Finite Group Databasebeta

← #15675049

Subgroups — #15675049

Order 2944.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092989C211yesmaximal, characteristic
2#13092398C211yesmaximal, characteristic
3#13092389C211yesmaximal, characteristic
4#13092208C211yesmaximal, characteristic, complemented
5#13092207C211yesmaximal, characteristic, complemented
6#13092206C211yesmaximal, characteristic, complemented
7C23×#352C211yesmaximal, characteristic, complemented
8C2×#67290C2211yescharacteristic
9C22×Dic46C411yescharacteristic, complemented
10C23×#123C2211yescharacteristic
11#10625106C2211yescharacteristic
12#10625100C411yescharacteristic, complemented
13M16×D23—21no—
14#10625067—21no—
15#10625059—21no—
16#10625057C411yescharacteristic, complemented
17#10625056—21no—
18#10625049—21no—
19#10625048—21no—
20#10625048C411yescharacteristic, complemented
21C23×#100C2211yescharacteristic
22C23×#99C2211yescharacteristic
23#10625016C2211yescharacteristic
24#10625015C2211yescharacteristic
25#10625006—21no—
26#10624988—21no—
27C2×D4×C23C2311yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C2×C22⋊D23C2×C411yescharacteristic
30C2×C22⋊D23D411yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C22×Dic23C2×C411yescharacteristic
33C22×Dic23D411yescharacteristic
34#67290—41no—
35#67290—41no—
36C2×C4×D23D411yescharacteristic
37C2×Dic46—21no—
38C2×Dic46—21no—
39C2×Dic46—41no—
40C2×Dic46—41no—
41C2×Dic46D411yescharacteristic
42M16×C23—21no—
43C4⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23C2×C411yescharacteristic
47C22⋊Dic23—21no—
48C22⋊Dic23—21no—
49C22⋊Dic23C2×C411yescharacteristic
50(C2×D23)⋊C4—21no—
51(C2×D23)⋊C4—21no—
52C4⋊Dic23—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—41no—
57C4×Dic23—21no—
58C4×Dic23—41no—
59#67267—21no—
60#67262—41no—
61C8×D23—41no—
62C23×C23C22×C411yescharacteristic
63C23×C23C2×D411yescharacteristic
64C22×D23C22⋊C411yescharacteristic
65D4×C23—41no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C2×D411yescharacteristic
71C22⋊D23—41no—
72C22⋊D23—41no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23C22⋊C411yescharacteristic
82C2×Dic23C22⋊C411yescharacteristic
83C2×Dic23C22⋊C411yescharacteristic
84C4×D23—21no—
85C4×D23—21no—
86Dic46—41no—
87Dic46—42no—
88Dic46—41no—
89Dic46—41no—
90C8×C23—41no—
91C23⋊C8—41no—
92#2123—231nomaximal, Sylow
93C22×C23—21no—
94C22×C23—21no—
95C22×C23—41no—
96C22×C23—41no—
97C22×C23C2×C22⋊C411yescharacteristic
98C2×D23—21no—
99C2×D23—41no—
100C4×C23—21no—
101C4×C23—41no—
102C4×C23—41no—
103C4×C23—81no—
104Dic23—21no—
105Dic23—21no—
106Dic23—41no—
107Dic23—41no—
108Dic23—81no—
109Dic23#9911yescharacteristic
110Dic23#9911yescharacteristic
111#536—231no—
112#413—231no—
113#410—231no—
114#352—231no—
115#352—231no—
116#352—231no—
117#352D2311yescharacteristic, complemented
118C2×C23—21no—
119C2×C23—41no—
120C2×C23—41no—
121C2×C23C2×#9911yescharacteristic
122D23—41no—
123C2×#41—231no—
124C22×Q8—231no—
125C2×M16—461no—
126C4⋊Q8—461no—
127#124—461no—
128#123—231no—
129#123—231no—
130#123—231no—
131#123C2×D2311yescharacteristic
132C22⋊Q8—461no—
133C22⋊Q8—461no—
134#117—231no—
135#117—461no—
136#101—461no—
137#100—231no—
138#100C2×D2311yescharacteristic
139#99—231no—
140#99—461no—
141#99C2×D2311yescharacteristic
142C23#212311yescharacteristic, complemented, Sylow
143#41—921no—
144#41—921no—
145C2×Q8—231no—
146C2×Q8—461no—
147C2×Q8—461no—
148C2×Q8—921no—
149C2×Q8—921no—
150C2×D4—231no—
151C2×D4—231no—
152C2×D4C22×D2311yescharacteristic
153C22×C4—231no—
154C22×C4—231no—
155C22×C4—231no—
156C22×C4—231no—
157C22×C4C4×D2311yescharacteristic
158M16—21no—
159M16—461no—
160M16—921no—
161C2×C8—921no—
162C4⋊C4—21no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C4⋊C4—461no—
166C4⋊C4—461no—
167C4⋊C4—921no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—231no—
171C22⋊C4—461no—
172C22⋊C4—461no—
173C22⋊C4—461no—
174C22⋊C4—461no—
175C22⋊C4C4×D2311yescharacteristic
176C42—461no—
177C42—921no—
178C23—231no—
179C23C2×C4×D2311yescharacteristic
180C23D4×D2311yescharacteristic
181Q8—921no—
182Q8—921no—
183Q8—921no—
184Q8—922no—
185D4—41no—
186D4—921no—
187D4—921no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—231no—
193C2×C4—231no—
194C2×C4—231no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—461no—
198C2×C4—461no—
199C2×C4—461no—
200C2×C4—461no—
201C2×C4—461no—
202C2×C4—461no—
203C2×C4—921no—
204C2×C4—921no—
205C2×C4D4×D2311yescharacteristic
206C8—41no—
207C8—921no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—461no—
213C22—921no—
214C22C22⋊C4×D2311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—231no—
220C4—231no—
221C4—461no—
222C4—461no—
223C4—921no—
224C4—921no—
225C4—1841no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—921no—
230C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#352C2
socleC2×C23C2×#99
prime radicalC2×#67290C22
cosocleC2×D4×C23C23
hypercenter#352D23
hypocenterC23#2123
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #13092208C2semidirect
5. #13092207C2semidirect
6. #13092206C2semidirect
7. C23×#352C2semidirect
9. C22×Dic46C4semidirect
12. #10625100C4semidirect
16. #10625057C4semidirect
20. #10625048C4semidirect
117. #352D23semidirect
142. C23#2123semidirect

Maximal subgroups

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

subgroupindex
#130929892
#130923982
#130923892
#130922082
#130922072
#130922062
C23×#3522
#212323