Finite Group Databasebeta

← C2×C4×#3792 #11857149

Subgroups — C2×C4×#3792 #11857149

Order 1152.

1154 conjugacy classes of subgroups; only the 322 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 322 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×#3792C212yesmaximal
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic
3C4×#3792C218yesmaximal, direct product factor
4C2×#63777C212yesmaximal, complemented
5C2×C4×#622C212yesmaximal, complemented
6C23×C32×C4C411yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C2×#3792C4116yesdirect product factor
10C2×#3792C2218yes—
11C22×#622C2214yes—
12C2×C4×C3⋊Dic3C414yes—
13C2×C4×C3⋊Dic3C411yescharacteristic
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2214yes—
18#63777C2218yescomplemented
19C4×#622C2218yescomplemented
20C22×C4×Dic3—62no—
21C24×C32C2×C411yescharacteristic
22C22×C32×C4—24no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C414yes—
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3—24no—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C414yes—
29C22×C3⋊Dic3C2×C412yes—
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C418yes—
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2311yescharacteristic
34C22×C3⋊Dic3C2312yes—
35#3792C2×C4132yesdirect product factor
36C2×#622C2×C4116yescomplemented
37C2×#622C2318yes—
38C4×C3⋊Dic3C2×C412yes—
39C4×C3⋊Dic3C2×C414yes—
40C4×C3⋊Dic3C2×C414yes—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3C2312yes—
43C4×C3⋊Dic3C2312yes—
44C2×C4×M16—91nomaximal, Sylow
45C23×C3×C4—22no—
46C23×Dic3—62no—
47C23×Dic3—62no—
48C2×C4×Dic3—62no—
49C2×C4×Dic3—68no—
50C2×C4×Dic3—62no—
51C2×C4×Dic3—62no—
52C2×C4×Dic3—68no—
53C2×C4×Dic3—62no—
54C23×C32—22no—
55C23×C32—22no—
56C23×C32C4214yes—
57C23×C32C22×C412yes—
58C23×C32C22×C411yescharacteristic
59C2×C32×C4—22no—
60C2×C32×C4—28no—
61C2×C32×C4M1614yescomplemented
62C2×C32×C4C22×C412yes—
63C2×C32×C4C22×C412yes—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—28no—
66C2×C3⋊Dic3C4218yes—
67C2×C3⋊Dic3C4214yes—
68C2×C3⋊Dic3M1614yescomplemented
69C2×C3⋊Dic3C22×C412yes—
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C22×C412yes—
72C2×C3⋊Dic3C22×C414yes—
73C2×C3⋊Dic3C22×C418yes—
74C2×C3⋊Dic3C22×C412yes—
75C2×C3⋊Dic3C2411yescharacteristic
76#622C22×C4116yescomplemented
77C22×M16—92no—
78C22×C42—91no—
79C4×M16—98no—
80C2×#97—92no—
81C2×C4×C8—92no—
82C24×C3—22no—
83C22×C3×C4—216no—
84C22×C3×C4—22no—
85C22×C3×C4—28no—
86C22×C3×C4—22no—
87C22×Dic3—64no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—68no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C22×Dic3—64no—
94C22×Dic3—616no—
95C22×Dic3—616no—
96C4×Dic3—68no—
97C4×Dic3—64no—
98C4×Dic3—64no—
99C4×Dic3—68no—
100C4×Dic3—64no—
101C4×Dic3—64no—
102C22×C32—22no—
103C22×C32—22no—
104C22×C32—28no—
105C22×C32C2×C4214yes—
106C22×C32C2×C4212yes—
107C22×C32C2×M1612yes—
108C22×C32C2×M1612yes—
109C22×C32C23×C411yescharacteristic
110C32×C4—22no—
111C32×C4C2×M1614yescomplemented
112C3⋊Dic3—22no—
113C3⋊Dic3C2×C4212yes—
114C3⋊Dic3C2×C4214yes—
115C3⋊Dic3C2×M1614yescomplemented
116C3⋊Dic3C23×C412yes—
117C23×C4—91no—
118C23×C4—91no—
119C23×C4#15711yescharacteristic
