Finite Group Databasebeta

← #15673708

Subgroups — #15673708

Order 2944.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10625068C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic
3C2×#10624998C211yesmaximal, characteristic, complemented
4C2×#10624992C211yesmaximal, characteristic, complemented
5C2×(C2×D23)⋊C8C211yesmaximal, characteristic
6#13092179C211yesmaximal, characteristic, complemented
7C23×#340C211yesmaximal, characteristic, complemented
8C22×C4×D23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C22×C8×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×(C2×D23)⋊C4—21no—
15C2×C4⋊Dic23—21no—
16C2×C4⋊Dic23C2211yescharacteristic
17C2×C4×Dic23—21no—
18C22×C23⋊C8C2211yescharacteristic
19#10625068—22no—
20#10625068C414yescomplemented
21#10625063—22no—
22#10625063—22no—
23(C2×D23)⋊C8—22no—
24#10624998—22no—
25#10624992—22no—
26C23×D23D411yescharacteristic
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×C4×D23—21no—
36C2×C4×D23—21no—
37C2×C4×D23C2×C412yes—
38C2×C4×D23D412yes—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46—21no—
42C2×Dic46—21no—
43C2×Dic46—21no—
44C2×Dic46C2×C412yes—
45C2×C8×C23—21no—
46C2×C8×C23—21no—
47C2×C8×C23—21no—
48C4⋊C4×C23—21no—
49C4⋊C4×C23—21no—
50C4⋊C4×C23C2×C412yes—
51C4⋊C4×C23D412yes—
52(C2×D23)⋊C4—24no—
53(C2×D23)⋊C4—24no—
54C4⋊Dic23—21no—
55C4⋊Dic23—24no—
56C4⋊Dic23D412yes—
57C4×Dic23—24no—
58C2×C23⋊C8—21no—
59C2×C23⋊C8—21no—
60C2×C23⋊C8—21no—
61C23×C23C2×D411yescharacteristic
62C22×D23—21no—
63C22×D23—21no—
64C22×D23—21no—
65C22×D23—21no—
66C22×D23—21no—
67C22×D23—21no—
68C22×D23C22⋊C412yes—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23C22×C411yescharacteristic
76C2×C4×C23C2×D411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23#4111yescharacteristic
80C2×C4×C23#4111yescharacteristic
81C2×Dic23—21no—
82C2×Dic23—21no—
83C2×Dic23—22no—
84C2×Dic23—22no—
85C2×Dic23—41no—
86C2×Dic23—41no—
87C2×Dic23—41no—
88C2×Dic23—41no—
89C2×Dic23C22⋊C412yes—
90C4×D23—22no—
91C4×D23—22no—
92C4×D23—22no—
93C4×D23—22no—
94Dic46—22no—
95Dic46—22no—
96Dic46—41no—
97Dic46—41no—
98C8×C23—41no—
99C23⋊C8—41no—
100#1873—231nomaximal, Sylow
101C22×C23C2×C22⋊C411yescharacteristic
102C22×C23#12011yescharacteristic
103C22×C23#12311yescharacteristic
104C22×C23#13511yescharacteristic
105C22×C23#13511yescharacteristic
106C22×C23#13711yescharacteristic
107C22×C23#13711yescharacteristic
108C2×D23—22no—
109C2×D23—22no—
110C2×D23—22no—
111C2×D23—41no—
112C2×D23—41no—
113C2×D23—41no—
114C2×D23—41no—
115C4×C23—42no—
116C4×C23—42no—
117C4×C23C4×D411yescharacteristic
118C4×C23C4×D411yescharacteristic
119C4×C23#12111yescharacteristic
120C4×C23#12111yescharacteristic
121Dic23—22no—
122Dic23—42no—
123Dic23—42no—
124C2×C22⋊Q8—231no—
125C2×#117—231no—
126C2×#103—231no—
127C2×#103—231no—
128C2×C22⋊C8—231no—
129#340—231no—
130#340D2311yescharacteristic, complemented
131C2×C23#38611yescharacteristic
132C2×C23#41611yescharacteristic
133C2×C23#41911yescharacteristic
134C2×C23#45211yescharacteristic
135C2×C23#45211yescharacteristic
136C2×C23#48511yescharacteristic
