Finite Group Databasebeta

← C4×#63781 #11773144

Subgroups — C4×#63781 #11773144

Order 1152.

1250 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 254 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
1C22×C4×#157C212yesmaximal
2C2×C42×C3⋊D3C211yesmaximal, characteristic
3C2×#63781C214yesmaximal
4C23×#157C2214yes—
5C22×C4×C3⋊D3C2212yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C4×#157—24no—
8C2×C4×#157—24no—
9C2×C4×#157C418yescomplemented
10C2×C32×C42C411yescharacteristic, complemented
11C2×C4×C3⋊Dic3C411yescharacteristic, complemented
12C2×C4×C3⋊Dic3C412yescomplemented
13C42×C3⋊D3—24no—
14#63781C4116yesdirect product factor
15C2×C42×D3—62no—
16C23×C3⋊D3C2311yescharacteristic
17C22×#157—24no—
18C22×#157—24no—
19C22×#157—28no—
20C22×#157C2×C418yes—
21C22×#157C2×C4116yes—
22C22×C32×C4C2×C412yes—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2×C411yescharacteristic
26C2×C4×C3⋊D3—24no—
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C418yes—
29C2×C4×C3⋊D3C2×C414yes—
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3D414yes—
32C2×C4×C3⋊D3Q812yes—
33C4×#157—216no—
34C32×C42—22no—
35C4×C3⋊Dic3—22no—
36C4×C3⋊Dic3—24no—
37C4×#95—91nomaximal, Sylow
38C22×C4×D3—62no—
39C22×C4×D3—64no—
40C2×C3×C42—22no—
41C2×C4×Dic3—64no—
42C2×C4×Dic3—62no—
43C42×D3—616no—
44C23×C32C22×C411yescharacteristic
45C22×C3⋊D3C22×C412yes—
46C22×C3⋊D3C22×C414yes—
47C22×C3⋊D3C2×D411yescharacteristic
48C22×C3⋊D3C2×D412yes—
49C22×C3⋊D3C2×Q811yescharacteristic
50C22×C3⋊D3#4114yes—
51C2×#157—28no—
52C2×#157—28no—
53C2×#157—216no—
54C2×#157—216no—
55C2×#157C42116yescomplemented
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4C4212yes—
59C2×C32×C4C4214yescomplemented
60C2×C32×C4C22⋊C412yes—
61C2×C32×C4C4⋊C412yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C4212yes—
65C2×C3⋊Dic3C4214yescomplemented
66C2×C3⋊Dic3C22⋊C412yes—
67C2×C3⋊Dic3C4⋊C412yes—
68C4×C3⋊D3—216no—
69C4×C3⋊D3C22⋊C418yes—
70C4×C3⋊D3C4⋊C418yes—
71C22×C42—92no—
72C22×C42—91no—
73C2×#95—94no—
74C23×D3—62no—
75C22×C3×C4—24no—
76C22×C3×C4—22no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C2×C4×D3—68no—
80C2×C4×D3—68no—
81C2×C4×D3—616no—
82C2×C4×D3—64no—
83C2×C4×D3—64no—
84C2×C4×D3—616no—
85C2×C4×D3—616no—
86C3×C42—28no—
87C4×Dic3—616no—
88C4×Dic3—68no—
89C22×C32C2×C4211yescharacteristic
90C22×C32C2×C4212yes—
91C22×C32C2×C22⋊C411yescharacteristic
92C22×C32C2×C4⋊C411yescharacteristic
93C22×C32#11712yes—
94C2×C3⋊D3C2×C4214yes—
95C2×C3⋊D3C2×C22⋊C412yes—
96C2×C3⋊D3C2×C4⋊C412yes—
97C2×C3⋊D3#11714yes—
98C2×C3⋊D3C4×D414yes—
99C2×C3⋊D3C4×D418yes—
100C2×C3⋊D3C4×Q814yes—
101#157—216no—
102C32×C4—24no—
103C32×C4#9514yescomplemented
104C3⋊Dic3—24no—
105C3⋊Dic3#9514yescomplemented
106C23×C4—91no—
107C23×C4—94no—
108C23×C4—92no—
109C2×C42—98no—
110C2×C42—92no—
111C2×C42—91no—
112C2×C42—184no—
113C2×C42—184no—
114C2×C42—184no—
115C2×C42#15711yescharacteristic, complemented
116#95—916no—
117C23×C3—22no—
118C22×D3—64no—
119C22×D3—68no—
120C22×D3—64no—
121C22×D3—62no—
