Finite Group Databasebeta

← #15672626

Subgroups — #15672626

Order 2944.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093133C211yesmaximal, characteristic
2#13092767C211yesmaximal, characteristic, complemented
3#13092698C211yesmaximal, characteristic, complemented
4#13092623C211yesmaximal, characteristic, complemented
5#13092144C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#333C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9#10625118—22no—
10C2×#67263—21no—
11#10625066—21no—
12#10625066—21no—
13#10625063—21no—
14#10625063—21no—
15C4×D92C2211yescharacteristic
16C4×D92C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20#10625017—22no—
21#10625003—21no—
22#10625000—21no—
23#10624998—21no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23D412yes—
26C2×D92—22no—
27C2×D92D411yescharacteristic
28C2×D92D411yescharacteristic
29C2×C4×D23—21no—
30C2×C4×D23—21no—
31C2×Dic46—21no—
32C2×C8×C23—21no—
33C2×C8×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C42×C23C2311yescharacteristic
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23D411yescharacteristic
44C4⋊Dic23D411yescharacteristic
45C4×Dic23—22no—
46C2×C23⋊C8—21no—
47#67263—42no—
48C22×D23—21no—
49C22×D23—21no—
50Q8×C23—42no—
51C2×C4×C23—22no—
52C2×C4×C23C2×D411yescharacteristic
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23C2×D411yescharacteristic
55C2×Dic23—21no—
56C2×Dic23—21no—
57C2×Dic23—41no—
58D92—21no—
59D92—21no—
60D92—21no—
61D92—21no—
62D92—82no—
63C4×D23—41no—
64C4×D23—41no—
65C4×D23—41no—
66C4×D23—41no—
67Dic46—41no—
68Dic46—41no—
69C8×C23—41no—
70C8×C23—41no—
71C23⋊C8—41no—
72#1646—231nomaximal, Sylow
73C22×C23#12011yescharacteristic
74C2×D23—41no—
75C2×D23—41no—
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—41no—
79C2×D23—41no—
80C4×C23—21no—
81C4×C23—42no—
82C4×C23#13511yescharacteristic
83C4×C23#13511yescharacteristic
84C4×C23AGL(1,ℤ/8)11yescharacteristic
85C4×C23#13711yescharacteristic
86Dic23—41no—
87Dic23—41no—
88Dic23—81no—
89#555—231no—
90#487—231no—
91#474—231no—
92#461—231no—
93#333D2311yescharacteristic, complemented
94D4⋊C8—231no—
95D4⋊C8—231no—
96C2×C23#44911yescharacteristic
97C2×C23#45211yescharacteristic
98C2×C23#45511yescharacteristic
99D23—81no—
100D23—81no—
101C2×SD16—461no—
102C4⋊Q8—231no—
103C4⋊Q8C2×D2311yescharacteristic
104#124—462no—
105#121—461no—
106#121—461no—
107C4×D4—231no—
108C4×D4—231no—
109#117—461no—
110#117—461no—
111#107—461no—
112C4⋊C8C2×D2311yescharacteristic
113C4⋊C8C2×D2311yescharacteristic
114#103—461no—
115#103—462no—
116#102—461no—
117C4×C8—231no—
118C23#164611yescharacteristic, complemented, Sylow
119C2×Q8—461no—
120C2×Q8D9212yes—
121C2×D4—231no—
122C2×D4—231no—
123C2×D4—462no—
124C22×C4—461no—
125C22×C4—461no—
126SD16—922no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—461no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—231no—
133C4⋊C4—231no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C22⋊C4—462no—
137C22⋊C4—462no—
138C22⋊C4—461no—
139C22⋊C4—461no—
140C42—462no—
141C42C22×D2311yescharacteristic
142C23—461no—
143C23—461no—
144Q8—42no—
145Q8—921no—
146Q8—921no—
147D4—461no—
148D4—461no—
149D4—461no—
150D4—461no—
151D4—1842no—
152C2×C4—22no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—921no—
156C2×C4—921no—
157C2×C4—921no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4C2×D9211yescharacteristic
161C2×C4D4×D2311yescharacteristic
162C2×C4D4×D2311yescharacteristic
163C8—41no—
164C8—41no—
165C8—921no—
166C22—921no—
167C22—921no—
168C22—921no—
169C22—921no—
170C22—921no—
171C22—921no—
172C22#1062505311yescharacteristic
173C4—21no—
174C4—42no—
175C4—921no—
176C4—921no—
177C4—1841no—
178C4#1062508511yescharacteristic
179C4#1062508711yescharacteristic
180C4#1062508911yescharacteristic
181C4#1062509011yescharacteristic
182C2—1841no—
183C2—1841no—
184C2#1309256511yescharacteristic
185C2#1309258211yescharacteristic
186C2#1309259711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#333C2
socleC22×C23#120
prime radical#13093133C2
hypercenter#333D23
hypocenterC23#1646
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #13092767C2semidirect
3. #13092698C2semidirect
4. #13092623C2semidirect
5. #13092144C2semidirect
6. #13092144C2semidirect
7. C23×#333C2semidirect
93. #333D23semidirect
118. C23#1646semidirect

Maximal subgroups

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

subgroupindex
#130931332
#130927672
#130926982
#130926232
#130921442
C23×#3332
#164623