Finite Group Databasebeta

← #15671993

Subgroups — #15671993

Order 2944.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D23C211yesmaximal, characteristic
2#13092472C211yesmaximal, characteristic, complemented
3#13092369C211yesmaximal, characteristic, complemented
4#13092157C211yesmaximal, characteristic, complemented
5#13092156C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#329C211yesmaximal, characteristic, complemented
8C2×Q8×D23C411yescharacteristic
9C2×D4×D23C411yescharacteristic
10C23×#124C2211yescharacteristic
11#10625118C411yescharacteristic
12#10625107C411yescharacteristic
13C2×#67262—21no—
14#10625056—21no—
15#10625056—21no—
16C22⋊C4×D23—21no—
17C22⋊C4×D23—21no—
18#10625046C2211yescharacteristic
19C42×D23C2211yescharacteristic
20C23×#97C2211yescharacteristic, complemented
21C23×#97C2211yescharacteristic, complemented
22(C2×D23)⋊C8—21no—
23Dic23⋊C8—21no—
24C8×Dic23—21no—
25#10624985C2211yescharacteristic, complemented
26#10624985C2211yescharacteristic, complemented
27C23×D23—21no—
28C2×Q8×C23C2×C411yescharacteristic
29C2×D4×C23C2×C411yescharacteristic
30C2×C22⋊D23—21no—
31Q8×D23—42no—
32D4×D23—42no—
33C2×D92C2×C411yescharacteristic
34C2×C4×D23—21no—
35C2×C4×D23C2×C411yescharacteristic
36C2×C4×D23D411yescharacteristic
37C2×C4×D23D411yescharacteristic
38C2×Dic46—21no—
39C2×Dic46C2×C411yescharacteristic
40C2×C8×C23—21no—
41C2×C8×C23—21no—
42C22⋊C4×C23—21no—
43C22⋊C4×C23—21no—
44C42×C23C2311yescharacteristic
45C22⋊Dic23—21no—
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50(C2×D23)⋊C4—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56#67262—24no—
57C23×C23—21no—
58C22×D23—21no—
59C22×D23—42no—
60C22×D23—42no—
61C22×D23—42no—
62C22×D23C22⋊C411yescharacteristic
63Q8×C23—41no—
64D4×C23—41no—
65C2×C4×C23—21no—
66C2×C4×C23C22×C411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—42no—
70C2×Dic23—21no—
71C2×Dic23C22⋊C411yescharacteristic
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74D92—41no—
75C4×D23—22no—
76C4×D23—22no—
77C4×D23—41no—
78C4×D23—42no—
79Dic46—42no—
80Dic46—41no—
81C8×C23—22no—
82C8×C23—41no—
83C23⋊C8—22no—
84C23⋊C8—41no—
85#1527—231nomaximal, Sylow
86C22×C23—41no—
87C22×C23—41no—
88C22×C23—41no—
89C22×C23C2×C22⋊C411yescharacteristic
90C2×D23—21no—
91C2×D23—21no—
92C2×D23—41no—
93C2×D23—41no—
94C2×D23—41no—
95C2×D23—84no—
96C2×D23#10412yes—
97C4×C23—21no—
98C4×C23—21no—
99C4×C23—21no—
100C4×C23—41no—
101Dic23—21no—
102Dic23—21no—
103Dic23—41no—
104Dic23#10012yes—
105C2×#124—231no—
106#432—231no—
107C4×M16—231no—
108#329—231no—
109#329—231no—
110#329—231no—
111#329D2311yescharacteristic, complemented
112C2×C23—81no—
113C2×C23C2×#10011yescharacteristic
114C2×C23C2×#10411yescharacteristic
115C2×C23#42111yescharacteristic
116D23—22no—
117D23—81no—
118C22×Q8—231no—
119C22×D4—231no—
120C2×M16—461no—
121#124—231no—
122#124—231no—
123#124—231no—
124#124—461no—
125#124—461no—
126#124C2×D2311yescharacteristic
127C2×C22⋊C4—461no—
128C2×C22⋊C4—461no—
129C2×C42—231no—
130C4⋊C8—461no—
131C22⋊C8—461no—
132#97—231no—
133#97—231no—
134#97C2×D2311yescharacteristic, complemented
135#97C2×D2311yescharacteristic, complemented
136C4×C8—461no—
137C23#152711yescharacteristic, complemented, Sylow
138C24—461no—
139C2×Q8—231no—
140C2×Q8—461no—
141C2×Q8—922no—
142C2×Q8C4×D2311yescharacteristic
143C2×D4—231no—
144C2×D4—461no—
145C2×D4—922no—
146C2×D4C4×D2311yescharacteristic
147C22×C4—231no—
148C22×C4—231no—
149C22×C4—231no—
150C22×C4—461no—
151M16—464no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—461no—
155C2×C8—461no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C42—231no—
165C42—231no—
166C42—231no—
167C42C22×D2311yescharacteristic
168C23—21no—
169C23—231no—
170C23—461no—
171C23—922no—
172C23—922no—
173C23—922no—
174Q8—41no—
175Q8—921no—
176Q8—922no—
177D4—41no—
178D4—921no—
179D4—922no—
180C2×C4—21no—
181C2×C4—231no—
182C2×C4—231no—
183C2×C4—231no—
184C2×C4—462no—
185C2×C4—462no—
186C2×C4—461no—
187C2×C4—921no—
188C2×C4—922no—
189C2×C4C2×C4×D2311yescharacteristic
190C2×C4D4×D2311yescharacteristic
191C2×C4D4×D2311yescharacteristic
192C8—22no—
193C8—41no—
194C8—462no—
195C8—921no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—232no—
200C22—461no—
201C22—461no—
202C22—921no—
203C22—921no—
204C22—921no—
205C22—1844no—
206C22C22⋊C4×D2311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—232no—
212C4—461no—
213C4—461no—
214C4—921no—
215C2—81no—
216C2—462no—
217C2—1841no—
218C2#100×D2311yescharacteristic
219C2#104×D2311yescharacteristic
220C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23C2×C22⋊C4
prime radicalC2×D4×D23C4
cosocleC42×C23C23
hypercenter#329D23
hypocenterC23#1527
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #13092472C2semidirect
3. #13092369C2semidirect
4. #13092157C2semidirect
5. #13092156C2semidirect
6. #13092156C2semidirect
7. C23×#329C2semidirect
20. C23×#97C22semidirect
21. C23×#97C22semidirect
25. #10624985C22semidirect
26. #10624985C22semidirect
111. #329D23semidirect
134. #97C2×D23semidirect
135. #97C2×D23semidirect
137. C23#1527semidirect

Maximal subgroups

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

subgroupindex
#124×D232
#130924722
#130923692
#130921572
#130921562
C23×#3292
#152723