Finite Group Databasebeta

← #16831509

Subgroups — #16831509

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#14271848C211yesmaximal, characteristic, complemented
2D4×C22⋊D29C211yesmaximal, characteristic
3#14271526C211yesmaximal, characteristic, complemented
4#14271486C211yesmaximal, characteristic, complemented
5#14271476C211yesmaximal, characteristic, complemented
6#14271465C211yesmaximal, characteristic, complemented
7#14271408C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271362C211yesmaximal, characteristic, complemented
10#14271315C211yesmaximal, characteristic, complemented
11#14271314C211yesmaximal, characteristic, complemented
12#14271260C211yesmaximal, characteristic, complemented
13#14271234C211yesmaximal, characteristic, complemented
14#14271166C211yesmaximal, characteristic, complemented
15C2×C29×#102C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C22×C22⋊D29—21no—
18C2×D4×D29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic, complemented
20C2×C4⋊C4×C29C2211yescharacteristic, complemented
21#11745315—21no—
22#11745302C2211yescharacteristic
23#11745301—21no—
24#11745300C2211yescharacteristic
25#11745299—21no—
26D4×Dic29C2211yescharacteristic
27C2×#90783C2211yescharacteristic
28C2×#90783C2211yescharacteristic, complemented
29#11745292C2211yescharacteristic
30#11745291—21no—
31C4×C22⋊D29C2211yescharacteristic
32#11745288—21no—
33#11745286C2211yescharacteristic, complemented
34C2×#90773C2211yescharacteristic, complemented
35C2×#90772C2211yescharacteristic, complemented
36#11745260—21no—
37#11745259C2211yescharacteristic, complemented
38#11745254C2211yescharacteristic, complemented
39#11745252C2211yescharacteristic, complemented
40#11745251—21no—
41#11745249C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic, complemented
45C29×#102C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic, complemented
48C22⋊#6597C2211yescharacteristic, complemented
49#11745169C2211yescharacteristic, complemented
50#11745168C2211yescharacteristic, complemented
51#11745165C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54#11745162C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C24×C29—21no—
60C23×D29—21no—
61C2×D4×C29—22no—
62C2×D4×C29—21no—
63C2×D4×C29—41no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—44no—
74C2×C22⋊D29D411yescharacteristic
75C22×Dic29—21no—
76D4×D29—22no—
77D4×D29—41no—
78C2×D116C2311yescharacteristic
79C2×C4×D29C2311yescharacteristic
80C2×Dic58C2311yescharacteristic
81C2×C8×C29—41no—
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C4⋊C4×C29—21no—
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29D411yescharacteristic
91#90783—22no—
92#90783—41no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110#90773—41no—
111#90772—41no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—42no—
115C23×C29—42no—
116C23×C29—81no—
117C23×C29C2×D411yescharacteristic
118C22×D29—21no—
119C22×D29—42no—
120C22×D29—42no—
121C22×D29—81no—
122C22×D29C2×D411yescharacteristic
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—42no—
127D4×C29#4112yes—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—42no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—22no—
136C22⋊D29—42no—
137C22⋊D29—42no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C22⋊D29—81no—
141C2×Dic29—21no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—42no—
145C2×Dic29C2×D411yescharacteristic
146C2×Dic29C2×D411yescharacteristic
147C2×Dic29C2×D411yescharacteristic
148D116—21no—
149D116—21no—
150C4×D29—21no—
151C4×D29—21no—
152Dic58—21no—
153Dic58—21no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3310—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—22no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—84no—
168C22×C29AGL(1,ℤ/8)12yes—
169C22×C29C22×D411yescharacteristic
170C2×D29—21no—
171C2×D29—21no—
172C2×D29—21no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—41no—
176C2×D29—84no—
177C4×C29—21no—
178C4×C29—41no—
179C4×C29—41no—
180C4×C29C2×#4111yescharacteristic
181C4×C29H(5,𝔽2)11yescharacteristic
182Dic29—21no—
183Dic29—21no—
184Dic29—21no—
185Dic29—41no—
186Dic29—41no—
187Dic29—41no—
188#552—291no—
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×#102D2911yescharacteristic, complemented
203C2×C29—22no—
