Finite Group Databasebeta

← #15674562

Subgroups — #15674562

Order 2944.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#13093043C211yesmaximal, characteristic, complemented
2#13092272C211yesmaximal, characteristic
3#13092272C212yesmaximal
4#13092183C212yesmaximal, complemented
5C23×#342C211yesmaximal, characteristic, complemented
6C24×D23C2211yescharacteristic
7C2×C22⋊C4×C23C2212yes—
8C2×C22⋊C4×C23C2211yescharacteristic
9C2×C22⋊Dic23C2211yescharacteristic
10C2×C22⋊Dic23C2212yes—
11C2×(C2×D23)⋊C4—22no—
12C2×(C2×D23)⋊C4—24no—
13#10625095—22no—
14#10625049—24no—
15C24×C23C2311yescharacteristic
16C23×D23—21no—
17C23×D23—22no—
18C23×D23—22no—
19C23×D23—21no—
20C23×D23—44no—
21C23×D23Q812yescomplemented
22C22×C4×C23—22no—
23C22×C4×C23D412yes—
24C22×Dic23—21no—
25C22×Dic23D414yes—
26C2×Dic46—22no—
27C22⋊C4×C23—22no—
28C22⋊C4×C23—22no—
29C22⋊C4×C23—22no—
30C22⋊Dic23—22no—
31C22⋊Dic23—22no—
32C22⋊Dic23—22no—
33(C2×D23)⋊C4—48no—
34(C2×D23)⋊C4—44no—
35C4⋊Dic23—22no—
36Dic23⋊C4—24no—
37C23×C23—42no—
38C23×C23C2×D411yescharacteristic
39C23×C23C2×D412yes—
40C23×C23C2×Q811yescharacteristic
41C23×C23#4112yes—
42C23×C23#4111yescharacteristic
43C22×D23—24no—
44C22×D23—28no—
45C22×D23—24no—
46C22×D23—22no—
47C22×D23—44no—
48C22×D23—48no—
49C22×D23—44no—
50C22×D23—42no—
51C22×D23—44no—
52C22×D23—41no—
53C22×D23—41no—
54C22×D23—42no—
55C2×C4×C23—22no—
56C2×C4×C23—42no—
57C2×C4×C23—44no—
58C2×C4×C23—42no—
59C2×Dic23—24no—
60C2×Dic23—44no—
61C2×Dic23—42no—
62C2×Dic23—41no—
63Dic46—82no—
64#2029—231nomaximal, Sylow
65C22×C23—22no—
66C22×C23—24no—
67C22×C23—41no—
68C22×C23—42no—
69C22×C23—41no—
70C22×C23#12011yescharacteristic
71C22×C23C22⋊Q812yes—
72C22×C23C22⋊Q811yescharacteristic
73C22×C23#12411yescharacteristic
74C22×C23#12412yes—
75C2×D23—28no—
76C2×D23—24no—
77C2×D23—44no—
78C2×D23—48no—
79C2×D23—44no—
80C2×D23—42no—
81C2×D23—42no—
82C2×D23—44no—
83C4×C23—42no—
84C4×C23—82no—
85Dic23—44no—
86Dic23—81no—
87#543—231no—
88#379—232no—
89#379—231no—
90#342—232no—
91#342D2311yescharacteristic, complemented
92C2×C23—21no—
93C2×C23—22no—
94C2×C23—22no—
95C2×C23—21no—
96C2×C23#39311yescharacteristic
97C2×C23B(4,𝔽2)12yes—
98D23—44no—
99C25—231no—
100C22⋊Q8—464no—
101C22⋊Q8—462no—
102C2×C22⋊C4—232no—
103C2×C22⋊C4—231no—
104C2×C22⋊C4—464no—
105C2×C22⋊C4—462no—
106C2×C22⋊C4C2×D2312yes—
107C2×C22⋊C4C2×D2311yescharacteristic
108C23#202911yescharacteristic, complemented, Sylow
109C24—232no—
110C24—461no—
111C24—462no—
112C24—462no—
113C24—461no—
114C24—924no—
115C24C22×D2311yescharacteristic
116C2×Q8—462no—
117C22×C4—22no—
118C22×C4—234no—
119C22×C4—461no—
120C22×C4D9212yes—
121C4⋊C4—464no—
122C4⋊C4—462no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—462no—
127C22⋊C4—462no—
128C22⋊C4—462no—
129C22⋊C4—924no—
130C22⋊C4—928no—
131C23—42no—
132C23—464no—
133C23—468no—
134C23—464no—
135C23—462no—
136C23—922no—
137C23—924no—
138C23—924no—
139C23—928no—
140C23—924no—
141C23—921no—
142C23—921no—
143C23—922no—
144C23C2×D9211yescharacteristic
145C23#6728812yes—
146C23D4×D2312yes—
147C23#6729011yescharacteristic
148C23Q8×D2311yescharacteristic
149Q8—1842no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—464no—
155C2×C4—924no—
156C2×C4—922no—
157C2×C4—921no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—468no—
164C22—464no—
165C22—928no—
166C22—924no—
167C22—924no—
168C22—922no—
169C22—922no—
170C22—924no—
171C22#1062504611yescharacteristic
172C22#1062505311yescharacteristic
173C22#1062505612yes—
174C22#1062506712yes—
175C22#1062506811yescharacteristic
176C4—42no—
177C4—82no—
178C4—924no—
179C4—1841no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—924no—
185C2#1309233011yescharacteristic
186C2#1309260512yes—
subgroupG/H
centerC22#10625053
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23#120
prime radicalC24×D23C22
hypercenter#342D23
hypocenterC23#2029
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #13093043C2semidirect
4. #13092183C2semidirect
5. C23×#342C2semidirect
21. C23×D23Q8semidirect
91. #342D23semidirect
108. C23#2029semidirect

Maximal subgroups

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

subgroupindex
#130930432
#130922722
#130921832
C23×#3422
#202923