Finite Group Databasebeta

← #15671967

Subgroups — #15671967

Order 2944.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22⋊Q8×D23C211yesmaximal, characteristic
2C22⋊C8×D23C211yesmaximal, characteristic
3#13092276C211yesmaximal, characteristic
4#13092155C211yesmaximal, characteristic, complemented
5#13092154C211yesmaximal, characteristic, complemented
6#13092153C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D23C411yescharacteristic, complemented
9C22×C4×D23C2211yescharacteristic
10C23×C22⋊Q8C2211yescharacteristic
11#10625117C411yescharacteristic, complemented
12C2×(C2×D23)⋊C4—21no—
13#10625095C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15C2×C8×D23—21no—
16#10625068C411yescharacteristic, complemented
17#10625067—21no—
18C4⋊C4×D23—21no—
19C4⋊C4×D23C411yescharacteristic, complemented
20C22⋊C4×D23—21no—
21#10625049—21no—
22C23×C22⋊C8C2211yescharacteristic
23C23×#95C2211yescharacteristic
24C23⋊#95C2211yescharacteristic
25C22⋊(C23⋊C8)C2211yescharacteristic
26(C2×D23)⋊C8—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23C2×C411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33Q8×D23—42no—
34C2×C4×D23—21no—
35C2×C4×D23—21no—
36C2×C4×D23—42no—
37C2×C4×D23C2×C411yescharacteristic
38C2×C4×D23C2×C411yescharacteristic
39C2×C4×D23D411yescharacteristic
40C2×C4×D23D411yescharacteristic
41C2×Dic46—21no—
42C2×Dic46C2×C411yescharacteristic
43C2×C8×C23—21no—
44C4⋊C4×C23—21no—
45C4⋊C4×C23C2×C411yescharacteristic
46C22⋊C4×C23—21no—
47C22⋊Dic23—21no—
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50(C2×D23)⋊C4—42no—
51C4⋊Dic23—21no—
52C4⋊Dic23C2×C411yescharacteristic
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—42no—
57C2×C23⋊C8—21no—
58C8×D23—42no—
59C23×C23C2×D411yescharacteristic
60C22×D23—41no—
61C22×D23—41no—
62C22×D23C22⋊C411yescharacteristic
63C22×D23C22⋊C411yescharacteristic
64C22×D23SD1612yes—
65C22×D23Q1612yes—
66Q8×C23—41no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23C22×C411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C2×Dic23—22no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23C22⋊C411yescharacteristic
82C2×Dic23C22⋊C411yescharacteristic
83C4×D23—22no—
84C4×D23—22no—
85C4×D23—41no—
86C4×D23—41no—
87C4×D23—42no—
88C4×D23—42no—
89Dic46—42no—
90Dic46—41no—
91C8×C23—41no—
92C23⋊C8—41no—
93#1520—231nomaximal, Sylow
94C22×C23—21no—
95C22×C23—21no—
96C22×C23C2×C22⋊C411yescharacteristic
97C22×C23C2×SD1611yescharacteristic
98C22×C23C2×Q1611yescharacteristic
99C2×D23—21no—
100C2×D23—21no—
101C2×D23—21no—
102C2×D23—21no—
103C2×D23—42no—
104C2×D23—42no—
105C2×D23#10312yes—
106C2×D23#10312yes—
107C4×C23—21no—
108C4×C23—21no—
109C4×C23—41no—
110C4×C23—41no—
111C4×C23—81no—
112Dic23—21no—
113Dic23—41no—
114Dic23—41no—
115Dic23—81no—
116Dic23#9912yes—
117C2×C22⋊Q8—231no—
118C2×C22⋊C8—231no—
119#380—231no—
120#328—231no—
121#328—231no—
122#328—231no—
123#328D2311yescharacteristic, complemented
124C2×C23—21no—
125C2×C23—21no—
126C2×C23C2×#9911yescharacteristic
127C2×C23C2×#10311yescharacteristic
128C2×C23#42111yescharacteristic
129D23—22no—
130D23—22no—
131C22×Q8—231no—
132C23×C4—231no—
133C22×C8—461no—
134C22⋊Q8—231no—
135C22⋊Q8—231no—
136C22⋊Q8—231no—
137C22⋊Q8—461no—
138C22⋊Q8—461no—
139C22⋊Q8C2×D2311yescharacteristic
140C2×C4⋊C4—231no—
141C2×C4⋊C4—461no—
142C2×C4⋊C4—461no—
143C2×C22⋊C4—461no—
144C2×C22⋊C4—461no—
145C22⋊C8—231no—
146C22⋊C8—461no—
147C22⋊C8C2×D2311yescharacteristic
148#95—231no—
149#95C2×D2311yescharacteristic
150C23#152011yescharacteristic, complemented, Sylow
151C24—231no—
152C2×Q8—231no—
153C2×Q8—461no—
154C2×Q8—922no—
155C2×Q8C4×D2311yescharacteristic
156C22×C4—21no—
157C22×C4—231no—
158C22×C4—231no—
159C22×C4—231no—
160C22×C4—231no—
161C22×C4—231no—
162C22×C4—461no—
163C22×C4—461no—
164C22×C4—461no—
165C22×C4—922no—
166C22×C4C22×D2311yescharacteristic
167C2×C8—21no—
168C2×C8—461no—
169C2×C8—922no—
170C4⋊C4—21no—
171C4⋊C4—231no—
172C4⋊C4—461no—
173C4⋊C4—461no—
174C4⋊C4—461no—
175C4⋊C4—461no—
176C4⋊C4—922no—
177C4⋊C4C4×D2311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—461no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—922no—
183C23—231no—
184C23—231no—
185C23—232no—
186C23—232no—
187C23—921no—
188C23—921no—
189C23D4×D2311yescharacteristic
190Q8—41no—
191Q8—921no—
192Q8—922no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—231no—
200C2×C4—231no—
201C2×C4—462no—
202C2×C4—462no—
203C2×C4—462no—
204C2×C4—461no—
205C2×C4—461no—
206C2×C4—921no—
207C2×C4—921no—
208C2×C4—922no—
209C2×C4—922no—
210C2×C4—921no—
211C2×C4—921no—
212C2×C4—921no—
213C2×C4C2×C4×D2311yescharacteristic
214C2×C4D4×D2311yescharacteristic
215C8—41no—
216C8—921no—
217C22—21no—
218C22—21no—
219C22—232no—
220C22—232no—
221C22—461no—
222C22—461no—
223C22—461no—
224C22—461no—
225C22—922no—
226C22—922no—
227C22C22⋊C4×D2311yescharacteristic
228C22SD16×D2311yescharacteristic
229C22Q16×D2311yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—232no—
236C4—461no—
237C4—921no—
238C4—921no—
239C4—1841no—
240C2—21no—
241C2—21no—
242C2—462no—
243C2—462no—
244C2#99×D2311yescharacteristic
245C2#103×D2311yescharacteristic
246C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23D4
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1520
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #13092155C2semidirect
5. #13092154C2semidirect
6. #13092153C2semidirect
7. C23×#328C2semidirect
8. C2×Q8×D23C4semidirect
11. #10625117C4semidirect
16. #10625068C4semidirect
19. C4⋊C4×D23C4semidirect
123. #328D23semidirect
150. C23#1520semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D232
C22⋊C8×D232
#130922762
#130921552
#130921542
#130921532
C23×#3282
#152023