Finite Group Databasebeta

← #15673854

Subgroups — #15673854

Order 2944.

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

normal subgroups only

This group has 378 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
1C2×#10625057C211yesmaximal, characteristic
2C2×#10625048C211yesmaximal, characteristic, complemented
3C2×#10624988C211yesmaximal, characteristic
4C2×#10624988C211yesmaximal, characteristic
5#13092278C211yesmaximal, characteristic, complemented
6#13092184C211yesmaximal, characteristic, complemented
7C23×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D23C2211yescharacteristic
9C23×Dic23C2211yescharacteristic
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊Dic23C2211yescharacteristic
14C2×C22⋊Dic23C2211yescharacteristic
15C2×(C2×D23)⋊C4C412yescomplemented
16C2×C4⋊Dic23C412yescomplemented
17C2×Dic23⋊C4—21no—
18C2×C4×Dic23—21no—
19#10625057—21no—
20#10625057—21no—
21#10625057—22no—
22#10625048—22no—
23#10625048—22no—
24C23⋊#95—22no—
25#10624988—22no—
26#10624988—22no—
27C24×C23C2311yescharacteristic
28C23×D23C2×C411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23—21no—
31C22×C4×C23C2×C412yes—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C2×C22⋊D23—21no—
37C2×C22⋊D23—21no—
38C22×Dic23—21no—
39C22×Dic23—21no—
40C22×Dic23—21no—
41C22×Dic23—21no—
42C22×Dic23—21no—
43C22×Dic23—21no—
44C22×Dic23C2×C411yescharacteristic
45C22×Dic23C2×C412yes—
46C22×Dic23D411yescharacteristic
47C22×Dic23D411yescharacteristic
48C22×Dic23D412yes—
49C22⋊C4×C23—21no—
50C22⋊C4×C23—21no—
51C22⋊C4×C23—21no—
52C22⋊C4×C23—21no—
53C22⋊C4×C23—21no—
54C22⋊C4×C23D412yes—
55C22⋊Dic23—21no—
56C22⋊Dic23—21no—
57C22⋊Dic23—21no—
58C22⋊Dic23D412yes—
59(C2×D23)⋊C4—22no—
60(C2×D23)⋊C4—22no—
61C4⋊Dic23—22no—
62C4⋊Dic23—22no—
63Dic23⋊C4—24no—
64C4×Dic23—24no—
65C23×C23—42no—
66C23×C23C22×C411yescharacteristic
67C23×C23C2×D411yescharacteristic
68C23×C23C2×D411yescharacteristic
69C23×C23C2×D411yescharacteristic
70C23×C23C2×D411yescharacteristic
71C23×C23#4111yescharacteristic
72C23×C23#4111yescharacteristic
73C22×D23—21no—
74C22×D23—21no—
75C22×D23—21no—
76C22×D23—42no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—42no—
80C2×C4×C23—42no—
81C2×C4×C23—42no—
82C2×C4×C23—41no—
83C22⋊D23—41no—
84C22⋊D23—41no—
85C22⋊D23—41no—
86C22⋊D23—41no—
87C2×Dic23—22no—
88C2×Dic23—22no—
89C2×Dic23—21no—
90C2×Dic23—21no—
91C2×Dic23—22no—
92C2×Dic23—22no—
93C2×Dic23—21no—
94C2×Dic23—21no—
95C2×Dic23—21no—
96C2×Dic23—21no—
97C2×Dic23—21no—
98C2×Dic23—22no—
99C2×Dic23—42no—
100C2×Dic23—42no—
101C2×Dic23—41no—
102C2×Dic23C22⋊C412yes—
103C2×Dic23C22⋊C412yes—
104#1899—231nomaximal, Sylow
105C22×C23—22no—
106C22×C23—22no—
107C22×C23—22no—
108C22×C23—41no—
109C22×C23—41no—
110C22×C23—41no—
111C22×C23—41no—
112C22×C23C2×C22⋊C411yescharacteristic
113C22×C23C4×D411yescharacteristic
114C22×C23C4×D411yescharacteristic
115C22×C23#12011yescharacteristic
116C22×C23#12111yescharacteristic
117C22×C23#12111yescharacteristic
118C22×C23#12311yescharacteristic
119C2×D23—41no—
120C2×D23—42no—
121C2×D23—81no—
122C2×D23—81no—
123C4×C23—42no—
124C4×C23—42no—
125C4×C23—81no—
126Dic23—22no—
127Dic23—22no—
