Finite Group Databasebeta

← #44537314

Subgroups — #44537314

Order 31424.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30628332C211yesmaximal, characteristic, complemented
2#30628325C211yesmaximal, characteristic, complemented
3#30628323C211yesmaximal, characteristic, complemented
4#30628322C211yesmaximal, characteristic, complemented
5#30628319C211yesmaximal, characteristic, complemented
6#30628315C211yesmaximal, characteristic, complemented
7#30628312C211yesmaximal, characteristic, complemented
8#30628312C211yesmaximal, characteristic, complemented
9#30628310C211yesmaximal, characteristic, complemented
10#30628307C211yesmaximal, characteristic, complemented
11#30628307C211yesmaximal, characteristic, complemented
12C4×D1964C211yesmaximal, characteristic, complemented
13#30628299C211yesmaximal, characteristic, complemented
14C22⋊C4×D491C211yesmaximal, characteristic, complemented
15#126×C491C211yesmaximal, characteristic, complemented
16C23×D491C2211yescharacteristic
17C2×Dic982C2211yescharacteristic, complemented
18C2×D1964C2211yescharacteristic
19C2×D1964C2211yescharacteristic
20C2×D1964C2211yescharacteristic
21C2×D1964C2211yescharacteristic
22C2×D1964C2211yescharacteristic, complemented
23C2×C22⋊D491C2211yescharacteristic
24C2×C22⋊D491C2211yescharacteristic
25C2×C4×D491C2211yescharacteristic
26C2×C4×D491C2211yescharacteristic
27C2×C4×D491C2211yescharacteristic, complemented
28C2×C4×D491C2211yescharacteristic, complemented
29C4⋊Dic491C2211yescharacteristic, complemented
30Dic491⋊C4C2211yescharacteristic, complemented
31Dic491⋊C4C2211yescharacteristic, complemented
32C22⋊Dic491C2211yescharacteristic
33(C2×D491)⋊C4C2211yescharacteristic
34(C2×D491)⋊C4C2211yescharacteristic
35(C2×D491)⋊C4C2211yescharacteristic
36(C2×D491)⋊C4C2211yescharacteristic
37(C2×D491)⋊C4C2211yescharacteristic
38(C2×D491)⋊C4C2211yescharacteristic
39(C2×D491)⋊C4C2211yescharacteristic, complemented
40(C2×D491)⋊C4C2211yescharacteristic, complemented
41(C2×D491)⋊C4C2211yescharacteristic, complemented
42(C2×D491)⋊C4C2211yescharacteristic, complemented
43C4×Dic491C2211yescharacteristic, complemented
44C4⋊C4×C491C2211yescharacteristic, complemented
45C4⋊C4×C491C2211yescharacteristic, complemented
46C4⋊C4×C491C2211yescharacteristic, complemented
47C22⋊C4×C491C2211yescharacteristic
48C22⋊C4×C491C2211yescharacteristic
49C22⋊C4×C491C2211yescharacteristic
50C42×C491C2211yescharacteristic, complemented
51C22×D491—22no—
52C22×D491—41no—
53C22×D491—41no—
54C22×D491C2311yescharacteristic
55C22×D491C2311yescharacteristic
56C22×D491C2311yescharacteristic
57C22×D491C2311yescharacteristic
58Dic982—41no—
59D1964—22no—
60D1964—22no—
61D1964—41no—
62D1964—41no—
63D1964—41no—
64C22⋊D491—41no—
65C22⋊D491—41no—
66C2×Dic491C2311yescharacteristic
67C2×Dic491C2311yescharacteristic
68C2×Dic491C2311yescharacteristic
69C2×Dic491C2311yescharacteristic
70C4×D491—41no—
71C4×D491—41no—
72C4×D491—41no—
73C4×D491—41no—
74C23×C491C2311yescharacteristic
75C2×C4×C491C2311yescharacteristic
76C2×C4×C491C2311yescharacteristic
77C2×C4×C491C2311yescharacteristic
78C2×C4×C491C2311yescharacteristic
79C2×C4×C491C2311yescharacteristic
80C2×C4×C491C2311yescharacteristic
81C22×C491—21no—
82C22×C491—21no—
83C22×C491—21no—
84C22×C491C2411yescharacteristic
85C2×D491—21no—
86C2×D491—21no—
87C2×D491—21no—
88C2×D491—21no—
89C2×D491—21no—
90C2×D491—21no—
91C2×D491—21no—
92C2×D491—21no—
93C2×D491—21no—
94C2×D491—21no—
95C2×D491—21no—
96C2×D491—44no—
97C2×D491#4112yes—
98C4×C491—21no—
99C4×C491—21no—
100C4×C491—21no—
101C4×C491—21no—
102C4×C491—21no—
103C4×C491—21no—
104Dic491—21no—
105Dic491—21no—
106Dic491—21no—
107Dic491—21no—
108C2×C491—41no—
109C2×C491C2×#4111yescharacteristic
