Finite Group Databasebeta

← #15673802

Subgroups — #15673802

Order 2944.

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

normal subgroups only

This group has 578 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×#10625124C211yesmaximal, characteristic
2#13092890C211yesmaximal, characteristic, complemented
3C2×#10624988C211yesmaximal, characteristic, complemented
4#13092273C211yesmaximal, characteristic, complemented
5#13092184C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C23×#379C211yesmaximal, characteristic, complemented
8C25×C23C2211yescharacteristic
9C22×C22⋊D23—21no—
10C22×C22⋊D23C2211yescharacteristic
11C2×C22⋊C4×C23—22no—
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊C4×C23C2211yescharacteristic
14#10625124—22no—
15#10625124C414yescomplemented
16C2×C22⋊Dic23—21no—
17C2×C22⋊Dic23—22no—
18C2×C22⋊Dic23C2211yescharacteristic
19C2×C22⋊Dic23C2211yescharacteristic
20C2×C22⋊Dic23C2211yescharacteristic
21C4×C22⋊D23—22no—
22(C22⋊D23)⋊C4—22no—
23C22⋊C4×D23—21no—
24#10625048—21no—
25#10624988—22no—
26C24×C23—21no—
27C24×C23—21no—
28C24×C23—21no—
29C24×C23—21no—
30C24×C23—21no—
31C24×C23—21no—
32C24×C23—44no—
33C24×C23C2×C412yescomplemented
34C24×C23C2311yescharacteristic
35C23×D23D411yescharacteristic
36C22×C4×C23—21no—
37C22×C4×C23D412yescomplemented
38C2×C22⋊D23—21no—
39C2×C22⋊D23—21no—
40C2×C22⋊D23—21no—
41C2×C22⋊D23—21no—
42C2×C22⋊D23—24no—
43C2×C22⋊D23—44no—
44C2×C22⋊D23C2×C412yes—
45C2×C22⋊D23D412yes—
46C22×Dic23—21no—
47C22×Dic23—21no—
48C22×Dic23D411yescharacteristic
49C22×Dic23D412yescomplemented
50C2×C4×D23—22no—
51C22⋊C4×C23—21no—
52C22⋊C4×C23—21no—
53C22⋊C4×C23—21no—
54C22⋊C4×C23—21no—
55C22⋊C4×C23—44no—
56C22⋊Dic23—21no—
57C22⋊Dic23—21no—
58C22⋊Dic23—21no—
59C22⋊Dic23—24no—
60C22⋊Dic23—21no—
61C22⋊Dic23—21no—
62C22⋊Dic23—44no—
63C22⋊Dic23C2×C412yescomplemented
64(C2×D23)⋊C4—22no—
65Dic23⋊C4—22no—
66C4×Dic23—22no—
67C23×C23—24no—
68C23×C23—24no—
69C23×C23—24no—
70C23×C23—22no—
71C23×C23—22no—
72C23×C23—22no—
73C23×C23—44no—
74C23×C23—42no—
75C23×C23—42no—
76C23×C23—42no—
77C23×C23—42no—
78C23×C23—44no—
79C23×C23—44no—
80C23×C23—44no—
81C23×C23—41no—
82C23×C23—41no—
83C23×C23—41no—
84C23×C23—41no—
85C23×C23C22×C411yescharacteristic
86C23×C23C2×D411yescharacteristic
87C23×C23C2×D411yescharacteristic
88C23×C23C2×D411yescharacteristic
89C23×C23C2×D411yescharacteristic
90C23×C23#4111yescharacteristic
91C23×C23#4111yescharacteristic
92C22×D23—21no—
93C22×D23—21no—
94C22×D23—42no—
95C22×D23C22⋊C412yescomplemented
96C2×C4×C23—22no—
97C2×C4×C23—42no—
98C2×C4×C23—42no—
99C2×C4×C23—41no—
100C22⋊D23—22no—
101C22⋊D23—22no—
102C22⋊D23—22no—
103C22⋊D23—22no—
104C22⋊D23—48no—
105C2×Dic23—21no—
106C2×Dic23—21no—
107C2×Dic23—22no—
108C2×Dic23—22no—
109C2×Dic23—42no—
110C2×Dic23—42no—
111C2×Dic23—42no—
112C2×Dic23—41no—
113C2×Dic23C22⋊C412yescomplemented
114C4×D23—82no—
115#1889—231nomaximal, Sylow
116C22×C23—22no—
117C22×C23—22no—
118C22×C23—22no—
119C22×C23—24no—
120C22×C23—24no—
121C22×C23—24no—
122C22×C23—41no—
123C22×C23—41no—
124C22×C23—41no—
125C22×C23—41no—
126C22×C23—42no—
127C22×C23—44no—
128C22×C23—44no—
129C22×C23—44no—
130C22×C23—42no—
131C22×C23—42no—
132C22×C23—42no—
133C22×C23—44no—
134C22×C23C2×C22⋊C411yescharacteristic
135C22×C23C4×D411yescharacteristic
136C22×C23C4×D411yescharacteristic
137C22×C23#12011yescharacteristic
138C22×C23#12111yescharacteristic
139C22×C23#12111yescharacteristic
140C22×C23#12311yescharacteristic
141C2×D23—22no—
142C2×D23—42no—
143C2×D23—42no—
144C2×D23—81no—
145C4×C23—42no—
146C4×C23—81no—
147Dic23—22no—
148Dic23—42no—
149Dic23—42no—
150Dic23—81no—
151C2×#120—231no—
152#518—231no—
