Finite Group Databasebeta

← #15676689

Subgroups — #15676689

Order 2944.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10625058C211yesmaximal, characteristic
2C2×#10625058C211yesmaximal, characteristic
3#13092351C212yesmaximal
4#13092348C211yesmaximal, characteristic
5#13092338C211yesmaximal, characteristic
6#13092337C212yesmaximal
7#13092337C211yesmaximal, characteristic
8C4⋊C4×Dic23C212yesmaximal
9#13092268C212yesmaximal
10#13092262C211yesmaximal, characteristic
11C23×#398C211yesmaximal, characteristic
12C22×Dic46C2211yescharacteristic
13C22×Dic46C2211yescharacteristic
14C2×C4⋊C4×C23C2211yescharacteristic
15C2×C4⋊C4×C23C2211yescharacteristic
16C2×C4⋊C4×C23C2212yes—
17C2×C4⋊Dic23C2212yes—
18C2×Dic23⋊C4C2212yes—
19C2×Dic23⋊C4C2211yescharacteristic
20C2×Dic23⋊C4C2211yescharacteristic
21C2×Dic23⋊C4C2212yes—
22C2×Dic23⋊C4C2212yes—
23C2×C4×Dic23C2211yescharacteristic
24C2×C4×Dic23C2212yes—
25C2×C4×Dic23C2211yescharacteristic
26C2×C4×Dic23C2211yescharacteristic
27C2×C4×Dic23C2212yes—
28#10625058—24no—
29#10625058—24no—
30C23×#95C2211yescharacteristic
31C23×#95C2212yes—
32C23⋊#95C2211yescharacteristic
33C23⋊#95C2212yes—
34C23⋊#95C2212yes—
35C23⋊#95C2212yes—
36C23⋊#95C2212yes—
37C22×C4×C23C2311yescharacteristic
38C22×C4×C23C2312yes—
39C22×C4×C23C2311yescharacteristic
40C22×C4×C23C2312yes—
41C22×C4×C23C2311yescharacteristic
42C22×Dic23C2311yescharacteristic
43C22×Dic23C2311yescharacteristic
44C22×Dic23C2312yes—
45C22×Dic23C2311yescharacteristic
46C22×Dic23C2312yes—
47C22×Dic23C2311yescharacteristic
48C2×Dic46—22no—
49C2×Dic46—22no—
50C2×Dic46—22no—
51C2×Dic46—22no—
52C2×Dic46—24no—
53C4⋊C4×C23—22no—
54C4⋊C4×C23—22no—
55C4⋊C4×C23—24no—
56C4⋊Dic23—24no—
57Dic23⋊C4—22no—
58Dic23⋊C4—24no—
59Dic23⋊C4—22no—
60Dic23⋊C4—24no—
61Dic23⋊C4—24no—
62C4×Dic23—22no—
63C4×Dic23—24no—
64C4×Dic23—22no—
65C4×Dic23D414yes—
66C4×Dic23Q818yescomplemented
67C23×C23C2411yescharacteristic
68C2×C4×C23—21no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—22no—
72C2×C4×C23—21no—
73C2×C4×C23—21no—
74C2×C4×C23—22no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23C2×D412yes—
79C2×C4×C23C2×Q814yes—
80C2×C4×C23#4112yes—
81C2×Dic23—21no—
82C2×Dic23—22no—
83C2×Dic23—22no—
84C2×Dic23—22no—
85C2×Dic23—21no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23—22no—
89C2×Dic23—21no—
90C2×Dic23—22no—
91C2×Dic23C2×D412yes—
92C2×Dic23C2×D412yes—
93C2×Dic23C2×Q814yes—
94C2×Dic23C2×Q814yes—
95C2×Dic23#4112yes—
96C2×Dic23#4114yes—
97Dic46—28no—
98Dic46—28no—
99#2399—231nomaximal, Sylow
100C22×C23C22×D411yescharacteristic
101C22×C23C22×Q812yes—
102C22×C23C2×#4111yescharacteristic
103C22×C23C2×#4112yes—
104C22×C23C2×#4111yescharacteristic
105C4×C23—22no—
106C4×C23—22no—
107C4×C23—24no—
108C4×C23—41no—
109C4×C23—42no—
