Finite Group Databasebeta

← #15683194

Subgroups — #15683194

Order 2944.

440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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
1#13092974C211yesmaximal, characteristic, complemented
2#13092717C214yesmaximal, complemented
3#13092707C212yesmaximal, complemented
4#13092697C212yesmaximal, complemented
5#13092457C212yesmaximal, complemented
6#13092441C211yesmaximal, characteristic, complemented
7#13092422C212yesmaximal
8C2×C4×D4×C23C211yesmaximal, characteristic
9C22×D4×C23C2211yescharacteristic
10C23×C4×C23—21no—
11C4×D4×C23—21no—
12C4×D4×C23—21no—
13C4×D4×C23C2212yes—
14C4×D4×C23C2212yes—
15C2×C4⋊C4×C23C2211yescharacteristic
16C2×C22⋊C4×C23—21no—
17C2×C42×C23C2211yescharacteristic
18#10625097C2212yes—
19#10625095—21no—
20#10625095—21no—
21C2×#67267C2212yes—
22#10625041C2212yescomplemented
23#10625040C2211yescharacteristic, complemented
24#10625040C2211yescharacteristic, complemented
25C4×Dic46—21no—
26C4×Dic46—21no—
27#10625014C2214yes—
28#10625014C2214yes—
29#10624990C2214yescomplemented
30#10624989C2214yescomplemented
31C4⋊(C23⋊C8)C2212yescomplemented
32C4⋊(C23⋊C8)C2212yescomplemented
33C24×C23—21no—
34C2×D4×C23—21no—
35C2×D4×C23—22no—
36C2×D4×C23Q814yescomplemented
37C2×D4×C23C2312yes—
38C22×C4×C23—21no—
39C22×C4×C23—22no—
40C22×C4×C23—22no—
41C22×C4×C23—44no—
42C22×C4×C23D411yescharacteristic
43C22×C4×C23D411yescharacteristic
44C22×C4×C23C2311yescharacteristic
45C2×Dic46—21no—
46C2×Dic46—21no—
47C4⋊C4×C23—21no—
48C4⋊C4×C23C2312yes—
49C22⋊C4×C23—22no—
50C22⋊C4×C23—22no—
51C42×C23D411yescharacteristic
52C42×C23D411yescharacteristic
53C42×C23C2311yescharacteristic
54C42×C23C2311yescharacteristic
55C22⋊Dic23—22no—
56C4⋊Dic23—21no—
57C4⋊Dic23—21no—
58C4⋊Dic23C2312yes—
59C4⋊Dic23C2312yes—
60Dic23⋊C4—22no—
61Dic23⋊C4—22no—
62C4×Dic23—22no—
63#67267—24no—
64C2×C23⋊C8C2314yes—
65C23×C23—24no—
66C23×C23—22no—
67C23×C23—42no—
68C23×C23—42no—
69C23×C23C2×D411yescharacteristic
70D4×C23—24no—
71D4×C23—22no—
72D4×C23C2×Q814yes—
73C2×C4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23—41no—
76C2×C4×C23—44no—
77C2×C4×C23—42no—
78C2×C4×C23—44no—
79C2×C4×C23C2×D411yescharacteristic
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2×Q812yes—
85C2×C4×C23#4112yes—
86C2×C4×C23C2411yescharacteristic
87C2×Dic23—22no—
88C2×Dic23—22no—
89Dic46—42no—
90Dic46—42no—
91C23⋊C8—24no—
92#3077—231nomaximal, Sylow
93C22×C23—21no—
94C22×C23—21no—
95C22×C23—24no—
96C22×C23—48no—
97C22×C23—42no—
98C22×C23—42no—
99C22×C23C22⋊Q812yes—
100C22×C23C22×D411yescharacteristic
101C4×C23—21no—
102C4×C23—21no—
103C4×C23—21no—
104C4×C23—42no—
105C4×C23C22⋊Q812yes—
106C4×C23AGL(1,ℤ/8)12yes—
107C4×C23C22×Q811yescharacteristic
108C4×C23C2×#4111yescharacteristic
109Dic23—42no—
110Dic23—42no—
111#533—231no—
112C2×C4×D4D2311yescharacteristic
113#478—234no—
114#476—232no—
115#474—232no—
116#428—232no—
117#423—231no—
118#418—232no—
119C2×C23—22no—
120C2×C23—44no—
121C2×C23C2×C22⋊Q811yescharacteristic
