Finite Group Databasebeta

← #16829403

Subgroups — #16829403

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271670C211yesmaximal, characteristic
2#117×D29C211yesmaximal, characteristic, complemented
3#14271503C211yesmaximal, characteristic, complemented
4#14271502C211yesmaximal, characteristic, complemented
5#14271497C211yesmaximal, characteristic, complemented
6#14271492C211yesmaximal, characteristic, complemented
7#14271486C211yesmaximal, characteristic, complemented
8#14271485C211yesmaximal, characteristic, complemented
9#14271480C211yesmaximal, characteristic, complemented
10#14271475C211yesmaximal, characteristic, complemented
11#14271201C211yesmaximal, characteristic, complemented
12#14271199C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14C2×#11745168C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×C4×D29C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C29×#117C2211yescharacteristic
20#11745308C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745300C2211yescharacteristic
23#11745300C2211yescharacteristic
24#11745299—21no—
25#11745297—21no—
26C4×C22⋊D29—21no—
27C4×C22⋊D29—21no—
28#11745288C2211yescharacteristic
29#11745288C2211yescharacteristic
30C22×#6597C2211yescharacteristic
31#11745254C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34C4⋊C4×D29C2211yescharacteristic
35C22⋊C4×D29—21no—
36#11745239—21no—
37#11745234—21no—
38C42×D29—21no—
39C29×#103C2211yescharacteristic, complemented
40C29×#103C2211yescharacteristic, complemented
41C29×#102C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic, complemented
43#11745183C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic, complemented
47#11745168C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745166C2211yescharacteristic, complemented
52#11745166C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29D411yescharacteristic
60#41×C29—22no—
61#41×C29—22no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C22×Dic29D411yescharacteristic
70C2×C4×D29—22no—
71C2×C4×D29—22no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29D411yescharacteristic
75C2×C4×D29D411yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×C4×D29C2311yescharacteristic
78C2×C8×C29—22no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29—21no—
105C2×#6597—22no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—22no—
111C22×D29—22no—
112C22×D29—41no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—42no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—42no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29#4112yes—
126C2×C4×C29#4112yes—
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—42no—
130C2×Dic29—22no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C4×D29—22no—
138C4×D29—22no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—42no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3091—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29#12312yes—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—44no—
163C2×D29#13512yes—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29#12312yes—
168C4×C29C2×#4111yescharacteristic
169C4×C29C2×#4111yescharacteristic
170Dic29—21no—
171Dic29—21no—
172Dic29—41no—
173Dic29—41no—
174Dic29—41no—
175Dic29—41no—
176#525—291no—
177C2×#117—291no—
178#485—291no—
179#485—291no—
180#484—291no—
181#483—291no—
182#482—291no—
183#482—291no—
184#481—291no—
185#480—291no—
186#427—291no—
187#427—291no—
188#416—291no—
189#416D2911yescharacteristic, complemented
190C2×C22⋊C8—291no—
191C2×C29—22no—
192C2×C29—81no—
193C2×C29C2×#12311yescharacteristic
194C2×C29C2×#13511yescharacteristic
195C2×C29#57511yescharacteristic
196D29—22no—
197D29—41no—
198C2×#41C2×D2911yescharacteristic
199C23×C4—291no—
200C22×C8—291no—
201C22×C8C2×D2911yescharacteristic
202#123—581no—
203C22⋊Q8—291no—
204C22⋊Q8—291no—
205#121—291no—
206#121—291no—
207#120—581no—
