Finite Group Databasebeta

← #15674561

Subgroups — #15674561

Order 2944.

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

normal subgroups only

This group has 466 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#13093043C211yesmaximal, characteristic, complemented
2#13092273C212yesmaximal
3#13092184C211yesmaximal, characteristic, complemented
4#13092183C212yesmaximal, complemented
5C23×#379C211yesmaximal, characteristic
6C25×C23C2211yescharacteristic
7C2×C22⋊C4×C23—22no—
8C2×C22⋊C4×C23C2211yescharacteristic
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊Dic23—24no—
11C2×C22⋊Dic23C2212yes—
12C2×C22⋊Dic23C2212yes—
13#10625095—22no—
14#10625049—24no—
15C24×C23—22no—
16C24×C23—21no—
17C24×C23—21no—
18C24×C23—22no—
19C24×C23—44no—
20C24×C23Q812yescomplemented
21C24×C23C2311yescharacteristic
22C22×C4×C23—21no—
23C22×C4×C23D412yes—
24C22×Dic23—22no—
25C22×Dic23D414yes—
26C2×Dic46—22no—
27C22⋊C4×C23—22no—
28C22⋊C4×C23—22no—
29C22⋊C4×C23—44no—
30C22⋊Dic23—22no—
31C22⋊Dic23—22no—
32C22⋊Dic23—22no—
33C22⋊Dic23—22no—
34C22⋊Dic23—48no—
35C4⋊Dic23—22no—
36Dic23⋊C4—24no—
37C23×C23—28no—
38C23×C23—24no—
39C23×C23—24no—
40C23×C23—22no—
41C23×C23—44no—
42C23×C23—42no—
43C23×C23—44no—
44C23×C23—42no—
45C23×C23—44no—
46C23×C23—48no—
47C23×C23—41no—
48C23×C23—42no—
49C23×C23—41no—
50C23×C23C2×D412yes—
51C23×C23C2×D411yescharacteristic
52C23×C23C2×Q811yescharacteristic
53C23×C23#4111yescharacteristic
54C23×C23#4112yes—
55C2×C4×C23—22no—
56C2×C4×C23—42no—
57C2×C4×C23—42no—
58C2×C4×C23—41no—
59C2×Dic23—24no—
60C2×Dic23—44no—
61C2×Dic23—44no—
62C2×Dic23—42no—
63Dic46—82no—
64#2029—231nomaximal, Sylow
65C22×C23—24no—
66C22×C23—22no—
67C22×C23—28no—
68C22×C23—24no—
69C22×C23—41no—
70C22×C23—41no—
71C22×C23—42no—
72C22×C23—48no—
73C22×C23—44no—
74C22×C23—44no—
75C22×C23—42no—
76C22×C23—42no—
77C22×C23—44no—
78C22×C23#12011yescharacteristic
79C22×C23C22⋊Q812yes—
80C22×C23C22⋊Q811yescharacteristic
81C22×C23#12412yes—
82C22×C23#12411yescharacteristic
83C4×C23—42no—
84C4×C23—81no—
85Dic23—44no—
86Dic23—82no—
87#543—231no—
88#379—232no—
89#379D2311yescharacteristic
90#342—232no—
91#342—231no—
92C2×C23—22no—
93C2×C23—21no—
94C2×C23—22no—
95C2×C23—21no—
96C2×C23—44no—
97C2×C23#39311yescharacteristic
98C2×C23B(4,𝔽2)12yes—
99C25C2×D2311yescharacteristic
100C22⋊Q8—464no—
101C22⋊Q8—462no—
102C2×C22⋊C4—22no—
103C2×C22⋊C4—232no—
104C2×C22⋊C4—232no—
105C2×C22⋊C4—464no—
106C2×C22⋊C4C2×D2311yescharacteristic
107C2×C22⋊C4C2×D2311yescharacteristic
108C23#202911yescharacteristic, complemented, Sylow
109C24—22no—
110C24—21no—
111C24—21no—
112C24—22no—
113C24—44no—
114C24Dic4612yescomplemented
115C24C22×D2311yescharacteristic
116C2×Q8—462no—
117C22×C4—21no—
118C22×C4—234no—
119C22×C4—462no—
120C22×C4C22⋊D2312yes—
121C4⋊C4—464no—
122C4⋊C4—462no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—462no—
127C22⋊C4—462no—
128C22⋊C4—462no—
129C22⋊C4—462no—
130C22⋊C4—928no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—44no—
140C23—48no—
141C23—42no—
142C23—41no—
143C23—41no—
144C23C2×Dic4611yescharacteristic
145C23#6728811yescharacteristic
146C23D4×D2312yes—
147C23#6729012yes—
148C23C2×C22⋊D2311yescharacteristic
149Q8—1842no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—464no—
155C2×C4—924no—
156C2×C4—924no—
157C2×C4—922no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1062504912yes—
172C22#1062505612yes—
173C22#1062509511yescharacteristic
174C22#1062510711yescharacteristic
175C22#1062510811yescharacteristic
176C4—42no—
177C4—81no—
178C4—924no—
179C4—1842no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#1309232911yescharacteristic
186C2#1309260312yes—
subgroupG/H
centerC22#10625108
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#379C2
socleC22×C23#120
prime radicalC25×C23C22
hypercenter#379D23
hypocenterC23#2029
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #13093043C2semidirect
3. #13092184C2semidirect
4. #13092183C2semidirect
20. C24×C23Q8semidirect
108. C23#2029semidirect
114. C24Dic46semidirect

Maximal subgroups

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

subgroupindex
#130930432
#130922732
#130921842
#130921832
C23×#3792
#202923