Finite Group Databasebeta

← #15672436

Subgroups — #15672436

Order 2944.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092998C211yesmaximal, characteristic
2#13092736C212yesmaximal, complemented
3#13092356C211yesmaximal, characteristic, complemented
4#13092152C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C2×C4⋊C4×C23C2211yescharacteristic
8#10625101—21no—
9#10625101C2212yes—
10C2×C4⋊Dic23C2211yescharacteristic
11#10625068—22no—
12#10625066—22no—
13C23×C22⋊C8C2212yes—
14C23⋊#95—21no—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17#10625003—22no—
18#10624999—22no—
19C22×C4×C23D411yescharacteristic
20C22×C4×C23D411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C2×C22⋊D23—22no—
23C22×Dic23—21no—
24C22×Dic23—21no—
25#67288—42no—
26#67288—42no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D412yes—
30C2×C4×D23—22no—
31C2×Dic46—21no—
32C2×C8×C23—22no—
33C4⋊C4×C23—22no—
34(C2×D23)⋊C4—22no—
35(C2×D23)⋊C4—22no—
36C4⋊Dic23—21no—
37C4⋊Dic23—22no—
38C4⋊Dic23D412yes—
39C23×C23C2×D411yescharacteristic
40C22×D23—22no—
41C2×C4×C23—21no—
42C2×C4×C23—21no—
43C2×C4×C23—21no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23SD1612yes—
47C2×C4×C23C2×D412yes—
48C22⋊D23—42no—
49C22⋊D23—42no—
50C2×Dic23—22no—
51C2×Dic23—41no—
52C2×Dic23—41no—
53C2×Dic23—42no—
54C2×Dic23—41no—
55C2×Dic23—41no—
56D92—42no—
57D92—42no—
58D92—81no—
59C4×D23—44no—
60Dic46—42no—
61C8×C23—42no—
62#1616—231nomaximal, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23#12011yescharacteristic
66C22×C23C2×SD1611yescharacteristic
67C22×C23AGL(1,ℤ/8)11yescharacteristic
68C2×D23—42no—
69C2×D23—42no—
70C2×D23—42no—
71C4×C23—22no—
72C4×C23—22no—
73C4×C23—41no—
74Dic23—42no—
75Dic23—81no—
76Dic23—81no—
77#537—231no—
78#481—232no—
79#400—231no—
80#327—232no—
81#324D2311yescharacteristic, complemented
82C2×C23—21no—
83C2×C23—21no—
84C2×C23#45011yescharacteristic
85C2×C23#45411yescharacteristic
86C2×C23#45811yescharacteristic
87D23—82no—
88C2×#41—461no—
89C22⋊Q8—462no—
90#121—232no—
91#121—462no—
92#121—461no—
93C2×C4⋊C4—231no—
94C2×C4⋊C4C2×D2311yescharacteristic
95#106—462no—
96#102—462no—
97C22⋊C8C2×D2312yes—
98#95—231no—
99#95—461no—
100#95—461no—
101C23#161611yescharacteristic, complemented, Sylow
102#41—922no—
103#41—922no—
104C2×Q8—461no—
105C2×D4—232no—
106C2×D4—461no—
107C2×D4—461no—
108C2×D4—462no—
109C22×C4—462no—
110C22×C4—461no—
111C22×C4—461no—
112C22×C4D9211yescharacteristic
113C22×C4D9211yescharacteristic
114C22×C4C22×D2311yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—232no—
118C4⋊C4—461no—
119C4⋊C4—462no—
120C22⋊C4—462no—
121C22⋊C4—462no—
122C23—462no—
123C23C2×D9211yescharacteristic
124Q8—922no—
125D4—922no—
126D4—922no—
127D4—922no—
128D4—922no—
129D4—1841no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—462no—
136C2×C4—924no—
137C2×C4—921no—
138C2×C4—921no—
139C2×C4—922no—
140C2×C4—921no—
141C2×C4—921no—
142C2×C4#6726312yes—
143C2×C4D4×D2312yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—922no—
148C22—922no—
149C22—922no—
150C22#1062505311yescharacteristic
151C22C2×#6726311yescharacteristic
152C22#1062507911yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—922no—
157C4—1841no—
158C4—1841no—
159C2—21no—
160C2—21no—
161C2—1842no—
162C2#1309257011yescharacteristic
163C2#1309259211yescharacteristic
164C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#324D23
hypocenterC23#1616
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092736C2semidirect
3. #13092356C2semidirect
4. #13092152C2semidirect
5. C23×#324C2semidirect
81. #324D23semidirect
101. C23#1616semidirect

Maximal subgroups

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

subgroupindex
#130929982
#130927362
#130923562
#130921522
C23×#3242
#161623