Finite Group Databasebeta

← #15672697

Subgroups — #15672697

Order 2944.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#13093171C211yesmaximal, characteristic, complemented
2#13092806C211yesmaximal, characteristic
3#13092783C211yesmaximal, characteristic, complemented
4#13092782C211yesmaximal, characteristic, complemented
5#13092158C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#330C211yesmaximal, characteristic, complemented
8C23×#125C2211yescharacteristic
9C2×D184—21no—
10C2×#67263—21no—
11#10625069—21no—
12#10625069—21no—
13#10625068—21no—
14#10625067—21no—
15#10625065—21no—
16#10625059—21no—
17#10625046C2211yescharacteristic
18#10625045C2211yescharacteristic
19#10625041C2211yescharacteristic
20C23×#97C2211yescharacteristic
21C23×#97C2211yescharacteristic
22#10625003—21no—
23#10625003—21no—
24#10624991—21no—
25#10624991—21no—
26#10624985C2211yescharacteristic
27C2×D92—21no—
28C2×D92—21no—
29C2×D92—21no—
30C2×D92D411yescharacteristic
31C2×C4×D23—21no—
32C2×Dic46—21no—
33C2×Dic46D411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23D411yescharacteristic
39C4⋊C4×C23D411yescharacteristic
40C42×C23C2311yescharacteristic
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48C4⋊Dic23D411yescharacteristic
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52C4×Dic23—21no—
53C2×C23⋊C8—21no—
54D184—42no—
55#67263—42no—
56C22×D23—21no—
57C22×D23—41no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66D92—41no—
67D92—41no—
68D92—41no—
69D92—42no—
70D92—42no—
71C4×D23—81no—
72Dic46—41no—
73Dic46—81no—
74C8×C23—22no—
75C8×C23—41no—
76C23⋊C8—41no—
77#1657—231nomaximal, Sylow
78C22×C23#12011yescharacteristic
79C2×D23—41no—
80C2×D23—41no—
81C2×D23—41no—
82C2×D23—81no—
83C2×D23—81no—
84C2×D23—81no—
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—21no—
88C4×C23—41no—
89C4×C23—41no—
90Dic23—41no—
91Dic23—41no—
92Dic23—41no—
93#563—231no—
94#496—231no—
95#490—231no—
96#490—231no—
97#330—231no—
98#330D2311yescharacteristic, complemented
99#329—231no—
100C2×C23#45311yescharacteristic
101C2×C23#45411yescharacteristic
102C2×C23#45411yescharacteristic
103D23—81no—
104D23—161no—
105C2×SD16—461no—
106C2×D8—461no—
107C4⋊Q8—461no—
108#127—231no—
109#126—461no—
110#126—461no—
111#125—231no—
112#125C2×D2311yescharacteristic
113#124—231no—
114#123—461no—
115C22⋊Q8—461no—
116C22⋊Q8—461no—
117#102—461no—
118#102—461no—
119#102—461no—
120#102—461no—
121#97—231no—
122#97C2×D2311yescharacteristic
123#97C2×D2311yescharacteristic
124C23#165711yescharacteristic, complemented, Sylow
125C2×Q8—231no—
126C2×Q8—461no—
127C2×D4—231no—
128C2×D4—461no—
129C2×D4—461no—
130C2×D4—461no—
131C22×C4—461no—
132SD16—922no—
133D8—922no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—461no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—231no—
140C4⋊C4—231no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4D9211yescharacteristic
146C4⋊C4D9211yescharacteristic
147C22⋊C4—461no—
148C22⋊C4—461no—
149C22⋊C4—461no—
150C22⋊C4—461no—
151C22⋊C4—461no—
152C42—461no—
153C42C22×D2311yescharacteristic
154C23—461no—
155C23—921no—
156Q8—921no—
157Q8—1841no—
158D4—921no—
159D4—921no—
160D4—921no—
161D4—922no—
162D4—922no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—461no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—1841no—
169C2×C4C2×D9211yescharacteristic
170C2×C4D4×D2311yescharacteristic
171C2×C4D4×D2311yescharacteristic
172C8—22no—
173C8—41no—
174C8—921no—
175C22—921no—
176C22—921no—
177C22—921no—
178C22—1841no—
179C22—1841no—
180C22—1841no—
181C22#1062505311yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—921no—
188C4—921no—
189C4—921no—
190C2—3681no—
191C2—1841no—
192C2#1309258611yescharacteristic
193C2#1309259111yescharacteristic
194C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#330C2
socleC22×C23#120
prime radical#13092806C2
hypercenter#330D23
hypocenterC23#1657
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #13093171C2semidirect
3. #13092783C2semidirect
4. #13092782C2semidirect
5. #13092158C2semidirect
6. #13092156C2semidirect
7. C23×#330C2semidirect
98. #330D23semidirect
124. C23#1657semidirect

Maximal subgroups

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

subgroupindex
#130931712
#130928062
#130927832
#130927822
#130921582
#130921562
C23×#3302
#165723