Finite Group Databasebeta

← #45690771

Subgroups — #45690771

Order 33472.

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×#22552641C211yesmaximal, characteristic, complemented
2C2×D4×D523C211yesmaximal, characteristic, complemented
3#30660369C212yesmaximal, complemented
4#30660359C212yesmaximal, complemented
5#30660348C211yesmaximal, characteristic, complemented
6#30660347C211yesmaximal, characteristic, complemented
7#30660344C211yesmaximal, characteristic, complemented
8#30660343C212yesmaximal, complemented
9#30660341C212yesmaximal, complemented
10#30660331C211yesmaximal, characteristic, complemented
11#121×C523C211yesmaximal, characteristic, complemented
12C23×D523C2212yes—
13#22552641—24no—
14C2×Dic1046C2211yescharacteristic, complemented
15C2×D2092C2211yescharacteristic
16C2×D2092C2211yescharacteristic
17C2×D2092C2212yescomplemented
18C2×C22⋊D523C2212yes—
19C2×C22⋊D523C2211yescharacteristic
20C2×C22⋊D523C2211yescharacteristic, complemented
21C2×C22⋊D523C2212yescomplemented
22C2×C22⋊D523C2212yescomplemented
23D4×D523—24no—
24C2×C4×D523C2211yescharacteristic
25C2×C4×D523C2211yescharacteristic, complemented
26C4⋊Dic523C2211yescharacteristic, complemented
27C22⋊Dic523C2212yescomplemented
28(C2×D523)⋊C4C2212yes—
29(C2×D523)⋊C4C2212yescomplemented
30(C2×D523)⋊C4C2212yescomplemented
31C4×Dic523C2212yescomplemented
32C2×D4×C523C2211yescharacteristic
33C2×D4×C523C2212yescomplemented
34C22×C4×C523C2211yescharacteristic, complemented
35C4⋊C4×C523C2211yescharacteristic, complemented
36C22⋊C4×C523C2212yescomplemented
37C22×D523—24no—
38C22×D523—42no—
39C22×D523—42no—
40C22×D523C2312yes—
41C22×D523C2311yescharacteristic
42C22×D523C2311yescharacteristic
43Dic1046—22no—
44D2092—22no—
45D2092—22no—
46D2092—42no—
47C22⋊D523—22no—
48C22⋊D523—24no—
49C22⋊D523—22no—
50C22⋊D523—42no—
51C22⋊D523—42no—
52C2×Dic523C2312yes—
53C2×Dic523C2311yescharacteristic
54C2×Dic523C2311yescharacteristic
55C4×D523—22no—
56C4×D523D414yescomplemented
57C23×C523C2312yes—
58C23×C523C2311yescharacteristic
59D4×C523—22no—
60D4×C523—42no—
61C2×C4×C523—22no—
62C2×C4×C523C2311yescharacteristic
63C2×C4×C523C2312yes—
64C2×C4×C523C2311yescharacteristic
65C22×C523—21no—
66C22×C523—22no—
67C22×C523—21no—
68C22×C523—22no—
69C22×C523—21no—
70C22×C523—22no—
71C22×C523C2411yescharacteristic
72C2×D523—21no—
73C2×D523—21no—
74C2×D523—21no—
75C2×D523—22no—
76C2×D523—21no—
77C2×D523—22no—
78C2×D523—21no—
79C2×D523—22no—
80C2×D523—48no—
81C2×D523C2×D412yes—
82C4×C523—21no—
83C4×C523—22no—
84C4×C523C2×D412yes—
85Dic523—21no—
86Dic523—22no—
87Dic523C2×D412yes—
88C2×C523—42no—
89C2×C523—41no—
90C2×C523C22×D411yescharacteristic
91C2×C523H(5,𝔽2)11yescharacteristic
92C2×C523H(5,𝔽2)11yescharacteristic
93D523—22no—
94D523—41no—
95D523—42no—
96C523#53511yescharacteristic, complemented, Sylow
97#535—5231nomaximal, Sylow
98C2×#41—5231no—
99C22×D4—5231no—
100#127—5232no—
101#124—5232no—
102#121—5231no—
103#121—5231no—
104#121—5231no—