110C2×C491H(5,𝔽2)11yescharacteristic
111C2×C491H(5,𝔽2)11yescharacteristic
112D491—22no—
113D491—41no—
114D491—41no—
115D491—41no—
116C491#53811yescharacteristic, complemented, Sylow
117#538—4911nomaximal, Sylow
118#126—4911no—
119#126D49111yescharacteristic, complemented
120#124—4911no—
121#124—4911no—
122#123—4911no—
123#123—4911no—
124C22⋊Q8—4911no—
125#121—4911no—
126#121—4911no—
127#121—4911no—
128#120—4911no—
129#120—4911no—
130C4×D4—4911no—
131C4×D4—4911no—
132C2×C22⋊C4—4911no—
133C24—4911no—
134C2×Q8—4911no—
135C2×D4—4911no—
136C2×D4—4911no—
137C2×D4—4911no—
138C2×D4—4911no—
139C2×D4—4911no—
140C2×D4—4911no—
141C2×D4—4911no—
142C22×C4—4911no—
143C22×C4—4911no—
144C22×C4—4911no—
145C22×C4—4911no—
146C4⋊C4—4911no—
147C4⋊C4—4911no—
148C4⋊C4—4911no—
149C4⋊C4C2×D49111yescharacteristic, complemented
150C4⋊C4C2×D49111yescharacteristic, complemented
151C4⋊C4C2×D49111yescharacteristic, complemented
152C22⋊C4—4911no—
153C22⋊C4—4911no—
154C22⋊C4—4911no—
155C22⋊C4—4911no—
156C22⋊C4—4911no—
157C22⋊C4—4911no—
158C22⋊C4—4911no—
159C22⋊C4—4911no—
160C22⋊C4—4911no—
161C22⋊C4—4911no—
162C22⋊C4—4911no—
163C22⋊C4C2×D49111yescharacteristic
164C22⋊C4C2×D49111yescharacteristic
165C22⋊C4C2×D49111yescharacteristic
166C42—4911no—
167C42C2×D49111yescharacteristic, complemented
168C23—19641no—
169C23—19641no—
170C23—9822no—
171C23—4911no—
172C23—4911no—
173C23—4911no—
174C23—4911no—
175C23C22×D49111yescharacteristic
176Q8—19641no—
177D4—19641no—
178D4—19641no—
179D4—19641no—
180D4—19641no—
181D4—19641no—
182D4—9822no—
183D4—9822no—
184C2×C4—19641no—
185C2×C4—19641no—
186C2×C4—19641no—
187C2×C4—19641no—
188C2×C4—4911no—
189C2×C4—4911no—
190C2×C4—4911no—
191C2×C4—4911no—
192C2×C4C22×D49111yescharacteristic
193C2×C4C22×D49111yescharacteristic
194C2×C4C22×D49111yescharacteristic
195C2×C4C22×D49111yescharacteristic
196C2×C4C22×D49111yescharacteristic
197C2×C4C22×D49111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—19644no—
202C22—9821no—
203C22—9821no—
204C22—9821no—
205C22—9821no—
206C22—9821no—
207C22—9821no—
208C22—9821no—
209C22—9821no—
210C22—9821no—
211C22—9821no—
212C22—9821no—
213C22—4912no—
214C22C23×D49111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—9821no—
222C4—9821no—
223C4—9821no—
224C4—9821no—
225C2—41no—
226C2—19641no—
227C2—19641no—
228C2—19641no—
229C2—9822no—
230C2#41×D49111yescharacteristic
231C2#3062838311yescharacteristic
232C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#126×C491C2
hypercenter#126D491
hypocenterC491#538
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #30628332C2semidirect
2. #30628325C2semidirect
3. #30628323C2semidirect
4. #30628322C2semidirect
5. #30628319C2semidirect
6. #30628315C2semidirect
7. #30628312C2semidirect
8. #30628312C2semidirect
9. #30628310C2semidirect
10. #30628307C2semidirect
11. #30628307C2semidirect
12. C4×D1964C2semidirect
13. #30628299C2semidirect
14. C22⋊C4×D491C2semidirect
15. #126×C491C2semidirect
17. C2×Dic982C22semidirect
22. C2×D1964C22semidirect
27. C2×C4×D491C22semidirect
28. C2×C4×D491C22semidirect
29. C4⋊Dic491C22semidirect
30. Dic491⋊C4C22semidirect
31. Dic491⋊C4C22semidirect
39. (C2×D491)⋊C4C22semidirect
40. (C2×D491)⋊C4C22semidirect
41. (C2×D491)⋊C4C22semidirect
42. (C2×D491)⋊C4C22semidirect
43. C4×Dic491C22semidirect
44. C4⋊C4×C491C22semidirect
45. C4⋊C4×C491C22semidirect
46. C4⋊C4×C491C22semidirect
50. C42×C491C22semidirect
116. C491#538semidirect
119. #126D491semidirect
149. C4⋊C4C2×D491semidirect
150. C4⋊C4C2×D491semidirect
151. C4⋊C4C2×D491semidirect
167. C42C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283322
#306283252
#306283232
#306283222
#306283192
#306283152
#306283122
#306283102
#306283072
C4×D19642
#306282992
C22⋊C4×D4912
#126×C4912
#538491