153C2×#99—231no—
154#379—231no—
155#379D2311yescharacteristic, complemented
156#342—231no—
157#342—231no—
158C2×C23—21no—
159C2×C23—21no—
160C2×C23—21no—
161C2×C23—21no—
162C2×C23—21no—
163C2×C23—21no—
164C2×C23—44no—
165C2×C23#38611yescharacteristic
166C2×C23B(4,𝔽2)12yes—
167D23—42no—
168C25C2×D2311yescharacteristic
169C22×D4—231no—
170C22×D4—461no—
171#120—234no—
172#120—462no—
173C4×D4—462no—
174C4×D4—462no—
175#117—461no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—231no—
178C2×C22⋊C4—231no—
179C2×C22⋊C4—231no—
180C2×C22⋊C4—461no—
181C2×C22⋊C4—461no—
182C2×C22⋊C4—462no—
183C2×C22⋊C4C2×D2311yescharacteristic
184C2×C22⋊C4C2×D2311yescharacteristic
185#99—462no—
186C23#188911yescharacteristic, complemented, Sylow
187C24—21no—
188C24—21no—
189C24—21no—
190C24—21no—
191C24—21no—
192C24—21no—
193C24—44no—
194C24—231no—
195C24C4×D2312yescomplemented
196C24C22×D2311yescharacteristic
197C2×D4—232no—
198C2×D4—232no—
199C2×D4—461no—
200C2×D4—461no—
201C2×D4—461no—
202C2×D4—461no—
203C2×D4—464no—
204C2×D4—924no—
205C22×C4—21no—
206C22×C4—231no—
207C22×C4—232no—
208C22×C4—462no—
209C22×C4—461no—
210C22×C4—461no—
211C22×C4C22⋊D2312yescomplemented
212C4⋊C4—462no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—44no—
218C22⋊C4—232no—
219C22⋊C4—462no—
220C22⋊C4—464no—
221C22⋊C4—461no—
222C22⋊C4—461no—
223C22⋊C4—461no—
224C22⋊C4—461no—
225C22⋊C4—461no—
226C22⋊C4—924no—
227C42—462no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—44no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—232no—
247C23—461no—
248C23—461no—
249C23—922no—
250C23C2×C4×D2311yescharacteristic
251C23#6728811yescharacteristic
252C23D4×D2311yescharacteristic
253C23D4×D2311yescharacteristic
254C23D4×D2311yescharacteristic
255C23#6729011yescharacteristic
256C23C2×C22⋊D2311yescharacteristic
257D4—462no—
258D4—462no—
259D4—462no—
260D4—462no—
261D4—928no—
262C2×C4—22no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—232no—
267C2×C4—461no—
268C2×C4—461no—
269C2×C4—462no—
270C2×C4—462no—
271C2×C4—922no—
272C2×C4—922no—
273C2×C4—922no—
274C2×C4—921no—
275C2×C4—1842no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—24no—
280C22—24no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—44no—
287C22—42no—
288C22—44no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—42no—
293C22—44no—
294C22—462no—
295C22—922no—
296C22—922no—
297C22—1841no—
298C22C22⋊C4×D2311yescharacteristic
299C22(C22⋊D23)⋊C411yescharacteristic
300C22#1062505411yescharacteristic
301C22#1062505511yescharacteristic
302C22C4×C22⋊D2311yescharacteristic
303C22#1062510811yescharacteristic
304C22#1062510911yescharacteristic
305C4—42no—
306C4—81no—
307C4—462no—
308C4—922no—
309C4—922no—
310C4—1841no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—44no—
318C2—922no—
319C2#1309229311yescharacteristic
320C2#1309260312yes—
subgroupG/H
centerC22#10625108
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#379C2
socleC22×C23#120
prime radicalC2×#10625124C2
cosocleC24×C23C23
hypercenter#379D23
hypocenterC23#1889
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #13092890C2semidirect
3. C2×#10624988C2semidirect
4. #13092273C2semidirect
5. #13092184C2semidirect
6. #13092183C2semidirect
7. C23×#379C2semidirect
15. #10625124C4semidirect
33. C24×C23C2×C4semidirect
37. C22×C4×C23D4semidirect
49. C22×Dic23D4semidirect
63. C22⋊Dic23C2×C4semidirect
95. C22×D23C22⋊C4semidirect
113. C2×Dic23C22⋊C4semidirect
155. #379D23semidirect
186. C23#1889semidirect
195. C24C4×D23semidirect
211. C22×C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251242
#130928902
C2×#106249882
#130922732
#130921842
#130921832
C23×#3792
#188923