Finite Group Databasebeta

← #38734612

Subgroups — #38734612

Order 24896.

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×#20261967C211yesmaximal, characteristic, complemented
2C22×C4×D389C211yesmaximal, characteristic, complemented
3#27159369C212yesmaximal, complemented
4#27159360C211yesmaximal, characteristic, complemented
5#27159359C211yesmaximal, characteristic, complemented
6#27159358C211yesmaximal, characteristic, complemented
7#27159354C212yesmaximal, complemented
8#27159346C212yesmaximal, complemented
9#27159344C212yesmaximal, complemented
10#27159342C211yesmaximal, characteristic, complemented
11C22⋊Q8×C389C211yesmaximal, characteristic, complemented
12C23×D389C2211yescharacteristic
13#20261967—24no—
14C2×D1556C2212yes—
15C2×D1556C2212yes—
16C2×D1556C2211yescharacteristic, complemented
17C2×C22⋊D389C2212yes—
18C22×Dic389C2211yescharacteristic
19C2×C4×D389—24no—
20C2×C4×D389C2211yescharacteristic
21C2×C4×D389C2211yescharacteristic
22C2×C4×D389C2211yescharacteristic
23C2×C4×D389C2211yescharacteristic
24C2×C4×D389C2212yescomplemented
25C4⋊Dic389C2211yescharacteristic, complemented
26#20261945C2212yescomplemented
27#20261943C2212yes—
28#20261943C2212yes—
29#20261943C2212yescomplemented
30#20261943C2212yescomplemented
31C4×Dic389C2212yescomplemented
32C2×Q8×C389C2211yescharacteristic, complemented
33C22×C4×C389C2211yescharacteristic
34C4⋊C4×C389C2211yescharacteristic, complemented
35C4⋊C4×C389C2212yescomplemented
36C22⋊C4×C389C2212yes—
37C22×D389—22no—
38C22×D389—22no—
39C22×D389—22no—
40C22×D389C2312yes—
41C22×D389C2311yescharacteristic
42C22×D389C2311yescharacteristic
43D1556—24no—
44D1556—24no—
45D1556—22no—
46C22⋊D389—24no—
47C2×Dic389—22no—
48C2×Dic389C2312yes—
49C2×Dic389C2311yescharacteristic
50C2×Dic389C2311yescharacteristic
51C4×D389—22no—
52C4×D389—22no—
53C4×D389—22no—
54C4×D389—24no—
55C4×D389D414yescomplemented
56C23×C389C2311yescharacteristic
57Q8×C389—22no—
58C2×C4×C389—22no—
59C2×C4×C389C2312yes—
60C2×C4×C389C2312yes—
61C2×C4×C389C2311yescharacteristic
62C2×C4×C389C2311yescharacteristic
63C22×C389—21no—
64C22×C389—21no—
65C22×C389#4112yescomplemented
66C22×C389C2411yescharacteristic
67C2×D389—28no—
68C2×D389—21no—
69C2×D389—21no—
70C2×D389—21no—
71C2×D389—21no—
72C2×D389—22no—
73C2×D389—22no—
74C2×D389—22no—
75C2×D389C2×D412yes—
76C2×D389#4112yescomplemented
77C4×C389—22no—
78C4×C389—21no—
79C4×C389—22no—
80C4×C389C2×D412yes—
81Dic389—21no—
82Dic389—22no—
83Dic389C2×D412yes—
84C2×C389—22no—
85C2×C389C22×D411yescharacteristic
86C2×C389C2×#4111yescharacteristic
87C2×C389C2×#4111yescharacteristic
88D389—22no—
89D389—22no—
90D389—42no—
91C389#52511yescharacteristic, complemented, Sylow
92#525—3891nomaximal, Sylow
93C2×#41—3891no—
94C23×C4—3891no—
95#123—3892no—
96C22⋊Q8—3891no—
97C22⋊Q8D38911yescharacteristic, complemented
