Finite Group Databasebeta

← #15673676

Subgroups — #15673676

Order 2944.

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

normal subgroups only

This group has 374 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#13092890C211yesmaximal, characteristic
2C2×#10624988C211yesmaximal, characteristic
3#13092296C211yesmaximal, characteristic
4#13092290C211yesmaximal, characteristic, complemented
5#13092184C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C23×#385C211yesmaximal, characteristic, complemented
8C23×C4×C23C2211yescharacteristic
9C22×C22⋊D23C2211yescharacteristic
10C2×C4⋊C4×C23—21no—
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊Dic23C2211yescharacteristic
14C2×C22⋊Dic23C2211yescharacteristic
15C2×C22⋊Dic23C2211yescharacteristic
16C4×C22⋊D23—21no—
17C4×C22⋊D23—21no—
18C2×(C2×D23)⋊C4—21no—
19C2×Dic23⋊C4—21no—
20(C22⋊D23)⋊C4—21no—
21(C22⋊D23)⋊C4—21no—
22C22⋊C4×D23—21no—
23#10625048—21no—
24C23×#95—21no—
25C23⋊#95—21no—
26C23⋊#95—21no—
27#10624988C414yescomplemented
28C24×C23C2311yescharacteristic
29C23×D23D411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23—21no—
32C22×C4×C23—21no—
33C22×C4×C23—21no—
34C22×C4×C23—42no—
35C22×C4×C23D411yescharacteristic
36C22×C4×C23D411yescharacteristic
37C2×C22⋊D23—21no—
38C2×C22⋊D23—21no—
39C2×C22⋊D23—21no—
40C2×C22⋊D23—21no—
41C2×C22⋊D23C2×C412yes—
42C2×C22⋊D23Q812yes—
43C22×Dic23—21no—
44C22×Dic23—21no—
45C22×Dic23D411yescharacteristic
46C22×Dic23D411yescharacteristic
47C22×Dic23D411yescharacteristic
48C2×C4×D23—21no—
49C2×C4×D23—21no—
50C4⋊C4×C23—42no—
51C22⋊C4×C23—21no—
52C22⋊C4×C23—21no—
53C22⋊C4×C23—21no—
54C22⋊C4×C23C2×C412yescomplemented
55C22⋊Dic23—21no—
56C22⋊Dic23—21no—
57C22⋊Dic23—21no—
58C22⋊Dic23—21no—
59C22⋊Dic23—21no—
60C22⋊Dic23C2×C412yescomplemented
61(C2×D23)⋊C4—21no—
62(C2×D23)⋊C4—21no—
63(C2×D23)⋊C4—42no—
64Dic23⋊C4—21no—
65Dic23⋊C4—21no—
66Dic23⋊C4—42no—
67C4×Dic23—21no—
68C4×Dic23—21no—
69C23×C23—41no—
70C23×C23—41no—
71C23×C23C22×C411yescharacteristic
72C23×C23C2×D411yescharacteristic
73C23×C23C2×D411yescharacteristic
74C23×C23C2×D411yescharacteristic
75C23×C23C2×Q811yescharacteristic
76C23×C23#4111yescharacteristic
77C23×C23#4111yescharacteristic
78C22×D23—21no—
79C22×D23—21no—
80C22×D23—41no—
81C22×D23—41no—
82C22×D23C4⋊C412yescomplemented
83C2×C4×C23—22no—
84C2×C4×C23—22no—
85C2×C4×C23—22no—
86C2×C4×C23—22no—
87C2×C4×C23—21no—
88C2×C4×C23—21no—
89C2×C4×C23—41no—
90C2×C4×C23—41no—
91C2×C4×C23—41no—
92C2×C4×C23—41no—
93C2×C4×C23—41no—
94C2×C4×C23—41no—
95C2×C4×C23—41no—
96C2×C4×C23—41no—
97C22⋊D23—22no—
98C22⋊D23—22no—
99C22⋊D23—22no—
100C22⋊D23—22no—
101C2×Dic23—21no—
102C2×Dic23—21no—
103C2×Dic23—22no—
104C2×Dic23—21no—
105C2×Dic23—21no—
106C2×Dic23—41no—
107C2×Dic23—41no—
108C2×Dic23—41no—
109C2×Dic23—41no—
110C2×Dic23—41no—
111C2×Dic23—41no—
112C2×Dic23—41no—
113C2×Dic23C4⋊C412yescomplemented
114C4×D23—81no—
115C4×D23—81no—
116#1867—231nomaximal, Sylow
117C22×C23—21no—
118C22×C23—21no—
119C22×C23—21no—
120C22×C23—21no—
121C22×C23—21no—
122C22×C23—21no—
123C22×C23—41no—
124C22×C23—41no—
125C22×C23—41no—
126C22×C23—41no—
127C22×C23C2×C4⋊C411yescharacteristic
128C22×C23C4×D411yescharacteristic
129C22×C23C4×D411yescharacteristic
130C22×C23#12011yescharacteristic
131C22×C23C22⋊Q811yescharacteristic
132C22×C23C22⋊Q811yescharacteristic
133C22×C23#12311yescharacteristic
134C2×D23—22no—
135C2×D23—41no—
136C2×D23—41no—
137C2×D23—42no—
138C2×D23—81no—
139C4×C23—42no—
140C4×C23—41no—
141C4×C23—42no—
142C4×C23—41no—
143Dic23—22no—
144Dic23—42no—
