Finite Group Databasebeta

← #44537402

Subgroups — #44537402

Order 31424.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#30628332C211yesmaximal, characteristic, complemented
3#30628326C211yesmaximal, characteristic, complemented
4#30628322C211yesmaximal, characteristic, complemented
5#30628322C211yesmaximal, characteristic, complemented
6#30628321C211yesmaximal, characteristic, complemented
7#30628313C211yesmaximal, characteristic, complemented
8#30628307C211yesmaximal, characteristic
9#30628299C211yesmaximal, characteristic, complemented
10C4×C22⋊D491C211yesmaximal, characteristic, complemented
11#30628295C211yesmaximal, characteristic, complemented
12#30628293C211yesmaximal, characteristic, complemented
13C2×(C2×D491)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D491C211yesmaximal, characteristic, complemented
15C22⋊Q8×C491C211yesmaximal, characteristic, complemented
16C23×D491C2211yescharacteristic
17C2×D1964C2211yescharacteristic
18C2×D1964C2211yescharacteristic
19C2×C22⋊D491C2211yescharacteristic
20C22×Dic491C2211yescharacteristic
21C2×C4×D491C2211yescharacteristic
22C2×C4×D491C2211yescharacteristic
23C2×C4×D491C2211yescharacteristic, complemented
24C4⋊Dic491C2211yescharacteristic, complemented
25C4⋊Dic491C2211yescharacteristic, complemented
26Dic491⋊C4C2211yescharacteristic, complemented
27Dic491⋊C4C2211yescharacteristic, complemented
28Dic491⋊C4C2211yescharacteristic, complemented
29C22⋊Dic491C2211yescharacteristic
30(C2×D491)⋊C4C2211yescharacteristic
31(C2×D491)⋊C4C2211yescharacteristic
32(C2×D491)⋊C4C2211yescharacteristic
33(C2×D491)⋊C4C2211yescharacteristic
34(C2×D491)⋊C4C2211yescharacteristic
35(C2×D491)⋊C4C2211yescharacteristic
36(C2×D491)⋊C4C2211yescharacteristic
37(C2×D491)⋊C4C2211yescharacteristic
38(C2×D491)⋊C4C2211yescharacteristic, complemented
39(C2×D491)⋊C4C2211yescharacteristic, complemented
40(C2×D491)⋊C4C2211yescharacteristic, complemented
41C4×Dic491C2211yescharacteristic, complemented
42C4×Dic491C2211yescharacteristic, complemented
43C4×Dic491C2211yescharacteristic, complemented
44C2×Q8×C491C2211yescharacteristic, complemented
45C22×C4×C491C2211yescharacteristic
46C4⋊C4×C491C2211yescharacteristic, complemented
47C4⋊C4×C491C2211yescharacteristic, complemented
48C4⋊C4×C491C2211yescharacteristic, complemented
49C22⋊C4×C491C2211yescharacteristic
50C22⋊C4×C491C2211yescharacteristic
51C22×D491—22no—
52C22×D491—22no—
53C22×D491—41no—
54C22×D491C2311yescharacteristic
55C22×D491C2311yescharacteristic
56C22×D491C2311yescharacteristic
57D1964—22no—
58D1964—41no—
59C22⋊D491—22no—
60C2×Dic491—22no—
61C2×Dic491C2311yescharacteristic
62C2×Dic491C2311yescharacteristic
63C2×Dic491C2311yescharacteristic
64C2×Dic491C2311yescharacteristic
65C2×Dic491C2311yescharacteristic
66C4×D491—22no—
67C4×D491—41no—
68C4×D491—41no—
69C23×C491C2311yescharacteristic
70Q8×C491—41no—
71C2×C4×C491—41no—
72C2×C4×C491C2311yescharacteristic
73C2×C4×C491C2311yescharacteristic
74C2×C4×C491C2311yescharacteristic
75C2×C4×C491C2311yescharacteristic
76C2×C4×C491C2311yescharacteristic
77C2×C4×C491C2311yescharacteristic
78C22×C491—21no—
79C22×C491—21no—
80C22×C491#4112yes—
81C22×C491C2411yescharacteristic
82C2×D491—21no—
83C2×D491—21no—
84C2×D491—21no—
85C2×D491—21no—
86C2×D491—21no—
87C2×D491—21no—
88C2×D491—21no—
89C2×D491—21no—
90C2×D491—44no—
91C2×D491#4112yes—
92C4×C491—21no—
93C4×C491—21no—
94C4×C491—21no—
95C4×C491—21no—
96C4×C491—21no—
97C4×C491—21no—
98Dic491—21no—
99Dic491—21no—
100Dic491—21no—
101Dic491—21no—
102Dic491—21no—
103C2×C491—22no—
104C2×C491C2×#4111yescharacteristic
105C2×C491C2×#4111yescharacteristic
106C2×C491H(5,𝔽2)11yescharacteristic