128Dic23—42no—
129Dic23—41no—
130Dic23—81no—
131C2×#123—231no—
132C2×#117—231no—
133C2×#99—231no—
134C2×#99—231no—
135#381—231no—
136#342—231no—
137#342D2311yescharacteristic, complemented
138C2×C23—21no—
139C2×C23—21no—
140C2×C23—21no—
141C2×C23—21no—
142C2×C23—21no—
143C2×C23—21no—
144C2×C23#38611yescharacteristic
145C2×C23#41012yes—
146D23—81no—
147C22×D4—231no—
148C23×C4—231no—
149#123—462no—
150#123—461no—
151#123—461no—
152#117—462no—
153#117—462no—
154C2×C4⋊C4—232no—
155C2×C4⋊C4—461no—
156C2×C22⋊C4—231no—
157C2×C22⋊C4—232no—
158C2×C22⋊C4—231no—
159C2×C22⋊C4C2×D2311yescharacteristic
160C2×C22⋊C4C2×D2311yescharacteristic
161C2×C22⋊C4C2×D2311yescharacteristic
162C2×C42—461no—
163#99—462no—
164#99—462no—
165#95—462no—
166C23#189911yescharacteristic, complemented, Sylow
167C24—231no—
168C24C22×D2311yescharacteristic
169C2×D4—461no—
170C2×D4—461no—
171C2×D4—461no—
172C2×D4—461no—
173C2×D4—461no—
174C2×D4—461no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—232no—
178C22×C4—232no—
179C22×C4—231no—
180C22×C4—231no—
181C22×C4—231no—
182C22×C4—461no—
183C22×C4—461no—
184C22×C4—461no—
185C22×C4—461no—
186C22×C4—461no—
187C22×C4—461no—
188C22×C4C4×D2312yes—
189C4⋊C4—462no—
190C4⋊C4—462no—
191C4⋊C4—464no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—232no—
198C22⋊C4—462no—
199C22⋊C4—462no—
200C22⋊C4—461no—
201C22⋊C4—461no—
202C22⋊C4—461no—
203C22⋊C4D9212yes—
204C42—464no—
205C23—42no—
206C23—461no—
207C23—461no—
208C23—461no—
209C23—922no—
210C23C2×C4×D2311yescharacteristic
211C23C2×D9211yescharacteristic
212C23#6728811yescharacteristic
213C23D4×D2311yescharacteristic
214C23D4×D2311yescharacteristic
215C23D4×D2311yescharacteristic
216C23#6729211yescharacteristic
217D4—921no—
218D4—921no—
219D4—921no—
220D4—921no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—232no—
228C2×C4—232no—
229C2×C4—462no—
230C2×C4—461no—
231C2×C4—461no—
232C2×C4—462no—
233C2×C4—462no—
234C2×C4—461no—
235C2×C4—461no—
236C2×C4—462no—
237C2×C4—461no—
238C2×C4—461no—
239C2×C4—462no—
240C2×C4—461no—
241C2×C4—922no—
242C2×C4—922no—
243C2×C4—921no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—922no—
252C22—921no—
253C22—1841no—
254C22—1841no—
255C22C4×D9211yescharacteristic
256C22C22⋊C4×D2311yescharacteristic
257C22#1062505311yescharacteristic
258C22#1062505511yescharacteristic
259C22#1062506411yescharacteristic
260C22#1062506511yescharacteristic
261C22#1062506611yescharacteristic
262C4—42no—
263C4—42no—
264C4—81no—
265C4—462no—
266C4—462no—
267C4—922no—
268C4—921no—
269C4—1841no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—1841no—
277C2#1309229511yescharacteristic
278C2#1309238912yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C22
cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1899
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#10625048C2semidirect
5. #13092278C2semidirect
6. #13092184C2semidirect
7. C23×#342C2semidirect
15. C2×(C2×D23)⋊C4C4semidirect
16. C2×C4⋊Dic23C4semidirect
137. #342D23semidirect
166. C23#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#106250572
C2×#106250482
C2×#106249882
#130922782
#130921842
C23×#3422
#189923