Finite Group Databasebeta

← #15672546

Subgroups — #15672546

Order 2944.

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

normal subgroups only

This group has 234 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#13093071C211yesmaximal, characteristic
2#13092767C211yesmaximal, characteristic, complemented
3#13092704C211yesmaximal, characteristic, complemented
4#13092164C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#476C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×C4⋊Q8C2211yescharacteristic
10C4×D4×C23C2211yescharacteristic
11#10625101—21no—
12C2×C4⋊Dic23—21no—
13#10625068—21no—
14#10625057—22no—
15C4×D92C2211yescharacteristic
16#10625040C2211yescharacteristic
17C23×#106—21no—
18C23×C4⋊C8C2211yescharacteristic
19C23×#102—21no—
20#10625017—22no—
21#10624991—21no—
22#10624990—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23—21no—
28C2×C22⋊D23—22no—
29C22×Dic23—22no—
30#67290—42no—
31#67290—42no—
32C2×D92D411yescharacteristic
33C2×C4×D23—21no—
34C2×Dic46—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23D411yescharacteristic
39C22⋊C4×C23—21no—
40C42×C23C2311yescharacteristic
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23—22no—
44C4⋊Dic23—21no—
45C4⋊Dic23D412yes—
46C4⋊Dic23D411yescharacteristic
47C2×C23⋊C8—21no—
48C2×C23⋊C8—21no—
49C23×C23—21no—
50C22×D23—21no—
51Q8×C23—42no—
52D4×C23—21no—
53D4×C23SD1612yes—
54C2×C4×C23—21no—
55C2×C4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C22⋊D23—44no—
62C2×Dic23—22no—
63C2×Dic23—21no—
64C2×Dic23—44no—
65D92—21no—
66D92—21no—
67C4×D23—41no—
68C4×D23—41no—
69Dic46—41no—
70Dic46—41no—
71C8×C23—41no—
72C23⋊C8—41no—
73C23⋊C8—41no—
74#1635—231nomaximal, Sylow
75C22×C23—22no—
76C22×C23—41no—
77C22×C23—41no—
78C22×C23#12011yescharacteristic
79C2×D23—41no—
80C2×D23—41no—
81C2×D23—41no—
82C4×C23—21no—
83C4×C23—41no—
84C4×C23—81no—
85C4×C23C2×SD1611yescharacteristic
86C4×C23#13511yescharacteristic
87C4×C23AGL(1,ℤ/8)11yescharacteristic
88C4×C23#13711yescharacteristic
89Dic23—42no—
90Dic23—41no—
91#547—231no—
92#487—231no—
93#476—231no—
94#476D2311yescharacteristic, complemented
95#332—231no—
96D4⋊C8—231no—
97D4⋊C8—231no—
98C2×C23—42no—
99C2×C23#45011yescharacteristic
100C2×C23#45211yescharacteristic
101C2×C23#45411yescharacteristic
102D23—81no—
103C2×#41—461no—
104C4⋊Q8—231no—
105C4⋊Q8C2×D2311yescharacteristic
106#123—462no—
107C22⋊Q8—461no—
108#121—461no—
109C4×D4—231no—
110C4×D4C2×D2311yescharacteristic
111C2×C4⋊C4—461no—
112#106—21no—
113#106—461no—
114C4⋊C8—231no—
115C4⋊C8C2×D2311yescharacteristic
116#103—462no—
117#102—21no—
118#102—461no—
119C4×C8—231no—
120C23#163511yescharacteristic, complemented, Sylow
121#41—922no—
122#41—922no—
123C2×Q8—21no—
124C2×Q8—461no—
125C2×D4—231no—
126C2×D4—462no—
127C2×D4C22⋊D2311yescharacteristic
128C22×C4—21no—
129C22×C4—462no—
130C22×C4—461no—
131C2×C8—21no—
132C2×C8—461no—
133C2×C8—461no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—232no—
137C4⋊C4—231no—
138C4⋊C4—462no—
139C4⋊C4—461no—
140C4⋊C4C22⋊D2311yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—462no—
143C22⋊C4—461no—
144C42C22×D2311yescharacteristic
145C23—21no—
146C23—461no—
147Q8—42no—
148Q8—921no—
149Q8—921no—
150D4—21no—
151D4—461no—
152D4—461no—
153D4—924no—
154D4#6727412yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—461no—
160C2×C4—462no—
161C2×C4—924no—
162C2×C4—921no—
163C2×C4—921no—
164C2×C4D4×D2311yescharacteristic
165C2×C4D4×D2311yescharacteristic
166C2×C4C2×C22⋊D2311yescharacteristic
167C8—41no—
168C8—921no—
169C8—921no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—921no—
174C22—921no—
175C22—921no—
176C22#1062510811yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—921no—
181C4—922no—
182C4#1062508611yescharacteristic
183C4#1062508711yescharacteristic
184C4C2×#6727411yescharacteristic
185C4#1062512011yescharacteristic
186C2—42no—
187C2—1841no—
188C2#1309256711yescharacteristic
189C2#1309257611yescharacteristic
190C2#1309258811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#476C2
socleC22×C23#120
prime radical#13093071C2
hypercenter#476D23
hypocenterC23#1635
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #13092767C2semidirect
3. #13092704C2semidirect
4. #13092164C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×#476C2semidirect
94. #476D23semidirect
120. C23#1635semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130927672
#130927042
#130921642
D4⋊(C23⋊C8)2
#130921442
C23×#4762
#163523