Finite Group Databasebeta

← #46830681

Subgroups — #46830681

Order 34624.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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
2C23×Dic541C211yesmaximal, characteristic, complemented
3#31772612C211yesmaximal, characteristic, complemented
4#31772609C211yesmaximal, characteristic, complemented
5#31772605C212yesmaximal, complemented
6#31772600C212yesmaximal, complemented
7#31772597C211yesmaximal, characteristic, complemented
8D4×Dic541C212yesmaximal, complemented
9#31772588C212yesmaximal, complemented
10#31772584C211yesmaximal, characteristic, complemented
11#120×C541C211yesmaximal, characteristic, complemented
12#22575835—24no—
13C2×Dic1082C2211yescharacteristic, complemented
14C2×C22⋊D541C2212yes—
15C2×C22⋊D541C2211yescharacteristic
16C2×C22⋊D541C2211yescharacteristic, complemented
17C22×Dic541—24no—
18C22×Dic541C2212yes—
19C22×Dic541C2212yes—
20C22×Dic541C2211yescharacteristic
21C22×Dic541C2211yescharacteristic
22C22×Dic541C2211yescharacteristic, complemented
23C2×C4×D541C2211yescharacteristic, complemented
24C4⋊Dic541C2212yescomplemented
25#22575815C2212yescomplemented
26#22575815C2212yescomplemented
27C22⋊Dic541C2211yescharacteristic
28C22⋊Dic541C2212yes—
29C22⋊Dic541C2212yescomplemented
30#22575813C2212yescomplemented
31C4×Dic541C2212yescomplemented
32C24×C541C2211yescharacteristic
33C2×D4×C541C2212yes—
34C2×D4×C541C2211yescharacteristic
35C22⋊C4×C541C2211yescharacteristic
36C22⋊C4×C541C2212yes—
37C22×D541C2311yescharacteristic
38Dic1082—22no—
39C22⋊D541—22no—
40C22⋊D541—24no—
41C22⋊D541—22no—
42C2×Dic541—22no—
43C2×Dic541—24no—
44C2×Dic541—24no—
45C2×Dic541—22no—
46C2×Dic541D414yescomplemented
47C2×Dic541C2312yes—
48C2×Dic541C2312yes—
49C2×Dic541C2311yescharacteristic
50C2×Dic541C2311yescharacteristic
51C2×Dic541C2311yescharacteristic
52C4×D541—22no—
53C23×C541—22no—
54C23×C541—24no—
55C23×C541C2311yescharacteristic
56C23×C541C2311yescharacteristic
57C23×C541C2312yes—
58D4×C541—22no—
59D4×C541—24no—
60C2×C4×C541C2312yes—
61C2×C4×C541C2311yescharacteristic
62C22×C541—28no—
63C22×C541—22no—
64C22×C541—22no—
65C22×C541—22no—
66C22×C541—21no—
67C22×C541—22no—
68C22×C541C2×D412yes—
69C22×C541#4114yescomplemented
70C22×C541C2411yescharacteristic
71C2×D541—21no—
72C2×D541—22no—
73C4×C541—21no—
74C4×C541—22no—
75Dic541—22no—
76Dic541—21no—
77Dic541—22no—
78Dic541C2×D412yes—
79Dic541C2×D412yes—
80C2×C541—22no—
81C2×C541—24no—
82C2×C541—41no—
83C2×C541C22×D411yescharacteristic
84C2×C541C2×#4112yes—
85D541—41no—
86C541#52511yescharacteristic, complemented, Sylow
87#525—5411nomaximal, Sylow
88C2×#41—5411no—
89C23×C4—5411no—
90#123—5411no—
91#123—5411no—
92C22⋊Q8—5412no—
93#121—5412no—
94#120—5411no—
95#120D54111yescharacteristic, complemented
96C4×D4—5412no—
97C4×D4—5412no—
98#117—5411no—
99C24C2×D54111yescharacteristic
100#41—10824no—
101C2×Q8—5411no—
102C2×D4—5412no—
103C2×D4—5411no—
104C2×D4—5411no—
105C2×D4C2×D54112yes—
106C2×D4C2×D54111yescharacteristic
107C22×C4—5411no—
108C22×C4—5412no—
109C22×C4—5411no—
110C22×C4—5412no—
111C22×C4—5411no—
112C22×C4—5411no—
113C22×C4—10824no—
114C4⋊C4—5412no—
115C4⋊C4—5412no—
116C4⋊C4—5412no—
117C22⋊C4—5411no—
118C22⋊C4—5412no—
119C22⋊C4—5412no—
120C22⋊C4—5412no—
121C22⋊C4C2×D54111yescharacteristic
122C22⋊C4C2×D54112yes—
123C42—5412no—
124C23—22no—
125C23—24no—
126C23—5411no—
127C23C22×D54111yescharacteristic
128C23C22×D54111yescharacteristic
129C23C22×D54112yes—
130Q8—10822no—
131D4—22no—
132D4—24no—
133D4—10822no—
134D4—10822no—
135D4—10824no—
136C2×C4—5414no—
137C2×C4—5411no—
138C2×C4—5411no—
139C2×C4—5412no—
140C2×C4—5412no—
141C2×C4—5411no—
142C2×C4—10822no—
143C2×C4—10824no—
144C2×C4—10824no—
145C2×C4—10822no—
146C2×C4—10822no—
147C2×C4C22×D54112yes—
148C2×C4C22×D54111yescharacteristic
149C22—28no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—22no—
155C22—10821no—
156C22—10822no—
157C22D4×D54112yes—
158C22#2257583514yescomplemented
159C22C23×D54111yescharacteristic
160C4—21no—
161C4—22no—
162C4—5412no—
163C4—5412no—
164C4—10822no—
165C4—10821no—
166C4—10822no—
167C2—22no—
168C2—24no—
169C2—41no—
170C2—21641no—
171C2C2×D4×D54111yescharacteristic
172C2C2×#2257583512yes—
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#120×C541C2
hypercenter#120D541
hypocenterC541#525
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. C23×Dic541C2semidirect
3. #31772612C2semidirect
4. #31772609C2semidirect
5. #31772605C2semidirect
6. #31772600C2semidirect
7. #31772597C2semidirect
8. D4×Dic541C2semidirect
9. #31772588C2semidirect
10. #31772584C2semidirect
11. #120×C541C2semidirect
13. C2×Dic1082C22semidirect
16. C2×C22⋊D541C22semidirect
22. C22×Dic541C22semidirect
23. C2×C4×D541C22semidirect
24. C4⋊Dic541C22semidirect
25. #22575815C22semidirect
26. #22575815C22semidirect
29. C22⋊Dic541C22semidirect
30. #22575813C22semidirect
31. C4×Dic541C22semidirect
46. C2×Dic541D4semidirect
69. C22×C541#41semidirect
86. C541#525semidirect
95. #120D541semidirect
158. C22#22575835semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
C23×Dic5412
#317726122
#317726092
#317726052
#317726002
#317725972
D4×Dic5412
#317725882
#317725842
#120×C5412
#525541