98#121—3891no—
99#121—3891no—
100#120—3892no—
101C4×D4—3892no—
102C4×D4—3892no—
103#117—3891no—
104C24—3891no—
105#41—7784no—
106C2×Q8C2×D38911yescharacteristic, complemented
107C2×D4—3892no—
108C2×D4—3892no—
109C2×D4—3892no—
110C2×D4—3891no—
111C22×C4—7784no—
112C22×C4—3891no—
113C22×C4—3891no—
114C22×C4—3891no—
115C22×C4—3891no—
116C22×C4—3892no—
117C22×C4—3891no—
118C22×C4C2×D38911yescharacteristic
119C4⋊C4—3892no—
120C4⋊C4—3891no—
121C4⋊C4C2×D38911yescharacteristic, complemented
122C4⋊C4C2×D38912yescomplemented
123C22⋊C4—3892no—
124C22⋊C4—3892no—
125C22⋊C4—3892no—
126C22⋊C4—3892no—
127C22⋊C4C2×D38912yes—
128C42—3892no—
129C23—7782no—
130C23—7782no—
131C23—7782no—
132C23—3892no—
133C23—3891no—
134C23—3891no—
135C23C22×D38911yescharacteristic
136Q8—22no—
137D4—7784no—
138D4—7784no—
139D4—7784no—
140D4—7782no—
141C2×C4—22no—
142C2×C4—7782no—
143C2×C4—7782no—
144C2×C4—7784no—
145C2×C4—7782no—
146C2×C4—7782no—
147C2×C4—3892no—
148C2×C4—3891no—
149C2×C4—3891no—
150C2×C4—3894no—
151C2×C4C22×D38912yes—
152C2×C4C22×D38911yescharacteristic
153C2×C4C22×D38912yes—
154C2×C4C22×D38911yescharacteristic
155C22—21no—
156C22—21no—
157C22—7788no—
158C22—7781no—
159C22—7781no—
160C22—7781no—
161C22—7781no—
162C22—7782no—
163C22—7782no—
164C22—7782no—
165C22—3892no—
166C22—3892no—
167C22#2026196712yescomplemented
168C22C23×D38911yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—7781no—
173C4—7782no—
174C4—3892no—
175C4D4×D38912yes—
176C2—22no—
177C2—7782no—
178C2—7782no—
179C2—15562no—
180C2C2×D4×D38911yescharacteristic
181C2#41×D38911yescharacteristic
182C2C2×#2026196711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
FittingC22⋊Q8×C389C2
hypercenterC22⋊Q8D389
hypocenterC389#525
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#20261967C2semidirect
2. C22×C4×D389C2semidirect
3. #27159369C2semidirect
4. #27159360C2semidirect
5. #27159359C2semidirect
6. #27159358C2semidirect
7. #27159354C2semidirect
8. #27159346C2semidirect
9. #27159344C2semidirect
10. #27159342C2semidirect
11. C22⋊Q8×C389C2semidirect
16. C2×D1556C22semidirect
24. C2×C4×D389C22semidirect
25. C4⋊Dic389C22semidirect
26. #20261945C22semidirect
29. #20261943C22semidirect
30. #20261943C22semidirect
31. C4×Dic389C22semidirect
32. C2×Q8×C389C22semidirect
34. C4⋊C4×C389C22semidirect
35. C4⋊C4×C389C22semidirect
55. C4×D389D4semidirect
65. C22×C389#41semidirect
76. C2×D389#41semidirect
91. C389#525semidirect
97. C22⋊Q8D389semidirect
106. C2×Q8C2×D389semidirect
121. C4⋊C4C2×D389semidirect
122. C4⋊C4C2×D389semidirect
167. C22#20261967semidirect

Maximal subgroups

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

subgroupindex
C2×#202619672
C22×C4×D3892
#271593692
#271593602
#271593592
#271593582
#271593542
#271593462
#271593442
#271593422
C22⋊Q8×C3892
#525389