Finite Group Databasebeta

← #15673495

Subgroups — #15673495

Order 2944.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#117×D23C211yesmaximal, characteristic
2#13092380C211yesmaximal, characteristic
3C4×(C2×D23)⋊C4C211yesmaximal, characteristic
4#13092178C211yesmaximal, characteristic, complemented
5#13092177C211yesmaximal, characteristic, complemented
6#13092176C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C22×C4×D23C2211yescharacteristic
9C2×M16×C23C2211yescharacteristic
10C23×#117C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12C2×(C2×D23)⋊C4—21no—
13#10625097C2211yescharacteristic
14C2×C4×Dic23C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16#10625063C411yescharacteristic, complemented
17#10625063C411yescharacteristic, complemented
18C4⋊C4×D23C411yescharacteristic, complemented
19C4⋊C4×D23C411yescharacteristic, complemented
20C22⋊C4×D23—21no—
21#10625048—21no—
22#10625043—21no—
23C42×D23—21no—
24C23⋊#95—21no—
25(C2×D23)⋊C8—21no—
26(C2×D23)⋊C8—21no—
27C23×D23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C2×C4×D23—21no—
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×C4×D23—21no—
36C2×C4×D23—21no—
37C2×C4×D23—21no—
38C2×C4×D23C2×C411yescharacteristic
39C2×C4×D23C2×C411yescharacteristic
40C2×C4×D23D411yescharacteristic
41C2×C4×D23D411yescharacteristic
42M16×C23—21no—
43M16×C23—21no—
44C2×C8×C23—21no—
45C4⋊C4×C23C2×C411yescharacteristic
46C4⋊C4×C23C2×C411yescharacteristic
47C22⋊C4×C23—21no—
48C42×C23—21no—
49C42×C23—21no—
50C42×C23—21no—
51C22⋊Dic23—21no—
52(C2×D23)⋊C4—24no—
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55C4⋊Dic23C2×C411yescharacteristic
56C4⋊Dic23C2×C411yescharacteristic
57Dic23⋊C4—21no—
58Dic23⋊C4—21no—
59C4×Dic23—21no—
60C4×Dic23—21no—
61C4×Dic23—21no—
62C4×Dic23—21no—
63C4×Dic23—21no—
64#67267—21no—
65#67267—21no—
66C2×C23⋊C8—21no—
67C23×C23C2×D411yescharacteristic
68C22×D23—21no—
69C22×D23—21no—
70C22×D23—22no—
71C22×D23—41no—
72C22×D23C22⋊C411yescharacteristic
73C22×D23C22⋊C411yescharacteristic
74C2×C4×C23—22no—
75C2×C4×C23—21no—
76C2×C4×C23—21no—
77C2×C4×C23—41no—
78C2×C4×C23—41no—
79C2×C4×C23C22×C411yescharacteristic
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23#4111yescharacteristic
82C2×C4×C23#4111yescharacteristic
83C2×C4×C23#4111yescharacteristic
84C2×C4×C23#4111yescharacteristic
85C2×Dic23—21no—
86C2×Dic23—21no—
87C2×Dic23—22no—
88C2×Dic23—21no—
89C2×Dic23—21no—
90C2×Dic23—41no—
91C2×Dic23—41no—
92C2×Dic23C22⋊C411yescharacteristic
93C2×Dic23C22⋊C411yescharacteristic
94C4×D23—21no—
95C4×D23—21no—
96C4×D23—21no—
97C4×D23—21no—
98C4×D23—21no—
99C4×D23—21no—
100C4×D23—21no—
101C4×D23—21no—
102C4×D23—42no—
103C4×D23—42no—
104C8×C23—41no—
105C23⋊C8—41no—
106#1826—231nomaximal, Sylow
107C22×C23—21no—
108C22×C23—21no—
109C22×C23C2×C22⋊C411yescharacteristic
110C22×C23#12311yescharacteristic
111C22×C23#12311yescharacteristic
112C2×D23—21no—
113C2×D23—21no—
114C2×D23—21no—
115C2×D23—21no—
116C2×D23—21no—
117C2×D23—42no—
118C2×D23—42no—
119C2×D23#10412yes—
120C4×C23—42no—
121C4×C23—41no—
122C4×C23—41no—
123C4×C23#11711yescharacteristic
124C4×C23#11711yescharacteristic
125C4×C23#12311yescharacteristic
126C4×C23#12311yescharacteristic
127Dic23—21no—
128Dic23—21no—
129Dic23—42no—
130Dic23—41no—
131Dic23—41no—
132C2×#117—231no—
