Finite Group Databasebeta

← #15686114

Subgroups — #15686114

Order 2944.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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#13093137C211yesmaximal, characteristic, complemented
2#13093082C211yesmaximal, characteristic, complemented
3#13092775C212yesmaximal, complemented
4#13092769C211yesmaximal, characteristic, complemented
5#13092711C212yesmaximal, complemented
6#13092631C212yesmaximal
7#13092623C211yesmaximal, characteristic, complemented
8#13092544C211yesmaximal, characteristic, complemented
9#13092516C212yesmaximal, complemented
10C4×#67272C211yesmaximal, characteristic
11C23×#474C211yesmaximal, characteristic, complemented
12C2×Q8×D23—21no—
13C23×C4⋊Q8C2211yescharacteristic
14C4×D4×C23C2211yescharacteristic
15#10625117—21no—
16#10625107C2212yes—
17C2×#67272C2211yescharacteristic
18#10625097—21no—
19#10625095—21no—
20C2×#67263C2212yes—
21#10625067—22no—
22#10625064C2212yes—
23#10625059C2212yes—
24#10625058C2212yes—
25#10625050—22no—
26C4×D92C2211yescharacteristic
27#10625040C2211yescharacteristic
28C4×Dic46C2211yescharacteristic
29C23×#107C2212yes—
30C23×C4⋊C8C2211yescharacteristic
31C23×#102C2212yes—
32#10625014C2211yescharacteristic
33#10624998C2212yes—
34#10624997C2212yes—
35Dic23⋊C8C2212yes—
36#10624992C2212yes—
37#10624992C2212yes—
38#10624991C2211yescharacteristic
39#10624989C2211yescharacteristic
40C4×C23⋊C8C2211yescharacteristic
41C2×Q8×C23—21no—
42C2×D4×C23C2311yescharacteristic
43C22×C4×C23—21no—
44Q8×D23—44no—
45C2×D92C2311yescharacteristic
46C2×C4×D23—21no—
47C2×C4×D23—22no—
48C2×Dic46—22no—
49C2×Dic46D411yescharacteristic
50C2×Dic46C2312yes—
51C2×C8×C23C2312yes—
52C4⋊C4×C23—21no—
53C4⋊C4×C23C2312yes—
54C4⋊C4×C23C2311yescharacteristic
55C22⋊C4×C23—21no—
56C42×C23C2311yescharacteristic
57C22⋊Dic23—22no—
58C22⋊Dic23—22no—
59#67272—22no—
60(C2×D23)⋊C4—21no—
61(C2×D23)⋊C4—22no—
62C4⋊Dic23—21no—
63C4⋊Dic23—21no—
64C4⋊Dic23D411yescharacteristic
65C4⋊Dic23C2311yescharacteristic
66Dic23⋊C4—22no—
67Dic23⋊C4—22no—
68Dic23⋊C4D412yes—
69C4×Dic23—22no—
70C4×Dic23C2312yes—
71C2×C23⋊C8C2311yescharacteristic
72C2×C23⋊C8C2311yescharacteristic
73#67263—24no—
74C23×C23—21no—
75C22×D23—21no—
76Q8×C23—42no—
77D4×C23—21no—
78D4×C23—21no—
79C2×C4×C23—21no—
80C2×C4×C23—22no—
81C2×C4×C23—42no—
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2411yescharacteristic
85C2×Dic23—22no—
86C2×Dic23—21no—
87C2×Dic23C2×D412yes—
88C2×Dic23C2×D412yes—
89D92—21no—
90D92#4112yes—
91C4×D23—44no—
92C4×D23—42no—
93Dic46—22no—
94Dic46—22no—
95Dic46—22no—
96Dic46—44no—
97C8×C23—22no—
98C23⋊C8—21no—
99C23⋊C8—21no—
100#3367—231nomaximal, Sylow
101C22×C23—41no—
102C22×C23—41no—
103C22×C23—41no—
104C22×C23C22×D411yescharacteristic
105C2×D23—22no—
106C2×D23—41no—
107C2×D23—41no—
108C4×C23—21no—
109C4×C23—42no—
110C4×C23—41no—
111C4×C23AGL(1,ℤ/8)12yes—
112C4×C23C2×#4111yescharacteristic
113C4×C232−1+411yescharacteristic
114Dic23—22no—
115Dic23—22no—
116Dic23—42no—
117Dic23—41no—
118#556—231no—
