Finite Group Databasebeta

← #46830741

Subgroups — #46830741

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×#22575836C211yesmaximal, characteristic, complemented
2C2×D4×D541C211yesmaximal, characteristic, complemented
3#31772624C212yesmaximal, complemented
4#31772614C212yesmaximal, complemented
5#31772603C211yesmaximal, characteristic, complemented
6#31772602C211yesmaximal, characteristic, complemented
7#31772599C211yesmaximal, characteristic, complemented
8#31772598C212yesmaximal, complemented
9#31772596C212yesmaximal, complemented
10#31772586C211yesmaximal, characteristic, complemented
11#121×C541C211yesmaximal, characteristic, complemented
12C23×D541C2212yes—
13#22575836—24no—
14C2×Dic1082C2211yescharacteristic, complemented
15C2×D2164C2211yescharacteristic
16C2×D2164C2211yescharacteristic
17C2×D2164C2212yescomplemented
18C2×C22⋊D541C2211yescharacteristic
19C2×C22⋊D541C2212yes—
20C2×C22⋊D541C2211yescharacteristic, complemented
21C2×C22⋊D541C2212yescomplemented
22C2×C22⋊D541C2212yescomplemented
23D4×D541—24no—
24C2×C4×D541C2211yescharacteristic
25C2×C4×D541C2211yescharacteristic, complemented
26C4⋊Dic541C2211yescharacteristic, complemented
27C22⋊Dic541C2212yescomplemented
28#22575813C2212yes—
29#22575813C2212yescomplemented
30#22575813C2212yescomplemented
31C4×Dic541C2212yescomplemented
32C2×D4×C541C2211yescharacteristic
33C2×D4×C541C2212yescomplemented
34C22×C4×C541C2211yescharacteristic, complemented
35C4⋊C4×C541C2211yescharacteristic, complemented
36C22⋊C4×C541C2212yescomplemented
37C22×D541—24no—
38C22×D541—42no—
39C22×D541—42no—
40C22×D541C2312yes—
41C22×D541C2311yescharacteristic
42C22×D541C2311yescharacteristic
43Dic1082—22no—
44D2164—22no—
45D2164—22no—
46D2164—42no—
47C22⋊D541—22no—
48C22⋊D541—24no—
49C22⋊D541—22no—
50C22⋊D541—42no—
51C22⋊D541—42no—
52C2×Dic541C2312yes—
53C2×Dic541C2311yescharacteristic
54C2×Dic541C2311yescharacteristic
55C4×D541—22no—
56C4×D541D414yescomplemented
57C23×C541C2312yes—
58C23×C541C2311yescharacteristic
59D4×C541—22no—
60D4×C541—42no—
61C2×C4×C541—22no—
62C2×C4×C541C2311yescharacteristic
63C2×C4×C541C2312yes—
64C2×C4×C541C2311yescharacteristic
65C22×C541—21no—
66C22×C541—22no—
67C22×C541—21no—
68C22×C541—22no—
69C22×C541—22no—
70C22×C541—21no—
71C22×C541C2411yescharacteristic
72C2×D541—21no—
73C2×D541—21no—
74C2×D541—21no—
75C2×D541—22no—
76C2×D541—21no—
77C2×D541—22no—
78C2×D541—21no—
79C2×D541—22no—
80C2×D541—48no—
81C2×D541C2×D412yes—
82C4×C541—21no—
83C4×C541—22no—
84C4×C541C2×D412yes—
85Dic541—21no—
86Dic541—22no—
87Dic541C2×D412yes—
88C2×C541—42no—
89C2×C541—41no—
90C2×C541C22×D411yescharacteristic
91C2×C541H(5,𝔽2)11yescharacteristic
92C2×C541H(5,𝔽2)11yescharacteristic
93D541—22no—
94D541—41no—
95D541—42no—
96C541#53511yescharacteristic, complemented, Sylow
97#535—5411nomaximal, Sylow
98C2×#41—5411no—
99C22×D4—5411no—
100#127—5412no—
101#124—5412no—
102#121—5411no—
103#121—5411no—
