Finite Group Databasebeta

← #15673622

Subgroups — #15673622

Order 2944.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#13092898C211yesmaximal, characteristic
2#13092457C211yesmaximal, characteristic, complemented
3C2×#10624987C211yesmaximal, characteristic
4#13092416C211yesmaximal, characteristic
5#13092186C211yesmaximal, characteristic, complemented
6#13092177C211yesmaximal, characteristic, complemented
7C23×#384C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C2×C4⋊C4×C23—22no—
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13C4×C22⋊D23—22no—
14#10625097C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16C2×#67267C2211yescharacteristic
17#10625064—21no—
18#10625063—21no—
19C4⋊C4×D23—21no—
20#10625058—21no—
21#10624992—21no—
22#10624991—21no—
23#10624990—21no—
24#10624989—21no—
25#10624987C414yescomplemented
26C22×C4×C23—21no—
27C22×C4×C23—21no—
28C22×C4×C23D412yes—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31#67288—21no—
32#67288—21no—
33#67288C2×C412yes—
34#67288Q812yes—
35C2×D92D411yescharacteristic
36C2×C4×D23—21no—
37C2×C4×D23—22no—
38C2×Dic46D411yescharacteristic
39C4⋊C4×C23—21no—
40C4⋊C4×C23—21no—
41C4⋊C4×C23—21no—
42C4⋊C4×C23—21no—
43C4⋊C4×C23—44no—
44C42×C23—21no—
45C42×C23C2×C412yescomplemented
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—22no—
48C4⋊Dic23D411yescharacteristic
49C4⋊Dic23D411yescharacteristic
50Dic23⋊C4—22no—
51C4×Dic23—22no—
52C4×Dic23—21no—
53#67267—21no—
54#67267—21no—
55#67267—21no—
56#67267C2×C412yescomplemented
57C2×C23⋊C8—21no—
58C2×C23⋊C8—21no—
59C23×C23C2×D411yescharacteristic
60C22×D23—21no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—22no—
65C2×C4×C23—42no—
66C2×C4×C23—42no—
67C2×C4×C23—41no—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×Q811yescharacteristic
72C2×C4×C23#4111yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C22⋊D23—22no—
75C22⋊D23—22no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79D92—21no—
80D92C4⋊C412yescomplemented
81C4×D23—22no—
82C4×D23—22no—
83C4×D23—82no—
84Dic46—21no—
85Dic46C4⋊C412yescomplemented
86C23⋊C8—22no—
87C23⋊C8—41no—
88#1859—231nomaximal, Sylow
89C22×C23—21no—
90C22×C23—21no—
91C22×C23C4×D411yescharacteristic
92C22×C23#12011yescharacteristic
93C22×C23C22⋊Q811yescharacteristic
94C2×D23—22no—
95C2×D23—41no—
96C2×D23—41no—
97C4×C23—24no—
98C4×C23—42no—
99C4×C23—81no—
100C4×C23C2×C4⋊C411yescharacteristic
101C4×C23C4×D411yescharacteristic
102C4×C23C22⋊Q811yescharacteristic
103C4×C23#12311yescharacteristic
104Dic23—22no—
105Dic23—41no—
106Dic23—41no—
107#520—231no—
108#428—231no—
109C2×#104—231no—
110#417—231no—
111#384D2311yescharacteristic, complemented
112#343—231no—
113#339—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23#38511yescharacteristic
117C2×C23#45311yescharacteristic
118C2×C23#45611yescharacteristic
119D23—42no—
120C2×#41—231no—
121C2×M16—231no—
122C2×M16—231no—
123C4×Q8—461no—
124C4×D4—461no—
125C4×D4—462no—
126#117—231no—
127#117—461no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—461no—
130C2×C4⋊C4C2×D2311yescharacteristic
131C2×C4⋊C4C2×D2311yescharacteristic
132C2×C42C2×D2311yescharacteristic
133#107—461no—
134#106—461no—
135#104—234no—
136#103—461no—
137#102—461no—
138C23#185911yescharacteristic, complemented, Sylow
139#41—232no—
140#41—232no—
141#41—461no—
142#41—461no—
143C2×Q8—231no—
144C2×D4—231no—
145C2×D4—461no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—462no—
149C22×C4—461no—
150C22×C4C22⋊D2312yes—
151C22×C4C22×D2311yescharacteristic
152M16—232no—
153M16—461no—
154M16—461no—
155M16—461no—
156C2×C8—461no—
157C2×C8—461no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—44no—
163C4⋊C4—231no—
164C4⋊C4—231no—
165C4⋊C4—462no—
166C22⋊C4—462no—
167C22⋊C4—461no—
168C42—21no—
169C42—462no—
170C42—461no—
171C42C4×D2312yescomplemented
172C23—461no—
173C23C2×C22⋊D2311yescharacteristic
174Q8—232no—
175Q8—461no—
176D4—232no—
177D4—462no—
178D4—462no—
179D4—461no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—461no—
188C2×C4—462no—
189C2×C4—462no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—1842no—
193C2×C4C2×C4×D2311yescharacteristic
194C2×C4#6728811yescharacteristic
195C2×C4D4×D2311yescharacteristic
196C2×C4D4×D2311yescharacteristic
197C2×C4Q8×D2311yescharacteristic
198C2×C4#6729211yescharacteristic
199C8—462no—
200C8—921no—
201C22—21no—
202C22—21no—
203C22—462no—
204C22—921no—
205C22—921no—
206C22C4×C22⋊D2311yescharacteristic
207C22#1062510811yescharacteristic
208C22#1062511711yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—462no—
213C4—921no—
214C4—921no—
215C4C4⋊C4×D2311yescharacteristic
216C4#1062506411yescharacteristic
217C4#1062506511yescharacteristic
218C4#1062506711yescharacteristic
219C2—21no—
220C2—21no—
221C2—922no—
222C2#1309228811yescharacteristic
223C2#1309258411yescharacteristic
224C2#1309259911yescharacteristic
subgroupG/H
centerC22#10625108
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#384C2
socleC22×C23#120
prime radicalC2×#67288C22
cosocleC22×C4×C23C23
hypercenter#384D23
hypocenterC23#1859
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #13092457C2semidirect
5. #13092186C2semidirect
6. #13092177C2semidirect
7. C23×#384C2semidirect
25. #10624987C4semidirect
45. C42×C23C2×C4semidirect
56. #67267C2×C4semidirect
80. D92C4⋊C4semidirect
85. Dic46C4⋊C4semidirect
111. #384D23semidirect
138. C23#1859semidirect
171. C42C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130928982
#130924572
C2×#106249872
#130924162
#130921862
#130921772
C23×#3842
#185923