Finite Group Databasebeta

← #15672402

Subgroups — #15672402

Order 2944.

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

normal subgroups only

This group has 254 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#13092731C212yesmaximal, complemented
3#13092347C211yesmaximal, characteristic, complemented
4#13092152C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C2×C4⋊C4×C23C2211yescharacteristic
8#10625101—21no—
9#10625101C2212yes—
10C2×C4⋊Dic23C2211yescharacteristic
11C2×Dic23⋊C4—21no—
12#10625068—22no—
13#10625066—22no—
14C23×C22⋊C8C2212yes—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17#10625003—22no—
18#10625000—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—
39Dic23⋊C4—42no—
40C23×C23C2×D411yescharacteristic
41C22×D23—22no—
42C2×C4×C23—21no—
43C2×C4×C23—21no—
44C2×C4×C23—21no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23D812yes—
48C2×C4×C23C2×D412yes—
49C22⋊D23—42no—
50C22⋊D23—42no—
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—41no—
54C2×Dic23—41no—
55C2×Dic23—41no—
56C2×Dic23—41no—
57C2×Dic23—41no—
58D92—42no—
59D92—42no—
60D92—81no—
61C4×D23—44no—
62Dic46—42no—
63C8×C23—42no—
64#1610—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—21no—
67C22×C23#12011yescharacteristic
68C22×C23C2×D811yescharacteristic
69C22×C23AGL(1,ℤ/8)11yescharacteristic
70C2×D23—42no—
71C2×D23—42no—
72C2×D23—42no—
73C4×C23—22no—
74C4×C23—22no—
75C4×C23—41no—
76Dic23—42no—
77Dic23—42no—
78Dic23—81no—
79#537—231no—
80#480—232no—
81#398—231no—
82#327—232no—
83#324D2311yescharacteristic, complemented
84C2×C23—21no—
85C2×C23—21no—
86C2×C23#44711yescharacteristic
87C2×C23#45611yescharacteristic
88C2×C23#45811yescharacteristic
89D23—82no—
90C2×#41—461no—
91C22⋊Q8—462no—
92#121—232no—
93#121—462no—
94#121—461no—
95C2×C4⋊C4—231no—
96C2×C4⋊C4—461no—
97C2×C4⋊C4C2×D2311yescharacteristic
98#107—462no—
99#102—462no—
100C22⋊C8C2×D2312yes—
101#95—231no—
102#95—461no—
103C23#161011yescharacteristic, complemented, Sylow
104#41—922no—
105#41—922no—
106C2×Q8—461no—
107C2×D4—232no—
108C2×D4—461no—
109C2×D4—461no—
110C2×D4—462no—
111C22×C4—462no—
112C22×C4—461no—
113C22×C4—461no—
114C22×C4D9211yescharacteristic
115C22×C4D9211yescharacteristic
116C22×C4C22×D2311yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—232no—
120C4⋊C4—461no—
121C4⋊C4—462no—
122C4⋊C4—922no—
123C22⋊C4—462no—
124C22⋊C4—462no—
125C23—462no—
126C23C2×D9211yescharacteristic
127Q8—922no—
128D4—922no—
129D4—922no—
130D4—922no—
131D4—922no—
132D4—1841no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—462no—
139C2×C4—462no—
140C2×C4—924no—
141C2×C4—921no—
142C2×C4—921no—
143C2×C4—921no—
144C2×C4—921no—
145C2×C4—921no—
146C2×C4D18412yes—
147C2×C4D4×D2312yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—922no—
152C22—922no—
153C22—922no—
154C22#1062505311yescharacteristic
155C22C2×D18411yescharacteristic
156C22#1062507911yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—922no—
161C4—922no—
162C4—1841no—
163C2—21no—
164C2—21no—
165C2—1842no—
166C2#1309255311yescharacteristic
167C2#1309260211yescharacteristic
168C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#324D23
hypocenterC23#1610
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. #13092731C2semidirect
3. #13092347C2semidirect
4. #13092152C2semidirect
5. C23×#324C2semidirect
83. #324D23semidirect
103. C23#1610semidirect

Maximal subgroups

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

subgroupindex
#130929982
#130927312
#130923472
#130921522
C23×#3242
#161023