107D491—22no—
108D491—41no—
109D491—41no—
110C491#55111yescharacteristic, complemented, Sylow
111#551—4911nomaximal, Sylow
112#126—4911no—
113#126—4911no—
114#124—4911no—
115#123—4911no—
116#123—4911no—
117#123—4911no—
118C22⋊Q8—4911no—
119C22⋊Q8D49111yescharacteristic, complemented
120#120—4911no—
121C4×D4—4911no—
122C4×D4—4911no—
123#117—4911no—
124#117—4911no—
125C2×C22⋊C4—4911no—
126C2×C22⋊C4—4911no—
127C24—4911no—
128C2×Q8C2×D49111yescharacteristic, complemented
129C2×D4—4911no—
130C2×D4—4911no—
131C2×D4—4911no—
132C22×C4—4911no—
133C22×C4—4911no—
134C22×C4—4911no—
135C22×C4—4911no—
136C22×C4C2×D49111yescharacteristic
137C4⋊C4—4911no—
138C4⋊C4—4911no—
139C4⋊C4—4911no—
140C4⋊C4—4911no—
141C4⋊C4—4911no—
142C4⋊C4C2×D49111yescharacteristic, complemented
143C4⋊C4C2×D49111yescharacteristic, complemented
144C4⋊C4C2×D49111yescharacteristic, complemented
145C22⋊C4—4911no—
146C22⋊C4—4911no—
147C22⋊C4—4911no—
148C22⋊C4—4911no—
149C22⋊C4—4911no—
150C22⋊C4—4911no—
151C22⋊C4—4911no—
152C22⋊C4—4911no—
153C22⋊C4—4911no—
154C22⋊C4—4911no—
155C22⋊C4—4911no—
156C22⋊C4—4911no—
157C22⋊C4C2×D49111yescharacteristic
158C22⋊C4C2×D49111yescharacteristic
159C42—4911no—
160C42—4911no—
161C42—4911no—
162C23—19641no—
163C23—9822no—
164C23—9822no—
165C23—4911no—
166C23—4911no—
167C23—4911no—
168C23C22×D49111yescharacteristic
169Q8—41no—
170D4—19641no—
171D4—9822no—
172D4—9822no—
173C2×C4—41no—
174C2×C4—19641no—
175C2×C4—19641no—
176C2×C4—9822no—
177C2×C4—9822no—
178C2×C4—4911no—
179C2×C4—4911no—
180C2×C4—4911no—
181C2×C4—4911no—
182C2×C4—4911no—
183C2×C4C22×D49111yescharacteristic
184C2×C4C22×D49111yescharacteristic
185C2×C4C22×D49111yescharacteristic
186C2×C4C22×D49111yescharacteristic
187C2×C4C22×D49111yescharacteristic
188C2×C4C22×D49111yescharacteristic
189C22—21no—
190C22—21no—
191C22—19644no—
192C22—9821no—
193C22—9821no—
194C22—9821no—
195C22—9821no—
196C22—9821no—
197C22—9821no—
198C22—9821no—
199C22—9821no—
200C22—4912no—
201C22#2146332912yes—
202C22C23×D49111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—9821no—
210C4—9821no—
211C4—9821no—
212C4—9821no—
213C4—9821no—
214C2—22no—
215C2—19641no—
216C2—19641no—
217C2—9822no—
218C2#41×D49111yescharacteristic
219C2C2×#2146332911yescharacteristic
220C2#3062838211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC22⋊Q8×C491C2
prime radical#30628307C2
hypercenterC22⋊Q8D491
hypocenterC491#551
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #30628332C2semidirect
2. #30628332C2semidirect
3. #30628326C2semidirect
4. #30628322C2semidirect
5. #30628322C2semidirect
6. #30628321C2semidirect
7. #30628313C2semidirect
9. #30628299C2semidirect
10. C4×C22⋊D491C2semidirect
11. #30628295C2semidirect
12. #30628293C2semidirect
13. C2×(C2×D491)⋊C4C2semidirect
14. C22⋊C4×D491C2semidirect
15. C22⋊Q8×C491C2semidirect
23. C2×C4×D491C22semidirect
24. C4⋊Dic491C22semidirect
25. C4⋊Dic491C22semidirect
26. Dic491⋊C4C22semidirect
27. Dic491⋊C4C22semidirect
28. Dic491⋊C4C22semidirect
38. (C2×D491)⋊C4C22semidirect
39. (C2×D491)⋊C4C22semidirect
40. (C2×D491)⋊C4C22semidirect
41. C4×Dic491C22semidirect
42. C4×Dic491C22semidirect
43. C4×Dic491C22semidirect
44. C2×Q8×C491C22semidirect
46. C4⋊C4×C491C22semidirect
47. C4⋊C4×C491C22semidirect
48. C4⋊C4×C491C22semidirect
110. C491#551semidirect
119. C22⋊Q8D491semidirect
128. C2×Q8C2×D491semidirect
142. C4⋊C4C2×D491semidirect
143. C4⋊C4C2×D491semidirect
144. C4⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283322
#306283262
#306283222
#306283212
#306283132
#306283072
#306282992
C4×C22⋊D4912
#306282952
#306282932
C2×(C2×D491)⋊C42
C22⋊C4×D4912
C22⋊Q8×C4912
#551491