Finite Group Databasebeta

← #38734607

Subgroups — #38734607

Order 24896.

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×#20261965C211yesmaximal, characteristic, complemented
2C22×C4×D389C211yesmaximal, characteristic, complemented
3#27159367C211yesmaximal, characteristic, complemented
4#27159362C212yesmaximal, complemented
5#27159357C212yesmaximal, complemented
6#27159354C211yesmaximal, characteristic, complemented
7#27159352C211yesmaximal, characteristic, complemented
8#27159346C212yesmaximal, complemented
9#27159344C212yesmaximal, complemented
10#27159340C211yesmaximal, characteristic, complemented
11#123×C389C211yesmaximal, characteristic, complemented
12C23×D389C2211yescharacteristic
13#20261965—24no—
14C2×Dic778C2211yescharacteristic, complemented
15C2×D1556C2212yes—
16C2×C22⋊D389C2212yes—
17C2×C22⋊D389C2211yescharacteristic
18C2×C22⋊D389C2211yescharacteristic, complemented
19C22×Dic389C2211yescharacteristic
20C22×Dic389C2211yescharacteristic, complemented
21C2×C4×D389—24no—
22C2×C4×D389C2212yes—
23C2×C4×D389C2212yes—
24C2×C4×D389C2211yescharacteristic, complemented
25#20261945C2212yescomplemented
26#20261945C2212yescomplemented
27C22⋊Dic389C2211yescharacteristic
28#20261943C2212yes—
29#20261943C2212yes—
30#20261943C2212yescomplemented
31C4×Dic389C2212yescomplemented
32C2×D4×C389C2211yescharacteristic
33C22×C4×C389C2211yescharacteristic
34C4⋊C4×C389C2212yescomplemented
35C22⋊C4×C389C2211yescharacteristic
36C22⋊C4×C389C2212yescomplemented
37C22×D389—22no—
38C22×D389—24no—
39C22×D389C2311yescharacteristic
40C22×D389C2312yes—
41Dic778—22no—
42D1556—24no—
43C22⋊D389—22no—
44C22⋊D389—24no—
45C22⋊D389—22no—
46C2×Dic389—22no—
47C2×Dic389D414yescomplemented
48C2×Dic389C2312yes—
49C2×Dic389C2311yescharacteristic
50C2×Dic389C2311yescharacteristic
51C2×Dic389C2311yescharacteristic
52C4×D389—24no—
53C4×D389—24no—
54C4×D389—22no—
55C23×C389C2311yescharacteristic
56C23×C389C2311yescharacteristic
57D4×C389—22no—
58C2×C4×C389—22no—
59C2×C4×C389C2312yes—
60C2×C4×C389C2312yes—
61C2×C4×C389C2311yescharacteristic
62C22×C389—22no—
63C22×C389—21no—
64C22×C389—22no—
65C22×C389C2×D412yes—
66C22×C389C2411yescharacteristic
67C2×D389—28no—
68C2×D389—22no—
69C2×D389—22no—
70C2×D389—21no—
71C2×D389—22no—
72C2×D389#4114yescomplemented
73C4×C389—21no—
74C4×C389—22no—
75C4×C389—22no—
76Dic389—21no—
77Dic389—22no—
78Dic389C2×D412yes—
79Dic389C2×D412yes—
80C2×C389—22no—
81C2×C389—41no—
82C2×C389C22×D411yescharacteristic
83C2×C389C2×#4112yes—
84D389—24no—
85D389—41no—
86C389#52511yescharacteristic, complemented, Sylow
87#525—3891nomaximal, Sylow
88C2×#41—3891no—
89C23×C4—3891no—
90#123—3891no—
91#123D38911yescharacteristic, complemented
92C22⋊Q8—3892no—
93#121—3892no—
94#120—3891no—
95#120—3891no—
96C4×D4—3892no—
97C4×D4—3892no—
98#117—3891no—
99C24—3891no—
100#41—7784no—
101C2×Q8—3891no—
102C2×D4—3892no—
103C2×D4—3891no—
104C2×D4—3891no—
105C2×D4—3892no—
106C2×D4C2×D38911yescharacteristic
107C22×C4—7784no—
108C22×C4—3891no—
109C22×C4—3892no—
110C22×C4—3892no—
111C22×C4—3891no—
112C22×C4—3891no—
113C22×C4C2×D38911yescharacteristic
114C4⋊C4—3892no—
115C4⋊C4—3892no—
116C4⋊C4C2×D38912yescomplemented
117C22⋊C4—3891no—
118C22⋊C4—3892no—
119C22⋊C4—3892no—
120C22⋊C4—3892no—
121C22⋊C4C2×D38911yescharacteristic
122C22⋊C4C2×D38912yescomplemented
123C42—3892no—
124C23—7784no—
125C23—7782no—
126C23—3891no—
127C23—3892no—
128C23C22×D38911yescharacteristic
129C23C22×D38911yescharacteristic
130Q8—7782no—
131D4—22no—
132D4—7784no—
133D4—7784no—
134D4—7782no—
135D4—7782no—
136C2×C4—22no—
137C2×C4—7784no—
138C2×C4—7784no—
139C2×C4—7782no—
140C2×C4—7782no—
141C2×C4—3892no—
142C2×C4—3891no—
143C2×C4—3894no—
144C2×C4—3891no—
145C2×C4—3891no—
146C2×C4C22×D38912yes—
147C2×C4C22×D38911yescharacteristic
148C2×C4C22×D38912yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—7788no—
153C22—7782no—
154C22—7782no—
155C22—7781no—
156C22—7782no—
157C22—3894no—
158C22D4×D38912yes—
159C22C23×D38911yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—7781no—
164C4—7782no—
165C4—3892no—
166C4—3892no—
167C2—22no—
168C2—41no—
169C2—7784no—
170C2—15561no—
171C2C2×D4×D38911yescharacteristic
172C2#41×D38912yes—
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#123×C389C2
hypercenter#123D389
hypocenterC389#525
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#20261965C2semidirect
2. C22×C4×D389C2semidirect
3. #27159367C2semidirect
4. #27159362C2semidirect
5. #27159357C2semidirect
6. #27159354C2semidirect
7. #27159352C2semidirect
8. #27159346C2semidirect
9. #27159344C2semidirect
10. #27159340C2semidirect
11. #123×C389C2semidirect
14. C2×Dic778C22semidirect
18. C2×C22⋊D389C22semidirect
20. C22×Dic389C22semidirect
24. C2×C4×D389C22semidirect
25. #20261945C22semidirect
26. #20261945C22semidirect
30. #20261943C22semidirect
31. C4×Dic389C22semidirect
34. C4⋊C4×C389C22semidirect
36. C22⋊C4×C389C22semidirect
47. C2×Dic389D4semidirect
72. C2×D389#41semidirect
86. C389#525semidirect
91. #123D389semidirect
116. C4⋊C4C2×D389semidirect
122. C22⋊C4C2×D389semidirect

Maximal subgroups

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

subgroupindex
C2×#202619652
C22×C4×D3892
#271593672
#271593622
#271593572
#271593542
#271593522
#271593462
#271593442
#271593402
#123×C3892
#525389