Finite Group Databasebeta

← #15672472

Subgroups — #15672472

Order 2944.

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

normal subgroups only

This group has 236 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#13093127C211yesmaximal, characteristic, complemented
2#13092790C211yesmaximal, characteristic, complemented
3#13092617C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic
5#13092165C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C23C2211yescharacteristic
9#10625117—21no—
10C2×#67274—21no—
11C2×D184—21no—
12C2×#67263—22no—
13#10625067—22no—
14C4⋊C4×D23—21no—
15#10625045C2211yescharacteristic
16C4×D92—21no—
17C4×D92C2211yescharacteristic
18#10625041—21no—
19#10625040C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21C4×C8×C23C2211yescharacteristic
22#10625003—21no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26C2×D92—21no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D411yescharacteristic
30C2×C4×D23—21no—
31C2×C4×D23—22no—
32C2×Dic46D412yes—
33C2×C8×C23—21no—
34C2×C8×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23D411yescharacteristic
37C42×C23—21no—
38C42×C23C2311yescharacteristic
39#67274—42no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23D411yescharacteristic
45Dic23⋊C4—22no—
46Dic23⋊C4—22no—
47C2×C23⋊C8—21no—
48D184—42no—
49#67263—44no—
50C22×D23—21no—
51C22×D23—41no—
52Q8×C23—21no—
53Q8×C23—21no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—22no—
61D92—21no—
62D92—42no—
63D92—41no—
64D92—41no—
65D92—41no—
66D92—41no—
67D92SD1612yescomplemented
68C4×D23—41no—
69C4×D23—41no—
70C4×D23—82no—
71Dic46—42no—
72C8×C23—22no—
73C8×C23—41no—
74C23⋊C8—41no—
75#1622—231nomaximal, Sylow
76C22×C23#12011yescharacteristic
77C2×D23—22no—
78C2×D23—41no—
79C2×D23—41no—
80C2×D23—81no—
81C2×D23—81no—
82C2×D23—81no—
83C4×C23—21no—
84C4×C23—41no—
85C4×C23—41no—
86C4×C23C2×SD1611yescharacteristic
87C4×C23#13511yescharacteristic
88C4×C23AGL(1,ℤ/8)11yescharacteristic
89C4×C23#13711yescharacteristic
90Dic23—41no—
91Dic23—42no—
92#554—231no—
93#492—231no—
94#460—231no—
95#459—231no—
96#333—231no—
97Q8⋊C8D2311yescharacteristic, complemented
98D4⋊C8—231no—
99C2×C23#44811yescharacteristic
100C2×C23#44911yescharacteristic
101C2×C23#45311yescharacteristic
102D23—42no—
103D23—161no—
104C2×SD16—462no—
105C2×SD16—461no—
106C2×D8—461no—
107C4⋊Q8—231no—
108#127—231no—
109#125—461no—
110C22⋊Q8—462no—
111C22⋊Q8—461no—
112C4×Q8C2×D2311yescharacteristic
113C4×D4—231no—
114C4×D4—461no—
115C2×C4⋊C4—461no—
116C4⋊C8—231no—
117C4⋊C8C2×D2311yescharacteristic
118#102—461no—
119#102—461no—
120C4×C8C2×D2311yescharacteristic
121C23#162211yescharacteristic, complemented, Sylow
122C2×Q8—232no—
123C2×Q8D9211yescharacteristic
124C2×D4—231no—
125C2×D4—461no—
126C2×D4—461no—
127C2×D4—461no—
128C22×C4—462no—
129C22×C4—461no—
130SD16—924no—
131SD16—922no—
132D8—922no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—461no—
136C4⋊C4—21no—
137C4⋊C4—231no—
138C4⋊C4—462no—
139C4⋊C4—462no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4D9211yescharacteristic
143C22⋊C4—462no—
144C22⋊C4—461no—
145C42—21no—
146C42C22×D2311yescharacteristic
147C23—461no—
148C23—921no—
149Q8—21no—
150Q8—21no—
151Q8—922no—
152D4—232no—
153D4—461no—
154D4—922no—
155D4—921no—
156D4—921no—
157D4—921no—
158D4—921no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—461no—
162C2×C4—462no—
163C2×C4—921no—
164C2×C4—921no—
165C2×C4—1842no—
166C2×C4C2×D9211yescharacteristic
167C2×C4D4×D2311yescharacteristic
168C2×C4D4×D2311yescharacteristic
169C8—22no—
170C8—41no—
171C8—921no—
172C22—462no—
173C22—921no—
174C22—921no—
175C22—1841no—
176C22—1841no—
177C22—1841no—
178C22#1062505311yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—921no—
183C4—922no—
184C4#1062507511yescharacteristic
185C4#1062507911yescharacteristic
186C4SD16×D2311yescharacteristic
187C4#1062508911yescharacteristic
188C2—922no—
189C2—3681no—
190C2#1309255711yescharacteristic
191C2#1309256411yescharacteristic
192C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radical#13092613C2
hypercenterQ8⋊C8D23
hypocenterC23#1622
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #13093127C2semidirect
2. #13092790C2semidirect
3. #13092617C2semidirect
5. #13092165C2semidirect
6. #13092146C2semidirect
7. C23×Q8⋊C8C2semidirect
67. D92SD16semidirect
97. Q8⋊C8D23semidirect
121. C23#1622semidirect

Maximal subgroups

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

subgroupindex
#130931272
#130927902
#130926172
#130926132
#130921652
#130921462
C23×Q8⋊C82
#162223