Finite Group Databasebeta

← #15674380

Subgroups — #15674380

Order 2944.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10625049C211yesmaximal, characteristic
2#13092275C211yesmaximal, characteristic
3C22⋊C4×Dic23C211yesmaximal, characteristic
4#13092184C211yesmaximal, characteristic
5#13092183C211yesmaximal, characteristic
6#13092183C211yesmaximal, characteristic
7C23×#342C211yesmaximal, characteristic
8C23×Dic23C2211yescharacteristic
9C22×Dic46C411yescharacteristic, complemented
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊Dic23C2211yescharacteristic
14C2×C22⋊Dic23C2211yescharacteristic
15C2×C22⋊Dic23C2211yescharacteristic
16C2×C4⋊Dic23C411yescharacteristic, complemented
17C2×Dic23⋊C4—21no—
18C2×Dic23⋊C4C411yescharacteristic, complemented
19C2×Dic23⋊C4C411yescharacteristic, complemented
20C2×C4×Dic23—21no—
21#10625049—21no—
22#10625049—21no—
23#10625049—21no—
24#10625049—21no—
25C23⋊#95—21no—
26C23⋊#95—21no—
27C24×C23C2311yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23—21no—
30C22×C4×C23C2×C411yescharacteristic
31C22×C4×C23C2×C411yescharacteristic
32C22×Dic23—21no—
33C22×Dic23—21no—
34C22×Dic23—42no—
35C22×Dic23C2×C411yescharacteristic
36C22×Dic23C2×C411yescharacteristic
37C22×Dic23C2×C411yescharacteristic
38C22×Dic23C2×C411yescharacteristic
39C22×Dic23D411yescharacteristic
40C22×Dic23D411yescharacteristic
41C22×Dic23D411yescharacteristic
42C22×Dic23D411yescharacteristic
43C2×Dic46—21no—
44C2×Dic46—21no—
45C2×Dic46—42no—
46C22⋊C4×C23—21no—
47C22⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C22⋊C4×C23—21no—
50C22⋊C4×C23—21no—
51C22⋊C4×C23Q812yescomplemented
52C22⋊Dic23—21no—
53C22⋊Dic23—21no—
54C22⋊Dic23—21no—
55C22⋊Dic23—21no—
56C22⋊Dic23—21no—
57C22⋊Dic23Q812yescomplemented
58C4⋊Dic23—21no—
59C4⋊Dic23—21no—
60Dic23⋊C4—21no—
61Dic23⋊C4—21no—
62Dic23⋊C4—21no—
63Dic23⋊C4—21no—
64Dic23⋊C4—42no—
65C4×Dic23—42no—
66C23×C23—41no—
67C23×C23—41no—
68C23×C23C22×C411yescharacteristic
69C23×C23C2×D411yescharacteristic
70C23×C23C2×D411yescharacteristic
71C23×C23C2×Q811yescharacteristic
72C23×C23C2×Q811yescharacteristic
73C23×C23#4111yescharacteristic
74C23×C23#4111yescharacteristic
75C2×C4×C23—21no—
76C2×C4×C23—21no—
77C2×C4×C23—22no—
78C2×C4×C23—41no—
79C2×C4×C23—41no—
80C2×C4×C23—41no—
81C2×C4×C23—41no—
82C2×C4×C23—41no—
83C2×C4×C23—41no—
84C2×C4×C23—41no—
85C2×Dic23—22no—
86C2×Dic23—22no—
87C2×Dic23—22no—
88C2×Dic23—21no—
89C2×Dic23—21no—
90C2×Dic23—22no—
91C2×Dic23—41no—
92C2×Dic23—41no—
93C2×Dic23—41no—
94C2×Dic23—41no—
95C2×Dic23—41no—
96C2×Dic23—41no—
97C2×Dic23—41no—
98C2×Dic23—41no—
99C2×Dic23—41no—
100C2×Dic23—41no—
101C2×Dic23C22⋊C411yescharacteristic
102C2×Dic23C22⋊C411yescharacteristic
103C2×Dic23C22⋊C411yescharacteristic
104C2×Dic23C22⋊C411yescharacteristic
105Dic46—42no—
106Dic46—42no—
107#1996—231nomaximal, Sylow
108C22×C23—21no—
109C22×C23—21no—
110C22×C23—21no—
111C22×C23—21no—
112C22×C23—21no—
113C22×C23—21no—
114C22×C23—41no—
115C22×C23—41no—
116C22×C23—41no—
117C22×C23—41no—
118C22×C23C2×C22⋊C411yescharacteristic
119C22×C23C4×Q811yescharacteristic
120C22×C23C4×Q811yescharacteristic
121C22×C23C22⋊Q811yescharacteristic
122C22×C23C22⋊Q811yescharacteristic
123C22×C23#12411yescharacteristic
124C22×C23C4⋊Q811yescharacteristic
125C4×C23—42no—
126C4×C23—41no—
127C4×C23—41no—
128C4×C23—81no—
129Dic23—21no—
130Dic23—21no—
131Dic23—21no—
