Finite Group Databasebeta

← #46830685

Subgroups — #46830685

Order 34624.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22575835C211yesmaximal, characteristic, complemented
2C22×C4×D541C211yesmaximal, characteristic, complemented
3#31772610C212yesmaximal, complemented
4#31772608C211yesmaximal, characteristic, complemented
5#31772607C211yesmaximal, characteristic, complemented
6#31772599C211yesmaximal, characteristic, complemented
7#31772596C212yesmaximal, complemented
8D4×Dic541C212yesmaximal, complemented
9#31772588C212yesmaximal, complemented
10#31772586C211yesmaximal, characteristic, complemented
11#121×C541C211yesmaximal, characteristic, complemented
12C23×D541C2211yescharacteristic
13#22575835—24no—
14C2×Dic1082C2211yescharacteristic, complemented
15C2×C22⋊D541C2212yes—
16C2×C22⋊D541C2212yes—
17C22×Dic541C2211yescharacteristic
18C22×Dic541C2212yescomplemented
19C2×C4×D541—24no—
20C2×C4×D541C2211yescharacteristic
21C2×C4×D541C2211yescharacteristic
22C2×C4×D541C2211yescharacteristic
23C2×C4×D541C2211yescharacteristic
24C4⋊Dic541C2211yescharacteristic, complemented
25C4⋊Dic541C2212yescomplemented
26#22575815C2212yescomplemented
27C22⋊Dic541C2212yes—
28C22⋊Dic541C2212yescomplemented
29#22575813C2212yes—
30#22575813C2212yes—
31C4×Dic541C2212yescomplemented
32C2×D4×C541C2212yes—
33C2×D4×C541C2211yescharacteristic, complemented
34C22×C4×C541C2211yescharacteristic
35C4⋊C4×C541C2211yescharacteristic, complemented
36C22⋊C4×C541C2212yescomplemented
37C22×D541—22no—
38C22×D541—22no—
39C22×D541—22no—
40C22×D541C2311yescharacteristic
41C22×D541C2311yescharacteristic
42Dic1082—22no—
43C22⋊D541—24no—
44C22⋊D541—24no—
45C2×Dic541—22no—
46C2×Dic541—24no—
47C2×Dic541C2312yes—
48C2×Dic541C2312yes—
49C2×Dic541C2311yescharacteristic
50C2×Dic541C2311yescharacteristic
51C4×D541—22no—
52C4×D541—22no—
53C4×D541—22no—
54C4×D541D414yescomplemented
55C23×C541C2312yes—
56C23×C541C2311yescharacteristic
57D4×C541—24no—
58D4×C541—22no—
59C2×C4×C541—22no—
60C2×C4×C541C2311yescharacteristic
61C2×C4×C541C2312yes—
62C2×C4×C541C2311yescharacteristic
63C22×C541—21no—
64C22×C541—21no—
65C22×C541—22no—
66C22×C541—22no—
67C22×C541—22no—
68C22×C541#4112yescomplemented
69C22×C541C2411yescharacteristic
70C2×D541—28no—
71C2×D541—21no—
72C2×D541—21no—
73C2×D541—21no—
74C2×D541—21no—
75C2×D541C2×D412yes—
76C2×D541#4112yescomplemented
77C4×C541—21no—
78C4×C541—22no—
79C4×C541C2×D412yes—
80Dic541—21no—
81Dic541—22no—
82Dic541—22no—
83Dic541C2×D412yes—
84C2×C541—22no—
85C2×C541—42no—
86C2×C541C22×D411yescharacteristic
87C2×C541C2×#4111yescharacteristic
88C2×C541C2×#4111yescharacteristic
89D541—22no—
90D541—22no—
91C541#52511yescharacteristic, complemented, Sylow
92#525—5411nomaximal, Sylow
93C2×#41—5411no—
94C23×C4—5411no—
95#123—5412no—
96C22⋊Q8—5411no—
97C22⋊Q8—5411no—
98#121—5411no—
99#121D54111yescharacteristic, complemented
100#120—5412no—
101C4×D4—5412no—
102C4×D4—5412no—
103#117—5411no—
104C24—5411no—
105#41—10824no—
106C2×Q8—5411no—
107C2×D4—5412no—
108C2×D4—5412no—
109C2×D4C2×D54112yes—
110C2×D4C2×D54111yescharacteristic, complemented
111C22×C4—5411no—
112C22×C4—5411no—
113C22×C4—5412no—
114C22×C4—5411no—
115C22×C4—5411no—
116C22×C4—5411no—
117C22×C4—10824no—
118C22×C4C2×D54111yescharacteristic
119C4⋊C4—5411no—
120C4⋊C4—5412no—
121C4⋊C4—5412no—
122C4⋊C4C2×D54111yescharacteristic, complemented
123C22⋊C4—5412no—
124C22⋊C4—5412no—
125C22⋊C4—5412no—
126C22⋊C4—5412no—
127C22⋊C4C2×D54112yescomplemented
128C42—5412no—
129C23—5411no—
130C23—5411no—
131C23—10822no—
132C23—10822no—
133C23—10822no—
134C23C22×D54112yes—
135C23C22×D54111yescharacteristic
136Q8—10822no—
137D4—24no—
138D4—22no—
139D4—10824no—
140D4—10824no—
141C2×C4—22no—
142C2×C4—5411no—
143C2×C4—5414no—
144C2×C4—5412no—
145C2×C4—5411no—
146C2×C4—5412no—
147C2×C4—10822no—
148C2×C4—10822no—
149C2×C4—10822no—
150C2×C4—10824no—
151C2×C4—10822no—
152C2×C4C22×D54112yes—
153C2×C4C22×D54111yescharacteristic
154C2×C4C22×D54111yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—5412no—
161C22—5412no—
162C22—10828no—
163C22—10821no—
164C22—10821no—
165C22—10821no—
166C22—10821no—
167C22#2257583512yescomplemented
168C22C23×D54111yescharacteristic
169C4—21no—
170C4—22no—
171C4—5412no—
172C4—10821no—
173C4—10822no—
174C4—10822no—
175C4D4×D54112yes—
176C2—22no—
177C2—42no—
178C2—10822no—
179C2—10822no—
180C2C2×D4×D54111yescharacteristic
181C2#41×D54111yescharacteristic
182C2C2×#2257583511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#121×C541C2
hypercenter#121D541
hypocenterC541#525
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22575835C2semidirect
2. C22×C4×D541C2semidirect
3. #31772610C2semidirect
4. #31772608C2semidirect
5. #31772607C2semidirect
6. #31772599C2semidirect
7. #31772596C2semidirect
8. D4×Dic541C2semidirect
9. #31772588C2semidirect
10. #31772586C2semidirect
11. #121×C541C2semidirect
14. C2×Dic1082C22semidirect
18. C22×Dic541C22semidirect
24. C4⋊Dic541C22semidirect
25. C4⋊Dic541C22semidirect
26. #22575815C22semidirect
28. C22⋊Dic541C22semidirect
31. C4×Dic541C22semidirect
33. C2×D4×C541C22semidirect
35. C4⋊C4×C541C22semidirect
36. C22⋊C4×C541C22semidirect
54. C4×D541D4semidirect
68. C22×C541#41semidirect
76. C2×D541#41semidirect
91. C541#525semidirect
99. #121D541semidirect
110. C2×D4C2×D541semidirect
122. C4⋊C4C2×D541semidirect
127. C22⋊C4C2×D541semidirect
167. C22#22575835semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
C22×C4×D5412
#317726102
#317726082
#317726072
#317725992
#317725962
D4×Dic5412
#317725882
#317725862
#121×C5412
#525541