no—
34#16839914—21no—
35#16839908—21no—
36C4×D488C2211yescharacteristic, complemented
37C8×D244C2211yescharacteristic
38#16839799C2211yescharacteristic, complemented
39#107×D61C2211yescharacteristic
40#16839587C2211yescharacteristic, complemented
41#16839567C2211yescharacteristic, complemented
42#16839565C2211yescharacteristic, complemented
43#16839565C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic, complemented
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic, complemented
51C4×#11758185C2211yescharacteristic, complemented
52C61×#499C2211yescharacteristic, complemented
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×C4⋊C16C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60C2×D4×D61—21no—
61#14519796—22no—
62#14519796—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×#11758200—21no—
66C2×D488C2311yescharacteristic
67C2×D488C2311yescharacteristic
68C2×#11758199—21no—
69D8×D61—22no—
70D8×D61—41no—
71C2×C8×D61C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519772—41no—
74#14519765—21no—
75#14519762—41no—
76#14519761—41no—
77#14519757—21no—
78#14519752—21no—
79#14519752—21no—
80#14519752—21no—
81#14519752—41no—
82#14519751—41no—
83#14519747—41no—
84C4×D244—21no—
85C4×D244D411yescharacteristic
86#14519739—41no—
87#14519735—21no—
88C4⋊C4×D61—21no—
89C2×#11758198—41no—
90#14519722—41no—
91D976—41no—
92#14519718—22no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—41no—
96C16×D61—41no—
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519708—21no—
100C4⋊#92418D411yescharacteristic
101#14519700—21no—
102#14519699—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519689D411yescharacteristic
107#14519689D411yescharacteristic
108C2×D8×C61C2311yescharacteristic
109#125×C61—21no—
110C4×D4×C61—21no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#106×C61—21no—
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C2×D4×C61—21no—
121C22×C4×C61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61—41no—
125#11758224—42no—
126#11758224—81no—
127D4×D61—42no—
128D4×D61—81no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244—41no—
132C2×D244—41no—
133C2×D244—41no—
134C2×D244D811yescharacteristic
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×Dic122—21no—
140D8×C61—21no—
141D8×C61#4112yes—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2411yescharacteristic
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—41no—
148C4⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C42×C61C2×D411yescharacteristic
151#11758200—42no—
152#11758199—42no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198D811yescharacteristic
162#11758198D811yescharacteristic
163C4⋊Dic61—21no—
164C4⋊Dic61—41no—
165C4⋊Dic61D811yescharacteristic
166#11758196—41no—
167C4×Dic61—41no—
168C2×#92418C2×D411yescharacteristic
169C2×#92418C2×D411yescharacteristic
170Dic244—21no—
171Dic244—21no—
172D488—21no—
173D488—21no—
174D488—21no—
175D488—21no—
176#11758190—81no—
177C8×D61—21no—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—82no—
189C22×D61—82no—
190C22×D61—161no—
191C22×D61C2×D811yescharacteristic
192C22×D61C2×D811yescharacteristic
193D4×C61—22no—
194D4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—161no—
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C22⋊D61—82no—
203C22⋊D61—82no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—82no—
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209D244—22no—
210D244—41no—
211D244—41no—
212D244—41no—
213D244—41no—
214D244—82no—
215D244—161no—
216D244—161no—
217C4×D61—21no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—161no—
222C4×D61—161no—
223Dic122—41no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33864—611nomaximal, Sylow
231C22×C61—42no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61C22×D811yescharacteristic
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—164no—
247C2×D61#50812yes—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—81no—
251C4×C61—81no—
252C4×C61—81no—
253C4×C61#54611yescharacteristic
254C4×C61#57711yescharacteristic
255Dic61—21no—
256Dic61—21no—
257Dic61—81no—
258Dic61—81no—
259#3339—611no—
260#3280—611no—
261#2242—611no—
262#2236—611no—
263#2234—611no—
264#2228D6111yescharacteristic, complemented
265#2217—611no—
266#2215—611no—
267#2210—611no—
268#2186—611no—
269#2184—611no—
270C4×D16—611no—
271D4×C16—611no—
272#2138—611no—
273C2×#357—611no—
274C2×C61—82no—
275C2×C61#329411yescharacteristic
276C2×C61C2×#50811yescharacteristic
277C2×C61#341511yescharacteristic
278D61—22no—
279D61—41no—
280D61—161no—
281D61—161no—
282C2×#135—611no—
283C22×D8—611no—
284#553—1221no—
285#546—1221no—
286C2×SD32—611no—
287C2×D16—611no—
288C2×D16—611no—
289C22×C16—611no—
290C22×C16—611no—
291#499C2×D6111yescharacteristic, complemented
292#495—611no—
293#482—1221no—
294#481—1221no—
295#478—1221no—
296#467—611no—
297#466—611no—
298#466—611no—
299#466—611no—
300#463—1221no—
301#450—1221no—
302#449—1221no—
303C4×D8—611no—
304C4×D8C2×D6111yescharacteristic
305C8×D4—611no—
306#427—611no—
307C2×#107—611no—
308#367C2×D6111yescharacteristic, complemented
309#366—611no—
310#366C2×D6111yescharacteristic, complemented