110Dic23—22no—
111Dic23—24no—
112Dic23—22no—
113Dic23—24no—
114Dic23—41no—
115Dic23C4⋊Q814yes—
116C2×C4×Q8—231no—
117C2×C4×Q8—231no—
118#398—231no—
119#398—232no—
120#398D2311yescharacteristic
121#395—232no—
122#395—231no—
123#395—231no—
124C4×C4⋊C4—232no—
125C4×C4⋊C4—232no—
126#376—231no—
127C2×C23#52511yescharacteristic
128C2×C23#52511yescharacteristic
129C2×C23C2×C4⋊Q811yescharacteristic
130C2×C23#53312yes—
131C2×C23#53312yes—
132C22×Q8—231no—
133C22×Q8—231no—
134C4×Q8—464no—
135C4×Q8—464no—
136C2×C4⋊C4—232no—
137C2×C4⋊C4—231no—
138C2×C4⋊C4—231no—
139C2×C4⋊C4—232no—
140C2×C4⋊C4—232no—
141C2×C4⋊C4—232no—
142C2×C4⋊C4C2×D2311yescharacteristic
143C2×C4⋊C4C2×D2311yescharacteristic
144C2×C4⋊C4C2×D2312yes—
145C2×C42—231no—
146C2×C42—232no—
147C2×C42—232no—
148C2×C42—231no—
149C2×C42—231no—
150#95—231no—
151#95—232no—
152#95—232no—
153#95—232no—
154#95—232no—
155#95C2×D2311yescharacteristic
156#95C2×D2312yes—
157C23#239911yescharacteristic, complemented, Sylow
158C2×Q8—462no—
159C2×Q8—464no—
160C2×Q8—462no—
161C2×Q8—462no—
162C2×Q8—462no—
163C22×C4—231no—
164C22×C4—232no—
165C22×C4—231no—
166C22×C4—231no—
167C22×C4—232no—
168C22×C4—231no—
169C22×C4C22×D2312yes—
170C22×C4C22×D2311yescharacteristic
171C22×C4C22×D2311yescharacteristic
172C22×C4C22×D2311yescharacteristic
173C22×C4C22×D2312yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—464no—
178C4⋊C4—462no—
179C4⋊C4—464no—
180C4⋊C4—464no—
181C4⋊C4—464no—
182C4⋊C4—462no—
183C42—234no—
184C42—238no—
185C42—462no—
186C42—462no—
187C42—464no—
188C23C23×D2311yescharacteristic
189Q8—468no—
190Q8—468no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—232no—
202C2×C4—234no—
203C2×C4—232no—
204C2×C4—234no—
205C2×C4—234no—
206C2×C4—232no—
207C2×C4—462no—
208C2×C4—461no—
209C2×C4—461no—
210C2×C4—461no—
211C2×C4—462no—
212C2×C4—462no—
213C2×C4—462no—
214C2×C4—461no—
215C2×C4—461no—
216C2×C4—462no—
217C2×C4D4×D2312yes—
218C2×C4#6729012yes—
219C2×C4Q8×D2314yes—
220C22C2×D4×D2311yescharacteristic
221C22C2×#6729011yescharacteristic
222C22C2×Q8×D2312yes—
223C22#41×D2312yes—
224C22#41×D2311yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—234no—
231C4—464no—
232C4—462no—
233C4—462no—
234C4—464no—
235C4—921no—
236C2#1309292511yescharacteristic
237C2#1309292711yescharacteristic
238C2C4⋊Q8×D2311yescharacteristic
239C2#1309296912yes—
240C2#1309297312yes—
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, prime radical, cosocleC23×C23C24
FittingC23×#398C2
hypercenter#398D23
hypocenterC23#2399
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
66. C4×Dic23Q8semidirect
157. C23#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#106250582
#130923512
#130923482
#130923382
#130923372
C4⋊C4×Dic232
#130922682
#130922622
C23×#3982
#239923