119D4×Q8—231no—
120#489—232no—
121#487—231no—
122#477—232no—
123#474D2311yescharacteristic, complemented
124#463—232no—
125#461—231no—
126#446—231no—
127#440—232no—
128C4×D8—231no—
129C2×C23—81no—
130C2×C23#54811yescharacteristic
131C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C23#57811yescharacteristic
133D23—42no—
134C22×Q8—461no—
135C2×SD16—232no—
136C2×D8—231no—
137C4⋊Q8—232no—
138C4⋊Q8—231no—
139C4⋊Q8C2×D2311yescharacteristic
140#126—462no—
141#124—232no—
142C22⋊Q8—462no—
143C22⋊Q8—461no—
144C22⋊Q8—461no—
145C4×Q8—231no—
146C4×Q8—232no—
147C4×D4—232no—
148C4×D4—231no—
149C4×D4C2×D2311yescharacteristic
150#117—461no—
151#107—231no—
152#107C2×D2312yes—
153C4⋊C8—232no—
154C4⋊C8C2×D2311yescharacteristic
155#103—232no—
156#103—232no—
157#103—232no—
158#102—231no—
159#102—231no—
160#102C2×D2312yes—
161#97—232no—
162C4×C8—231no—
163C23#336711yescharacteristic, complemented, Sylow
164C2×Q8—21no—
165C2×Q8—231no—
166C2×Q8—232no—
167C2×Q8—462no—
168C2×Q8—924no—
169C2×D4—231no—
170C2×D4C22×D2311yescharacteristic
171C22×C4—21no—
172C22×C4—462no—
173C22×C4—461no—
174SD16—464no—
175D8—462no—
176C2×C8—231no—
177C2×C8—231no—
178C2×C8C22×D2312yes—
179C4⋊C4—21no—
180C4⋊C4—231no—
181C4⋊C4—232no—
182C4⋊C4—231no—
183C4⋊C4—462no—
184C4⋊C4—462no—
185C4⋊C4—461no—
186C4⋊C4—461no—
187C4⋊C4C22×D2311yescharacteristic
188C4⋊C4C22×D2312yes—
189C22⋊C4—21no—
190C22⋊C4—462no—
191C22⋊C4—462no—
192C22⋊C4—462no—
193C22⋊C4—461no—
194C42—232no—
195C42—462no—
196C42C22×D2311yescharacteristic
197C23—21no—
198C23—461no—
199Q8—42no—
200Q8—462no—
201Q8—462no—
202Q8—462no—
203Q8—924no—
204D4—21no—
205D4—21no—
206D4—232no—
207D4—461no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—232no—
212C2×C4—232no—
213C2×C4—462no—
214C2×C4—461no—
215C2×C4—924no—
216C2×C4—922no—
217C2×C4D4×D2311yescharacteristic
218C2×C4D4×D2311yescharacteristic
219C2×C4C23×D2311yescharacteristic
220C8—22no—
221C8—461no—
222C8—461no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—462no—
227C22—921no—
228C22—921no—
229C22C2×D4×D2311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—462no—
234C4—462no—
235C4—921no—
236C4—922no—
237C4#1062508212yes—
238C4#1062515811yescharacteristic
239C4#41×D2311yescharacteristic
240C2—81no—
241C2—922no—
242C2#1309307711yescharacteristic
243C2C2×#1062508211yescharacteristic
244C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#474C2
socleC22×C23C22×D4
prime radicalC2×#67272C22
hypercenter#474D23
hypocenterC23#3367
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #13093137C2semidirect
2. #13093082C2semidirect
3. #13092775C2semidirect
4. #13092769C2semidirect
5. #13092711C2semidirect
7. #13092623C2semidirect
8. #13092544C2semidirect
9. #13092516C2semidirect
11. C23×#474C2semidirect
123. #474D23semidirect
163. C23#3367semidirect

Maximal subgroups

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

subgroupindex
#130931372
#130930822
#130927752
#130927692
#130927112
#130926312
#130926232
#130925442
#130925162
C4×#672722
C23×#4742
#336723