Finite Group Databasebeta

← #15671885

Subgroups — #15671885

Order 2944.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092927C211yesmaximal, characteristic
2C22⋊C8×D23C211yesmaximal, characteristic, complemented
3#13092264C211yesmaximal, characteristic, complemented
4#13092155C211yesmaximal, characteristic, complemented
5#13092153C211yesmaximal, characteristic, complemented
6#13092151C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×#67290C411yescharacteristic, complemented
9C22×C4×D23C2211yescharacteristic
10C23×#121C2211yescharacteristic
11#10625109C411yescharacteristic, complemented
12#10625108—21no—
13D4×Dic23—21no—
14C2×(C2×D23)⋊C4—21no—
15#10625095C2211yescharacteristic
16C2×C4×Dic23—21no—
17C2×C8×D23—21no—
18#10625068C411yescharacteristic, complemented
19#10625063C411yescharacteristic, complemented
20#10625054—21no—
21(C22⋊D23)⋊C4—21no—
22C23×C22⋊C8C2211yescharacteristic
23C23×#95C2211yescharacteristic
24C23⋊#95C2211yescharacteristic
25C22⋊(C23⋊C8)C2211yescharacteristic
26(C2×D23)⋊C8—21no—
27C23×D23D411yescharacteristic
28C2×D4×C23—21no—
29C2×D4×C23C2×C411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37#67290—42no—
38C2×C4×D23—42no—
39C2×C4×D23C2×C411yescharacteristic
40C2×C4×D23C2×C411yescharacteristic
41C2×C4×D23D411yescharacteristic
42C2×C4×D23D411yescharacteristic
43C2×Dic46C2×C411yescharacteristic
44C2×C8×C23—21no—
45C4⋊C4×C23C2×C411yescharacteristic
46C22⋊C4×C23—21no—
47C22⋊Dic23—21no—
48C22⋊Dic23—21no—
49(C2×D23)⋊C4—24no—
50(C2×D23)⋊C4—21no—
51(C2×D23)⋊C4—21no—
52C4⋊Dic23—21no—
53C4⋊Dic23C2×C411yescharacteristic
54Dic23⋊C4—21no—
55C4×Dic23—21no—
56C4×Dic23—42no—
57C2×C23⋊C8—21no—
58C8×D23—42no—
59C23×C23—21no—
60C23×C23C2×D411yescharacteristic
61C22×D23—21no—
62C22×D23—21no—
63C22×D23—22no—
64C22×D23—41no—
65C22×D23C22⋊C411yescharacteristic
66C22×D23C22⋊C411yescharacteristic
67D4×C23—41no—
68D4×C23—41no—
69D4×C23—41no—
70C2×C4×C23—22no—
71C2×C4×C23—21no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23C22×C411yescharacteristic
76C2×C4×C23C2×D411yescharacteristic
77C22⋊D23—42no—
78C22⋊D23—42no—
79C2×Dic23—22no—
80C2×Dic23—22no—
81C2×Dic23—21no—
82C2×Dic23—21no—
83C2×Dic23—41no—
84C2×Dic23—41no—
85C2×Dic23—42no—
86C2×Dic23C22⋊C411yescharacteristic
87C2×Dic23C22⋊C411yescharacteristic
88C4×D23—22no—
89C4×D23—22no—
90C4×D23—41no—
91C4×D23—41no—
92Dic46—41no—
93C8×C23—41no—
94C23⋊C8—41no—
95#1501—231nomaximal, Sylow
96C22×C23—21no—
97C22×C23—21no—
98C22×C23—41no—
99C22×C23—41no—
100C22×C23—41no—
101C22×C23C2×C22⋊C411yescharacteristic
102C22×C23#13511yescharacteristic
103C22×C23#13511yescharacteristic
104C2×D23—21no—
105C2×D23—21no—
106C2×D23—21no—
107C2×D23—21no—
108C2×D23—21no—
109C2×D23—42no—
110C2×D23—42no—
111C2×D23#10412yes—
112C4×C23—21no—
113C4×C23—21no—
114C4×C23—42no—
115C4×C23—41no—
116Dic23—21no—
117Dic23—42no—
118Dic23—41no—
119Dic23—41no—
120Dic23#9912yes—
121#525—231no—
122C2×C22⋊C8—231no—
123C4×C22⋊C4—231no—
124#328—231no—
125#328—231no—
