Finite Group Databasebeta

← #44537371

Subgroups — #44537371

Order 31424.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#21463328C211yesmaximal, characteristic, complemented
2C22×D1964C211yesmaximal, characteristic, complemented
3#30628325C211yesmaximal, characteristic, complemented
4#30628322C212yesmaximal, complemented
5#30628316C211yesmaximal, characteristic, complemented
6#30628311C211yesmaximal, characteristic, complemented
7#30628310C212yesmaximal, complemented
8#30628305C212yesmaximal, complemented
9C4×D1964C211yesmaximal, characteristic, complemented
10C22⋊C4×D491C212yesmaximal, complemented
11C4×D4×C491C211yesmaximal, characteristic, complemented
12C23×D491C2212yes—
13#21463328—24no—
14C2×Dic982C2211yescharacteristic, complemented
15C2×D1964—24no—
16C2×D1964C2212yes—
17C2×D1964C2211yescharacteristic
18C2×D1964C2211yescharacteristic
19C2×C22⋊D491C2212yescomplemented
20C2×C22⋊D491C2212yescomplemented
21C2×C4×D491C2212yescomplemented
22C2×C4×D491C2212yescomplemented
23C4⋊Dic491C2211yescharacteristic, complemented
24Dic491⋊C4C2212yescomplemented
25C22⋊Dic491C2212yes—
26(C2×D491)⋊C4C2212yescomplemented
27(C2×D491)⋊C4C2212yescomplemented
28(C2×D491)⋊C4C2212yescomplemented
29(C2×D491)⋊C4C2212yescomplemented
30C2×D4×C491C2211yescharacteristic
31C22×C4×C491C2211yescharacteristic
32C22×C4×C491C2211yescharacteristic, complemented
33C4⋊C4×C491C2211yescharacteristic, complemented
34C22⋊C4×C491C2211yescharacteristic
35C22⋊C4×C491C2211yescharacteristic, complemented
36C42×C491C2211yescharacteristic, complemented
37C22×D491—24no—
38C22×D491—24no—
39C22×D491—42no—
40C22×D491C2312yes—
41C22×D491C2312yes—
42Dic982—22no—
43D1964—24no—
44D1964—22no—
45D1964D414yescomplemented
46C22⋊D491—24no—
47C22⋊D491—42no—
48C2×Dic491C2312yes—
49C2×Dic491C2312yes—
50C4×D491—24no—
51C4×D491—42no—
52C23×C491C2311yescharacteristic
53C23×C491C2311yescharacteristic
54D4×C491—22no—
55C2×C4×C491—22no—
56C2×C4×C491—22no—
57C2×C4×C491C2311yescharacteristic
58C2×C4×C491C2311yescharacteristic
59C2×C4×C491C2311yescharacteristic
60C2×C4×C491C2311yescharacteristic
61C2×C4×C491C2311yescharacteristic
62C22×C491—21no—
63C22×C491—21no—
64C22×C491—21no—
65C22×C491—21no—
66C22×C491—21no—
67C22×C491#4112yescomplemented
68C22×C491C2411yescharacteristic
69C2×D491—22no—
70C2×D491—22no—
71C2×D491—22no—
72C2×D491—22no—
73C2×D491—22no—
74C2×D491—48no—
75C2×D491C2×D414yes—
76C4×C491—21no—
77C4×C491—21no—
78C4×C491—21no—
79C4×C491—21no—
80C4×C491C2×D412yes—
81Dic491—22no—
82Dic491—22no—
83C2×C491—22no—
84C2×C491—41no—
85C2×C491C22×D411yescharacteristic
86C2×C491C2×#4111yescharacteristic
87C2×C491H(5,𝔽2)11yescharacteristic
88D491—24no—
89D491—42no—
90C491#54611yescharacteristic, complemented, Sylow
91#546—4911nomaximal, Sylow
92C2×#41—4911no—
93C22×D4—4911no—
94#124—4911no—
95#123—4912no—
96C22⋊Q8—4911no—
97#121—4911no—
98#121—4912no—
99#120—4912no—
100C4×D4—4911no—
101C4×D4D49111yescharacteristic, complemented