132Dic23—42no—
133Dic23—41no—
134Dic23—41no—
135Dic23—81no—
136Dic23#9912yes—
137C2×C22⋊Q8—231no—
138#380—231no—
139C4×C22⋊C4—231no—
140#342—231no—
141#342—231no—
142#342—231no—
143#342D2311yescharacteristic
144C2×C23—21no—
145C2×C23—21no—
146C2×C23—21no—
147C2×C23—21no—
148C2×C23—21no—
149C2×C23—21no—
150C2×C23#39111yescharacteristic
151C2×C23C2×#9911yescharacteristic
152C2×C23#41011yescharacteristic
153C22×Q8—231no—
154C23×C4—231no—
155C22⋊Q8—461no—
156C22⋊Q8—461no—
157C22⋊Q8—461no—
158C22⋊Q8—461no—
159C2×C4⋊C4—231no—
160C2×C4⋊C4—231no—
161C2×C4⋊C4—231no—
162C2×C4⋊C4—461no—
163C2×C22⋊C4—231no—
164C2×C22⋊C4—231no—
165C2×C22⋊C4—231no—
166C2×C22⋊C4C2×D2311yescharacteristic
167C2×C22⋊C4C2×D2311yescharacteristic
168C2×C22⋊C4C2×D2311yescharacteristic
169C2×C42—461no—
170#95—461no—
171#95—461no—
172C23#199611yescharacteristic, complemented, Sylow
173C24C22×D2311yescharacteristic
174C2×Q8—461no—
175C2×Q8—461no—
176C2×Q8—922no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—231no—
180C22×C4—231no—
181C22×C4—231no—
182C22×C4—231no—
183C22×C4—231no—
184C22×C4—231no—
185C22×C4—231no—
186C22×C4—231no—
187C22×C4—461no—
188C22×C4—461no—
189C22×C4—922no—
190C22×C4C4×D2311yescharacteristic
191C22×C4C4×D2311yescharacteristic
192C4⋊C4—461no—
193C4⋊C4—461no—
194C4⋊C4—461no—
195C4⋊C4—461no—
196C4⋊C4—461no—
197C4⋊C4—461no—
198C4⋊C4—922no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—232no—
205C22⋊C4—461no—
206C22⋊C4—461no—
207C22⋊C4—461no—
208C22⋊C4—461no—
209C22⋊C4—461no—
210C22⋊C4Dic4612yescomplemented
211C42—922no—
212C23—41no—
213C23—41no—
214C23C2×Dic4611yescharacteristic
215C23C2×C4×D2311yescharacteristic
216C23#6728811yescharacteristic
217C23D4×D2311yescharacteristic
218C23D4×D2311yescharacteristic
219C23#6729011yescharacteristic
220C23Q8×D2311yescharacteristic
221Q8—922no—
222Q8—922no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—231no—
234C2×C4—231no—
235C2×C4—231no—
236C2×C4—231no—
237C2×C4—462no—
238C2×C4—462no—
239C2×C4—462no—
240C2×C4—461no—
241C2×C4—461no—
242C2×C4—462no—
243C2×C4—921no—
244C2×C4—921no—
245C2×C4—921no—
246C2×C4—921no—
247C2×C4—921no—
248C2×C4—921no—
249C2×C4—921no—
250C2×C4—921no—
251C2×C4—921no—
252C2×C4—921no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22C4×Dic4611yescharacteristic
264C22#1062504911yescharacteristic
265C22C22⋊C4×D2311yescharacteristic
266C22#1062505611yescharacteristic
267C22#1062505811yescharacteristic
268C22#1062505911yescharacteristic
269C22#1062506711yescharacteristic
270C4—42no—
271C4—41no—
272C4—41no—
273C4—81no—
274C4—232no—
275C4—461no—
276C4—461no—
277C4—461no—
278C4—922no—
279C4—921no—
280C4—921no—
281C4—1841no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—21no—
288C2#1309232111yescharacteristic
289C2#99×D2311yescharacteristic
290C2#1309238911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radical, cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1996
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
9. C22×Dic46C4semidirect
16. C2×C4⋊Dic23C4semidirect
18. C2×Dic23⋊C4C4semidirect
19. C2×Dic23⋊C4C4semidirect
51. C22⋊C4×C23Q8semidirect
57. C22⋊Dic23Q8semidirect
172. C23#1996semidirect
210. C22⋊C4Dic46semidirect

Maximal subgroups

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

subgroupindex
C2×#106250492
#130922752
C22⋊C4×Dic232
#130921842
#130921832
C23×#3422
#199623