Finite Group Databasebeta

← #15673845

Subgroups — #15673845

Order 2944.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#13092928C211yesmaximal, characteristic
2C2×#10624987C212yesmaximal, complemented
3#13092381C211yesmaximal, characteristic, complemented
4#13092177C212yesmaximal, complemented
5C2×C23×#117C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C2211yescharacteristic
8C23×#117—24no—
9C2×C4⋊C4×C23—21no—
10C2×C22⋊C4×C23—21no—
11C2×C42×C23C2212yes—
12#10625124—21no—
13#10625101C412yescomplemented
14#10625100—21no—
15C4×C22⋊D23—22no—
16#10625097C2211yescharacteristic
17#10625095C412yescomplemented
18C2×#67267C2212yes—
19C22⋊(C23⋊C8)—22no—
20#10624987—24no—
21C24×C23D411yescharacteristic
22C22×C4×C23—22no—
23C22×C4×C23—22no—
24C22×C4×C23—22no—
25C22×C4×C23C2×C412yes—
26C22×C4×C23D412yes—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23C2311yescharacteristic
29C2×C22⋊D23—22no—
30C2×C22⋊D23—21no—
31#67288—22no—
32#67288—22no—
33C2×D92C2×C411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46C2×C411yescharacteristic
36C4⋊C4×C23—24no—
37C22⋊C4×C23—24no—
38C42×C23—22no—
39C42×C23D414yescomplemented
40C22⋊Dic23—22no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—22no—
43C4⋊Dic23C2×C412yes—
44Dic23⋊C4—22no—
45C4×Dic23—21no—
46#67267—22no—
47#67267—22no—
48C2×C23⋊C8—22no—
49C23×C23—21no—
50C23×C23—21no—
51C23×C23—42no—
52C23×C23C22⋊C412yes—
53C23×C23C2×D411yescharacteristic
54C22×D23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—24no—
58C2×C4×C23—24no—
59C2×C4×C23—24no—
60C2×C4×C23—44no—
61C2×C4×C23C22⋊C412yes—
62C2×C4×C23C22×C411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D412yes—
65C2×C4×C23#4112yes—
66C22⋊D23—44no—
67C22⋊D23—41no—
68C22⋊D23—41no—
69C2×Dic23—22no—
70C2×Dic23—21no—
71D92—22no—
72C4×D23—42no—
73Dic46—22no—
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×C23C2×C22⋊C411yescharacteristic
83C22×C23#12011yescharacteristic
84C22×C23#12311yescharacteristic
85C2×D23—41no—
86C2×D23—42no—
87C4×C23—22no—
88C4×C23—44no—
89C4×C23C4×D412yes—
90C4×C23#12112yes—
91Dic23—41no—
92Dic23—42no—
93#525—231no—
94C2×#117D2311yescharacteristic, complemented
95C2×#104—232no—
96#407—231no—
97#339—232no—
98C2×C23—21no—
99C2×C23—21no—
100C2×C23—42no—
101C2×C23#38611yescharacteristic
102C2×C23#42112yes—
103D23—81no—
104C2×#41—231no—
105C23×C4C2×D2311yescharacteristic
106C2×M16—232no—
107#123—461no—
108C22⋊Q8—232no—
109#121—232no—
110#120—461no—
111C4×D4—462no—
112#117—24no—
113#117—231no—
114C2×C4⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C42C2×D2312yes—
117#104—464no—
118C22⋊C8—462no—
119C23#189711yescharacteristic, complemented, Sylow
120C24C22⋊D2311yescharacteristic
121#41—462no—
122#41—462no—
123C2×Q8—231no—
124C2×D4—231no—
125C2×D4—462no—
126C2×D4—461no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—461no—
131C22×C4C4×D2312yes—
132C22×C4D9212yes—
133C22×C4C22⋊D2311yescharacteristic
134C22×C4C22×D2311yescharacteristic
135M16—462no—
136M16—462no—
137C2×C8—462no—
138C4⋊C4—24no—
139C4⋊C4—232no—
140C4⋊C4—462no—
141C22⋊C4—24no—
142C22⋊C4—462no—
143C22⋊C4—461no—
144C22⋊C4—462no—
145C42—22no—
146C42—461no—
147C42C22⋊D2314yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—461no—
152C23(C2×D23)⋊C412yes—
153C23C2×C22⋊D2311yescharacteristic
154Q8—462no—
155D4—462no—
156D4—924no—
157D4—921no—
158D4—921no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—462no—
166C2×C4—461no—
167C2×C4—922no—
168C2×C4(C2×D23)⋊C412yes—
169C2×C4C2×C4×D2311yescharacteristic
170C2×C4C2×D9211yescharacteristic
171C2×C4#6728812yes—
172C2×C4C2×C22⋊D2312yes—
173C8—922no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—922no—
181C22—921no—
182C22C2×(C2×D23)⋊C411yescharacteristic
183C22#1062510011yescharacteristic
184C22#1062512411yescharacteristic
185C4—22no—
186C4—44no—
187C4—922no—
188C4—921no—
189C4C4×C22⋊D2312yes—
190C4#1062510112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—1841no—
195C2#1309229611yescharacteristic
196C2#1309243512yes—
subgroupG/H
centerC2×C4C2×D92
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#117C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenterC2×#117D23
hypocenterC23#1897
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10624987C2semidirect
3. #13092381C2semidirect
4. #13092177C2semidirect
5. C2×C23×#117C2semidirect
13. #10625101C4semidirect
17. #10625095C4semidirect
39. C42×C23D4semidirect
94. C2×#117D23semidirect
119. C23#1897semidirect
147. C42C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929282
C2×#106249872
#130923812
#130921772
C2×C23×#1172
#189723