122C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C23#57511yescharacteristic
124C22×D4C2×D2311yescharacteristic
125C23×C4—21no—
126C2×M16—232no—
127C4⋊Q8—231no—
128C4⋊Q8—231no—
129#125—232no—
130C22⋊Q8—461no—
131C22⋊Q8—461no—
132C4×Q8—461no—
133C4×Q8—461no—
134C4×D4—21no—
135C4×D4—21no—
136C4×D4C2×D2312yes—
137C4×D4C2×D2312yes—
138#117—232no—
139C2×C4⋊C4C2×D2311yescharacteristic
140C2×C22⋊C4—21no—
141C2×C42C2×D2311yescharacteristic
142#107—234no—
143#106—234no—
144C4⋊C8—232no—
145C4⋊C8—232no—
146#102—234no—
147#102—234no—
148C23#307711yescharacteristic, complemented, Sylow
149C24—21no—
150C2×Q8—461no—
151C2×Q8—461no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4Dic4614yescomplemented
155C2×D4C22×D2312yes—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—44no—
160C22×C4C22⋊D2311yescharacteristic
161C22×C4C22⋊D2311yescharacteristic
162C22×C4C22×D2311yescharacteristic
163M16—464no—
164C2×C8—234no—
165C4⋊C4—21no—
166C4⋊C4—232no—
167C4⋊C4—232no—
168C4⋊C4—462no—
169C4⋊C4—462no—
170C4⋊C4—461no—
171C4⋊C4—461no—
172C4⋊C4C22×D2312yes—
173C22⋊C4—22no—
174C22⋊C4—22no—
175C22⋊C4—462no—
176C42—462no—
177C42C22⋊D2311yescharacteristic
178C42C22⋊D2311yescharacteristic
179C42C22×D2311yescharacteristic
180C42C22×D2311yescharacteristic
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23C2×C22⋊D2311yescharacteristic
186Q8—922no—
187Q8—922no—
188D4—24no—
189D4—22no—
190D4C2×Dic4614yes—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—462no—
198C2×C4—462no—
199C2×C4C2×Dic4612yes—
200C2×C4#6728812yes—
201C2×C4C2×C22⋊D2311yescharacteristic
202C2×C4C2×C22⋊D2311yescharacteristic
203C2×C4C2×C22⋊D2311yescharacteristic
204C2×C4C2×C22⋊D2311yescharacteristic
205C2×C4C2×C22⋊D2311yescharacteristic
206C2×C4C23×D2311yescharacteristic
207C8—464no—
208C22—21no—
209C22—21no—
210C22—24no—
211C22—48no—
212C22—42no—
213C22—42no—
214C22#1062509512yes—
215C22C22×C22⋊D2311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—922no—
221C4—922no—
222C4#1062509512yes—
223C4#1062510312yes—
224C4C22×Dic4611yescharacteristic
225C4C2×#6728811yescharacteristic
226C2—22no—
227C2—44no—
228C2C2×#1062509511yescharacteristic
229C2C2×#1062510311yescharacteristic
230C2#1309321511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C4×D4×C23C2
socleC22×C23C22×D4
prime radicalC22×D4×C23C22
hypercenterC2×C4×D4D23
hypocenterC23#3077
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13092974C2semidirect
2. #13092717C2semidirect
3. #13092707C2semidirect
4. #13092697C2semidirect
5. #13092457C2semidirect
6. #13092441C2semidirect
22. #10625041C22semidirect
23. #10625040C22semidirect
24. #10625040C22semidirect
29. #10624990C22semidirect
30. #10624989C22semidirect
31. C4⋊(C23⋊C8)C22semidirect
32. C4⋊(C23⋊C8)C22semidirect
36. C2×D4×C23Q8semidirect
148. C23#3077semidirect
154. C2×D4Dic46semidirect

Maximal subgroups

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

subgroupindex
#130929742
#130927172
#130927072
#130926972
#130924572
#130924412
#130924222
C2×C4×D4×C232
#307723