Finite Group Databasebeta

← #15675408

Subgroups — #15675408

Order 2944.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093170C211yesmaximal, characteristic, complemented
2#13092607C211yesmaximal, characteristic
3#13092595C211yesmaximal, characteristic
4#13092211C211yesmaximal, characteristic, complemented
5#13092207C211yesmaximal, characteristic, complemented
6#13092206C211yesmaximal, characteristic, complemented
7C23×#458C211yesmaximal, characteristic
8C23×H(5,𝔽2)C2211yescharacteristic
9C23×#123—21no—
10C23×#123C2211yescharacteristic
11#10625122—21no—
12#10625107C2211yescharacteristic
13#10625106—21no—
14#10625106C2211yescharacteristic
15#10625095—21no—
16#10625060—21no—
17#10625059—21no—
18#10625050—21no—
19#10625050—21no—
20#10625049—21no—
21C23×#99—21no—
22C23×#99C2211yescharacteristic
23#10625019—21no—
24#10625016—21no—
25#10625016C2211yescharacteristic
26#10625015C2211yescharacteristic
27#41×C23—21no—
28#41×C23—41no—
29C2×D4×C23—21no—
30C2×D4×C23—21no—
31C2×D4×C23—41no—
32C2×D4×C23C2311yescharacteristic
33C22×C4×C23D411yescharacteristic
34C22×Dic23D411yescharacteristic
35C2×Dic46—21no—
36C2×Dic46D411yescharacteristic
37C4⋊C4×C23—21no—
38C4⋊C4×C23—41no—
39C22⋊C4×C23—21no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23—41no—
42C22⋊C4×C23D411yescharacteristic
43C22⋊Dic23—21no—
44C22⋊Dic23—21no—
45C22⋊Dic23—21no—
46C22⋊Dic23—21no—
47C22⋊Dic23—41no—
48C22⋊Dic23D411yescharacteristic
49#67275—41no—
50#67273—41no—
51C4⋊Dic23—21no—
52C4⋊Dic23—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—21no—
57Dic23⋊C4—21no—
58Dic23⋊C4—41no—
59C4×Dic23—21no—
60C4×Dic23D411yescharacteristic
61#67267—21no—
62C23×C23—21no—
63C23×C23—21no—
64C23×C23C2×D411yescharacteristic
65C23×C23C2×D411yescharacteristic
66Q8×C23—21no—
67D4×C23—21no—
68D4×C23—41no—
69D4×C23—41no—
70D4×C23—41no—
71D4×C23—41no—
72C2×C4×C23—21no—
73C2×C4×C23—21no—
74C2×C4×C23—21no—
75C2×C4×C23—21no—
76C2×C4×C23—41no—
77C2×C4×C23—41no—
78C2×C4×C23—41no—
79C2×C4×C23C2×D411yescharacteristic
80C2×Dic23—21no—
81C2×Dic23—21no—
82C2×Dic23—21no—
83C2×Dic23—21no—
84C2×Dic23—41no—
85C2×Dic23—41no—
86Dic46—41no—
87Dic46—81no—
88C23⋊C8—41no—
89#2201—231nomaximal, Sylow
90C22×C23—21no—
91C22×C23—21no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23—41no—
95C22×C23—81no—
96C22×C23—81no—
97C22×C23#12011yescharacteristic
98C4×C23—21no—
99C4×C23—41no—
100C4×C23—41no—
101C4×C23—41no—
102C4×C23—81no—
103Dic23—41no—
104Dic23—41no—
105Dic23—41no—
106Dic23—41no—
107Dic23—81no—
108#563—231no—
109#458—231no—
110#458D2311yescharacteristic
111#455—231no—
112#354—231no—
113#352—231no—
114#352—231no—
115C2×C23—21no—
116C2×C23—41no—
117C2×C23—41no—
118C2×C23—81no—
119C2×C23B(4,𝔽2)11yescharacteristic
120H(5,𝔽2)C2×D2311yescharacteristic
121#137—461no—
122C4⋊Q8—461no—
123#126—461no—
124#126—461no—
125#125—461no—
126#124—231no—
127#123—21no—
128#123—231no—
129#123—461no—
130#123C2×D2311yescharacteristic
131C22⋊Q8—461no—
132C22⋊Q8—461no—
133#104—461no—
134#100—231no—
135#99—21no—
136#99—231no—
137#99—461no—
138#99C2×D2311yescharacteristic
139C23#220111yescharacteristic, complemented, Sylow
140#41—21no—
141#41—41no—
142C2×Q8—231no—
143C2×Q8—461no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D2311yescharacteristic
148C22×C4—231no—
149C22×C4C22⋊D2311yescharacteristic
150Q16—921no—
151SD16—921no—
152M16—461no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—461no—
160C4⋊C4—461no—
161C4⋊C4—461no—
162C4⋊C4—921no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—231no—
167C22⋊C4—461no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C22⋊C4—461no—
171C22⋊C4—921no—
172C22⋊C4C22⋊D2311yescharacteristic
173C42—231no—
174C42—461no—
175C23—21no—
176C23—21no—
177C23D4×D2311yescharacteristic
178C23C2×C22⋊D2311yescharacteristic
179Q8—21no—
180Q8—921no—
181Q8—1841no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—461no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—461no—
198C2×C4—921no—
199C2×C4—921no—
200C2×C4D4×D2311yescharacteristic
201C8—921no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1062510811yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—921no—
216C4—921no—
217C4—921no—
218C4—921no—
219C4—1841no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×D4×C23C23
FrattiniC2×D4C22×D23
FittingC23×#458C2
socleC2×C23B(4,𝔽2)
prime radicalC23×H(5,𝔽2)C22
hypercenter#458D23
hypocenterC23#2201
LCSG ▷ C2×D4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #13093170C2semidirect
4. #13092211C2semidirect
5. #13092207C2semidirect
6. #13092206C2semidirect
139. C23#2201semidirect

Maximal subgroups

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

subgroupindex
#130931702
#130926072
#130925952
#130922112
#130922072
#130922062
C23×#4582
#220123