Finite Group Databasebeta

← #15673938

Subgroups — #15673938

Order 2944.

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

normal subgroups only

This group has 380 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#13092979C211yesmaximal, characteristic
2#13092890C211yesmaximal, characteristic, complemented
3C2×#10624988C211yesmaximal, characteristic, complemented
4C2×#10624988C211yesmaximal, characteristic, complemented
5C2×#10624988C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C23×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D23C2211yescharacteristic
9C22×C22⋊D23C2211yescharacteristic
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊Dic23C2211yescharacteristic
14C2×C22⋊Dic23C2211yescharacteristic
15#10625101—22no—
16C4×C22⋊D23—22no—
17#10625057—21no—
18#10625057C412yescomplemented
19#10625053—21no—
20#10625053C412yescomplemented
21(C22⋊D23)⋊C4—22no—
22C22⋊C4×D23—21no—
23#10625048—21no—
24#10624988—22no—
25#10624988—22no—
26#10624988—22no—
27C24×C23C2311yescharacteristic
28C23×D23C2×C411yescharacteristic, complemented
29C23×D23D411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23—21no—
32C22×C4×C23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C2×C22⋊D23—21no—
37C2×C22⋊D23—21no—
38C2×C22⋊D23—21no—
39C2×C22⋊D23—21no—
40C2×C22⋊D23—21no—
41C2×C22⋊D23—21no—
42C2×C22⋊D23—21no—
43C2×C22⋊D23C2×C412yes—
44C2×C22⋊D23D412yes—
45C22×Dic23—21no—
46C22×Dic23—21no—
47C22×Dic23C2×C411yescharacteristic, complemented
48C22×Dic23D411yescharacteristic
49C2×D92—22no—
50C2×C4×D23—22no—
51C22⋊C4×C23—21no—
52C22⋊C4×C23—21no—
53C22⋊C4×C23—21no—
54C22⋊C4×C23—21no—
55C22⋊C4×C23C2×C412yescomplemented
56C22⋊C4×C23D412yescomplemented
57C22⋊Dic23—21no—
58C22⋊Dic23—21no—
59C22⋊Dic23—21no—
60C22⋊Dic23D412yescomplemented
61(C2×D23)⋊C4—22no—
62(C2×D23)⋊C4—22no—
63(C2×D23)⋊C4—22no—
64C4⋊Dic23—22no—
65Dic23⋊C4—22no—
66C4×Dic23—22no—
67C23×C23—81no—
68C23×C23C22×C411yescharacteristic
69C23×C23C2×D411yescharacteristic
70C23×C23C2×D411yescharacteristic
71C23×C23C2×D411yescharacteristic
72C23×C23C2×D411yescharacteristic
73C23×C23#4111yescharacteristic
74C23×C23#4111yescharacteristic
75C22×D23—21no—
76C22×D23—21no—
77C22×D23—21no—
78C22×D23—21no—
79C22×D23—21no—
80C22×D23—81no—
81C22×D23—81no—
82C22×D23C22⋊C412yes—
83C2×C4×C23—22no—
84C2×C4×C23—22no—
85C2×C4×C23—41no—
86C2×C4×C23—81no—
87C2×C4×C23—81no—
88C2×C4×C23—81no—
89C22⋊D23—22no—
90C22⋊D23—22no—
91C22⋊D23—22no—
92C22⋊D23—22no—
93C22⋊D23—41no—
94C22⋊D23—41no—
95C22⋊D23—41no—
96C22⋊D23—41no—
97C2×Dic23—21no—
98C2×Dic23—21no—
99C2×Dic23—21no—
100C2×Dic23—21no—
101C2×Dic23—21no—
102C2×Dic23—22no—
103C2×Dic23—41no—
104C2×Dic23—81no—
105C2×Dic23—81no—
106C2×Dic23C22⋊C412yes—
107D92—82no—
108C4×D23—82no—
109#1913—231nomaximal, Sylow
110C22×C23—41no—
111C22×C23—41no—
112C22×C23—41no—
113C22×C23—41no—
114C22×C23—41no—
115C22×C23—41no—
116C22×C23—41no—
117C22×C23C2×C22⋊C411yescharacteristic
118C22×C23C4×D411yescharacteristic
119C22×C23C4×D411yescharacteristic
120C22×C23#12011yescharacteristic
121C22×C23#12111yescharacteristic
122C22×C23#12111yescharacteristic
123C22×C23#12311yescharacteristic
124C2×D23—22no—
125C2×D23—42no—
126C2×D23—42no—
127C2×D23—42no—
128C2×D23—41no—
129C2×D23—81no—
130C2×D23—81no—
131C2×D23—81no—
132C4×C23—42no—
133C4×C23—42no—
134C4×C23—81no—
135Dic23—22no—
136Dic23—42no—
137Dic23—41no—
138Dic23—81no—
139#534—231no—
140#518—231no—
141C2×#99—231no—
142C2×#99—231no—
143C2×#99—231no—
144#342—231no—
