Finite Group Databasebeta

← #45690713

Subgroups — #45690713

Order 33472.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×#22552640C211yesmaximal, characteristic, complemented
2C22×C4×D523C211yesmaximal, characteristic, complemented
3#30660356C211yesmaximal, characteristic, complemented
4#30660351C212yesmaximal, complemented
5#30660346C212yesmaximal, complemented
6#30660343C211yesmaximal, characteristic, complemented
7#30660341C211yesmaximal, characteristic, complemented
8#30660335C212yesmaximal, complemented
9(C22⋊D523)⋊C4C212yesmaximal, complemented
10#30660329C211yesmaximal, characteristic, complemented
11#123×C523C211yesmaximal, characteristic, complemented
12C23×D523C2211yescharacteristic
13#22552640—24no—
14C2×Dic1046C2211yescharacteristic, complemented
15C2×D2092C2212yes—
16C2×C22⋊D523C2211yescharacteristic
17C2×C22⋊D523C2212yes—
18C2×C22⋊D523C2211yescharacteristic, complemented
19C22×Dic523C2211yescharacteristic
20C22×Dic523C2211yescharacteristic, complemented
21C2×C4×D523—24no—
22C2×C4×D523C2212yes—
23C2×C4×D523C2212yes—
24C2×C4×D523C2211yescharacteristic, complemented
25Dic523⋊C4C2212yescomplemented
26Dic523⋊C4C2212yescomplemented
27C22⋊Dic523C2211yescharacteristic
28(C2×D523)⋊C4C2212yes—
29(C2×D523)⋊C4C2212yes—
30(C2×D523)⋊C4C2212yescomplemented
31C4×Dic523C2212yescomplemented
32C2×D4×C523C2211yescharacteristic
33C22×C4×C523C2211yescharacteristic
34C4⋊C4×C523C2212yescomplemented
35C22⋊C4×C523C2211yescharacteristic
36C22⋊C4×C523C2212yescomplemented
37C22×D523—22no—
38C22×D523—24no—
39C22×D523C2311yescharacteristic
40C22×D523C2312yes—
41Dic1046—22no—
42D2092—24no—
43C22⋊D523—22no—
44C22⋊D523—24no—
45C22⋊D523—22no—
46C2×Dic523—22no—
47C2×Dic523D414yescomplemented
48C2×Dic523C2312yes—
49C2×Dic523C2311yescharacteristic
50C2×Dic523C2311yescharacteristic
51C2×Dic523C2311yescharacteristic
52C4×D523—24no—
53C4×D523—24no—
54C4×D523—22no—
55C23×C523C2311yescharacteristic
56C23×C523C2311yescharacteristic
57D4×C523—22no—
58C2×C4×C523—22no—
59C2×C4×C523C2312yes—
60C2×C4×C523C2312yes—
61C2×C4×C523C2311yescharacteristic
62C22×C523—22no—
63C22×C523—21no—
64C22×C523—22no—
65C22×C523C2×D412yes—
66C22×C523C2411yescharacteristic
67C2×D523—28no—
68C2×D523—22no—
69C2×D523—22no—
70C2×D523—21no—
71C2×D523—22no—
72C2×D523#4114yescomplemented
73C4×C523—22no—
74C4×C523—21no—
75C4×C523—22no—
76Dic523—21no—
77Dic523—22no—
78Dic523C2×D412yes—
79Dic523C2×D412yes—
80C2×C523—22no—
81C2×C523—41no—
82C2×C523C22×D411yescharacteristic
83C2×C523C2×#4112yes—
84D523—24no—
85D523—41no—
86C523#52511yescharacteristic, complemented, Sylow
87#525—5231nomaximal, Sylow
88C2×#41—5231no—
89C23×C4—5231no—
90#123—5231no—
91#123D52311yescharacteristic, complemented
92C22⋊Q8—5232no—
93#121—5232no—
94#120—5231no—
95#120—5231no—
96C4×D4—5232no—
97C4×D4—5232no—
98#117—5231no—
99C24—5231no—
100#41—10464no—
101C2×Q8—5231no—
102C2×D4—5232no—
103C2×D4—5231no—
104C2×D4—5231no—
105C2×D4—5232no—
106C2×D4C2×D52311yescharacteristic
107C22×C4—5231no—
108C22×C4—5231no—
109C22×C4—5232no—
110C22×C4—5232no—
111C22×C4—5231no—
112C22×C4—10464no—
113C22×C4C2×D52311yescharacteristic
114C4⋊C4—5232no—
115C4⋊C4—5232no—
116C4⋊C4C2×D52312yescomplemented
117C22⋊C4—5231no—
118C22⋊C4—5232no—
119C22⋊C4—5232no—
120C22⋊C4—5232no—
121C22⋊C4C2×D52311yescharacteristic
122C22⋊C4C2×D52312yescomplemented
123C42—5232no—
124C23—5232no—
125C23—5231no—
126C23—10464no—
127C23—10462no—
128C23C22×D52311yescharacteristic
129C23C22×D52311yescharacteristic
130Q8—10462no—
131D4—22no—
132D4—10464no—
133D4—10462no—
134D4—10464no—
135D4—10462no—
136C2×C4—22no—
137C2×C4—5234no—
138C2×C4—5231no—
139C2×C4—5231no—
140C2×C4—5232no—
141C2×C4—5231no—
142C2×C4—10464no—
143C2×C4—10464no—
144C2×C4—10462no—
145C2×C4—10462no—
146C2×C4C22×D52312yes—
147C2×C4C22×D52311yescharacteristic
148C2×C4C22×D52312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—5234no—
153C22—10468no—
154C22—10462no—
155C22—10462no—
156C22—10461no—
157C22—10462no—
158C22D4×D52312yes—
159C22C23×D52311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—5232no—
164C4—5232no—
165C4—10461no—
166C4—10462no—
167C2—22no—
168C2—41no—
169C2—10464no—
170C2—20921no—
171C2C2×D4×D52311yescharacteristic
172C2#41×D52312yes—
subgroupG/H
center, FrattiniC22C23×D523
commutator, socle, cosocleC22×C523C24
Fitting#123×C523C2
hypercenter#123D523
hypocenterC523#525
LCSG ▷ C22×C523 ▷ C523
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#22552640C2semidirect
2. C22×C4×D523C2semidirect
3. #30660356C2semidirect
4. #30660351C2semidirect
5. #30660346C2semidirect
6. #30660343C2semidirect
7. #30660341C2semidirect
8. #30660335C2semidirect
9. (C22⋊D523)⋊C4C2semidirect
10. #30660329C2semidirect
11. #123×C523C2semidirect
14. C2×Dic1046C22semidirect
18. C2×C22⋊D523C22semidirect
20. C22×Dic523C22semidirect
24. C2×C4×D523C22semidirect
25. Dic523⋊C4C22semidirect
26. Dic523⋊C4C22semidirect
30. (C2×D523)⋊C4C22semidirect
31. C4×Dic523C22semidirect
34. C4⋊C4×C523C22semidirect
36. C22⋊C4×C523C22semidirect
47. C2×Dic523D4semidirect
72. C2×D523#41semidirect
86. C523#525semidirect
91. #123D523semidirect
116. C4⋊C4C2×D523semidirect
122. C22⋊C4C2×D523semidirect

Maximal subgroups

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

subgroupindex
C2×#225526402
C22×C4×D5232
#306603562
#306603512
#306603462
#306603432
#306603412
#306603352
(C22⋊D523)⋊C42
#306603292
#123×C5232
#525523