Finite Group Databasebeta

← #15672031

Subgroups — #15672031

Order 2944.

238 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092967C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic, complemented
3#13092156C214yesmaximal, complemented
4C23×#432C211yesmaximal, characteristic, complemented
5C2×#67288C412yes—
6C2×C42×C23C2211yescharacteristic
7#10625101—21no—
8#10625101—21no—
9#10625046C2212yes—
10#10625045C411yescharacteristic
11C4×D92—21no—
12C4×D92—21no—
13#10625040C411yescharacteristic
14C23×C4⋊C8—21no—
15C23×C22⋊C8—21no—
16C23×#97C2212yes—
17C22⋊(C23⋊C8)—21no—
18C4⋊(C23⋊C8)—21no—
19#10624985C2212yes—
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23D411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C2×C22⋊D23—22no—
24#67288—44no—
25C2×D92—21no—
26C2×D92—21no—
27C2×D92C2×C412yes—
28C2×C4×D23—22no—
29C2×Dic46C2×C412yes—
30C2×C8×C23—22no—
31C42×C23C2×C411yescharacteristic
32C42×C23D411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23C2311yescharacteristic
35(C2×D23)⋊C4—22no—
36(C2×D23)⋊C4—22no—
37C4⋊Dic23—21no—
38C4⋊Dic23—21no—
39C2×C23⋊C8—22no—
40C23×C23C22⋊C411yescharacteristic
41C22×D23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23—41no—
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C22×C411yescharacteristic
49C2×C4×C23C2×D411yescharacteristic
50C2×C4×C23C2×D411yescharacteristic
51C22⋊D23—44no—
52C2×Dic23—22no—
53D92—42no—
54D92—42no—
55D92—42no—
56C4×D23—44no—
57Dic46—42no—
58C8×C23—42no—
59C23⋊C8—42no—
60#1536—231nomaximal, Sylow
61C22×C23—21no—
62C22×C23—21no—
63C22×C23—21no—
64C22×C23C2×C22⋊C411yescharacteristic
65C2×D23—42no—
66C2×D23—42no—
67C2×D23—42no—
68C4×C23—21no—
69C4×C23—21no—
70C4×C23—21no—
71C4×C23—21no—
72C4×C23—21no—
73C4×C23#10012yes—
74Dic23—42no—
75#532—231no—
76#432—231no—
77#432D2311yescharacteristic, complemented
78#329—234no—
79C2×C23—41no—
80C2×C23C2×#10011yescharacteristic
81C2×C23#42111yescharacteristic
82C2×C23#42111yescharacteristic
83D23—82no—
84C2×#41—232no—
85C4⋊Q8—231no—
86#127—231no—
87#124—232no—
88#121—461no—
89#121—461no—
90C4×D4—461no—
91C4×D4—461no—
92C2×C42C2×D2311yescharacteristic
93C4⋊C8—21no—
94C4⋊C8—461no—
95C22⋊C8—21no—
96C22⋊C8—461no—
97#97—232no—
98#97C2×D2312yes—
99C23#153611yescharacteristic, complemented, Sylow
100#41—924no—
101C2×Q8—232no—
102C2×D4—232no—
103C2×D4—462no—
104C2×D4—461no—
105C2×D4—461no—
106C22×C4—462no—
107C22×C4C4×D2311yescharacteristic
108C22×C4D9211yescharacteristic
109C22×C4C22⋊D2311yescharacteristic
110C2×C8—22no—
111C2×C8—462no—
112C4⋊C4—461no—
113C4⋊C4—461no—
114C22⋊C4—462no—
115C22⋊C4—462no—
116C42C4×D2311yescharacteristic
117C42D9211yescharacteristic
118C42C22⋊D2311yescharacteristic
119C42C22×D2311yescharacteristic
120C23—462no—
121C23(C2×D23)⋊C411yescharacteristic
122Q8—922no—
123D4—922no—
124D4—922no—
125D4—922no—
126D4—924no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—462no—
131C2×C4—924no—
132C2×C4(C2×D23)⋊C411yescharacteristic
133C2×C4(C2×D23)⋊C411yescharacteristic
134C2×C4(C2×D23)⋊C411yescharacteristic
135C2×C4C2×C4×D2311yescharacteristic
136C2×C4C2×D9211yescharacteristic
137C2×C4C2×C22⋊D2311yescharacteristic
138C8—42no—
139C8—922no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—922no—
144C22—922no—
145C22—922no—
146C22C2×(C2×D23)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—21no—
151C4—21no—
152C4—922no—
153C4#1062500512yes—
154C2—41no—
155C2—1842no—
156C2C2×#1062500511yescharacteristic
157C2#1309243311yescharacteristic
158C2#1309243511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radical#13092967C2
cosocleC42×C23C23
hypercenter#432D23
hypocenterC23#1536
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #13092474C2semidirect
3. #13092156C2semidirect
4. C23×#432C2semidirect
77. #432D23semidirect
99. C23#1536semidirect

Maximal subgroups

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

subgroupindex
#130929672
#130924742
#130921562
C23×#4322
#153623