Finite Group Databasebeta

← #44537233

Subgroups — #44537233

Order 31424.

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

normal subgroups only

This group has 330 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×#21463327C211yesmaximal, characteristic, complemented
2C22×C4×D491C211yesmaximal, characteristic, complemented
3#30628320C211yesmaximal, characteristic, complemented
4#30628315C212yesmaximal, complemented
5#30628310C212yesmaximal, complemented
6#30628307C211yesmaximal, characteristic, complemented
7#30628305C211yesmaximal, characteristic, complemented
8#30628299C212yesmaximal, complemented
9(C22⋊D491)⋊C4C212yesmaximal, complemented
10#30628293C211yesmaximal, characteristic, complemented
11#123×C491C211yesmaximal, characteristic, complemented
12C23×D491C2211yescharacteristic
13#21463327—24no—
14C2×Dic982C2211yescharacteristic, complemented
15C2×D1964C2212yes—
16C2×C22⋊D491C2211yescharacteristic
17C2×C22⋊D491C2212yes—
18C2×C22⋊D491C2211yescharacteristic, complemented
19C22×Dic491C2211yescharacteristic
20C22×Dic491C2211yescharacteristic, complemented
21C2×C4×D491—24no—
22C2×C4×D491C2212yes—
23C2×C4×D491C2212yes—
24C2×C4×D491C2211yescharacteristic, complemented
25Dic491⋊C4C2212yescomplemented
26Dic491⋊C4C2212yescomplemented
27C22⋊Dic491C2211yescharacteristic
28(C2×D491)⋊C4C2212yes—
29(C2×D491)⋊C4C2212yes—
30(C2×D491)⋊C4C2212yescomplemented
31C4×Dic491C2212yescomplemented
32C2×D4×C491C2211yescharacteristic
33C22×C4×C491C2211yescharacteristic
34C4⋊C4×C491C2212yescomplemented
35C22⋊C4×C491C2211yescharacteristic
36C22⋊C4×C491C2212yescomplemented
37C22×D491—22no—
38C22×D491—24no—
39C22×D491C2311yescharacteristic
40C22×D491C2312yes—
41Dic982—22no—
42D1964—24no—
43C22⋊D491—22no—
44C22⋊D491—24no—
45C22⋊D491—22no—
46C2×Dic491—22no—
47C2×Dic491D414yescomplemented
48C2×Dic491C2312yes—
49C2×Dic491C2311yescharacteristic
50C2×Dic491C2311yescharacteristic
51C2×Dic491C2311yescharacteristic
52C4×D491—24no—
53C4×D491—24no—
54C4×D491—22no—
55C23×C491C2311yescharacteristic
56C23×C491C2311yescharacteristic
57D4×C491—22no—
58C2×C4×C491—22no—
59C2×C4×C491C2312yes—
60C2×C4×C491C2311yescharacteristic
61C2×C4×C491C2312yes—
62C22×C491—22no—
63C22×C491—21no—
64C22×C491—22no—
65C22×C491C2×D412yes—
66C22×C491C2411yescharacteristic
67C2×D491—28no—
68C2×D491—22no—
69C2×D491—22no—
70C2×D491—21no—
71C2×D491—22no—
72C2×D491#4114yescomplemented
73C4×C491—22no—
74C4×C491—21no—
75C4×C491—22no—
76Dic491—21no—
77Dic491—22no—
78Dic491C2×D412yes—
79Dic491C2×D412yes—
80C2×C491—22no—
81C2×C491—41no—
82C2×C491C22×D411yescharacteristic
83C2×C491C2×#4112yes—
84D491—24no—
85D491—41no—
86C491#52511yescharacteristic, complemented, Sylow
87#525—4911nomaximal, Sylow
88C2×#41—4911no—
89C23×C4—4911no—
90#123—4911no—
91#123D49111yescharacteristic, complemented
92C22⋊Q8—4912no—
93#121—4912no—
94#120—4911no—
95#120—4911no—
96C4×D4—4912no—
97C4×D4—4912no—
98#117—4911no—
99C24—4911no—
100#41—9824no—
101C2×Q8—4911no—
102C2×D4—4912no—
103C2×D4—4911no—
104C2×D4—4911no—
105C2×D4—4912no—
106C2×D4C2×D49111yescharacteristic
107C22×C4—9824no—
108C22×C4—4911no—
109C22×C4—4912no—
110C22×C4—4912no—
111C22×C4—4911no—
112C22×C4—4911no—
113C22×C4C2×D49111yescharacteristic
114C4⋊C4—4912no—
115C4⋊C4—4912no—
116C4⋊C4C2×D49112yescomplemented
117C22⋊C4—4911no—
118C22⋊C4—4912no—
119C22⋊C4—4912no—
120C22⋊C4—4912no—
121C22⋊C4C2×D49111yescharacteristic
122C22⋊C4C2×D49112yescomplemented
123C42—4912no—
124C23—9824no—
125C23—9822no—
126C23—4911no—
127C23—4912no—
128C23C22×D49111yescharacteristic
129C23C22×D49111yescharacteristic
130Q8—9822no—
131D4—22no—
132D4—9824no—
133D4—9824no—
134D4—9822no—
135D4—9822no—
136C2×C4—22no—
137C2×C4—9824no—
138C2×C4—9824no—
139C2×C4—9822no—
140C2×C4—9822no—
141C2×C4—4912no—
142C2×C4—4911no—
143C2×C4—4914no—
144C2×C4—4911no—
145C2×C4—4911no—
146C2×C4C22×D49112yes—
147C2×C4C22×D49111yescharacteristic
148C2×C4C22×D49112yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—9828no—
153C22—9821no—
154C22—9822no—
155C22—9822no—
156C22—9822no—
157C22—4914no—
158C22D4×D49112yes—
159C22C23×D49111yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—9821no—
164C4—9822no—
165C4—4912no—
166C4—4912no—
167C2—22no—
168C2—41no—
169C2—19641no—
170C2—9824no—
171C2C2×D4×D49111yescharacteristic
172C2#41×D49112yes—
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#123×C491C2
hypercenter#123D491
hypocenterC491#525
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#21463327C2semidirect
2. C22×C4×D491C2semidirect
3. #30628320C2semidirect
4. #30628315C2semidirect
5. #30628310C2semidirect
6. #30628307C2semidirect
7. #30628305C2semidirect
8. #30628299C2semidirect
9. (C22⋊D491)⋊C4C2semidirect
10. #30628293C2semidirect
11. #123×C491C2semidirect
14. C2×Dic982C22semidirect
18. C2×C22⋊D491C22semidirect
20. C22×Dic491C22semidirect
24. C2×C4×D491C22semidirect
25. Dic491⋊C4C22semidirect
26. Dic491⋊C4C22semidirect
30. (C2×D491)⋊C4C22semidirect
31. C4×Dic491C22semidirect
34. C4⋊C4×C491C22semidirect
36. C22⋊C4×C491C22semidirect
47. C2×Dic491D4semidirect
72. C2×D491#41semidirect
86. C491#525semidirect
91. #123D491semidirect
116. C4⋊C4C2×D491semidirect
122. C22⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
C2×#214633272
C22×C4×D4912
#306283202
#306283152
#306283102
#306283072
#306283052
#306282992
(C22⋊D491)⋊C42
#306282932
#123×C4912
#525491