Finite Group Databasebeta

← #38734742

Subgroups — #38734742

Order 24896.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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
2C2×D4×D389C211yesmaximal, characteristic, complemented
3#27159366C212yesmaximal, complemented
4#27159360C211yesmaximal, characteristic, complemented
5#27159357C212yesmaximal, complemented
6#27159355C211yesmaximal, characteristic, complemented
7#27159354C212yesmaximal, complemented
8C4×D1556C211yesmaximal, characteristic, complemented
9C4×D1556C211yesmaximal, characteristic, complemented
10C22⋊C4×D389C212yesmaximal, complemented
11#124×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yes—
13#20261967—24no—
14C2×D1556C2211yescharacteristic
15C2×D1556C2211yescharacteristic
16C2×D1556C2212yescomplemented
17C2×C22⋊D389C2212yes—
18C2×C22⋊D389C2212yescomplemented
19D4×D389—24no—
20C2×C4×D389C2211yescharacteristic
21C2×C4×D389C2212yescomplemented
22C2×C4×D389C2211yescharacteristic, complemented
23C2×C4×D389C2212yescomplemented
24C4⋊Dic389C2211yescharacteristic, complemented
25C4⋊Dic389C2211yescharacteristic, complemented
26#20261945C2212yescomplemented
27C22⋊Dic389C2212yescomplemented
28#20261943C2211yescharacteristic
29#20261943C2212yes—
30#20261943C2212yescomplemented
31#20261943C2211yescharacteristic, complemented
32C2×Q8×C389C2211yescharacteristic, complemented
33C2×D4×C389C2211yescharacteristic
34C22⋊C4×C389C2212yescomplemented
35C22⋊C4×C389C2212yescomplemented
36C42×C389C2211yescharacteristic, complemented
37C22×D389—24no—
38C22×D389—24no—
39C22×D389—42no—
40C22×D389C2311yescharacteristic
41C22×D389C2312yes—
42C22×D389C2311yescharacteristic
43D1556—24no—
44D1556—22no—
45D1556D414yescomplemented
46C22⋊D389—24no—
47C22⋊D389—42no—
48C2×Dic389C2312yes—
49C2×Dic389C2311yescharacteristic
50C2×Dic389C2311yescharacteristic
51C4×D389—24no—
52C4×D389—22no—
53C4×D389—22no—
54C4×D389—42no—
55C23×C389C2312yes—
56Q8×C389—22no—
57D4×C389—22no—
58C2×C4×C389C2311yescharacteristic
59C2×C4×C389C2311yescharacteristic
60C2×C4×C389C2312yes—
61C2×C4×C389C2311yescharacteristic
62C22×C389—22no—
63C22×C389—22no—
64C22×C389—22no—
65C22×C389C2411yescharacteristic
66C2×D389—21no—
67C2×D389—22no—
68C2×D389—21no—
69C2×D389—22no—
70C2×D389—21no—
71C2×D389—21no—
72C2×D389—21no—
73C2×D389—48no—
74C2×D389C2×D414yes—
75C2×D389#4112yescomplemented
76C4×C389—22no—
77C4×C389—21no—
78C4×C389—21no—
79C4×C389C2×D412yes—
80Dic389—21no—
81Dic389—21no—
82Dic389—22no—
83C2×C389—42no—
84C2×C389C22×D411yescharacteristic
85C2×C389C2×#4111yescharacteristic
86C2×C389H(5,𝔽2)11yescharacteristic
87D389—22no—
88D389—24no—
89D389—41no—
90C389#54611yescharacteristic, complemented, Sylow
91#546—3891nomaximal, Sylow
92C2×#41—3891no—
93C22×D4—3891no—
94#124D38911yescharacteristic, complemented
95#123—3892no—
96C22⋊Q8—3891no—
97#121—3891no—
98#121—3892no—
99#120—3892no—
100C4×D4—3891no—
101C4×D4—3891no—
102C2×C22⋊C4—3892no—
103C24—3892no—
104#41—7784no—
105C2×Q8C2×D38911yescharacteristic, complemented
106C2×D4—7784no—
107C2×D4—3892no—
108C2×D4—3892no—
109C2×D4—3891no—
110C2×D4—3892no—
111C2×D4—3891no—
112C2×D4C2×D38911yescharacteristic
113C22×C4—3891no—
114C22×C4—3892no—
115C22×C4—3891no—
116C22×C4—3892no—
117C4⋊C4—3892no—
118C4⋊C4—3891no—
119C4⋊C4—3891no—
120C22⋊C4—3892no—
121C22⋊C4—3891no—
122C22⋊C4—3892no—
123C22⋊C4—3892no—
124C22⋊C4—3891no—
125C22⋊C4C2×D38912yescomplemented
126C22⋊C4C2×D38912yescomplemented
127C42C2×D38911yescharacteristic, complemented
128C23—7784no—
129C23—7784no—
130C23—15562no—
131C23—3891no—
132C23—3891no—
133C23—3892no—
134C23C22×D38912yes—
135Q8—22no—
136D4—22no—
137D4—7782no—
138D4—7784no—
139D4—7784no—
140D4—15562no—
141D4—3894no—
142C2×C4—7784no—
143C2×C4—7782no—
144C2×C4—7782no—
145C2×C4—15562no—
146C2×C4—3892no—
147C2×C4—3891no—
148C2×C4—3891no—
149C2×C4C22×D38911yescharacteristic
150C2×C4C22×D38911yescharacteristic
151C2×C4C22×D38912yes—
152C2×C4C22×D38911yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—7781no—
157C22—7782no—
158C22—7782no—
159C22—7781no—
160C22—7781no—
161C22—7781no—
162C22—7781no—
163C22—15568no—
164C22—3894no—
165C22—3892no—
166C22C23×D38911yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—7781no—
171C4—7781no—
172C4—7782no—
173C4D4×D38912yes—
174C2—42no—
175C2—7782no—
176C2—7784no—
177C2—15561no—
178C2C2×D4×D38911yescharacteristic
179C2#41×D38911yescharacteristic
180C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#124×C389C2
hypercenter#124D389
hypocenterC389#546
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#20261967C2semidirect
2. C2×D4×D389C2semidirect
3. #27159366C2semidirect
4. #27159360C2semidirect
5. #27159357C2semidirect
6. #27159355C2semidirect
7. #27159354C2semidirect
8. C4×D1556C2semidirect
9. C4×D1556C2semidirect
10. C22⋊C4×D389C2semidirect
11. #124×C389C2semidirect
16. C2×D1556C22semidirect
18. C2×C22⋊D389C22semidirect
21. C2×C4×D389C22semidirect
22. C2×C4×D389C22semidirect
23. C2×C4×D389C22semidirect
24. C4⋊Dic389C22semidirect
25. C4⋊Dic389C22semidirect
26. #20261945C22semidirect
27. C22⋊Dic389C22semidirect
30. #20261943C22semidirect
31. #20261943C22semidirect
32. C2×Q8×C389C22semidirect
34. C22⋊C4×C389C22semidirect
35. C22⋊C4×C389C22semidirect
36. C42×C389C22semidirect
45. D1556D4semidirect
75. C2×D389#41semidirect
90. C389#546semidirect
94. #124D389semidirect
105. C2×Q8C2×D389semidirect
125. C22⋊C4C2×D389semidirect
126. C22⋊C4C2×D389semidirect
127. C42C2×D389semidirect

Maximal subgroups

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

subgroupindex
C2×#202619672
C2×D4×D3892
#271593662
#271593602
#271593572
#271593552
#271593542
C4×D15562
C22⋊C4×D3892
#124×C3892
#546389