Finite Group Databasebeta

← #15676560

Subgroups — #15676560

Order 2944.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10625095C211yesmaximal, characteristic
2#13092321C212yesmaximal, complemented
3#13092312C212yesmaximal, complemented
4#13092311C212yesmaximal
5#13092305C212yesmaximal
6#13092300C212yesmaximal, complemented
7#13092298C212yesmaximal, complemented
8#13092280C211yesmaximal, characteristic
9C23×#380C211yesmaximal, characteristic
10C23×C4×C23C2211yescharacteristic
11C22×Dic46C2211yescharacteristic
12C2×C4⋊C4×C23C2212yes—
13C2×C22⋊C4×C23C2211yescharacteristic
14C2×C22⋊C4×C23C2211yescharacteristic
15C2×C22⋊Dic23C2212yes—
16C2×C22⋊Dic23C2212yes—
17C2×C4⋊Dic23C2211yescharacteristic
18#10625095C418yescomplemented
19C2×Dic23⋊C4C2212yes—
20C2×Dic23⋊C4C2212yes—
21C2×Dic23⋊C4C2212yes—
22C2×C4×Dic23C2212yes—
23C2×C4×Dic23C2212yes—
24C23×#95C2212yes—
25C23⋊#95C2211yescharacteristic
26C23⋊#95C2212yes—
27C23⋊#95C2211yescharacteristic
28C23⋊#95C2212yes—
29C23⋊#95C2212yes—
30C23⋊#95C2212yes—
31C23⋊#95C2212yes—
32C24×C23C2311yescharacteristic
33C22×C4×C23—42no—
34C22×C4×C23C2×C414yes—
35C22×C4×C23C2312yes—
36C22×C4×C23C2312yes—
37C22×C4×C23C2311yescharacteristic
38C22×C4×C23C2311yescharacteristic
39C22×Dic23C2312yes—
40C22×Dic23C2312yes—
41C22×Dic23C2312yes—
42C22×Dic23C2312yes—
43C2×Dic46—42no—
44C2×Dic46C2×C414yes—
45C4⋊C4×C23—42no—
46C22⋊C4×C23—41no—
47C22⋊C4×C23—41no—
48C22⋊Dic23—42no—
49C22⋊Dic23C2×C418yes—
50C4⋊Dic23C2×C414yes—
51Dic23⋊C4—42no—
52Dic23⋊C4—42no—
53Dic23⋊C4C2×C418yes—
54C4×Dic23—42no—
55C4×Dic23—42no—
56C23×C23—22no—
57C23×C23—21no—
58C23×C23—21no—
59C23×C23—22no—
60C23×C23C22×C412yes—
61C23×C23C2411yescharacteristic
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—22no—
65C2×C4×C23—22no—
66C2×C4×C23—22no—
67C2×C4×C23—22no—
68C2×C4×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—44no—
71C2×C4×C23C22×C412yes—
72C2×C4×C23C22×C412yes—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—22no—
76C2×Dic23—22no—
77C2×Dic23—22no—
78C2×Dic23—22no—
79C2×Dic23—22no—
80C2×Dic23—22no—
81C2×Dic23—22no—
82C2×Dic23—22no—
83C2×Dic23C22×C414yes—
84C2×Dic23C22×C414yes—
85Dic46—44no—
86#2378—231nomaximal, Sylow
87C22×C23—22no—
88C22×C23—22no—
89C22×C23—22no—
90C22×C23—42no—
91C22×C23—42no—
92C22×C23C23×C411yescharacteristic
93C22×C23H(5,𝔽2)12yes—
94C22×C23H(5,𝔽2)11yescharacteristic
95C22×C232−1+411yescharacteristic
96C22×C232−1+412yes—
97C4×C23—22no—
98C4×C23—22no—
99C4×C23—42no—
100C4×C23—42no—
101Dic23—24no—
102Dic23—24no—
103Dic23—42no—
104Dic23—42no—
105C2×C22⋊Q8—231no—
106#391—232no—
107#389—232no—
108#388—232no—
109#388—232no—
110#387—232no—
111#387—232no—
112#381—231no—
113#380D2311yescharacteristic
114C2×C23—42no—
115C2×C23#51811yescharacteristic
116C2×C23#51911yescharacteristic
117C2×C23#52011yescharacteristic
118C2×C23#56212yes—
119C2×C23#56312yes—
120C22×Q8—231no—
121C23×C4C2×D2311yescharacteristic
122C22⋊Q8—238no—
123C2×C4⋊C4—232no—
124C2×C4⋊C4—231no—
125C2×C4⋊C4—232no—
126C2×C4⋊C4—232no—
127C2×C4⋊C4C2×D2312yes—
128C2×C22⋊C4—232no—
129C2×C22⋊C4—232no—
130C2×C22⋊C4C2×D2311yescharacteristic
131C2×C22⋊C4C2×D2311yescharacteristic
132C2×C42—232no—
133C2×C42—232no—
134#95—231no—
135#95—232no—
136#95—231no—
137#95—232no—
138#95—232no—
139#95—232no—
140#95—232no—
141#95C2×D2312yes—
142C23#237811yescharacteristic, complemented, Sylow
143C24C22×D2311yescharacteristic
144C2×Q8—234no—
145C2×Q8—922no—
146C22×C4—42no—
147C22×C4—232no—
148C22×C4—232no—
149C22×C4—232no—
150C22×C4—232no—
151C22×C4C4×D2314yes—
152C22×C4C22×D2312yes—
153C22×C4C22×D2312yes—
154C22×C4C22×D2311yescharacteristic
155C22×C4C22×D2311yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—238no—
158C4⋊C4—234no—
159C4⋊C4—922no—
160C4⋊C4—922no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—238no—
164C22⋊C4—922no—
165C42—922no—
166C42—922no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23—22no—
171C23C2×C4×D2312yes—
172C23C23×D2311yescharacteristic
173Q8—924no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—234no—
184C2×C4—234no—
185C2×C4—462no—
186C2×C4—462no—
187C2×C4—462no—
188C2×C4—462no—
189C2×C4—462no—
190C2×C4—462no—
191C2×C4—462no—
192C2×C4—462no—
193C2×C4—462no—
194C2×C4—462no—
195C2×C4C2×C4×D2312yes—
196C2×C4C2×C4×D2312yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D2311yescharacteristic
203C22#1062515512yes—
204C22#1062515511yescharacteristic
205C22#1062515811yescharacteristic
206C22#1062516112yes—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—464no—
212C4—464no—
213C4—922no—
214C4—922no—
215C2—42no—
216C2#1309289011yescharacteristic
217C2#1309289411yescharacteristic
218C2#1309289811yescharacteristic
219C2#1309316212yes—
220C2#1309316812yes—
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#380C2
socle, cosocleC23×C23C24
prime radicalC24×C23C23
hypercenter#380D23
hypocenterC23#2378
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #13092321C2semidirect
3. #13092312C2semidirect
6. #13092300C2semidirect
7. #13092298C2semidirect
18. #10625095C4semidirect
142. C23#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#106250952
#130923212
#130923122
#130923112
#130923052
#130923002
#130922982
#130922802
C23×#3802
#237823