133#407—231no—
134C4×C22⋊C4—231no—
135#339—231no—
136#339—231no—
137#339—231no—
138#339D2311yescharacteristic, complemented
139C2×C23—21no—
140C2×C23—21no—
141C2×C23#38111yescharacteristic
142C2×C23C2×#10411yescharacteristic
143C2×C23#42111yescharacteristic
144D23—22no—
145D23—41no—
146C23×C4—231no—
147C2×M16—231no—
148C2×M16C2×D2311yescharacteristic
149#117—231no—
150#117—231no—
151#117—231no—
152#117—461no—
153#117—461no—
154#117C2×D2311yescharacteristic
155C2×C4⋊C4—231no—
156C2×C4⋊C4—231no—
157C2×C22⋊C4—461no—
158C2×C22⋊C4—461no—
159C2×C42—231no—
160C2×C42—461no—
161C2×C42C2×D2311yescharacteristic
162C22⋊C8—461no—
163C22⋊C8—461no—
164#95—461no—
165C23#182611yescharacteristic, complemented, Sylow
166C24—231no—
167C22×C4—21no—
168C22×C4—231no—
169C22×C4—231no—
170C22×C4—231no—
171C22×C4—231no—
172C22×C4—231no—
173C22×C4—461no—
174C22×C4—461no—
175C22×C4—461no—
176C22×C4—461no—
177C22×C4—461no—
178C22×C4—461no—
179C22×C4—461no—
180C22×C4C22×D2311yescharacteristic
181M16—21no—
182M16—21no—
183M16—461no—
184M16—461no—
185C2×C8—21no—
186C2×C8—461no—
187C4⋊C4—231no—
188C4⋊C4—231no—
189C4⋊C4—461no—
190C4⋊C4—461no—
191C4⋊C4C4×D2311yescharacteristic
192C4⋊C4C4×D2311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—461no—
195C22⋊C4—461no—
196C22⋊C4—464no—
197C22⋊C4—461no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—461no—
202C42—461no—
203C42—461no—
204C42—461no—
205C42—461no—
206C23—231no—
207C23—231no—
208C23—462no—
209C23—461no—
210C23—461no—
211C23—921no—
212C23D4×D2311yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—231no—
219C2×C4—231no—
220C2×C4—461no—
221C2×C4—461no—
222C2×C4—461no—
223C2×C4—461no—
224C2×C4—461no—
225C2×C4—461no—
226C2×C4—461no—
227C2×C4—461no—
228C2×C4—461no—
229C2×C4—461no—
230C2×C4—462no—
231C2×C4—461no—
232C2×C4—461no—
233C2×C4—922no—
234C2×C4—922no—
235C2×C4—921no—
236C2×C4—921no—
237C2×C4C2×C4×D2311yescharacteristic
238C2×C4#6728811yescharacteristic
239C2×C4#6728811yescharacteristic
240C2×C4D4×D2311yescharacteristic
241C2×C4#6729011yescharacteristic
242C2×C4#6729211yescharacteristic
243C8—41no—
244C8—921no—
245C22—21no—
246C22—21no—
247C22—232no—
248C22—461no—
249C22—461no—
250C22—461no—
251C22—461no—
252C22—461no—
253C22—922no—
254C22—922no—
255C22C22⋊C4×D2311yescharacteristic
256C22#1062505411yescharacteristic
257C22#1062506511yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—461no—
262C4—461no—
263C4—922no—
264C4—921no—
265C4—921no—
266C4#1062504311yescharacteristic
267C4#1062505411yescharacteristic
268C4#1062506311yescharacteristic
269C4#1062506511yescharacteristic
270C2—21no—
271C2—21no—
272C2—462no—
273C2—921no—
274C2#1309227911yescharacteristic
275C2#104×D2311yescharacteristic
276C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23D4
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1826
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #13092178C2semidirect
5. #13092177C2semidirect
6. #13092176C2semidirect
7. C23×#339C2semidirect
16. #10625063C4semidirect
17. #10625063C4semidirect
18. C4⋊C4×D23C4semidirect
19. C4⋊C4×D23C4semidirect
138. #339D23semidirect
165. C23#1826semidirect

Maximal subgroups

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

subgroupindex
#117×D232
#130923802
C4×(C2×D23)⋊C42
#130921782
#130921772
#130921762
C23×#3392
#182623