Finite Group Databasebeta

← #15673846

Subgroups — #15673846

Order 2944.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10625097C211yesmaximal, characteristic, complemented
2C2×#10625019C212yesmaximal, complemented
3#13092381C211yesmaximal, characteristic, complemented
4#13092176C212yesmaximal, complemented
5C23×#525C211yesmaximal, characteristic
6C2×#41×C23C2211yescharacteristic
7C23×C4×C23C2211yescharacteristic
8C23×#123—21no—
9C23×C22⋊Q8C412yescomplemented
10C23×#121C412yescomplemented
11C23×#120—21no—
12C4×D4×C23—22no—
13C23×#117C2211yescharacteristic
14C2×C22⋊Dic23—21no—
15#10625097—24no—
16C2×C4⋊Dic23—21no—
17C2×C4×Dic23C2212yes—
18C2×#67267C2212yes—
19#10625019—24no—
20C22⋊(C23⋊C8)—22no—
21C24×C23D411yescharacteristic
22#41×C23—22no—
23#41×C23—22no—
24C2×Q8×C23C2×C411yescharacteristic
25C2×D4×C23—22no—
26C2×D4×C23—21no—
27C2×D4×C23C2×C411yescharacteristic
28C22×C4×C23—22no—
29C22×C4×C23—22no—
30C22×C4×C23—21no—
31C22×C4×C23C2×C412yes—
32C22×C4×C23D411yescharacteristic
33C22×C4×C23D412yes—
34C22×C4×C23C2311yescharacteristic
35C22×Dic23—22no—
36C4⋊C4×C23—22no—
37C4⋊C4×C23C2×C412yes—
38C22⋊C4×C23—22no—
39C22⋊C4×C23—21no—
40C22⋊C4×C23—22no—
41C42×C23—21no—
42C22⋊Dic23—24no—
43C4⋊Dic23—24no—
44C4×Dic23—22no—
45C4×Dic23D414yescomplemented
46#67267—22no—
47#67267—22no—
48C2×C23⋊C8—22no—
49C23×C23—21no—
50C23×C23—21no—
51C23×C23—21no—
52C23×C23—42no—
53C23×C23C22⋊C412yes—
54C23×C23C2×D411yescharacteristic
55Q8×C23—22no—
56D4×C23—22no—
57D4×C23—44no—
58D4×C23—41no—
59D4×C23—41no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—24no—
63C2×C4×C23—24no—
64C2×C4×C23—22no—
65C2×C4×C23—21no—
66C2×C4×C23—42no—
67C2×C4×C23C22⋊C412yes—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D412yes—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23#4112yes—
72C2×Dic23—24no—
73C2×Dic23—44no—
74C23⋊C8—42no—
75#1897—231nomaximal, Sylow
76C22×C23—22no—
77C22×C23—22no—
78C22×C23—22no—
79C22×C23—22no—
80C22×C23—42no—
81C22×C23—42no—
82C22×C23—41no—
83C22×C23—42no—
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23#12011yescharacteristic
86C22×C23#12311yescharacteristic
87C4×C23—22no—
88C4×C23—41no—
89C4×C23—42no—
90C4×C23C4×D412yes—
91C4×C23#12112yes—
92Dic23—44no—
93#525D2311yescharacteristic
94C2×#117—231no—
95C2×#104—232no—
96#407—231no—
97#339—232no—
98C2×C23—21no—
99C2×C23—21no—
100C2×C23—42no—
101C2×C23—81no—
102C2×C23#38611yescharacteristic
103C2×C23#42112yes—
104C2×#41C2×D2311yescharacteristic
105C23×C4C2×D2311yescharacteristic
106C2×M16—232no—
107#123—21no—
108C22⋊Q8Dic2312yescomplemented
109#121Dic2312yescomplemented
110#120—21no—
111C4×D4—22no—
112#117—464no—
113#117C2×D2311yescharacteristic
114C2×C4⋊C4—461no—
115C2×C22⋊C4—461no—
116C2×C42—232no—
117#104—464no—
118C22⋊C8—462no—
119C23#189711yescharacteristic, complemented, Sylow
120C24C22⋊D2311yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic2311yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic2311yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—462no—
131C22×C4C2×Dic2312yes—
132C22×C4C22⋊D2311yescharacteristic
133C22×C4C22⋊D2312yes—
134C22×C4C22×D2311yescharacteristic
135M16—462no—
136M16—462no—
137C2×C8—462no—
138C4⋊C4—22no—
139C4⋊C4—464no—
140C4⋊C4C2×Dic2312yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—464no—
145C42—21no—
146C42—234no—
147C42—462no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic2312yes—
153C23C2×C22⋊D2311yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—464no—
167C2×C4—924no—
168C2×C4C22⋊Dic2312yes—
169C2×C4D4×D2312yes—
170C2×C4#6729012yes—
171C2×C4C22×Dic2311yescharacteristic
172C2×C4C2×C22⋊D2311yescharacteristic
173C8—922no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22#1062510611yescharacteristic
183C22#1062510811yescharacteristic
184C22C2×C22⋊Dic2311yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—924no—
189C4D4×Dic2312yes—
190C4#1062511012yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#1309229711yescharacteristic
196C2#1309243412yes—
subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#525C2
socleC22×C23C2×C22⋊C4
cosocleC22×C4×C23C23
hypercenter#525D23
hypocenterC23#1897
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#10625097C2semidirect
2. C2×#10625019C2semidirect
3. #13092381C2semidirect
4. #13092176C2semidirect
9. C23×C22⋊Q8C4semidirect
10. C23×#121C4semidirect
45. C4×Dic23D4semidirect
108. C22⋊Q8Dic23semidirect
109. #121Dic23semidirect
119. C23#1897semidirect

Maximal subgroups

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

subgroupindex
C2×#106250972
C2×#106250192
#130923812
#130921762
C23×#5252
#189723