311C4⋊C16C2×D6111yescharacteristic, complemented
312#358—611no—
313#358—611no—
314#358—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357C2×D6111yescharacteristic
321#357C2×D6111yescharacteristic
322C22⋊C16—611no—
323C22⋊C16—611no—
324C4×C16—611no—
325C61#3386411yescharacteristic, complemented, Sylow
326C2×#41—1221no—
327C22×D4—1221no—
328#135—1222no—
329#135—2441no—
330C2×Q16—611no—
331C2×SD16—1221no—
332C2×SD16—1221no—
333C2×D8—611no—
334C2×D8—611no—
335C2×D8—1221no—
336C2×D8—1222no—
337C2×D8—2441no—
338C2×D8C22×D6111yescharacteristic
339C22×C8—611no—
340C22×C8—611no—
341#126—2441no—
342#125—21no—
343#124—1221no—
344#123—2441no—
345#123—2441no—
346C22⋊Q8—1221no—
347#121—1221no—
348#121—1221no—
349#121—1221no—
350#121—2441no—
351#121—2441no—
352#120—2441no—
353C4×D4—21no—
354C4×D4—611no—
355C4×D4—1221no—
356C4×D4—2441no—
357#117—1221no—
358C2×C4⋊C4—1221no—
359C2×C22⋊C4—2441no—
360SD32—2441no—
361D16—1222no—
362D16—2441no—
363C2×C16—611no—
364C2×C16—611no—
365C2×C16—2441no—
366C2×C16—2441no—
367C2×C16C22×D6111yescharacteristic
368C2×C16C22×D6111yescharacteristic
369#107—611no—
370#107—1221no—
371#107C22×D6111yescharacteristic
372#107C22×D6111yescharacteristic
373#107C22×D6111yescharacteristic
374#106—21no—
375#106—1221no—
376C4⋊C8—611no—
377#103—1221no—
378#102—21no—
379#102—1221no—
380#102—1221no—
381#102—1221no—
382#102—1221no—
383C22⋊C8—611no—
384C22⋊C8—611no—
385C4×C8C22×D6111yescharacteristic
386C24—2441no—
387#41—4881no—
388#41—2442no—
389C2×Q8—1221no—
390C2×D4—21no—
391C2×D4—611no—
392C2×D4—1221no—
393C2×D4—1221no—
394C2×D4—4881no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2442no—
400C2×D4—2441no—
401C22×C4—41no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407Q16—1221no—
408Q16—1221no—
409SD16—4881no—
410SD16—2442no—
411D8—21no—
412D8—1221no—
413D8—1221no—
414D8—1221no—
415D8—1221no—
416D8—2442no—
417D8#1175822612yes—
418C2×C8—611no—
419C2×C8—611no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8—1221no—
423C2×C8—1221no—
424C2×C8D4×D6111yescharacteristic
425C2×C8C23×D6111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—611no—
432C4⋊C4—1221no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C22⋊C4—41no—
436C22⋊C4—611no—
437C22⋊C4—611no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C22⋊C4—2441no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C42—2441no—
447C42D4×D6111yescharacteristic
448C16—21no—
449C16—21no—
450C16—1221no—
451C16—1221no—
452C23—41no—
453C23—611no—
454C23—611no—
455C23—9761no—
456C23—4882no—
457C23—4882no—
458C23—2441no—
459C23—2441no—
460Q8—2441no—
461Q8—2441no—
462D4—22no—
463D4—41no—
464D4—1222no—
465D4—9761no—
466D4—9761no—
467D4—4882no—
468D4—4882no—
469D4—4882no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473D4—2441no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—161no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—9761no—
485C2×C4—9761no—
486C2×C4—4882no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4D8×D6111yescharacteristic
490C2×C4D8×D6111yescharacteristic
491C2×C4C2×D4×D6111yescharacteristic
492C8—21no—
493C8—1221no—
494C8—1221no—
495C8C2×#1175822611yescharacteristic
496C8#1451982311yescharacteristic
497C22—42no—
498C22—81no—
499C22—81no—
500C22—612no—
501C22—1221no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—9764no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22—4881no—
512C22—4881no—
513C22C2×D8×D6111yescharacteristic
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—1221no—
520C4—1221no—
521C4—4881no—
522C4—4881no—
523C4#1684040311yescharacteristic
524C4#1684057111yescharacteristic
525C2—82no—
526C2—1222no—
527C2—9761no—
528C2—9761no—
529C2—2441no—
530C2#2145762911yescharacteristic
531C2#508×D6111yescharacteristic
532C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
hypercenter#2228D61
hypocenterC61#33864
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21458220C2semidirect
2. #21457505C2semidirect
3. #21448053C2semidirect
4. #21448023C2semidirect
5. #21448012C2semidirect
6. #21447916C2semidirect
7. #21447906C2semidirect
8. #21447875C2semidirect
9. #21447743C2semidirect
10. #21447732C2semidirect
11. C4×#14519718C2semidirect
12. #21447638C2semidirect
13. #21447523C2semidirect
14. #357×D61C2semidirect
15. C61×#2228C2semidirect
20. C2×#14519722C22semidirect
24. C2×C16×D61C22semidirect
32. #16839999C22semidirect
36. C4×D488C22semidirect
38. #16839799C22semidirect
40. #16839587C22semidirect
41. #16839567C22semidirect
42. #16839565C22semidirect
43. #16839565C22semidirect
48. #16839562C22semidirect
50. #16839541C22semidirect
51. C4×#11758185C22semidirect
52. C61×#499C22semidirect
54. C61×#367C22semidirect
55. C61×#366C22semidirect
56. C61×C4⋊C16C22semidirect
264. #2228D61semidirect
291. #499C2×D61semidirect
308. #367C2×D61semidirect
310. #366C2×D61semidirect
311. C4⋊C16C2×D61semidirect
325. C61#33864semidirect

Maximal subgroups

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

subgroupindex
#214582202
#214575052
#214480532
#214480232
#214480122
#214479162
#214479062
#214478752
#214477432
#214477322
C4×#145197182
#214476382
#214475232
#357×D612
C61×#22282
#3386461