Finite Group Databasebeta

← #15672525

Subgroups — #15672525

Order 2944.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093087C211yesmaximal, characteristic
2#13092789C211yesmaximal, characteristic, complemented
3#13092713C211yesmaximal, characteristic, complemented
4#13092708C211yesmaximal, characteristic, complemented
5#13092147C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#331C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×#127C2211yescharacteristic
10#10625111—21no—
11#10625110—22no—
12#10625109—21no—
13D4×Dic23—21no—
14C2×#67273—22no—
15C4×D92C2211yescharacteristic
16#10625040C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20#10625003—21no—
21#10625000—21no—
22#10624999—21no—
23#10624998—21no—
24C4×C23⋊C8C2211yescharacteristic
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23D412yes—
28C2×C22⋊D23—22no—
29C2×C22⋊D23—22no—
30C22×Dic23—22no—
31#67290—42no—
32#67290—42no—
33C2×D92D411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46—21no—
36C2×Dic46D411yescharacteristic
37C2×C8×C23—21no—
38C2×C8×C23—21no—
39C42×C23C2311yescharacteristic
40C22⋊Dic23—22no—
41#67273—44no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23D411yescharacteristic
46C4⋊Dic23D411yescharacteristic
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C2×C23⋊C8—21no—
50C23×C23—22no—
51C22×D23—21no—
52D4×C23—42no—
53D4×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56D4×C23—41no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—44no—
61C22⋊D23—82no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—44no—
66C2×Dic23—41no—
67D92—21no—
68D92—21no—
69C4×D23—41no—
70C4×D23—41no—
71Dic46—21no—
72Dic46—42no—
73Dic46SD1612yescomplemented
74C8×C23—41no—
75C8×C23—41no—
76C23⋊C8—22no—
77#1631—231nomaximal, Sylow
78C22×C23—42no—
79C22×C23—42no—
80C22×C23—42no—
81C22×C23#12011yescharacteristic
82C2×D23—41no—
83C2×D23—41no—
84C2×D23—41no—
85C4×C23—21no—
86C4×C23C2×SD1611yescharacteristic
87C4×C23#13511yescharacteristic
88C4×C23AGL(1,ℤ/8)11yescharacteristic
89C4×C23#13711yescharacteristic
90Dic23—22no—
91Dic23—41no—
92Dic23—41no—
93Dic23—81no—
94#550—231no—
95#492—231no—
96#477—231no—
97#476—231no—
98#331D2311yescharacteristic, complemented
99Q8⋊C8—231no—
100D4⋊C8—231no—
101C2×C23—82no—
102C2×C23#45011yescharacteristic
103C2×C23#45211yescharacteristic
104C2×C23#45311yescharacteristic
105D23—81no—
106C2×#41—461no—
107C2×SD16—462no—
108C4⋊Q8—231no—
109#127—461no—
110#127C2×D2311yescharacteristic
111#121—461no—
112#121—462no—
113C4×Q8—231no—
114C4×D4—231no—
115C4×D4—461no—
116#107—461no—
117#106—461no—
118C4⋊C8C2×D2311yescharacteristic
119C4⋊C8C2×D2311yescharacteristic
120#103—461no—
121#102—461no—
122C4×C8—231no—
123C23#163111yescharacteristic, complemented, Sylow
124#41—922no—
125#41—922no—
126C2×Q8—231no—
127C2×Q8—461no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—231no—
131C2×D4—462no—
132C2×D4—462no—
133C2×D4D9212yes—
134C22×C4—462no—
135C22×C4—461no—
136SD16—924no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—461no—
140C4⋊C4—231no—
141C4⋊C4—231no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C22⋊C4—462no—
146C22⋊C4—461no—
147C42—461no—
148C42C22×D2311yescharacteristic
149C23—22no—
150C23—461no—
151Q8—232no—
152Q8—461no—
153Q8—922no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—461no—
160D4—461no—
161D4—924no—
162D4—1842no—
163C2×C4—461no—
164C2×C4—461no—
165C2×C4—461no—
166C2×C4—924no—
167C2×C4—921no—
168C2×C4—921no—
169C2×C4—921no—
170C2×C4C2×D9211yescharacteristic
171C2×C4D4×D2311yescharacteristic
172C2×C4D4×D2311yescharacteristic
173C8—41no—
174C8—41no—
175C8—462no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—921no—
180C22—921no—
181C22—921no—
182C22#1062505311yescharacteristic
183C4—21no—
184C4—462no—
185C4—921no—
186C4—921no—
187C4—1841no—
188C4#1062508211yescharacteristic
189C4#1062508311yescharacteristic
190C4SD16×D2311yescharacteristic
191C4#1062508611yescharacteristic
192C2—82no—
193C2—1841no—
194C2#1309256911yescharacteristic
195C2#1309258011yescharacteristic
196C2#1309258711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#331C2
socleC22×C23#120
prime radical#13093087C2
hypercenter#331D23
hypocenterC23#1631
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #13092789C2semidirect
3. #13092713C2semidirect
4. #13092708C2semidirect
5. #13092147C2semidirect
6. #13092144C2semidirect
7. C23×#331C2semidirect
73. Dic46SD16semidirect
98. #331D23semidirect
123. C23#1631semidirect

Maximal subgroups

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

subgroupindex
#130930872
#130927892
#130927132
#130927082
#130921472
#130921442
C23×#3312
#163123