208C4×D4—581no—
209C4×D4—581no—
210#117—291no—
211#117—291no—
212#117—291no—
213#117—291no—
214#117—581no—
215#117—581no—
216#117C2×D2911yescharacteristic
217C2×C4⋊C4—291no—
218C2×C4⋊C4—291no—
219C2×C22⋊C4—581no—
220C2×C42—581no—
221#107—291no—
222#107—291no—
223#107—291no—
224#107—291no—
225#106—291no—
226#106—291no—
227#106—291no—
228#106—291no—
229#103—291no—
230#103—291no—
231#103C2×D2911yescharacteristic, complemented
232#103C2×D2911yescharacteristic, complemented
233#102—291no—
234#102—291no—
235#102C2×D2911yescharacteristic, complemented
236#102C2×D2911yescharacteristic, complemented
237C22⋊C8—291no—
238C22⋊C8—291no—
239C22⋊C8—291no—
240C22⋊C8—291no—
241C29#309111yescharacteristic, complemented, Sylow
242C24—291no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—21no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C22×C4—21no—
251C22×C4—291no—
252C22×C4—291no—
253C22×C4—291no—
254C22×C4—291no—
255C22×C4—291no—
256C22×C4—581no—
257C22×C4—581no—
258C22×C4—582no—
259C22×C4—582no—
260C22×C4C22×D2911yescharacteristic
261C2×C8—22no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8—582no—
265C2×C8C22×D2911yescharacteristic
266C2×C8C22×D2911yescharacteristic
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—291no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—21no—
287C42—581no—
288C42—581no—
289C42—581no—
290C42—581no—
291C23—21no—
292C23—291no—
293C23—291no—
294C23—582no—
295C23—582no—
296C23—1161no—
297C23D4×D2911yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—1162no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—291no—
310C2×C4—291no—
311C2×C4—582no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—582no—
317C2×C4—582no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—1162no—
323C2×C4—1162no—
324C2×C4#9080512yes—
325C2×C4D4×D2911yescharacteristic
326C2×C4#9080712yes—
327C2×C4C23×D2911yescharacteristic
328C8—21no—
329C8—21no—
330C8—581no—
331C8—581no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—292no—
338C22—581no—
339C22—581no—
340C22—581no—
341C22—581no—
342C22—581no—
343C22—1164no—
344C22#1174524512yes—
345C22C2×D4×D2911yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—581no—
350C4—581no—
351C4—1161no—
352C4—1161no—
353C4—1161no—
354C4—1161no—
355C4#1174524512yes—
356C4C2×#9080511yescharacteristic
357C4C2×#9080711yescharacteristic
358C2—22no—
359C2—81no—
360C2—582no—
361C2—1161no—
362C2C2×#1174524511yescharacteristic
363C2#135×D2911yescharacteristic
364C2#1427196011yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#416C2
socleC22×C29C22×D4
prime radical#14271670C2
hypercenter#416D29
hypocenterC29#3091
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D29C2semidirect
3. #14271503C2semidirect
4. #14271502C2semidirect
5. #14271497C2semidirect
6. #14271492C2semidirect
7. #14271486C2semidirect
8. #14271485C2semidirect
9. #14271480C2semidirect
10. #14271475C2semidirect
11. #14271201C2semidirect
12. #14271199C2semidirect
13. #14271159C2semidirect
14. C2×#11745168C2semidirect
15. C29×#416C2semidirect
39. C29×#103C22semidirect
40. C29×#103C22semidirect
41. C29×#102C22semidirect
42. C29×#102C22semidirect
43. #11745183C22semidirect
44. #11745183C22semidirect
45. #11745180C22semidirect
46. #11745180C22semidirect
51. #11745166C22semidirect
52. #11745166C22semidirect
53. #11745165C22semidirect
54. #11745165C22semidirect
55. #11745156C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. #11745155C22semidirect
189. #416D29semidirect
231. #103C2×D29semidirect
232. #103C2×D29semidirect
235. #102C2×D29semidirect
236. #102C2×D29semidirect
241. C29#3091semidirect

Maximal subgroups

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

subgroupindex
#142716702
#117×D292
#142715032
#142715022
#142714972
#142714922
#142714862
#142714852
#142714802
#142714752
#142712012
#142711992
#142711592
C2×#117451682
C29×#4162
#309129