Finite Group Databasebeta

← #46855514

Subgroups — #46855514

Order 35008.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22576777C211yesmaximal, characteristic, complemented
2C22×C4×D547C211yesmaximal, characteristic, complemented
3#31775987C212yesmaximal, complemented
4#31775978C211yesmaximal, characteristic, complemented
5#31775977C211yesmaximal, characteristic, complemented
6#31775976C211yesmaximal, characteristic, complemented
7#31775972C212yesmaximal, complemented
8#31775964C212yesmaximal, complemented
9(C22⋊D547)⋊C4C212yesmaximal, complemented
10#31775960C211yesmaximal, characteristic, complemented
11C22⋊Q8×C547C211yesmaximal, characteristic, complemented
12C23×D547C2211yescharacteristic
13#22576777—24no—
14C2×D2188C2212yes—
15C2×D2188C2212yes—
16C2×D2188C2211yescharacteristic, complemented
17C2×C22⋊D547C2212yes—
18C22×Dic547C2211yescharacteristic
19C2×C4×D547—24no—
20C2×C4×D547C2211yescharacteristic
21C2×C4×D547C2211yescharacteristic
22C2×C4×D547C2211yescharacteristic
23C2×C4×D547C2211yescharacteristic
24C2×C4×D547C2212yescomplemented
25C4⋊Dic547C2211yescharacteristic, complemented
26Dic547⋊C4C2212yescomplemented
27(C2×D547)⋊C4C2212yes—
28(C2×D547)⋊C4C2212yes—
29(C2×D547)⋊C4C2212yescomplemented
30(C2×D547)⋊C4C2212yescomplemented
31C4×Dic547C2212yescomplemented
32C2×Q8×C547C2211yescharacteristic, complemented
33C22×C4×C547C2211yescharacteristic
34C4⋊C4×C547C2211yescharacteristic, complemented
35C4⋊C4×C547C2212yescomplemented
36C22⋊C4×C547C2212yes—
37C22×D547—22no—
38C22×D547—22no—
39C22×D547—22no—
40C22×D547C2312yes—
41C22×D547C2311yescharacteristic
42C22×D547C2311yescharacteristic
43D2188—24no—
44D2188—24no—
45D2188—22no—
46C22⋊D547—24no—
47C2×Dic547—22no—
48C2×Dic547C2312yes—
49C2×Dic547C2311yescharacteristic
50C2×Dic547C2311yescharacteristic
51C4×D547—22no—
52C4×D547—22no—
53C4×D547—22no—
54C4×D547—24no—
55C4×D547D414yescomplemented
56C23×C547C2311yescharacteristic
57Q8×C547—22no—
58C2×C4×C547—22no—
59C2×C4×C547C2312yes—
60C2×C4×C547C2312yes—
61C2×C4×C547C2311yescharacteristic
62C2×C4×C547C2311yescharacteristic
63C22×C547—21no—
64C22×C547—21no—
65C22×C547#4112yescomplemented
66C22×C547C2411yescharacteristic
67C2×D547—28no—
68C2×D547—21no—
69C2×D547—21no—
70C2×D547—21no—
71C2×D547—21no—
72C2×D547—22no—
73C2×D547—22no—
74C2×D547—22no—
75C2×D547C2×D412yes—
76C2×D547#4112yescomplemented
77C4×C547—21no—
78C4×C547—22no—
79C4×C547—22no—
80C4×C547C2×D412yes—
81Dic547—21no—
82Dic547—22no—
83Dic547C2×D412yes—
84C2×C547—22no—
85C2×C547C22×D411yescharacteristic
86C2×C547C2×#4111yescharacteristic
87C2×C547C2×#4111yescharacteristic
88D547—22no—
89D547—22no—
90D547—42no—
91C547#52511yescharacteristic, complemented, Sylow
92#525—5471nomaximal, Sylow
93C2×#41—5471no—
94C23×C4—5471no—
95#123—5472no—
96C22⋊Q8—5471no—
97C22⋊Q8D54711yescharacteristic, complemented
98#121—5471no—
99#121—5471no—
