Finite Group Databasebeta

← #15673476

Subgroups — #15673476

Order 2944.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4⋊C4×D23C211yesmaximal, characteristic
2#13092380C212yesmaximal
3#13092186C211yesmaximal, characteristic, complemented
4#13092185C212yesmaximal, complemented
5C23×#343C211yesmaximal, characteristic, complemented
6C22×C4×D23C412yes—
7C22×C4×D23C2211yescharacteristic
8C2×M16×C23C2212yes—
9C2×C4⋊C4×C23C2211yescharacteristic
10C2×C4⋊Dic23C2211yescharacteristic
11C2×Dic23⋊C4C412yes—
12C2×#67267C2212yes—
13C4⋊C4×D23—22no—
14C4⋊C4×D23—22no—
15(C2×D23)⋊C8—22no—
16(C2×D23)⋊C8—22no—
17C23×D23C2×C411yescharacteristic
18C22×C4×C23C2×C412yes—
19C22×C4×C23C2311yescharacteristic
20C22×Dic23C2×C411yescharacteristic
21C22×Dic23C2×C412yes—
22C2×C4×D23—22no—
23C2×C4×D23—21no—
24C2×C4×D23—21no—
25C2×C4×D23—22no—
26C2×C4×D23—22no—
27C2×C4×D23—44no—
28C2×C4×D23D412yes—
29C2×C4×D23D412yes—
30M16×C23—22no—
31M16×C23—22no—
32C2×C8×C23—22no—
33C4⋊C4×C23—22no—
34C4⋊Dic23—22no—
35Dic23⋊C4—24no—
36#67267—22no—
37#67267—22no—
38C2×C23⋊C8—22no—
39C23×C23C22×C411yescharacteristic
40C22×D23—21no—
41C22×D23—21no—
42C22×D23—22no—
43C22×D23—22no—
44C22×D23C22⋊C411yescharacteristic
45C22×D23C22⋊C411yescharacteristic
46C2×C4×C23—22no—
47C2×C4×C23—42no—
48C2×C4×C23C2×D412yes—
49C2×C4×C23#4112yes—
50C2×C4×C23#4111yescharacteristic
51C2×C4×C23#4111yescharacteristic
52C2×Dic23—21no—
53C2×Dic23—21no—
54C2×Dic23—22no—
55C2×Dic23—42no—
56C2×Dic23C22⋊C412yes—
57C4×D23—22no—
58C4×D23—22no—
59C4×D23—22no—
60C4×D23—22no—
61C4×D23—44no—
62C4×D23—44no—
63C8×C23—42no—
64C23⋊C8—42no—
65#1821—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—21no—
68C22×C23C2×C22⋊C411yescharacteristic
69C22×C23#11711yescharacteristic
70C22×C23#11711yescharacteristic
71C2×D23—24no—
72C2×D23—24no—
73C2×D23—21no—
74C2×D23—21no—
75C2×D23—21no—
76C2×D23—21no—
77C2×D23#10012yes—
78C2×D23#10112yes—
79C4×C23—42no—
80C4×C23#12312yes—
81C4×C23#12312yes—
82Dic23—22no—
83Dic23—42no—
84C22×C4⋊C4—231no—
85#407—232no—
86#343—232no—
87#343—231no—
88#343D2311yescharacteristic, complemented
89C2×C23—21no—
90C2×C23—21no—
91C2×C23#38111yescharacteristic
92C2×C23C2×#10011yescharacteristic
93C2×C23C2×#10111yescharacteristic
94D23—22no—
95D23—22no—
96C23×C4—231no—
97C23×C4—232no—
98C2×M16—232no—
99C2×M16C2×D2312yes—
100C2×C4⋊C4—232no—
101C2×C4⋊C4—231no—
102C2×C4⋊C4—462no—
103C2×C4⋊C4—462no—
104C2×C4⋊C4C2×D2311yescharacteristic
105C22⋊C8—462no—
106C22⋊C8—462no—
107C23#182111yescharacteristic, complemented, Sylow
108C24—231no—
109C22×C4—231no—
110C22×C4—232no—
111C22×C4—232no—
112C22×C4—232no—
113C22×C4—462no—
114C22×C4—462no—
115C22×C4—462no—
116C22×C4—461no—
117C22×C4—461no—
118C22×C4—924no—
119C22×C4C4×D2312yes—
120C22×C4C22×D2311yescharacteristic
121M16—22no—
122M16—22no—
123M16—462no—
124M16—462no—
125C2×C8—22no—
126C2×C8—462no—
127C4⋊C4—22no—
128C4⋊C4—464no—
129C4⋊C4—462no—
130C23—231no—
131C23—231no—
132C23—462no—
133C23—462no—
134C23—461no—
135C23—461no—
136C23C2×C4×D2311yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—232no—
140C2×C4—461no—
141C2×C4—461no—
142C2×C4—462no—
143C2×C4—462no—
144C2×C4—462no—
145C2×C4—462no—
146C2×C4—462no—
147C2×C4—924no—
148C2×C4—924no—
149C2×C4—922no—
150C2×C4#6728812yes—
151C2×C4D4×D2312yes—
152C2×C4#6729011yescharacteristic
153C2×C4#6729211yescharacteristic
154C8—42no—
155C8—922no—
156C22—21no—
157C22—21no—
158C22—232no—
159C22—232no—
160C22—464no—
161C22—464no—
162C22—461no—
163C22—461no—
164C22—461no—
165C22—461no—
166C22#1062504311yescharacteristic
167C22C22⋊C4×D2311yescharacteristic
168C22#1062506311yescharacteristic
169C4—42no—
170C4—462no—
171C4—922no—
172C4#1062505412yes—
173C4#1062506512yes—
174C2—21no—
175C2—21no—
176C2—462no—
177C2—462no—
178C2#1309227911yescharacteristic
179C2#100×D2311yescharacteristic
180C2#101×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#343D23
hypocenterC23#1821
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #13092186C2semidirect
4. #13092185C2semidirect
5. C23×#343C2semidirect
88. #343D23semidirect
107. C23#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D232
#130923802
#130921862
#130921852
C23×#3432
#182123