Finite Group Databasebeta

← #15671954

Subgroups — #15671954

Order 2944.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#13092280C211yesmaximal, characteristic, complemented
3#13092155C212yesmaximal, complemented
4#13092152C212yesmaximal, complemented
5C2×C23×C22⋊C8C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic, complemented
8C22×C8×C23—21no—
9#10625124—21no—
10C2×C22⋊Dic23—21no—
11#10625101C411yescharacteristic, complemented
12#10625101C2211yescharacteristic
13#10625100—21no—
14C4×C22⋊D23—21no—
15C4×C22⋊D23—21no—
16#10625097C411yescharacteristic, complemented
17#10625095C411yescharacteristic, complemented
18#10625095C2211yescharacteristic
19C23×C22⋊C8—21no—
20C23×C22⋊C8C2212yes—
21C23⋊#95—21no—
22C23⋊#95C2212yes—
23C24×C23D411yescharacteristic
24C22×C4×C23—42no—
25C22×C4×C23C2×C411yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—22no—
35#67288—42no—
36C2×D92C2×C411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46C2×C411yescharacteristic
39C2×C8×C23—22no—
40C2×C8×C23—42no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—21no—
44C22⋊Dic23—42no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47C4⋊Dic23C2×C411yescharacteristic
48C4⋊Dic23C2×C411yescharacteristic
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23—21no—
52C23×C23—22no—
53C23×C23—22no—
54C23×C23—41no—
55C23×C23C22⋊C411yescharacteristic
56C23×C23C22⋊C411yescharacteristic
57C23×C23C2×D411yescharacteristic
58C22×D23—21no—
59C2×C4×C23—22no—
60C2×C4×C23—22no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23C22⋊C411yescharacteristic
66C2×C4×C23C22⋊C411yescharacteristic
67C2×C4×C23C22×C411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—42no—
70C22⋊D23—42no—
71C22⋊D23—42no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—42no—
76C2×Dic23—42no—
77C2×Dic23—42no—
78D92—41no—
79C4×D23—42no—
80Dic46—41no—
81C8×C23—42no—
82#1516—231nomaximal, Sylow
83C22×C23—21no—
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—44no—
91C22×C23#9912yes—
92C22×C23C2×C22⋊C411yescharacteristic
93C22×C23#13512yes—
94C2×D23—41no—
95C2×D23—41no—
96C2×D23—41no—
97C4×C23—21no—
98C4×C23—21no—
99C4×C23—21no—
100C4×C23—21no—
101Dic23—41no—
102Dic23—41no—
103Dic23—41no—
104Dic23—82no—
105#525—231no—
106C2×C22⋊C8D2311yescharacteristic, complemented
107#381—231no—
108#328—232no—
109#327—232no—
110C2×C23—22no—
111C2×C23—22no—
112C2×C23—41no—
113C2×C23C2×#9911yescharacteristic
114C2×C23#41611yescharacteristic
115C2×C23#42111yescharacteristic
116D23—81no—
117C2×#41—231no—
118C23×C4C2×D2311yescharacteristic
119C22×C8—21no—
120#123—461no—
121C22⋊Q8—231no—
122C22⋊Q8—231no—
123#121—231no—
124#121—231no—
125#120—461no—
126C4×D4—461no—
127C4×D4—461no—
128#117—231no—
129C2×C22⋊C4—461no—
130C22⋊C8—21no—
131C22⋊C8C2×D2312yes—
132#95—232no—
133#95—461no—
134C23#151611yescharacteristic, complemented, Sylow
135C24D9211yescharacteristic
136#41—922no—
137C2×Q8—231no—
138C2×D4—231no—
139C2×D4—461no—
140C2×D4—461no—
141C2×D4—461no—
142C22×C4—42no—
143C22×C4—461no—
144C22×C4—462no—
145C22×C4C4×D2311yescharacteristic
146C22×C4C4×D2311yescharacteristic
147C22×C4D9211yescharacteristic
148C22×C4C22⋊D2311yescharacteristic
149C22×C4C22⋊D2311yescharacteristic
150C22×C4C22×D2311yescharacteristic
151C2×C8—22no—
152C2×C8—42no—
153C4⋊C4—231no—
154C4⋊C4—231no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—922no—
163C42—461no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—461no—
168C23(C2×D23)⋊C411yescharacteristic
169C23(C2×D23)⋊C411yescharacteristic
170C23C2×D9211yescharacteristic
171Q8—921no—
172D4—921no—
173D4—922no—
174D4—922no—
175D4—922no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—461no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—922no—
186C2×C4—922no—
187C2×C4—922no—
188C2×C4—922no—
189C2×C4(C2×D23)⋊C411yescharacteristic
190C2×C4(C2×D23)⋊C411yescharacteristic
191C2×C4C2×C4×D2311yescharacteristic
192C2×C4C2×C22⋊D2311yescharacteristic
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—921no—
203C22—921no—
204C22—921no—
205C22#1062498812yes—
206C22#1062507512yes—
207C22C2×(C2×D23)⋊C411yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—921no—
213C4—921no—
214C4—921no—
215C4—1842no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—1841no—
220C2C2×#1062498811yescharacteristic
221C2#1309241411yescharacteristic
222C2#1309243311yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×C22⋊C8C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenterC2×C22⋊C8D23
hypocenterC23#1516
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092280C2semidirect
3. #13092155C2semidirect
4. #13092152C2semidirect
5. C2×C23×C22⋊C8C2semidirect
7. C2×#67288C4semidirect
11. #10625101C4semidirect
16. #10625097C4semidirect
17. #10625095C4semidirect
106. C2×C22⋊C8D23semidirect
134. C23#1516semidirect

Maximal subgroups

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

subgroupindex
#130929282
#130922802
#130921552
#130921522
C2×C23×C22⋊C82
#151623