204C2×C29—42no—
205C2×C29—81no—
206C2×C29#54611yescharacteristic
207C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C29#57711yescharacteristic
209D29—41no—
210D29—81no—
211C22×D4—291no—
212C22×D4—581no—
213C22×D4C2×D2911yescharacteristic
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×M16—291no—
218C22×C8C2×D2911yescharacteristic, complemented
219#127—291no—
220#126—581no—
221#125—291no—
222#125—581no—
223#123—581no—
224C22⋊Q8—291no—
225C22⋊Q8—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230#120—581no—
231C4×Q8—291no—
232C4×D4—291no—
233C4×D4—291no—
234#117—291no—
235#117—581no—
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#102C2×D2911yescharacteristic
248#102C2×D2911yescharacteristic
249#102C2×D2911yescharacteristic, complemented
250#102C2×D2911yescharacteristic, complemented
251C22⋊C8—291no—
252C22⋊C8—291no—
253#97—291no—
254C29#331011yescharacteristic, complemented, Sylow
255C24—21no—
256C24—581no—
257C2×Q8—291no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—291no—
262C2×D4—291no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4—582no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—1161no—
270C2×D4—1164no—
271C2×D4C22×D2911yescharacteristic
272C2×D4C22×D2911yescharacteristic
273C22×C4—21no—
274C22×C4—291no—
275C22×C4—581no—
276C22×C4C22×D2911yescharacteristic
277SD16—582no—
278SD16—1161no—
279SD16—1161no—
280M16—1161no—
281C2×C8—41no—
282C2×C8—291no—
283C2×C8—291no—
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—291no—
298C22⋊C4—291no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C42—291no—
306C42—581no—
307C42—581no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—291no—
314C23—581no—
315C23—1162no—
316C23—1162no—
317C23—2321no—
318C23D4×D2911yescharacteristic
319Q8—581no—
320Q8—581no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—582no—
326D4—581no—
327D4—581no—
328D4—1162no—
329D4—1162no—
330D4—1162no—
331D4—1162no—
332D4—2321no—
333D4#9080512yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—291no—
340C2×C4—291no—
341C2×C4—291no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—581no—
345C2×C4—581no—
346C2×C4—581no—
347C2×C4—1162no—
348C2×C4D4×D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—581no—
353C8—581no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—84no—
363C22—581no—
364C22—581no—
365C22—581no—
366C22—1161no—
367C22—1161no—
368C22—1161no—
369C22—2324no—
370C22#1174527312yes—
371C22C2×D4×D2911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—581no—
376C4—581no—
377C4—581no—
378C4—1161no—
379C4—1161no—
380C4—1161no—
381C4C2×#9080511yescharacteristic
382C4#1174535911yescharacteristic
383C2—22no—
384C2—42no—
385C2—81no—
386C2—1161no—
387C2—2321no—
388C2#1427180311yescharacteristic
389C2C2×#1174527311yescharacteristic
390C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC22×C29C22×D4
prime radicalD4×C22⋊D29C2
hypercenterC2×#102D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14271848C2semidirect
3. #14271526C2semidirect
4. #14271486C2semidirect
5. #14271476C2semidirect
6. #14271465C2semidirect
7. #14271408C2semidirect
8. #14271392C2semidirect
9. #14271362C2semidirect
10. #14271315C2semidirect
11. #14271314C2semidirect
12. #14271260C2semidirect
13. #14271234C2semidirect
14. #14271166C2semidirect
15. C2×C29×#102C2semidirect
19. C22×C8×C29C22semidirect
20. C2×C4⋊C4×C29C22semidirect
28. C2×#90783C22semidirect
33. #11745286C22semidirect
34. C2×#90773C22semidirect
35. C2×#90772C22semidirect
37. #11745259C22semidirect
38. #11745254C22semidirect
39. #11745252C22semidirect
41. #11745249C22semidirect
44. C29×#102C22semidirect
45. C29×#102C22semidirect
47. #11745180C22semidirect
48. C22⋊#6597C22semidirect
49. #11745169C22semidirect
50. #11745168C22semidirect
51. #11745165C22semidirect
52. #11745164C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
55. #11745157C22semidirect
56. #11745157C22semidirect
57. #11745155C22semidirect
58. #11745155C22semidirect
202. C2×#102D29semidirect
218. C22×C8C2×D29semidirect
236. C2×C4⋊C4C2×D29semidirect
249. #102C2×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
#142718482
D4×C22⋊D292
#142715262
#142714862
#142714762
#142714652
#142714082
#142713922
#142713622
#142713152
#142713142
#142712602
#142712342
#142711662
C2×C29×#1022
#331029