122C22×D3—62no—
123C22×D3—68no—
124C2×C3×C4—28no—
125C2×C3×C4—28no—
126C2×C3×C4—24no—
127C2×C3×C4—28no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×Dic3—64no—
131C2×Dic3—68no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—68no—
135C2×Dic3—68no—
136C4×D3—616no—
137C4×D3—616no—
138C4×D3—664no—
139C2×C32C4311yescharacteristic
140C2×C32C2×#9511yescharacteristic
141C2×C32#37611yescharacteristic
142C2×C32C4×C22⋊C412yes—
143C2×C32C4×C4⋊C412yes—
144C3⋊D3C4×C22⋊C414yes—
145C3⋊D3C4×C4⋊C414yes—
146C24—91no—
147C22×C4—91no—
148C22×C4—94no—
149C22×C4—92no—
150C22×C4—92no—
151C22×C4—94no—
152C22×C4—916no—
153C22×C4—98no—
154C22×C4—92no—
155C22×C4—98no—
156C22×C4—184no—
157C22×C4—184no—
158C22×C4—184no—
159C22×C4—184no—
160C22×C4—188no—
161C22×C4C2×#15712yes—
162C22×C4C2×#15711yescharacteristic
163C42—22no—
164C42—184no—
165C42—1816no—
166C42—182no—
167C22×C3—22no—
168C22×C3—24no—
169C22×C3—22no—
170C22×C3—24no—
171C22×C3—22no—
172C2×D3—64no—
173C2×D3—64no—
174C2×D3—616no—
175C2×D3—68no—
176C2×D3—68no—
177C2×D3—68no—
178C2×D3—68no—
179C3×C4—216no—
180C3×C4—28no—
181Dic3—68no—
182Dic3—616no—
183C32C4×#9511yescharacteristic, complemented, Sylow
184C23—92no—
185C23—94no—
186C23—91no—
187C23—91no—
188C23—94no—
189C23—92no—
190C23C22×#15711yescharacteristic
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—92no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—98no—
197C2×C4—98no—
198C2×C4—916no—
199C2×C4—94no—
200C2×C4—1816no—
201C2×C4—188no—
202C2×C4—1816no—
203C2×C4—188no—
204C2×C4—1816no—
205C2×C4—182no—
206C2×C4—182no—
207C2×C4C4×#15712yes—
208C2×C4C4×#15714yescomplemented
209C2×C4C4⋊#15712yes—
210C2×C4C22⋊#15712yes—
211C2×C3—22no—
212C2×C3—24no—
213C2×C3—22no—
214C2×C3—22no—
215C2×C3—24no—
216D3—68no—
217D3—68no—
218C22—92no—
219C22—92no—
220C22—98no—
221C22—94no—
222C22—94no—
223C22—94no—
224C22—94no—
225C22C2×C4×#15711yescharacteristic
226C22C2×C4×#15712yes—
227C22C2×C4⋊#15711yescharacteristic
228C22#6428612yes—
229C22C2×C22⋊#15711yescharacteristic
230C4—24no—
231C4—94no—
232C4—1816no—
233C4—184no—
234C4#6378114yesdirect product factor
235C3—22no—
236C2—94no—
237C2—94no—
238C2C42×#15711yescharacteristic
239C2#1059373311yescharacteristic
240C2C4×C4⋊#15712yes—
241C2C2×#6378111yescharacteristic
242C2C4×C22⋊#15712yes—
subgroupG/H
centerC22×C4C2×#157
commutatorC2×C32C43
FrattiniC23C22×#157
FittingC2×C32×C42C4
socleC23×C32C22×C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C42#157
hypocenterC32C4×#95
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
9. C2×C4×#157C4semidirect
10. C2×C32×C42C4semidirect
11. C2×C4×C3⋊Dic3C4semidirect
12. C2×C4×C3⋊Dic3C4semidirect
14. #63781C4direct (N × H)
55. C2×#157C42semidirect
59. C2×C32×C4C42semidirect
65. C2×C3⋊Dic3C42semidirect
103. C32×C4#95semidirect
105. C3⋊Dic3#95semidirect
115. C2×C42#157semidirect
183. C32C4×#95semidirect
208. C2×C4C4×#157semidirect
234. C4#63781direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×C42×C3⋊D32
C2×#637812
C4×#959