Finite Group Databasebeta

← #16831508

Subgroups — #16831508

Order 3712.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271847C211yesmaximal, characteristic, complemented
2#14271797C211yesmaximal, characteristic
3#14271526C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271478C211yesmaximal, characteristic, complemented
6#14271466C211yesmaximal, characteristic, complemented
7#14271395C211yesmaximal, characteristic, complemented
8#14271361C211yesmaximal, characteristic, complemented
9#14271313C211yesmaximal, characteristic, complemented
10#14271312C211yesmaximal, characteristic, complemented
11#14271266C211yesmaximal, characteristic, complemented
12#14271232C211yesmaximal, characteristic, complemented
13#14271169C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#468C211yesmaximal, characteristic, complemented
16C2×D4×D29—21no—
17C2×D4×D29C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic, complemented
20C2×M16×C29C2211yescharacteristic, complemented
21C29×C22⋊Q8C2211yescharacteristic, complemented
22C29×#121C2211yescharacteristic
23#11745308C2211yescharacteristic, complemented
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90784C2211yescharacteristic
26C2×#90784C2211yescharacteristic, complemented
27#11745302C2211yescharacteristic
28#11745299—21no—
29C4×C22⋊D29C2211yescharacteristic
30#11745288C2211yescharacteristic, complemented
31C2×C8×D29C2211yescharacteristic, complemented
32#11745257C2211yescharacteristic
33#11745255C2211yescharacteristic
34#11745254—21no—
35C4⋊C4×D29C2211yescharacteristic, complemented
36#11745252C2211yescharacteristic, complemented
37#11745251—21no—
38#11745246—21no—
39#11745245—21no—
40#11745244—21no—
41#11745241—21no—
42C29×#107C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic, complemented
47C22⋊#6597C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic, complemented
51#11745169C2211yescharacteristic, complemented
52#11745168C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54#11745162C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C23×D29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29D411yescharacteristic
69D4×D29—22no—
70D4×D29—41no—
71D4×D29—44no—
72C2×D116—22no—
73C2×D116—21no—
74C2×D116—21no—
75C2×D116—41no—
76C2×D116C2311yescharacteristic
77C2×D116C2311yescharacteristic
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29C2311yescharacteristic
81SD16×C29—41no—
82M16×C29—41no—
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C4⋊C4×C29—21no—
86C4⋊C4×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29D411yescharacteristic
92#90784—22no—
93#90784—41no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781D411yescharacteristic
98C4⋊Dic29—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779D411yescharacteristic
106C4×Dic29—21no—
107C4×Dic29—21no—
108C4×Dic29C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C8×D29—41no—
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—42no—
120C22×D29—81no—
121C22×D29—81no—
122C22×D29C2×D411yescharacteristic
123Q8×C29—21no—
124Q8×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—42no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—22no—
136C22⋊D29—42no—
137C22⋊D29—42no—
138C22⋊D29—81no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144D116—21no—
145D116—21no—
146D116—21no—
147D116—42no—
148D116—42no—
149D116#4112yes—
150C4×D29—21no—
151C4×D29—21no—
152C4×D29—42no—
153C4×D29—42no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3310—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—21no—
167C2×D29—21no—
168C2×D29—22no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—84no—
175C2×D29—84no—
176C2×D29AGL(1,ℤ/8)12yes—
177C4×C29—21no—
178C4×C29—41no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29C2×#4111yescharacteristic
182C4×C29H(5,𝔽2)11yescharacteristic
183Dic29—21no—
184Dic29—21no—
185Dic29—21no—
186Dic29—41no—
187Dic29—41no—
188#552—291no—
189D42—291no—
190#490—291no—
191#482—291no—
192#480—291no—
193#478—291no—
194#468D2911yescharacteristic, complemented
195#465—291no—
196#460—291no—
197#450—291no—
198#450—291no—
199#440—291no—
200#435—291no—
201#418—291no—
202C2×#102—291no—
203C2×C29—41no—
204C2×C29—81no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—22no—
209D29—42no—
210D29—81no—
211C22×D4—291no—
212C22×D4—291no—
213C22×D4—581no—
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16C2×D2911yescharacteristic, complemented
217C2×M16C2×D2911yescharacteristic, complemented