120C2×M16—916no—
121C2×M16—98no—
122C22×C8—94no—
123C2×C42—91no—
124C2×C42—94no—
125C2×C42—91no—
126C2×C42—94no—
127C2×C42—91no—
128C2×C42—91no—
129#97—98no—
130C4×C8—98no—
131C23×C3—28no—
132C23×C3—28no—
133C23×C3—24no—
134C23×C3—22no—
135C23×C3—28no—
136C2×C3×C4—28no—
137C2×C3×C4—232no—
138C2×C3×C4—24no—
139C2×C3×C4—24no—
140C2×C3×C4—28no—
141C2×Dic3—616no—
142C2×Dic3—68no—
143C2×Dic3—68no—
144C2×Dic3—62no—
145C2×Dic3—64no—
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—68no—
149C2×Dic3—616no—
150C2×Dic3—62no—
151C2×Dic3—632no—
152C2×Dic3—68no—
153C2×C32—24no—
154C2×C32C4×M1614yescomplemented
155C2×C32C22×C4211yescharacteristic
156C2×C32C22×M1611yescharacteristic
157C2×C32C22×M1611yescharacteristic
158C24C2×#15711yescharacteristic
159C22×C4—24no—
160C22×C4—91no—
161C22×C4—92no—
162C22×C4—91no—
163C22×C4—92no—
164C22×C4—91no—
165C22×C4—98no—
166C22×C4—94no—
167C22×C4—91no—
168C22×C4—184no—
169C22×C4C2×#15711yescharacteristic
170C22×C4C2×#15714yes—
171C22×C4C2×#15711yescharacteristic
172M16—932no—
173C2×C8—98no—
174C2×C8—916no—
175C42—92no—
176C42—92no—
177C42—94no—
178C42—92no—
179C42—92no—
180C42—94no—
181C22×C3—28no—
182C22×C3—28no—
183C22×C3—232no—
184C22×C3—24no—
185C22×C3—28no—
186C22×C3—24no—
187C22×C3—24no—
188C22×C3—22no—
189C3×C4—28no—
190C3×C4—28no—
191Dic3—64no—
192Dic3—68no—
193Dic3—68no—
194Dic3—64no—
195Dic3—68no—
196C32C2×C4×M1611yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23C4×#15714yes—
200C23C22×#15712yes—
201C23C22×#15711yescharacteristic
202C2×C4—22no—
203C2×C4—28no—
204C2×C4—94no—
205C2×C4—94no—
206C2×C4—98no—
207C2×C4—98no—
208C2×C4—94no—
209C2×C4—91no—
210C2×C4—92no—
211C2×C4—91no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—188no—
215C2×C4—182no—
216C2×C4#379214yesdirect product factor
217C2×C4C22×#15712yes—
218C2×C4C22×#15712yes—
219C8—916no—
220C2×C3—216no—
221C2×C3—28no—
222C2×C3—22no—
223C2×C3—22no—
224C2×C3—22no—
225C22—28no—
226C22—22no—
227C22—22no—
228C22#6428312yes—
229C22C2×C4×#15714yes—
230C22C2×C4×#15712yes—
231C22C2×#379212yes—
232C22C23×#15711yescharacteristic
233C4—22no—
234C4—94no—
235C4—92no—
236C4—92no—
237C4—94no—
238C4—182no—
239C4C2×#379214yesdirect product factor
240C3—22no—
241C2—24no—
242C2C4×#379214yesdirect product factor
243C2C2×#6428311yescharacteristic
244C2C22×C4×#15711yescharacteristic
245C2C22×#379211yescharacteristic
subgroupG/H
centerC22×C4C2×#157
commutatorC2×C32C22×C42
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×C4×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C4×#3792C2direct (N × H)
4. C2×#63777C2semidirect
5. C2×C4×#622C2semidirect
9. C2×#3792C4direct (N × H)
18. #63777C22semidirect
19. C4×#622C22semidirect
35. #3792C2×C4direct (N × H)
36. C2×#622C2×C4semidirect
61. C2×C32×C4M16semidirect
68. C2×C3⋊Dic3M16semidirect
76. #622C22×C4semidirect
111. C32×C4C2×M16semidirect
115. C3⋊Dic3C2×M16semidirect
154. C2×C32C4×M16semidirect
196. C32C2×C4×M16semidirect
216. C2×C4#3792direct (N × H)
239. C4C2×#3792direct (N × H)
242. C2C4×#3792direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C22×C4×C3⋊Dic32
C4×#37922
C2×#637772
C2×C4×#6222
C2×C4×M169