145Dic23—41no—
146Dic23—41no—
147Dic23—81no—
148#518—231no—
149C2×#99—231no—
150#386—231no—
151#385—231no—
152#385D2311yescharacteristic, complemented
153#342—231no—
154#342—231no—
155C2×C23—21no—
156C2×C23—21no—
157C2×C23—21no—
158C2×C23—21no—
159C2×C23—21no—
160C2×C23—21no—
161C2×C23#38511yescharacteristic
162C2×C23B(4,𝔽2)11yescharacteristic
163C2×C23#45811yescharacteristic
164D23—42no—
165C22×D4—231no—
166C23×C4C2×D2311yescharacteristic
167C4×D4—461no—
168C4×D4—461no—
169C4×D4—461no—
170C4×D4—461no—
171#117—461no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—461no—
174C2×C22⋊C4—231no—
175C2×C22⋊C4—231no—
176C2×C22⋊C4—231no—
177C2×C22⋊C4—461no—
178C2×C22⋊C4—461no—
179C2×C22⋊C4C2×D2311yescharacteristic
180C2×C22⋊C4C2×D2311yescharacteristic
181#99—234no—
182#95—21no—
183#95—461no—
184#95—461no—
185C23#186711yescharacteristic, complemented, Sylow
186C24—231no—
187C24C22×D2311yescharacteristic
188C2×D4—232no—
189C2×D4—232no—
190C2×D4—461no—
191C2×D4—461no—
192C2×D4—461no—
193C2×D4—461no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—231no—
200C22×C4—231no—
201C22×C4—231no—
202C22×C4—461no—
203C22×C4—461no—
204C22×C4—461no—
205C22×C4—461no—
206C22×C4C22⋊D2311yescharacteristic
207C22×C4C22⋊D2311yescharacteristic
208C4⋊C4—42no—
209C4⋊C4—461no—
210C4⋊C4—461no—
211C4⋊C4—922no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—232no—
216C22⋊C4—461no—
217C22⋊C4—461no—
218C22⋊C4—461no—
219C22⋊C4—461no—
220C22⋊C4—461no—
221C22⋊C4—461no—
222C22⋊C4—461no—
223C22⋊C4—922no—
224C22⋊C4C4×D2312yescomplemented
225C42—461no—
226C42—461no—
227C23—41no—
228C23—41no—
229C23—232no—
230C23—461no—
231C23—461no—
232C23—921no—
233C23—921no—
234C23C2×C4×D2311yescharacteristic
235C23#6728811yescharacteristic
236C23D4×D2311yescharacteristic
237C23D4×D2311yescharacteristic
238C23Q8×D2311yescharacteristic
239C23#6729211yescharacteristic
240C23C2×C22⋊D2311yescharacteristic
241D4—462no—
242D4—462no—
243D4—462no—
244D4—462no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—232no—
260C2×C4—461no—
261C2×C4—461no—
262C2×C4—462no—
263C2×C4—461no—
264C2×C4—461no—
265C2×C4—921no—
266C2×C4—921no—
267C2×C4—921no—
268C2×C4—921no—
269C2×C4—921no—
270C2×C4—921no—
271C2×C4—921no—
272C2×C4—1841no—
273C2×C4—1841no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—462no—
285C22—922no—
286C22—921no—
287C22—921no—
288C22—1841no—
289C22C4⋊C4×D2311yescharacteristic
290C22#1062506411yescharacteristic
291C22#1062506511yescharacteristic
292C22#1062506711yescharacteristic
293C22C4×C22⋊D2311yescharacteristic
294C22#1062510811yescharacteristic
295C22#1062511711yescharacteristic
296C4—42no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—462no—
301C4—922no—
302C4—921no—
303C4—921no—
304C4—1841no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—922no—
312C2#1309228811yescharacteristic
313C2#1309260311yescharacteristic
314C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#385C2
socleC22×C23#120
prime radicalC22×C22⋊D23C22
cosocleC24×C23C23
hypercenter#385D23
hypocenterC23#1867
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #13092290C2semidirect
5. #13092184C2semidirect
6. #13092183C2semidirect
7. C23×#385C2semidirect
27. #10624988C4semidirect
54. C22⋊C4×C23C2×C4semidirect
60. C22⋊Dic23C2×C4semidirect
82. C22×D23C4⋊C4semidirect
113. C2×Dic23C4⋊C4semidirect
152. #385D23semidirect
185. C23#1867semidirect
224. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130928902
C2×#106249882
#130922962
#130922902
#130921842
#130921832
C23×#3852
#186723