218C22×C8—291no—
219#127—291no—
220#126—581no—
221#125—291no—
222#125—581no—
223#123—581no—
224C22⋊Q8—291no—
225C22⋊Q8C2×D2911yescharacteristic, complemented
226#121—291no—
227#121—581no—
228#121C2×D2911yescharacteristic
229#120—581no—
230#120—581no—
231C4×Q8—291no—
232C4×D4—291no—
233C4×D4—291no—
234#117—291no—
235#117—581no—
236C2×C4⋊C4—291no—
237#107—291no—
238#107C2×D2911yescharacteristic, complemented
239#106—291no—
240C4⋊C8—291no—
241#103C2×D2911yescharacteristic, complemented
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250#102C2×D2911yescharacteristic, complemented
251C22⋊C8—291no—
252C22⋊C8—291no—
253#97—291no—
254C29#331011yescharacteristic, complemented, Sylow
255C24—581no—
256C24—581no—
257C2×Q8C22×D2911yescharacteristic
258C2×D4—21no—
259C2×D4—291no—
260C2×D4—291no—
261C2×D4—291no—
262C2×D4—582no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—582no—
268C2×D4—581no—
269C2×D4—1161no—
270C2×D4—1161no—
271C2×D4—1164no—
272C2×D4C22×D2911yescharacteristic
273C22×C4—291no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4C22×D2911yescharacteristic
277SD16—41no—
278SD16—582no—
279SD16—1161no—
280M16—41no—
281C2×C8—291no—
282C2×C8—291no—
283C2×C8—1161no—
284C2×C8C22×D2911yescharacteristic
285C2×C8C22×D2911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—291no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—581no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4C22×D2911yescharacteristic
296C4⋊C4C22×D2911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—291no—
300C22⋊C4—291no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C42—291no—
306C42—581no—
307C42—581no—
308C23—21no—
309C23—291no—
310C23—581no—
311C23—581no—
312C23—1162no—
313C23—1162no—
314C23—1162no—
315C23—1162no—
316C23—2321no—
317C23—2321no—
318C23D4×D2911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—292no—
325D4—582no—
326D4—581no—
327D4—581no—
328D4—581no—
329D4—1162no—
330D4—1162no—
331D4—1162no—
332D4—1162no—
333D4—2321no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—291no—
340C2×C4—291no—
341C2×C4—291no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—581no—
345C2×C4—581no—
346C2×C4—1162no—
347C2×C4—1162no—
348C2×C4D4×D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—581no—
353C8—581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—292no—
361C22—581no—
362C22—581no—
363C22—582no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22—1161no—
369C22—2324no—
370C22—2324no—
371C22C2×D4×D2911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—581no—
377C4—581no—
378C4—581no—
379C4—1161no—
380C4—1161no—
381C4#1174535911yescharacteristic
382C4#41×D2911yescharacteristic
383C2—41no—
384C2—81no—
385C2—582no—
386C2—1162no—
387C2—2321no—
388C2#1427180211yescharacteristic
389C2AGL(1,ℤ/8)×D2911yescharacteristic
390C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#468C2
socleC22×C29C22×D4
prime radical#14271797C2
hypercenter#468D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #14271847C2semidirect
3. #14271526C2semidirect
4. #14271484C2semidirect
5. #14271478C2semidirect
6. #14271466C2semidirect
7. #14271395C2semidirect
8. #14271361C2semidirect
9. #14271313C2semidirect
10. #14271312C2semidirect
11. #14271266C2semidirect
12. #14271232C2semidirect
13. #14271169C2semidirect
14. #102×D29C2semidirect
15. C29×#468C2semidirect
19. C2×SD16×C29C22semidirect
20. C2×M16×C29C22semidirect
21. C29×C22⋊Q8C22semidirect
23. #11745308C22semidirect
24. Q8×Dic29C22semidirect
26. C2×#90784C22semidirect
30. #11745288C22semidirect
31. C2×C8×D29C22semidirect
35. C4⋊C4×D29C22semidirect
36. #11745252C22semidirect
42. C29×#107C22semidirect
43. C29×#103C22semidirect
44. C29×#102C22semidirect
45. #11745180C22semidirect
46. #11745180C22semidirect
47. C22⋊#6597C22semidirect
50. #11745169C22semidirect
51. #11745169C22semidirect
52. #11745168C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
56. #11745157C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
194. #468D29semidirect
216. C2×SD16C2×D29semidirect
217. C2×M16C2×D29semidirect
225. C22⋊Q8C2×D29semidirect
238. #107C2×D29semidirect
241. #103C2×D29semidirect
250. #102C2×D29semidirect
254. C29#3310semidirect

Maximal subgroups

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

subgroupindex
#142718472
#142717972
#142715262
#142714842
#142714782
#142714662
#142713952
#142713612
#142713132
#142713122
#142712662
#142712322
#142711692
#102×D292
C29×#4682
#331029