104#121—5411no—
105#121D54111yescharacteristic, complemented
106#120—5412no—
107#120—5412no—
108#117—5411no—
109C24—5412no—
110#41—10824no—
111C2×Q8—5411no—
112C2×D4—5411no—
113C2×D4—5412no—
114C2×D4—5411no—
115C2×D4—5412no—
116C2×D4—5412no—
117C2×D4—5411no—
118C2×D4—5411no—
119C2×D4—5412no—
120C2×D4—10824no—
121C2×D4C2×D54111yescharacteristic
122C2×D4C2×D54112yescomplemented
123C22×C4—5411no—
124C22×C4—5411no—
125C22×C4C2×D54111yescharacteristic, complemented
126C4⋊C4—5411no—
127C4⋊C4C2×D54111yescharacteristic, complemented
128C22⋊C4—5412no—
129C22⋊C4—5412no—
130C22⋊C4—5412no—
131C22⋊C4—5412no—
132C22⋊C4C2×D54112yescomplemented
133C42—5412no—
134C23—5411no—
135C23—5412no—
136C23—5411no—
137C23—10824no—
138C23—21642no—
139C23—21642no—
140C23C22×D54112yes—
141C23C22×D54111yescharacteristic
142Q8—10822no—
143D4—22no—
144D4—42no—
145D4—10822no—
146D4—10824no—
147D4—10822no—
148D4—10822no—
149D4—10822no—
150D4—21642no—
151D4—21642no—
152D4—21642no—
153C2×C4—22no—
154C2×C4—5411no—
155C2×C4—5414no—
156C2×C4—5412no—
157C2×C4—5411no—
158C2×C4—10822no—
159C2×C4C22×D54112yes—
160C2×C4C22×D54111yescharacteristic
161C2×C4C22×D54111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—5412no—
169C22—10821no—
170C22—10821no—
171C22—10821no—
172C22—10822no—
173C22—10821no—
174C22—10822no—
175C22—10821no—
176C22—10822no—
177C22—21648no—
178C22C23×D54111yescharacteristic
179C4—22no—
180C4—21no—
181C4—5412no—
182C4—10822no—
183C4—10821no—
184C4D4×D54112yes—
185C2—42no—
186C2—41no—
187C2—10822no—
188C2—21642no—
189C2—21641no—
190C2C2×D4×D54111yescharacteristic
191C2#3177267311yescharacteristic
192C2#3177267411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#121×C541C2
hypercenter#121D541
hypocenterC541#535
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22575836C2semidirect
2. C2×D4×D541C2semidirect
3. #31772624C2semidirect
4. #31772614C2semidirect
5. #31772603C2semidirect
6. #31772602C2semidirect
7. #31772599C2semidirect
8. #31772598C2semidirect
9. #31772596C2semidirect
10. #31772586C2semidirect
11. #121×C541C2semidirect
14. C2×Dic1082C22semidirect
17. C2×D2164C22semidirect
20. C2×C22⋊D541C22semidirect
21. C2×C22⋊D541C22semidirect
22. C2×C22⋊D541C22semidirect
25. C2×C4×D541C22semidirect
26. C4⋊Dic541C22semidirect
27. C22⋊Dic541C22semidirect
29. #22575813C22semidirect
30. #22575813C22semidirect
31. C4×Dic541C22semidirect
33. C2×D4×C541C22semidirect
34. C22×C4×C541C22semidirect
35. C4⋊C4×C541C22semidirect
36. C22⋊C4×C541C22semidirect
56. C4×D541D4semidirect
96. C541#535semidirect
105. #121D541semidirect
122. C2×D4C2×D541semidirect
125. C22×C4C2×D541semidirect
127. C4⋊C4C2×D541semidirect
132. C22⋊C4C2×D541semidirect

Maximal subgroups

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

subgroupindex
C2×#225758362
C2×D4×D5412
#317726242
#317726142
#317726032
#317726022
#317725992
#317725982
#317725962
#317725862
#121×C5412
#535541