Finite Group Databasebeta

← C22×#63778 #11857333

Subgroups — C22×#63778 #11857333

Order 1152.

2434 conjugacy classes of subgroups; only the 338 normal subgroups are shown.

normal subgroups only

This group has 2434 conjugacy classes of subgroups — too many to draw. Only its 338 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
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C23×#622C212yesmaximal, complemented
3C2×#63778C2112yesmaximal, direct product factor
4C24×C3⋊D3C411yescharacteristic
5C23×C32×C4C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C22×C4×C3⋊D3—28no—
8C22×C4×C3⋊D3C416yes—
9C22×C4×C3⋊D3C2216yes—
10C22×#622—28no—
11C22×#622C22112yescomplemented
12#63778C22116yesdirect product factor
13C23×C4×D3—62no—
14C24×C32C2×C411yescharacteristic
15C23×C3⋊D3—24no—
16C23×C3⋊D3—24no—
17C23×C3⋊D3C818yescomplemented
18C23×C3⋊D3C2×C416yes—
19C22×C32×C4—24no—
20C22×C32×C4C2×C416yes—
21C22×C3⋊Dic3C2×C413yes—
22C22×C3⋊Dic3D418yes—
23C22×C3⋊Dic3C2313yes—
24C2×C4×C3⋊D3—224no—
25C2×C4×C3⋊D3—224no—
26C2×C4×C3⋊D3C2×C4112yes—
27C2×C4×C3⋊D3C2314yes—
28C2×#622—224no—
29C2×#622C2318yescomplemented
30C22×C22⋊C8—91nomaximal, Sylow
31C24×D3—62no—
32C23×C3×C4—22no—
33C23×Dic3—62no—
34C22×C4×D3—612no—
35C22×C4×D3—612no—
36C22×C4×D3—632no—
37C23×C32C22⋊C414yes—
38C23×C32C2×C814yes—
39C23×C32M1614yes—
40C23×C32C22×C413yes—
41C22×C3⋊D3—232no—
42C22×C3⋊D3—212no—
43C22×C3⋊D3—212no—
44C22×C3⋊D3C2×C8124yescomplemented
45C22×C3⋊D3C22×C414yes—
46C2×C32×C4—212no—
47C2×C32×C4C22×C414yes—
48C2×C3⋊Dic3C22⋊C4112yes—
49C2×C3⋊Dic3C22×C413yes—
50C2×C3⋊Dic3C2×D4112yes—
51C2×C3⋊Dic3C2411yescharacteristic
52C4×C3⋊D3—224no—
53C4×C3⋊D3—28no—
54#622—28no—
55C24×C4—91no—
56C23×C8—92no—
57C2×C22⋊C8—912no—
58C24×C3—22no—
59C23×D3—616no—
60C23×D3—612no—
61C23×D3—616no—
62C23×D3—616no—
63C22×C3×C4—216no—
64C22×C3×C4—212no—
65C22×Dic3—66no—
66C22×Dic3—616no—
67C22×Dic3—66no—
68C2×C4×D3—624no—
69C2×C4×D3—68no—
70C2×C4×D3—696no—
71C2×C4×D3—696no—
72C22×C32C22⋊C8116yescomplemented
73C22×C32C2×C22⋊C416yes—
74C22×C32C22×C816yes—
75C22×C32C2×M1616yes—
76C22×C32C23×C411yescharacteristic
77C2×C3⋊D3—24no—
78C2×C3⋊D3—24no—
79C2×C3⋊D3—248no—
80C2×C3⋊D3C22×C818yescomplemented
81C32×C4—24no—
82C3⋊Dic3C2×C22⋊C416yes—
83C3⋊Dic3C22×D412yes—
84C25—91no—
85C23×C4—91no—
86C23×C4—96no—
87C23×C4—96no—
88C23×C4—188no—
89C23×C4#15711yescharacteristic
90C22×C8—912no—
91C22×C8—188no—
92C22⋊C8—916no—
93C23×C3—26no—
94C23×C3—28no—
95C23×C3—28no—
96C23×C3—28no—
97C22×D3—648no—
98C22×D3—68no—
99C22×D3—648no—
100C22×D3—648no—
101C22×D3—6128no—
102C2×C3×C4—248no—
103C2×C3×C4—28no—
104C2×Dic3—624no—
105C2×Dic3—66no—
106C2×Dic3—624no—
107C2×Dic3—62no—
108C4×D3—696no—
109C4×D3—632no—
110C2×C32C2×C22⋊C8112yescomplemented
111C2×C32C22×C22⋊C411yescharacteristic
112C2×C32C23×C811yescharacteristic
113C2×C32C22×M1611yescharacteristic
114C3⋊D3—28no—
115C24—96no—
116C24—98no—
117C24—184no—
118C24—184no—
119C24C2×#15711yescharacteristic
120C22×C4—24no—
121C22×C4—93no—
122C22×C4—93no—
123C22×C4—98no—
124C22×C4—94no—
125C22×C4—912no—
126C22×C4—1824no—
127C22×C4—1824no—
128C22×C4C2×#15716yes—
129C2×C8—98no—
130C2×C8—1824no—
131C22×C3—212no—
132C22×C3—212no—
133C22×C3—232no—
134C22×C3—212no—
135C22×C3—22no—
136C2×D3—616no—
137C2×D3—616no—
138C2×D3—6192no—
139C2×D3—616no—
140C3×C4—216no—
141Dic3—612no—
142Dic3—64no—
143C32C22×C22⋊C811yescharacteristic, complemented, Sylow
144C23—924no—
145C23—94no—
146C23—1812no—
147C23—1832no—
148C23—1812no—
149C23#378714yes—
150C23#378814yes—
151C23C22⋊#15714yes—
152C23C22×#15713yes—
153C2×C4—212no—
154C2×C4—912no—
155C2×C4—912no—
156C2×C4—91no—
157C2×C4—93no—
158C2×C4—188no—
159C2×C4—1824no—
160C2×C4C22×#15714yes—
161C8—188no—
162C2×C3—224no—
163C2×C3—22no—
164C2×C3—22no—
165C2×C3—22no—
166D3—632no—
167C22—98no—
168C22—1848no—
169C22—184no—
170C22—184no—
171C22#63778116yesdirect product factor
172C22C2×#378716yes—
173C22C2×#378816yes—
174C22C2×C22⋊#15716yes—
175C22C23×#15711yescharacteristic
176C4—24no—
177C4—92no—
178C4—96no—
179C3—22no—
180C2—188no—
181C2C2×#63778112yesdirect product factor
182C2C22×#378711yescharacteristic
183C2C22×#378811yescharacteristic
184C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC24C2×#157
commutatorC2×C32C23×C8
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC24×C32C2×C4
prime radicalC24×C3⋊D3C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C22×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×#622C2semidirect
3. C2×#63778C2direct (N × H)
11. C22×#622C22semidirect
12. #63778C22direct (N × H)
17. C23×C3⋊D3C8semidirect
29. C2×#622C23semidirect
44. C22×C3⋊D3C2×C8semidirect
72. C22×C32C22⋊C8semidirect
80. C2×C3⋊D3C22×C8semidirect
110. C2×C32C2×C22⋊C8semidirect
143. C32C22×C22⋊C8semidirect
171. C22#63778direct (N × H)
181. C2C2×#63778direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C23×#6222
C2×#637782
C22×C22⋊C89