100#120—5472no—
101C4×D4—5472no—
102C4×D4—5472no—
103#117—5471no—
104C24—5471no—
105#41—10944no—
106C2×Q8C2×D54711yescharacteristic, complemented
107C2×D4—5472no—
108C2×D4—5472no—
109C2×D4—5472no—
110C2×D4—5471no—
111C22×C4—5471no—
112C22×C4—5471no—
113C22×C4—5471no—
114C22×C4—5472no—
115C22×C4—5471no—
116C22×C4—5471no—
117C22×C4—10944no—
118C22×C4C2×D54711yescharacteristic
119C4⋊C4—5472no—
120C4⋊C4—5471no—
121C4⋊C4C2×D54711yescharacteristic, complemented
122C4⋊C4C2×D54712yescomplemented
123C22⋊C4—5472no—
124C22⋊C4—5472no—
125C22⋊C4—5472no—
126C22⋊C4—5472no—
127C22⋊C4C2×D54712yes—
128C42—5472no—
129C23—5471no—
130C23—5471no—
131C23—5472no—
132C23—10942no—
133C23—10942no—
134C23—10942no—
135C23C22×D54711yescharacteristic
136Q8—22no—
137D4—10944no—
138D4—10944no—
139D4—10944no—
140D4—10942no—
141C2×C4—22no—
142C2×C4—5471no—
143C2×C4—5474no—
144C2×C4—5472no—
145C2×C4—5471no—
146C2×C4—10942no—
147C2×C4—10944no—
148C2×C4—10942no—
149C2×C4—10942no—
150C2×C4—10942no—
151C2×C4C22×D54712yes—
152C2×C4C22×D54711yescharacteristic
153C2×C4C22×D54712yes—
154C2×C4C22×D54711yescharacteristic
155C22—21no—
156C22—21no—
157C22—5472no—
158C22—5472no—
159C22—10948no—
160C22—10941no—
161C22—10941no—
162C22—10941no—
163C22—10941no—
164C22—10942no—
165C22—10942no—
166C22—10942no—
167C22#2257677712yescomplemented
168C22C23×D54711yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—5472no—
173C4—10941no—
174C4—10942no—
175C4D4×D54712yes—
176C2—22no—
177C2—10942no—
178C2—10942no—
179C2—21882no—
180C2C2×D4×D54711yescharacteristic
181C2#41×D54711yescharacteristic
182C2C2×#2257677711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D547
commutator, socle, cosocleC22×C547C24
FittingC22⋊Q8×C547C2
hypercenterC22⋊Q8D547
hypocenterC547#525
LCSG ▷ C22×C547 ▷ C547
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#22576777C2semidirect
2. C22×C4×D547C2semidirect
3. #31775987C2semidirect
4. #31775978C2semidirect
5. #31775977C2semidirect
6. #31775976C2semidirect
7. #31775972C2semidirect
8. #31775964C2semidirect
9. (C22⋊D547)⋊C4C2semidirect
10. #31775960C2semidirect
11. C22⋊Q8×C547C2semidirect
16. C2×D2188C22semidirect
24. C2×C4×D547C22semidirect
25. C4⋊Dic547C22semidirect
26. Dic547⋊C4C22semidirect
29. (C2×D547)⋊C4C22semidirect
30. (C2×D547)⋊C4C22semidirect
31. C4×Dic547C22semidirect
32. C2×Q8×C547C22semidirect
34. C4⋊C4×C547C22semidirect
35. C4⋊C4×C547C22semidirect
55. C4×D547D4semidirect
65. C22×C547#41semidirect
76. C2×D547#41semidirect
91. C547#525semidirect
97. C22⋊Q8D547semidirect
106. C2×Q8C2×D547semidirect
121. C4⋊C4C2×D547semidirect
122. C4⋊C4C2×D547semidirect
167. C22#22576777semidirect

Maximal subgroups

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

subgroupindex
C2×#225767772
C22×C4×D5472
#317759872
#317759782
#317759772
#317759762
#317759722
#317759642
(C22⋊D547)⋊C42
#317759602
C22⋊Q8×C5472
#525547