Finite Group Databasebeta

← #15672501

Subgroups — #15672501

Order 2944.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#13093082C211yesmaximal, characteristic, complemented
2#13092765C211yesmaximal, characteristic, complemented
3#13092618C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic
5#13092147C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C23×C4⋊Q8C2211yescharacteristic
10#10625117—21no—
11C2×D184—21no—
12C2×#67263—21no—
13#10625067—22no—
14#10625064—21no—
15#10625059—21no—
16#10625045C2211yescharacteristic
17C4×D92C2211yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21#10625003—21no—
22#10625003—21no—
23#10624991—22no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26Q8×D23—42no—
27Q8×D23—42no—
28C2×D92—21no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92D411yescharacteristic
32C2×C4×D23—22no—
33C2×C4×D23—21no—
34C2×Dic46—22no—
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D412yes—
40C42×C23C2311yescharacteristic
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23D411yescharacteristic
44C4⋊Dic23D411yescharacteristic
45Dic23⋊C4—22no—
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48C2×C23⋊C8—21no—
49D184—42no—
50#67263—42no—
51C22×D23—21no—
52C22×D23—41no—
53Q8×C23—41no—
54Q8×C23—41no—
55C2×C4×C23—22no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—21no—
61C2×Dic23—21no—
62D92—21no—
63D92—42no—
64D92—41no—
65D92—41no—
66D92—41no—
67D92—41no—
68D92SD1612yescomplemented
69C4×D23—44no—
70C4×D23—41no—
71C4×D23—41no—
72Dic46—21no—
73Dic46—44no—
74Dic46D812yescomplemented
75C8×C23—41no—
76C8×C23—41no—
77C23⋊C8—41no—
78#1627—231nomaximal, Sylow
79C22×C23#12011yescharacteristic
80C2×D23—22no—
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—81no—
84C2×D23—81no—
85C2×D23—81no—
86C4×C23—21no—
87C4×C23—42no—
88C4×C23C2×D811yescharacteristic
89C4×C23C2×SD1611yescharacteristic
90C4×C23AGL(1,ℤ/8)11yescharacteristic
91C4×C23#13711yescharacteristic
92Dic23—22no—
93Dic23—41no—
94Dic23—41no—
95D4×Q8—231no—
96#486—231no—
97#460—231no—
98#459—231no—
99#332D2311yescharacteristic, complemented
100Q8⋊C8—231no—
101D4⋊C8—231no—
102C2×C23#44711yescharacteristic
103C2×C23#44811yescharacteristic
104C2×C23#45411yescharacteristic
105D23—42no—
106D23—161no—
107C22×Q8—461no—
108C2×SD16—461no—
109C2×D8—461no—
110C4⋊Q8—461no—
111C4⋊Q8C2×D2311yescharacteristic
112#127—231no—
113C22⋊Q8—461no—
114C22⋊Q8—462no—
115C4×Q8—231no—
116C4×D4—231no—
117C4×D4—461no—
118C4⋊C8C2×D2311yescharacteristic
119C4⋊C8C2×D2311yescharacteristic
120#102—461no—
121#102—461no—
122#102—462no—
123C4×C8—231no—
124C23#162711yescharacteristic, complemented, Sylow
125C2×Q8—21no—
126C2×Q8—231no—
127C2×Q8—462no—
128C2×Q8—922no—
129C2×Q8—922no—
130C2×D4—231no—
131C2×D4—461no—
132C2×D4—461no—
133C2×D4—461no—
134C22×C4—462no—
135C22×C4—461no—
136SD16—922no—
137D8—922no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—231no—
143C4⋊C4—231no—
144C4⋊C4—462no—
145C4⋊C4—461no—
146C4⋊C4D9212yes—
147C22⋊C4—462no—
148C22⋊C4—461no—
149C42—461no—
150C42C22×D2311yescharacteristic
151C23—461no—
152C23—921no—
153Q8—41no—
154Q8—41no—
155Q8—232no—
156Q8—461no—
157Q8—924no—
158D4—232no—
159D4—461no—
160D4—922no—
161D4—921no—
162D4—921no—
163D4—921no—
164D4—921no—
165C2×C4—22no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—461no—
169C2×C4—924no—
170C2×C4—921no—
171C2×C4—921no—
172C2×C4C2×D9211yescharacteristic
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C8—41no—
176C8—41no—
177C8—921no—
178C22—462no—
179C22—921no—
180C22—921no—
181C22—1841no—
182C22—1841no—
183C22—1841no—
184C22#1062505311yescharacteristic
185C4—21no—
186C4—42no—
187C4—462no—
188C4—921no—
189C4—921no—
190C4D8×D2311yescharacteristic
191C4SD16×D2311yescharacteristic
192C4#1062508511yescharacteristic
193C4#1062508911yescharacteristic
194C2—922no—
195C2—3681no—
196C2#1309255211yescharacteristic
197C2#1309255711yescharacteristic
198C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23#120
prime radical#13092613C2
hypercenter#332D23
hypocenterC23#1627
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #13093082C2semidirect
2. #13092765C2semidirect
3. #13092618C2semidirect
5. #13092147C2semidirect
6. #13092144C2semidirect
7. C23×#332C2semidirect
68. D92SD16semidirect
74. Dic46D8semidirect
99. #332D23semidirect
124. C23#1627semidirect

Maximal subgroups

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

subgroupindex
#130930822
#130927652
#130926182
#130926132
#130921472
#130921442
C23×#3322
#162723