Finite Group Databasebeta

← #46830740

Subgroups — #46830740

Order 34624.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×C22⋊D541C211yesmaximal, characteristic, complemented
3#31772624C212yesmaximal, complemented
4#31772614C212yesmaximal, complemented
5#31772601C212yesmaximal, complemented
6#31772600C212yesmaximal, complemented
7#31772598C211yesmaximal, characteristic, complemented
8#31772597C211yesmaximal, characteristic, complemented
9#31772596C211yesmaximal, characteristic, complemented
10#31772584C211yesmaximal, characteristic, complemented
11#120×C541C211yesmaximal, characteristic, complemented
12C23×D541C2211yescharacteristic
13#22575835—24no—
14C2×Dic1082C2211yescharacteristic, complemented
15C2×D2164C2212yescomplemented
16C2×C22⋊D541—24no—
17C2×C22⋊D541C2211yescharacteristic
18C2×C22⋊D541C2212yes—
19C2×C22⋊D541C2212yes—
20C2×C22⋊D541C2211yescharacteristic, complemented
21C2×C22⋊D541C2212yescomplemented
22C2×C22⋊D541C2212yescomplemented
23C22×Dic541C2211yescharacteristic
24C22×Dic541C2211yescharacteristic, complemented
25C2×C4×D541C2211yescharacteristic, complemented
26#22575815C2212yescomplemented
27C22⋊Dic541C2211yescharacteristic
28C22⋊Dic541C2212yescomplemented
29#22575813C2212yescomplemented
30#22575813C2212yescomplemented
31C4×Dic541C2212yescomplemented
32C24×C541C2211yescharacteristic
33C2×D4×C541C2211yescharacteristic
34C2×D4×C541C2212yescomplemented
35C22⋊C4×C541C2211yescharacteristic
36C22⋊C4×C541C2212yescomplemented
37C22×D541—22no—
38C22×D541—42no—
39C22×D541C2312yes—
40C22×D541C2311yescharacteristic
41Dic1082—22no—
42D2164—42no—
43C22⋊D541—22no—
44C22⋊D541—24no—
45C22⋊D541—24no—
46C22⋊D541—22no—
47C22⋊D541—42no—
48C22⋊D541—42no—
49C2×Dic541—22no—
50C2×Dic541D414yescomplemented
51C2×Dic541C2312yes—
52C2×Dic541C2311yescharacteristic
53C2×Dic541C2311yescharacteristic
54C2×Dic541C2311yescharacteristic
55C4×D541—22no—
56C23×C541—22no—
57C23×C541—42no—
58C23×C541C2312yes—
59C23×C541C2311yescharacteristic
60C23×C541C2311yescharacteristic
61D4×C541—22no—
62D4×C541—42no—
63C2×C4×C541C2312yes—
64C2×C4×C541C2311yescharacteristic
65C22×C541—22no—
66C22×C541—22no—
67C22×C541—21no—
68C22×C541—22no—
69C22×C541—22no—
70C22×C541—22no—
71C22×C541—44no—
72C22×C541C2×D412yes—
73C22×C541C2411yescharacteristic
74C2×D541—21no—
75C2×D541—22no—
76C2×D541—22no—
77C2×D541—22no—
78C2×D541—22no—
79C2×D541—44no—
80C4×C541—21no—
81C4×C541—22no—
82Dic541—21no—
83Dic541—22no—
84Dic541C2×D412yes—
85Dic541C2×D412yes—
86C2×C541—22no—
87C2×C541—41no—
88C2×C541—42no—
89C2×C541C22×D411yescharacteristic
90C2×C541H(5,𝔽2)12yes—
91D541—41no—
92D541—42no—
93C541#53511yescharacteristic, complemented, Sylow
94#535—5411nomaximal, Sylow
95C2×#41—5411no—
96C22×D4—5411no—
97#127—5412no—
98#124—5412no—
99#121—5412no—
100#121—5412no—
101#120—5411no—
102#120—5411no—
103#120—5411no—
104#120D54111yescharacteristic, complemented
105#117—5411no—
106C24—5411no—
107C24C2×D54111yescharacteristic
108#41—10824no—
109C2×Q8—5411no—
110C2×D4—5411no—
111C2×D4—5412no—
112C2×D4—5412no—
113C2×D4—5411no—
114C2×D4—5412no—
115C2×D4—5412no—
116C2×D4—5412no—
117C2×D4—10824no—
118C2×D4C2×D54111yescharacteristic
119C2×D4C2×D54112yescomplemented
120C22×C4—5411no—
121C22×C4—5411no—
122C22×C4—5411no—
123C4⋊C4—5412no—
124C22⋊C4—5411no—
125C22⋊C4—5412no—
126C22⋊C4—5412no—
127C22⋊C4—5412no—
128C22⋊C4C2×D54111yescharacteristic
129C22⋊C4C2×D54112yescomplemented
130C42—5412no—
131C23—22no—
132C23—42no—
133C23—5412no—
134C23—5411no—
135C23—10822no—
136C23—21642no—
137C23C22×D54112yes—
138C23C22×D54111yescharacteristic
139C23C22×D54111yescharacteristic
140Q8—10822no—
141D4—22no—
142D4—42no—
143D4—10824no—
144D4—10824no—
145D4—10822no—
146D4—10822no—
147D4—21642no—
148D4—21642no—
149D4—21642no—
150C2×C4—5414no—
151C2×C4—5411no—
152C2×C4—5411no—
153C2×C4—5412no—
154C2×C4—5411no—
155C2×C4—10822no—
156C2×C4—10822no—
157C2×C4C22×D54112yes—
158C2×C4C22×D54111yescharacteristic
159C22—22no—
160C22—22no—
161C22—22no—
162C22—22no—
163C22—21no—
164C22—22no—
165C22—44no—
166C22—10822no—
167C22—10822no—
168C22—10822no—
169C22—10821no—
170C22—10822no—
171C22—21644no—
172C22D4×D54112yes—
173C22C23×D54111yescharacteristic
174C4—22no—
175C4—21no—
176C4—5412no—
177C4—5412no—
178C4—10822no—
179C4—10821no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—21642no—
184C2—21641no—
185C2C2×D4×D54111yescharacteristic
186C2#3177267312yes—
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#120×C541C2
hypercenter#120D541
hypocenterC541#535
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#22575835C2semidirect
2. C22×C22⋊D541C2semidirect
3. #31772624C2semidirect
4. #31772614C2semidirect
5. #31772601C2semidirect
6. #31772600C2semidirect
7. #31772598C2semidirect
8. #31772597C2semidirect
9. #31772596C2semidirect
10. #31772584C2semidirect
11. #120×C541C2semidirect
14. C2×Dic1082C22semidirect
15. C2×D2164C22semidirect
20. C2×C22⋊D541C22semidirect
21. C2×C22⋊D541C22semidirect
22. C2×C22⋊D541C22semidirect
24. C22×Dic541C22semidirect
25. C2×C4×D541C22semidirect
26. #22575815C22semidirect
28. C22⋊Dic541C22semidirect
29. #22575813C22semidirect
30. #22575813C22semidirect
31. C4×Dic541C22semidirect
34. C2×D4×C541C22semidirect
36. C22⋊C4×C541C22semidirect
50. C2×Dic541D4semidirect
93. C541#535semidirect
104. #120D541semidirect
119. C2×D4C2×D541semidirect
129. C22⋊C4C2×D541semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
C22×C22⋊D5412
#317726242
#317726142
#317726012
#317726002
#317725982
#317725972
#317725962
#317725842
#120×C5412
#535541