137C2×C23#48511yescharacteristic
138D23—42no—
139C22×Q8—231no—
140C23×C4—231no—
141C22×C8—231no—
142C22×C8C2×D2311yescharacteristic
143C22⋊Q8—234no—
144C22⋊Q8—462no—
145#117—462no—
146#117—462no—
147C2×C4⋊C4—231no—
148C2×C4⋊C4—461no—
149C2×C4⋊C4C2×D2311yescharacteristic
150C2×C4⋊C4C2×D2311yescharacteristic
151C2×C22⋊C4—461no—
152C2×C22⋊C4—461no—
153C2×C42—461no—
154#103—462no—
155#103—462no—
156C22⋊C8—462no—
157C23#187311yescharacteristic, complemented, Sylow
158C24—231no—
159C2×Q8—232no—
160C2×Q8—461no—
161C2×Q8—461no—
162C2×Q8—461no—
163C2×Q8—461no—
164C2×Q8—461no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—231no—
168C22×C4—232no—
169C22×C4—232no—
170C22×C4—461no—
171C22×C4—461no—
172C22×C4—461no—
173C22×C4—461no—
174C22×C4—461no—
175C22×C4—461no—
176C22×C4C22×D2311yescharacteristic
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—461no—
181C2×C8—461no—
182C2×C8—461no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—232no—
186C4⋊C4—464no—
187C4⋊C4—461no—
188C4⋊C4C4×D2312yes—
189C4⋊C4D9212yes—
190C22⋊C4—464no—
191C22⋊C4—464no—
192C42—464no—
193C23—232no—
194C23—461no—
195C23—461no—
196C23—461no—
197C23—461no—
198C23—461no—
199C23—461no—
200C23D4×D2311yescharacteristic
201Q8—462no—
202Q8—462no—
203Q8—921no—
204Q8—921no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—232no—
212C2×C4—461no—
213C2×C4—461no—
214C2×C4—462no—
215C2×C4—462no—
216C2×C4—462no—
217C2×C4—462no—
218C2×C4—462no—
219C2×C4—462no—
220C2×C4—921no—
221C2×C4—921no—
222C2×C4—921no—
223C2×C4—921no—
224C2×C4C2×C4×D2311yescharacteristic
225C2×C4C2×D9211yescharacteristic
226C2×C4#6728811yescharacteristic
227C2×C4D4×D2311yescharacteristic
228C2×C4D4×D2311yescharacteristic
229C2×C4#6729211yescharacteristic
230C8—41no—
231C8—921no—
232C22—462no—
233C22—462no—
234C22—462no—
235C22—921no—
236C22—921no—
237C22—921no—
238C22—921no—
239C22C22⋊C4×D2311yescharacteristic
240C22#1062505311yescharacteristic
241C22#1062506511yescharacteristic
242C22#1062508311yescharacteristic
243C22#1062508611yescharacteristic
244C22#1062508711yescharacteristic
245C22#1062508911yescharacteristic
246C4—42no—
247C4—42no—
248C4—462no—
249C4—922no—
250C4—922no—
251C4C4×D9211yescharacteristic
252C4#1062505511yescharacteristic
253C4#1062506411yescharacteristic
254C4#1062506611yescharacteristic
255C2—922no—
256C2#1309229511yescharacteristic
257C2#1309241011yescharacteristic
258C2#1309242411yescharacteristic
259C2#1309258011yescharacteristic
260C2#1309258211yescharacteristic
261C2#1309276011yescharacteristic
262C2#1309276111yescharacteristic
subgroupG/H
centerC23D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#340C2
socleC23×C23C2×D4
prime radicalC23×D23D4
cosocleC22×C4×C23C23
hypercenter#340D23
hypocenterC23#1873
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×#10624998C2semidirect
4. C2×#10624992C2semidirect
6. #13092179C2semidirect
7. C23×#340C2semidirect
20. #10625068C4semidirect
130. #340D23semidirect
157. C23#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#106250682
C2×#106250632
C2×#106249982
C2×#106249922
C2×(C2×D23)⋊C82
#130921792
C23×#3402
#187323