102C2×C22⋊C4—4912no—
103C24—4912no—
104#41—9824no—
105C2×Q8—4911no—
106C2×D4—9824no—
107C2×D4—4912no—
108C2×D4—4912no—
109C2×D4—4912no—
110C2×D4—4911no—
111C2×D4—4911no—
112C2×D4C2×D49111yescharacteristic
113C22×C4—4912no—
114C22×C4—4912no—
115C22×C4C2×D49111yescharacteristic
116C22×C4C2×D49111yescharacteristic, complemented
117C4⋊C4—4912no—
118C4⋊C4—4911no—
119C4⋊C4C2×D49111yescharacteristic, complemented
120C22⋊C4—4912no—
121C22⋊C4—4912no—
122C22⋊C4—4912no—
123C22⋊C4—4912no—
124C22⋊C4—4912no—
125C22⋊C4C2×D49111yescharacteristic
126C22⋊C4C2×D49111yescharacteristic, complemented
127C42C2×D49111yescharacteristic, complemented
128C23—19642no—
129C23—9824no—
130C23—9824no—
131C23—4912no—
132C23—4912no—
133C23C22×D49111yescharacteristic
134C23C22×D49111yescharacteristic
135Q8—9822no—
136D4—22no—
137D4—19642no—
138D4—9824no—
139D4—9824no—
140D4—9822no—
141D4—4914no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—19642no—
145C2×C4—9824no—
146C2×C4—4912no—
147C2×C4—4912no—
148C2×C4C22×D49111yescharacteristic
149C2×C4C22×D49111yescharacteristic
150C2×C4C22×D49111yescharacteristic
151C2×C4C22×D49111yescharacteristic
152C2×C4C22×D49111yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—19648no—
159C22—9822no—
160C22—9822no—
161C22—9822no—
162C22—9822no—
163C22—9822no—
164C22—4914no—
165C22#2146332812yescomplemented
166C22C23×D49111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—9822no—
172C4—9822no—
173C4D4×D49112yes—
174C2—22no—
175C2—41no—
176C2—19642no—
177C2—9824no—
178C2C2×D4×D49111yescharacteristic
179C2C2×#2146332811yescharacteristic
180C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC4×D4×C491C2
hypercenterC4×D4D491
hypocenterC491#546
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#21463328C2semidirect
2. C22×D1964C2semidirect
3. #30628325C2semidirect
4. #30628322C2semidirect
5. #30628316C2semidirect
6. #30628311C2semidirect
7. #30628310C2semidirect
8. #30628305C2semidirect
9. C4×D1964C2semidirect
10. C22⋊C4×D491C2semidirect
11. C4×D4×C491C2semidirect
14. C2×Dic982C22semidirect
19. C2×C22⋊D491C22semidirect
20. C2×C22⋊D491C22semidirect
21. C2×C4×D491C22semidirect
22. C2×C4×D491C22semidirect
23. C4⋊Dic491C22semidirect
24. Dic491⋊C4C22semidirect
26. (C2×D491)⋊C4C22semidirect
27. (C2×D491)⋊C4C22semidirect
28. (C2×D491)⋊C4C22semidirect
29. (C2×D491)⋊C4C22semidirect
32. C22×C4×C491C22semidirect
33. C4⋊C4×C491C22semidirect
35. C22⋊C4×C491C22semidirect
36. C42×C491C22semidirect
45. D1964D4semidirect
67. C22×C491#41semidirect
90. C491#546semidirect
101. C4×D4D491semidirect
116. C22×C4C2×D491semidirect
119. C4⋊C4C2×D491semidirect
126. C22⋊C4C2×D491semidirect
127. C42C2×D491semidirect
165. C22#21463328semidirect

Maximal subgroups

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

subgroupindex
C2×#214633282
C22×D19642
#306283252
#306283222
#306283162
#306283112
#306283102
#306283052
C4×D19642
C22⋊C4×D4912
C4×D4×C4912
#546491