Finite Group Databasebeta

← #15675980

Subgroups — #15675980

Order 2944.

784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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
2C2×#10625063C211yesmaximal, characteristic
3C2×#10625043C211yesmaximal, characteristic
4#13092324C211yesmaximal, characteristic, complemented
5#13092323C211yesmaximal, characteristic, complemented
6#13092322C211yesmaximal, characteristic, complemented
7#13092321C214yesmaximal, complemented
8#13092279C214yesmaximal
9C23×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C23C2211yescharacteristic
11C2×Q8×D23—24no—
12C2×Q8×D23—24no—
13C2×Q8×D23C418yescomplemented
14C22×C4×D23C2212yes—
15C22×C4×D23C2211yescharacteristic
16C22×Dic46C2212yes—
17C22×Dic46C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×C42×C23C2211yescharacteristic
20C2×(C2×D23)⋊C4C2212yes—
21C2×(C2×D23)⋊C4C2212yes—
22C2×C4⋊Dic23C2211yescharacteristic
23C2×Dic23⋊C4C2212yes—
24C2×C4×Dic23C2211yescharacteristic
25C2×C4×Dic23C2212yes—
26#10625063—24no—
27#10625043—24no—
28C23×#95C2214yes—
29C23⋊#95C2214yes—
30C23⋊#95C2214yes—
31C23⋊#95C2214yes—
32C23×D23C2311yescharacteristic
33C2×Q8×C23—22no—
34C2×Q8×C23—22no—
35C2×Q8×C23C2×C414yes—
36C22×C4×C23C2312yes—
37C22×C4×C23C2312yes—
38C22×C4×C23C2312yes—
39C22×C4×C23C2311yescharacteristic
40C22×Dic23C2312yes—
41C22×Dic23C2312yes—
42C22×Dic23C2312yes—
43C22×Dic23C2311yescharacteristic
44Q8×D23—232no—
45C2×C4×D23—24no—
46C2×C4×D23—24no—
47C2×C4×D23C2×C418yes—
48C2×C4×D23C2×C414yes—
49C2×C4×D23D414yes—
50C2×C4×D23D414yes—
51C2×Dic46—22no—
52C2×Dic46—22no—
53C2×Dic46—24no—
54C2×Dic46—24no—
55C2×Dic46C2×C414yes—
56C2×Dic46C2×C418yes—
57C4⋊C4×C23—22no—
58C42×C23—22no—
59(C2×D23)⋊C4—24no—
60(C2×D23)⋊C4—24no—
61C4⋊Dic23—22no—
62Dic23⋊C4—24no—
63C4×Dic23—22no—
64C4×Dic23—24no—
65C23×C23C2411yescharacteristic
66C22×D23—22no—
67C22×D23—22no—
68C22×D23C22×C412yes—
69C22×D23C2×D412yes—
70C22×D23C2×D412yes—
71Q8×C23—28no—
72C2×C4×C23—22no—
73C2×C4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—24no—
78C2×C4×C23—22no—
79C2×C4×C23C22×C414yes—
80C2×C4×C23C22×C412yes—
81C2×C4×C23C2×D412yes—
82C2×C4×C23C2×D412yes—
83C2×Dic23—22no—
84C2×Dic23—22no—
85C2×Dic23—22no—
86C2×Dic23—22no—
87C2×Dic23—22no—
88C2×Dic23—24no—
89C2×Dic23—22no—
90C2×Dic23C22×C414yes—
91C2×Dic23C22×C412yes—
92C2×Dic23C2×D412yes—
93C2×Dic23C2×D412yes—
94C4×D23—216no—
95C4×D23C22⋊C4116yes—
96Dic46—28no—
97Dic46—216no—
98#2310—231nomaximal, Sylow
99C22×C23C23×C411yescharacteristic
100C22×C23C22×D411yescharacteristic
101C22×C23C22×D411yescharacteristic
102C22×C232−1+412yes—
103C22×C232−1+412yes—
104C2×D23—24no—
105C2×D23—22no—
106C2×D23—24no—
107C2×D23—22no—
108C2×D23C2×C22⋊C414yes—
109C4×C23—24no—
110C4×C23—42no—
111C4×C23—42no—
112C4×C23C2×C22⋊C414yes—
113Dic23—24no—
114Dic23—42no—
115Dic23—42no—
116Dic23C2×C22⋊C414yes—
117C23×Q8—231no—
118C2×#117—231no—
119C2×#117—231no—
