Finite Group Databasebeta

← #15675966

Subgroups — #15675966

Order 2944.

588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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×#10625115C211yesmaximal, characteristic
2C2×Q8×Dic23C211yesmaximal, characteristic
3C2×#10625058C211yesmaximal, characteristic
4#13092323C211yesmaximal, characteristic
5#13092314C214yesmaximal
6#13092286C211yesmaximal, characteristic
7#13092268C214yesmaximal
8C42×Dic23C211yesmaximal, characteristic
9C23×#391C211yesmaximal, characteristic
10C22×Q8×C23C2211yescharacteristic
11C22×Dic46C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×C42×C23C2211yescharacteristic
14Q8×Dic23—24no—
15#10625115C418yescomplemented
16C2×C4⋊Dic23C2211yescharacteristic
17C2×C4⋊Dic23C2212yes—
18C2×Dic23⋊C4C2212yes—
19C2×Dic23⋊C4C2214yes—
20C2×Dic23⋊C4C2214yes—
21C2×C4×Dic23C2212yes—
22C2×C4×Dic23C2212yes—
23C2×C4×Dic23C2212yes—
24C2×C4×Dic23C2211yescharacteristic
25C2×C4×Dic23C2211yescharacteristic
26C2×C4×Dic23C2212yes—
27#10625058—24no—
28C23×#95C2214yes—
29C23⋊#95C2214yes—
30C2×Q8×C23—22no—
31C2×Q8×C23—22no—
32C2×Q8×C23C2×C414yes—
33C22×C4×C23C2312yes—
34C22×C4×C23C2312yes—
35C22×C4×C23C2312yes—
36C22×C4×C23C2311yescharacteristic
37C22×Dic23C2312yes—
38C22×Dic23C2312yes—
39C22×Dic23C2311yescharacteristic
40C22×Dic23C2312yes—
41C22×Dic23C2311yescharacteristic
42C2×Dic46—22no—
43C2×Dic46—22no—
44C2×Dic46C2×C414yes—
45C4⋊C4×C23—22no—
46C42×C23—22no—
47C4⋊Dic23—22no—
48C4⋊Dic23—24no—
49Dic23⋊C4—24no—
50Dic23⋊C4—28no—
51Dic23⋊C4C2×C4116yes—
52C4×Dic23—24no—
53C4×Dic23—24no—
54C4×Dic23—24no—
55C4×Dic23C2×C414yes—
56C4×Dic23D414yes—
57C4×Dic23Q818yescomplemented
58C23×C23C2411yescharacteristic
59Q8×C23—28no—
60C2×C4×C23—22no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—22no—
65C2×C4×C23—24no—
66C2×C4×C23C22×C414yes—
67C2×C4×C23C22×C412yes—
68C2×C4×C23C2×D412yes—
69C2×C4×C23C2×Q814yes—
70C2×C4×C23#4112yes—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—24no—
76C2×Dic23C22×C414yes—
77C2×Dic23C22×C414yes—
78C2×Dic23C2×D412yes—
79C2×Dic23C2×D412yes—
80C2×Dic23C2×Q814yes—
81C2×Dic23C2×Q814yes—
82C2×Dic23#4114yes—
83Dic46—28no—
84C4×C4⋊Q8—231nomaximal, Sylow
85C22×C23C23×C411yescharacteristic
86C22×C23C22×D411yescharacteristic
87C22×C23C22×Q812yes—
88C22×C23C2×#4111yescharacteristic
89C22×C23C2×#4112yes—
90C4×C23—24no—
91C4×C23—24no—
92C4×C23—42no—
93C4×C23C4×D414yes—
94Dic23—24no—
95Dic23—22no—
96Dic23—42no—
97Dic23C4×Q818yescomplemented
98Dic23C4⋊Q814yescomplemented
99C2×C4⋊Q8—231no—
100C2×C4×Q8—231no—
101C2×C4×Q8—231no—
102#391—231no—
103#391D2311yescharacteristic
104#389—234no—
105#384—231no—
106C4×C4⋊C4—234no—
107C43—231no—
108C2×C23C2×C4×D411yescharacteristic
109C2×C23C2×C4×Q812yes—
110C2×C23C2×C4⋊Q811yescharacteristic
111C2×C23#53211yescharacteristic
112C2×C23#53312yes—
113C22×Q8—231no—
114C22×Q8C2×D2311yescharacteristic
115C4⋊Q8—238no—
116C4×Q8—464no—
117C4×Q8—464no—
118C2×C4⋊C4—234no—
119C2×C4⋊C4—232no—
120C2×C4⋊C4—231no—
121C2×C4⋊C4—232no—
122C2×C4⋊C4—234no—
123C2×C4⋊C4C2×D2311yescharacteristic
124C2×C42—231no—
125C2×C42—231no—
126C2×C42—232no—
127C2×C42—232no—
128C2×C42—232no—
129C2×C42—232no—
130C2×C42C2×D2311yescharacteristic
131#95—234no—
132#95C2×D2314yes—
133C23C4×C4⋊Q811yescharacteristic, complemented, Sylow
134C2×Q8—22no—
135C2×Q8—22no—
136C2×Q8—234no—
137C2×Q8—462no—
138C2×Q8—462no—
139C2×Q8C4×D2314yes—
140C22×C4—231no—
141C22×C4—232no—
142C22×C4—232no—
143C22×C4—231no—
144C22×C4—232no—
145C22×C4C22×D2312yes—
146C22×C4C22×D2312yes—
147C22×C4C22×D2312yes—
148C22×C4C22×D2311yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—2316no—
151C4⋊C4—464no—
152C4⋊C4—464no—
153C4⋊C4—468no—
154C4⋊C4—462no—
155C42—22no—
156C42—234no—
157C42—234no—
158C42—238no—
159C42—464no—
160C42—464no—
161C42—464no—
162C23C23×D2311yescharacteristic
163Q8—28no—
164Q8—468no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—234no—
172C2×C4—232no—
173C2×C4—234no—
174C2×C4—234no—
175C2×C4—234no—
176C2×C4—234no—
177C2×C4—232no—
178C2×C4—462no—
179C2×C4—462no—
180C2×C4—462no—
181C2×C4—462no—
182C2×C4—464no—
183C2×C4C2×C4×D2314yes—
184C2×C4C2×C4×D2312yes—
185C2×C4D4×D2312yes—
186C2×C4#6729012yes—
187C2×C4Q8×D2314yes—
188C22C22×C4×D2311yescharacteristic
189C22C2×D4×D2311yescharacteristic
190C22C2×#6729011yescharacteristic
191C22C2×Q8×D2312yes—
192C22#41×D2312yes—
193C4—24no—
194C4—24no—
195C4—42no—
196C4—238no—
197C4—234no—
198C4—464no—
199C4—462no—
200C4—922no—
201C4(C22⋊D23)⋊C414yes—
202C2C2×(C22⋊D23)⋊C411yescharacteristic
203C2C4×Q8×D2312yes—
204C2C4⋊Q8×D2311yescharacteristic
205C2#1309296611yescharacteristic
206C2#1309296912yes—
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#391C2
socle, prime radical, cosocleC23×C23C24
hypercenter#391D23
hypocenterC23C4×C4⋊Q8
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
15. #10625115C4semidirect
57. C4×Dic23Q8semidirect
97. Dic23C4×Q8semidirect
98. Dic23C4⋊Q8semidirect
133. C23C4×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#106251152
C2×Q8×Dic232
C2×#106250582
#130923232
#130923142
#130922862
#130922682
C42×Dic232
C23×#3912
C4×C4⋊Q823