Finite Group Databasebeta

← #16831507

Subgroups — #16831507

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
1D4×D116C211yesmaximal, characteristic
2#14271529C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271476C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271411C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271363C211yesmaximal, characteristic, complemented
9#14271313C211yesmaximal, characteristic, complemented
10#14271313C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271167C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#552C211yesmaximal, characteristic, complemented
16C2×D4×D29—21no—
17C22×D116C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C29×#126—21no—
20C29×#125—21no—
21C29×#125C2211yescharacteristic, complemented
22C29×#123—21no—
23C29×C22⋊Q8C2211yescharacteristic, complemented
24C29×C22⋊Q8C2211yescharacteristic, complemented
25C4×Q8×C29C2211yescharacteristic, complemented
26C4×D4×C29C2211yescharacteristic
27C29×#117—21no—
28C29×#117C2211yescharacteristic, complemented
29C2×C4⋊C4×C29C2211yescharacteristic, complemented
30C2×#90784C2211yescharacteristic
31C2×#90784C2211yescharacteristic, complemented
32C2×#90784C2211yescharacteristic, complemented
33#11745292C2211yescharacteristic
34#11745292C2211yescharacteristic
35C2×#90777C2211yescharacteristic, complemented
36C22×#6597C2211yescharacteristic, complemented
37#11745257—21no—
38#11745244—21no—
39#11745244—21no—
40#11745236C2211yescharacteristic
41C4×D116C2211yescharacteristic
42#11745183C2211yescharacteristic, complemented
43C22⋊#6597C2211yescharacteristic, complemented
44C22⋊#6597C2211yescharacteristic, complemented
45#11745157C2211yescharacteristic
46#11745157C2211yescharacteristic
47#11745157C2211yescharacteristic
48#11745157C2211yescharacteristic, complemented
49#11745157C2211yescharacteristic, complemented
50#11745157C2211yescharacteristic, complemented
51#11745157C2211yescharacteristic, complemented
52#11745157C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic, complemented
54#11745156C2211yescharacteristic, complemented
55#11745155C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C23×D29—21no—
60C23×D29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29D411yescharacteristic
63C22×C4×C29—21no—
64C22×C4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68D4×D29—44no—
69C2×D116—22no—
70C2×D116—22no—
71C2×D116—21no—
72C2×D116—21no—
73C2×D116—21no—
74C2×D116—21no—
75C2×D116—41no—
76C2×D116—41no—
77C2×D116C2311yescharacteristic
78C2×D116C2311yescharacteristic
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29—21no—
86C4⋊C4×C29—21no—
87C4⋊C4×C29D411yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C4⋊C4×C29C2311yescharacteristic
90C4⋊C4×C29C2311yescharacteristic
91C22⋊C4×C29—21no—
92C22⋊C4×C29—21no—
93C22⋊C4×C29—21no—
94C22⋊C4×C29D411yescharacteristic
95C22⋊C4×C29D411yescharacteristic
96C42×C29—21no—
97C42×C29—21no—
98C42×C29C2311yescharacteristic
99#90784—22no—
100#90784—41no—
101#90784—41no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105C4⋊Dic29C2311yescharacteristic
106#90777—41no—
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C2×#6597C2311yescharacteristic
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—21no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—42no—
120C22×D29—42no—
121C22×D29—81no—
122C22×D29—81no—
123Q8×C29—21no—
124Q8×C29—21no—
125D4×C29—22no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—42no—
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2411yescharacteristic
140C22⋊D29—42no—
141C22⋊D29—42no—
142C2×Dic29—21no—
143D116—21no—
144D116—21no—
145D116—21no—
146D116—21no—
147D116—21no—
148D116—42no—
149D116—42no—
150D116—42no—
151D116—81no—
152D116#4112yes—
153C4×D29—42no—
154#6597—21no—
155#6597—21no—
156#6597—21no—
157#6597—21no—
158#3310—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—21no—
164C22×C29AGL(1,ℤ/8)12yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—22no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—84no—
176C2×D29—84no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—41no—
182C4×C29—41no—
183C4×C29—41no—
184C4×C29—41no—
185C4×C29C2×#4111yescharacteristic
186C4×C29H(5,𝔽2)11yescharacteristic
187Dic29—41no—
188#552D2911yescharacteristic, complemented
189D42—291no—
190#490—291no—
191#482—291no—
192#480—291no—
193#478—291no—
194#468—291no—
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—22no—
204C2×C29—41no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—42no—
209D29—81no—
210D29—81no—
211C22×D4—291no—