120#391—231no—
121#391—231no—
122#391—231no—
123#391—234no—
124#391D2311yescharacteristic, complemented
125#381—234no—
126C2×C23C22×C22⋊C411yescharacteristic
127C2×C23#51912yes—
128C2×C23#53611yescharacteristic
129C2×C23#53612yes—
130C2×C23#53611yescharacteristic
131D23—24no—
132C22×Q8—238no—
133C22×Q8—232no—
134C22×Q8—231no—
135C22×Q8—464no—
136C22×Q8—464no—
137C22×Q8C2×D2311yescharacteristic
138C23×C4—231no—
139C23×C4—232no—
140#117—464no—
141#117—464no—
142C2×C4⋊C4—232no—
143C2×C4⋊C4—231no—
144C2×C4⋊C4C2×D2311yescharacteristic
145C2×C22⋊C4—232no—
146C2×C22⋊C4—232no—
147C2×C42—232no—
148C2×C42—231no—
149C2×C42C2×D2311yescharacteristic
150#95—234no—
151#95—234no—
152#95—234no—
153#95C2×D2314yes—
154C23#231011yescharacteristic, complemented, Sylow
155C24—231no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—238no—
159C2×Q8—234no—
160C2×Q8—464no—
161C2×Q8—464no—
162C2×Q8—4632no—
163C2×Q8—462no—
164C2×Q8—462no—
165C2×Q8C4×D2314yes—
166C22×C4—231no—
167C22×C4—234no—
168C22×C4—234no—
169C22×C4—234no—
170C22×C4—232no—
171C22×C4—238no—
172C22×C4—232no—
173C22×C4—232no—
174C22×C4—464no—
175C22×C4—464no—
176C22×C4C22×D2312yes—
177C22×C4C22×D2312yes—
178C22×C4C22×D2312yes—
179C22×C4C22×D2311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—464no—
182C4⋊C4—462no—
183C22⋊C4—464no—
184C22⋊C4—464no—
185C42—22no—
186C42—464no—
187C42—462no—
188C23—232no—
189C23—232no—
190C23—232no—
191C23—462no—
192C23—462no—
193C23C23×D2311yescharacteristic
194Q8—28no—
195Q8—4616no—
196Q8—468no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—232no—
205C2×C4—232no—
206C2×C4—232no—
207C2×C4—2316no—
208C2×C4—234no—
209C2×C4—4616no—
210C2×C4—462no—
211C2×C4—462no—
212C2×C4—462no—
213C2×C4—462no—
214C2×C4—462no—
215C2×C4—464no—
216C2×C4—462no—
217C2×C4C2×C4×D2314yes—
218C2×C4C2×C4×D2312yes—
219C2×C4D4×D2312yes—
220C2×C4D4×D2312yes—
221C22—234no—
222C22—464no—
223C22—462no—
224C22—464no—
225C22—462no—
226C22C22×C4×D2311yescharacteristic
227C22C2×D4×D2311yescharacteristic
228C22C2×D4×D2311yescharacteristic
229C22#1062515812yes—
230C22#1062516112yes—
231C4—24no—
232C4—42no—
233C4—42no—
234C4—234no—
235C4—464no—
236C4—922no—
237C4—922no—
238C4C22⋊C4×D2314yes—
239C2—464no—
240C2C2×C22⋊C4×D2311yescharacteristic
241C2#1309289312yes—
242C2#1309298711yescharacteristic
243C2#1309299012yes—
244C2#1309299211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#391C2
socle, cosocleC23×C23C24
prime radicalC23×D23C23
hypercenter#391D23
hypocenterC23#2310
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #13092324C2semidirect
5. #13092323C2semidirect
6. #13092322C2semidirect
7. #13092321C2semidirect
9. C23×#391C2semidirect
13. C2×Q8×D23C4semidirect
124. #391D23semidirect
154. C23#2310semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D232
C2×#106250632
C2×#106250432
#130923242
#130923232
#130923222
#130923212
#130922792
C23×#3912
#231023