105#121D52311yescharacteristic, complemented
106#120—5232no—
107#120—5232no—
108#117—5231no—
109C24—5232no—
110#41—10464no—
111C2×Q8—5231no—
112C2×D4—5231no—
113C2×D4—5232no—
114C2×D4—5231no—
115C2×D4—5232no—
116C2×D4—5232no—
117C2×D4—5231no—
118C2×D4—5231no—
119C2×D4—5232no—
120C2×D4—10464no—
121C2×D4C2×D52311yescharacteristic
122C2×D4C2×D52312yescomplemented
123C22×C4—5231no—
124C22×C4—5231no—
125C22×C4C2×D52311yescharacteristic, complemented
126C4⋊C4—5231no—
127C4⋊C4C2×D52311yescharacteristic, complemented
128C22⋊C4—5232no—
129C22⋊C4—5232no—
130C22⋊C4—5232no—
131C22⋊C4—5232no—
132C22⋊C4C2×D52312yescomplemented
133C42—5232no—
134C23—5231no—
135C23—5232no—
136C23—5231no—
137C23—10464no—
138C23—20922no—
139C23—20922no—
140C23C22×D52312yes—
141C23C22×D52311yescharacteristic
142Q8—10462no—
143D4—22no—
144D4—42no—
145D4—10462no—
146D4—10464no—
147D4—10462no—
148D4—10462no—
149D4—10462no—
150D4—20922no—
151D4—20922no—
152D4—20922no—
153C2×C4—22no—
154C2×C4—5231no—
155C2×C4—5234no—
156C2×C4—5232no—
157C2×C4—5231no—
158C2×C4—10462no—
159C2×C4C22×D52312yes—
160C2×C4C22×D52311yescharacteristic
161C2×C4C22×D52311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—5232no—
169C22—10461no—
170C22—10461no—
171C22—10461no—
172C22—10462no—
173C22—10461no—
174C22—10462no—
175C22—10461no—
176C22—10462no—
177C22—20928no—
178C22C23×D52311yescharacteristic
179C4—21no—
180C4—22no—
181C4—5232no—
182C4—10461no—
183C4—10462no—
184C4D4×D52312yes—
185C2—42no—
186C2—41no—
187C2—10462no—
188C2—20922no—
189C2—20921no—
190C2C2×D4×D52311yescharacteristic
191C2#3066041811yescharacteristic
192C2#3066041911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D523
commutator, socle, cosocleC22×C523C24
Fitting#121×C523C2
hypercenter#121D523
hypocenterC523#535
LCSG ▷ C22×C523 ▷ C523
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22552641C2semidirect
2. C2×D4×D523C2semidirect
3. #30660369C2semidirect
4. #30660359C2semidirect
5. #30660348C2semidirect
6. #30660347C2semidirect
7. #30660344C2semidirect
8. #30660343C2semidirect
9. #30660341C2semidirect
10. #30660331C2semidirect
11. #121×C523C2semidirect
14. C2×Dic1046C22semidirect
17. C2×D2092C22semidirect
20. C2×C22⋊D523C22semidirect
21. C2×C22⋊D523C22semidirect
22. C2×C22⋊D523C22semidirect
25. C2×C4×D523C22semidirect
26. C4⋊Dic523C22semidirect
27. C22⋊Dic523C22semidirect
29. (C2×D523)⋊C4C22semidirect
30. (C2×D523)⋊C4C22semidirect
31. C4×Dic523C22semidirect
33. C2×D4×C523C22semidirect
34. C22×C4×C523C22semidirect
35. C4⋊C4×C523C22semidirect
36. C22⋊C4×C523C22semidirect
56. C4×D523D4semidirect
96. C523#535semidirect
105. #121D523semidirect
122. C2×D4C2×D523semidirect
125. C22×C4C2×D523semidirect
127. C4⋊C4C2×D523semidirect
132. C22⋊C4C2×D523semidirect

Maximal subgroups

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

subgroupindex
C2×#225526412
C2×D4×D5232
#306603692
#306603592
#306603482
#306603472
#306603442
#306603432
#306603412
#306603312
#121×C5232
#535523