212C22×D4—291no—
213C22×D4—581no—
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×M16—291no—
218C22×C8—291no—
219#127—291no—
220#126—21no—
221#125—21no—
222#125C2×D2911yescharacteristic, complemented
223#123—21no—
224C22⋊Q8C2×D2911yescharacteristic, complemented
225C22⋊Q8C2×D2911yescharacteristic, complemented
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230#120—581no—
231C4×Q8C2×D2911yescharacteristic, complemented
232C4×D4—291no—
233C4×D4C2×D2911yescharacteristic
234#117—21no—
235#117C2×D2911yescharacteristic, complemented
236C2×C4⋊C4C2×D2911yescharacteristic, complemented
237#107—291no—
238#107—291no—
239#106—291no—
240C4⋊C8—291no—
241#103—291no—
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#102—291no—
251C22⋊C8—291no—
252C22⋊C8—291no—
253#97—291no—
254C29#331011yescharacteristic, complemented, Sylow
255C24—581no—
256C24—581no—
257C2×Q8C22×D2911yescharacteristic
258C2×D4—291no—
259C2×D4—291no—
260C2×D4—291no—
261C2×D4—582no—
262C2×D4—582no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—1161no—
270C2×D4—1161no—
271C2×D4—1164no—
272C2×D4C22⋊D2911yescharacteristic
273C22×C4—21no—
274C22×C4—581no—
275C22×C4C22×D2911yescharacteristic
276C22×C4C22×D2911yescharacteristic
277SD16—582no—
278SD16—1161no—
279SD16—1161no—
280M16—1161no—
281C2×C8—291no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—291no—
285C2×C8—1161no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—291no—
293C4⋊C4C22⋊D2911yescharacteristic
294C4⋊C4C22×D2911yescharacteristic
295C4⋊C4C22×D2911yescharacteristic
296C4⋊C4C22×D2911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4C22⋊D2911yescharacteristic
304C22⋊C4C22⋊D2911yescharacteristic
305C42—21no—
306C42—21no—
307C42C22×D2911yescharacteristic
308C23—581no—
309C23—581no—
310C23—581no—
311C23—1162no—
312C23—1162no—
313C23—1162no—
314C23—1162no—
315C23—2321no—
316C23—2321no—
317C23C2×C22⋊D2911yescharacteristic
318C23C2×C22⋊D2911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—22no—
322D4—292no—
323D4—581no—
324D4—581no—
325D4—581no—
326D4—581no—
327D4—581no—
328D4—1162no—
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—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—581no—
344C2×C4—1162no—
345C2×C4C2×C22⋊D2911yescharacteristic
346C2×C4C2×C22⋊D2911yescharacteristic
347C2×C4C2×C22⋊D2911yescharacteristic
348C2×C4C2×C22⋊D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—581no—
351C8—581no—
352C8—581no—
353C8—581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—582no—
360C22—1161no—
361C22—1161no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22—2324no—
369C22—2324no—
370C22#1174531112yes—
371C22C22×C22⋊D2911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1161no—
381C4#41×D2911yescharacteristic
382C4#1174536411yescharacteristic
383C2—22no—
384C2—41no—
385C2—1162no—
386C2—2321no—
387C2—2321no—
388C2#1427180111yescharacteristic
389C2C2×#1174531111yescharacteristic
390C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#552C2
socleC22×C29C22×D4
prime radicalD4×D116C2
hypercenter#552D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14271529C2semidirect
3. #14271487C2semidirect
4. #14271476C2semidirect
5. #14271460C2semidirect
6. #14271411C2semidirect
7. #14271394C2semidirect
8. #14271363C2semidirect
9. #14271313C2semidirect
10. #14271313C2semidirect
11. #14271261C2semidirect
12. #14271235C2semidirect
13. #14271167C2semidirect
14. C2×#11745157C2semidirect
15. C29×#552C2semidirect
21. C29×#125C22semidirect
23. C29×C22⋊Q8C22semidirect
24. C29×C22⋊Q8C22semidirect
25. C4×Q8×C29C22semidirect
28. C29×#117C22semidirect
29. C2×C4⋊C4×C29C22semidirect
31. C2×#90784C22semidirect
32. C2×#90784C22semidirect
35. C2×#90777C22semidirect
36. C22×#6597C22semidirect
42. #11745183C22semidirect
43. C22⋊#6597C22semidirect
44. C22⋊#6597C22semidirect
48. #11745157C22semidirect
49. #11745157C22semidirect
50. #11745157C22semidirect
51. #11745157C22semidirect
52. #11745157C22semidirect
53. #11745157C22semidirect
54. #11745156C22semidirect
55. #11745155C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. #11745151C22semidirect
188. #552D29semidirect
222. #125C2×D29semidirect
224. C22⋊Q8C2×D29semidirect
225. C22⋊Q8C2×D29semidirect
231. C4×Q8C2×D29semidirect
235. #117C2×D29semidirect
236. C2×C4⋊C4C2×D29semidirect
254. C29#3310semidirect

Maximal subgroups

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

subgroupindex
D4×D1162
#142715292
#142714872
#142714762
#142714602
#142714112
#142713942
#142713632
#142713132
#142712612
#142712352
#142711672
C2×#117451572
C29×#5522
#331029