126#327—231no—
127#327D2311yescharacteristic, complemented
128C2×C23—21no—
129C2×C23—21no—
130C2×C23—81no—
131C2×C23C2×#9911yescharacteristic
132C2×C23#41611yescharacteristic
133C2×C23C2×#10411yescharacteristic
134D23—22no—
135D23—41no—
136C2×#41—231no—
137C23×C4—231no—
138C22×C8—461no—
139#123—461no—
140C22⋊Q8—231no—
141C22⋊Q8—231no—
142#121—231no—
143#121C2×D2311yescharacteristic
144#120—461no—
145C4×D4—461no—
146C4×D4—461no—
147#117—231no—
148C2×C22⋊C4—461no—
149C2×C42—461no—
150C22⋊C8—231no—
151C22⋊C8—461no—
152C22⋊C8C2×D2311yescharacteristic
153#95—231no—
154#95C2×D2311yescharacteristic
155C23#150111yescharacteristic, complemented, Sylow
156C24—231no—
157#41—922no—
158C2×Q8—231no—
159C2×D4—21no—
160C2×D4—461no—
161C2×D4—461no—
162C2×D4C4×D2311yescharacteristic
163C22×C4—21no—
164C22×C4—231no—
165C22×C4—231no—
166C22×C4—231no—
167C22×C4—231no—
168C22×C4—231no—
169C22×C4—461no—
170C22×C4—461no—
171C22×C4—922no—
172C22×C4C22×D2311yescharacteristic
173C2×C8—21no—
174C2×C8—461no—
175C2×C8—922no—
176C4⋊C4—231no—
177C4⋊C4—461no—
178C4⋊C4—461no—
179C4⋊C4C4×D2311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—464no—
184C22⋊C4—461no—
185C22⋊C4—461no—
186C42—461no—
187C42—922no—
188C23—21no—
189C23—231no—
190C23—231no—
191C23—462no—
192C23—461no—
193C23—461no—
194C23—921no—
195C23D4×D2311yescharacteristic
196Q8—921no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—922no—
201D4—922no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—231no—
208C2×C4—231no—
209C2×C4—462no—
210C2×C4—462no—
211C2×C4—462no—
212C2×C4—462no—
213C2×C4—461no—
214C2×C4—461no—
215C2×C4—921no—
216C2×C4—921no—
217C2×C4—922no—
218C2×C4—921no—
219C2×C4—921no—
220C2×C4C2×C4×D2311yescharacteristic
221C2×C4D4×D2311yescharacteristic
222C8—41no—
223C8—921no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—232no—
230C22—461no—
231C22—461no—
232C22—461no—
233C22—461no—
234C22—461no—
235C22—922no—
236C22—922no—
237C22C22⋊C4×D2311yescharacteristic
238C22#1062508311yescharacteristic
239C22#1062508711yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—232no—
245C4—461no—
246C4—922no—
247C4—921no—
248C4—921no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—462no—
253C2—921no—
254C2#99×D2311yescharacteristic
255C2#1309241011yescharacteristic
256C2#104×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23C2×C22⋊C4
prime radical#13092927C2
cosocleC22×C4×C23C23
hypercenter#327D23
hypocenterC23#1501
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D23C2semidirect
3. #13092264C2semidirect
4. #13092155C2semidirect
5. #13092153C2semidirect
6. #13092151C2semidirect
7. C23×#327C2semidirect
8. C2×#67290C4semidirect
11. #10625109C4semidirect
18. #10625068C4semidirect
19. #10625063C4semidirect
127. #327D23semidirect
155. C23#1501semidirect

Maximal subgroups

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

subgroupindex
#130929272
C22⋊C8×D232
#130922642
#130921552
#130921532
#130921512
C23×#3272
#150123