145#342D2311yescharacteristic, complemented
146C2×C23—21no—
147C2×C23—21no—
148C2×C23—21no—
149C2×C23—21no—
150C2×C23—21no—
151C2×C23—21no—
152C2×C23—21no—
153C2×C23#38611yescharacteristic
154D23—42no—
155D23—81no—
156C22×D4—231no—
157C22×D4—231no—
158#123—232no—
159#123—461no—
160#121—462no—
161#120—232no—
162#120—461no—
163C4×D4—462no—
164C4×D4—462no—
165#117—461no—
166C2×C22⋊C4—231no—
167C2×C22⋊C4—231no—
168C2×C22⋊C4—461no—
169C2×C22⋊C4C2×D2311yescharacteristic
170C2×C22⋊C4C2×D2311yescharacteristic
171C2×C22⋊C4C2×D2311yescharacteristic
172#99—462no—
173#99—462no—
174#99—462no—
175C23#191311yescharacteristic, complemented, Sylow
176C24—231no—
177C24—231no—
178C24C22×D2311yescharacteristic
179C2×D4—232no—
180C2×D4—232no—
181C2×D4—462no—
182C2×D4—461no—
183C2×D4—461no—
184C2×D4—461no—
185C2×D4—461no—
186C2×D4—461no—
187C2×D4—461no—
188C2×D4—461no—
189C2×D4—461no—
190C2×D4—461no—
191C2×D4—461no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—231no—
196C22×C4—231no—
197C22×C4—462no—
198C22×C4—461no—
199C22×C4—461no—
200C4⋊C4—462no—
201C4⋊C4—462no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—232no—
207C22⋊C4—462no—
208C22⋊C4—462no—
209C22⋊C4—462no—
210C22⋊C4—461no—
211C22⋊C4—461no—
212C22⋊C4—461no—
213C22⋊C4C4×D2312yescomplemented
214C22⋊C4D9212yescomplemented
215C42—462no—
216C23—81no—
217C23—232no—
218C23—461no—
219C23—461no—
220C23—461no—
221C23—461no—
222C23—461no—
223C23—1841no—
224C23—1841no—
225C23C2×C4×D2311yescharacteristic
226C23C2×D9211yescharacteristic
227C23#6728811yescharacteristic
228C23D4×D2311yescharacteristic
229C23D4×D2311yescharacteristic
230C23D4×D2311yescharacteristic
231C23#6729211yescharacteristic
232D4—462no—
233D4—462no—
234D4—462no—
235D4—462no—
236D4—921no—
237D4—921no—
238D4—921no—
239D4—921no—
240D4—1842no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—232no—
248C2×C4—461no—
249C2×C4—461no—
250C2×C4—461no—
251C2×C4—461no—
252C2×C4—462no—
253C2×C4—461no—
254C2×C4—921no—
255C2×C4—1842no—
256C2×C4—1841no—
257C2×C4—1841no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—462no—
266C22—922no—
267C22—922no—
268C22—922no—
269C22—921no—
270C22—1841no—
271C22—1841no—
272C22—1841no—
273C22C4×D9211yescharacteristic
274C22C22⋊C4×D2311yescharacteristic
275C22#1062505311yescharacteristic
276C22#1062505511yescharacteristic
277C22#1062506411yescharacteristic
278C22#1062506511yescharacteristic
279C22#1062506611yescharacteristic
280C4—42no—
281C4—42no—
282C4—81no—
283C4—462no—
284C4—922no—
285C4—921no—
286C4—1841no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—922no—
295C2—1841no—
296C2#1309229511yescharacteristic
subgroupG/H
centerC2#13092295
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC2×C23#386
prime radical#13092979C2
cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1913
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #13092890C2semidirect
3. C2×#10624988C2semidirect
4. C2×#10624988C2semidirect
5. C2×#10624988C2semidirect
6. #13092183C2semidirect
7. C23×#342C2semidirect
18. #10625057C4semidirect
20. #10625053C4semidirect
28. C23×D23C2×C4semidirect
47. C22×Dic23C2×C4semidirect
55. C22⋊C4×C23C2×C4semidirect
56. C22⋊C4×C23D4semidirect
60. C22⋊Dic23D4semidirect
145. #342D23semidirect
175. C23#1913semidirect
213. C22⋊C4C4×D23semidirect
214. C22⋊C4D92semidirect

Maximal subgroups

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

subgroupindex
#130929792
#130928902
C2×#106249882
#130921832
C23×#3422
#191323