Finite Group Databasebeta

← #15672875

Subgroups — #15672875

Order 2944.

198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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#13092793C211yesmaximal, characteristic, complemented
2#13092613C211yesmaximal, characteristic, complemented
3#13092609C211yesmaximal, characteristic, complemented
4#13092494C211yesmaximal, characteristic, complemented
5#13092167C211yesmaximal, characteristic, complemented
6#13092160C211yesmaximal, characteristic, complemented
7C23×#331C211yesmaximal, characteristic, complemented
8C23×#127C2211yescharacteristic
9C2×#67272—21no—
10C2×#67272—21no—
11C2×#67272—21no—
12C2×D184—21no—
13C2×#67262—21no—
14#10625045C2211yescharacteristic
15C4×D92C2211yescharacteristic
16C23×C4⋊C8C2211yescharacteristic
17C23×C4⋊C8C2211yescharacteristic
18#10625014—21no—
19#10625003—21no—
20(C2×D23)⋊C8—21no—
21C4⋊(C23⋊C8)C2211yescharacteristic
22C4×C23⋊C8C2211yescharacteristic
23C2×D4×C23—21no—
24C2×D4×C23—21no—
25C2×D4×C23—21no—
26C2×D92—21no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D411yescharacteristic
30C2×C4×D23—21no—
31C2×C8×C23—21no—
32C2×C8×C23—21no—
33C42×C23C2311yescharacteristic
34#67272—42no—
35#67272—42no—
36#67272—42no—
37(C2×D23)⋊C4—21no—
38C4⋊Dic23D411yescharacteristic
39C2×C23⋊C8—21no—
40C2×C23⋊C8D411yescharacteristic
41C2×C23⋊C8D411yescharacteristic
42D184—42no—
43#67262—42no—
44C23×C23—41no—
45C22×D23—21no—
46C22×D23—41no—
47D4×C23—41no—
48D4×C23—41no—
49D4×C23—41no—
50D4×C23—41no—
51D4×C23—81no—
52C2×C4×C23C2×D411yescharacteristic
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23#4111yescharacteristic
55C2×Dic23—21no—
56D92—21no—
57D92—21no—
58D92—41no—
59D92—41no—
60D92—41no—
61D92—41no—
62D92—81no—
63C4×D23—41no—
64C4×D23—41no—
65C8×C23—41no—
66C8×C23—41no—
67C23⋊C8—21no—
68C23⋊C8—41no—
69C23⋊C8D812yescomplemented
70#1687—231nomaximal, Sylow
71C22×C23—81no—
72C22×C23—81no—
73C22×C23—81no—
74C22×C23#12111yescharacteristic
75C2×D23—41no—
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—81no—
79C2×D23—81no—
80C2×D23—81no—
81C4×C23—21no—
82C4×C23C2×D811yescharacteristic
83C4×C23AGL(1,ℤ/8)11yescharacteristic
84C4×C23AGL(1,ℤ/8)11yescharacteristic
85C4×C23AGL(1,ℤ/8)11yescharacteristic
86Dic23—41no—
87#493—231no—
88#459—231no—
89#459—231no—
90#436—231no—
91#334—231no—
92#331—231no—
93#331D2311yescharacteristic, complemented
94C2×C23—161no—
95C2×C23#45911yescharacteristic
96C2×C23#46911yescharacteristic
97C2×C23#47211yescharacteristic
98D23—81no—
99D23—161no—
100C2×D8—461no—
101C2×D8—461no—
102C2×D8—461no—
103C2×D8—461no—
104C2×M16—461no—
105#127—231no—
106#127C2×D2311yescharacteristic
107C4×D4—231no—
108C4⋊C8—231no—
109C4⋊C8C2×D2311yescharacteristic
110C4⋊C8C2×D2311yescharacteristic
111#102—461no—
112#102—461no—
113C22⋊C8—461no—
114C4×C8—231no—
115C23#168711yescharacteristic, complemented, Sylow
116C2×D4—21no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—231no—
120C2×D4—461no—
121C2×D4—461no—
122C2×D4—461no—
123C22×C4—461no—
124D8—922no—
125D8—922no—
126D8—922no—
127D8—922no—
128M16—922no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—231no—
132C2×C8—231no—
133C2×C8—461no—
134C4⋊C4—231no—
135C22⋊C4—461no—
136C42C22×D2311yescharacteristic
137C23—41no—
138C23—461no—
139C23—921no—
140D4—41no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—81no—
145D4—461no—
146D4—461no—
147D4—921no—
148D4—921no—
149D4—921no—
150D4—921no—
151D4—1841no—
152C2×C4—461no—
153C2×C4—921no—
154C2×C4—921no—
155C2×C4#6728811yescharacteristic
156C2×C4D4×D2311yescharacteristic
157C2×C4D4×D2311yescharacteristic
158C8—41no—
159C8—41no—
160C8—232no—
161C8—461no—
162C8—921no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22—921no—
167C22—921no—
168C22—921no—
169C22—1841no—
170C22—1841no—
171C22—1841no—
172C22#1062505511yescharacteristic
173C4—21no—
174C4—921no—
175C4D8×D2311yescharacteristic
176C4#1062508211yescharacteristic
177C4#1062508511yescharacteristic
178C4#1062508511yescharacteristic
179C2—161no—
180C2—3681no—
181C2—1841no—
182C2#1309261111yescharacteristic
183C2#1309266911yescharacteristic
184C2#1309268611yescharacteristic
subgroupG/H
centerC22#10625055
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#331C2
socleC22×C23#121
hypercenter#331D23
hypocenterC23#1687
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #13092793C2semidirect
2. #13092613C2semidirect
3. #13092609C2semidirect
4. #13092494C2semidirect
5. #13092167C2semidirect
6. #13092160C2semidirect
7. C23×#331C2semidirect
69. C23⋊C8D8semidirect
93. #331D23semidirect
115. C23#1687semidirect

Maximal subgroups

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

subgroupindex
#130927932
#130926132
#130926092
#130924942
#130921672
#130921602
C23×#3312
#168723