Finite Group Databasebeta

← #15672400

Subgroups — #15672400

Order 2944.

254 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 57 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#13092728C212yesmaximal, complemented
2#13092347C211yesmaximal, characteristic, complemented
3#13092151C212yesmaximal, complemented
4#13092143C211yesmaximal, characteristic, complemented
5C23×#537C211yesmaximal, characteristic
6C2×#41×C23—21no—
7C23×C22⋊Q8—22no—
8C23×#121—22no—
9C23×#121—21no—
10C23×#121C2212yes—
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊Dic23C2211yescharacteristic
13C2×Dic23⋊C4—21no—
14#10625014—22no—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17C22⋊(C23⋊C8)C2212yes—
18#10624989—22no—
19#41×C23—42no—
20#41×C23—42no—
21C2×Q8×C23—21no—
22C2×D4×C23—21no—
23C2×D4×C23—22no—
24C2×D4×C23—21no—
25C2×D4×C23D412yes—
26C22×C4×C23—22no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—22no—
34C4⋊C4×C23D412yes—
35C22⋊C4×C23—22no—
36C22⋊C4×C23—22no—
37C4⋊Dic23—22no—
38Dic23⋊C4—42no—
39C2×C23⋊C8—22no—
40C23×C23—22no—
41C23×C23C2×D411yescharacteristic
42Q8×C23—42no—
43D4×C23—42no—
44D4×C23—42no—
45D4×C23—42no—
46D4×C23—42no—
47D4×C23—81no—
48C2×C4×C23—21no—
49C2×C4×C23—21no—
50C2×C4×C23—21no—
51C2×C4×C23—22no—
52C2×C4×C23—41no—
53C2×C4×C23—44no—
54C2×C4×C23—41no—
55C2×C4×C23D812yes—
56C2×C4×C23C2×D412yes—
57C2×Dic23—22no—
58C2×Dic23—41no—
59C2×Dic23—41no—
60C2×Dic23—41no—
61C2×Dic23—41no—
62C2×Dic23—41no—
63C23⋊C8—42no—
64#1610—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—21no—
67C22×C23—42no—
68C22×C23—42no—
69C22×C23—42no—
70C22×C23#12011yescharacteristic
71C22×C23C2×D811yescharacteristic
72C22×C23AGL(1,ℤ/8)11yescharacteristic
73C4×C23—22no—
74C4×C23—22no—
75C4×C23—42no—
76C4×C23—41no—
77Dic23—42no—
78Dic23—81no—
79#537D2311yescharacteristic
80#480—232no—
81#398—231no—
82#327—232no—
83#324—231no—
84C2×C23—21no—
85C2×C23—21no—
86C2×C23—82no—
87C2×C23#44711yescharacteristic
88C2×C23#45611yescharacteristic
89C2×C23#45811yescharacteristic
90C2×#41—21no—
91C22⋊Q8—22no—
92#121—22no—
93#121—21no—
94#121C2×D2312yes—
95C2×C4⋊C4—231no—
96C2×C4⋊C4—461no—
97C2×C4⋊C4C2×D2311yescharacteristic
98#107—462no—
99#102—462no—
100C22⋊C8—232no—
101#95—231no—
102#95—461no—
103C23#161011yescharacteristic, complemented, Sylow
104#41—42no—
105#41—42no—
106C2×Q8—21no—
107C2×D4—21no—
108C2×D4—22no—
109C2×D4—21no—
110C2×D4C22⋊D2312yes—
111C22×C4—22no—
112C22×C4—461no—
113C22×C4—461no—
114C22×C4C22⋊D2311yescharacteristic
115C22×C4C22⋊D2311yescharacteristic
116C22×C4C22×D2311yescharacteristic
117C2×C8—462no—
118C4⋊C4—21no—
119C4⋊C4—22no—
120C4⋊C4—462no—
121C4⋊C4—922no—
122C4⋊C4C22⋊D2312yes—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C23—22no—
126C23C2×C22⋊D2311yescharacteristic
127Q8—42no—
128D4—42no—
129D4—42no—
130D4—42no—
131D4—42no—
132D4—81no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—44no—
139C2×C4—41no—
140C2×C4—462no—
141C2×C4—921no—
142C2×C4—921no—
143C2×C4—921no—
144C2×C4—921no—
145C2×C4—921no—
146C2×C4#6727212yes—
147C2×C4C2×C22⋊D2312yes—
148C8—922no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22C2×#6727211yescharacteristic
155C22#1062510311yescharacteristic
156C22#1062512411yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—922no—
162C4—1841no—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#1309255111yescharacteristic
167C2#1309260011yescharacteristic
168C2#1309260711yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#537C2
socleC22×C23#120
hypercenter#537D23
hypocenterC23#1610
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #13092728C2semidirect
2. #13092347C2semidirect
3. #13092151C2semidirect
4. #13092143C2semidirect
103. C23#1610semidirect

Maximal subgroups

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

subgroupindex
#130927282
#130923472
#130921512
#130921432
C23×#5372
#161023