Finite Group Databasebeta

← C2×#10593805 #11858243

Subgroups — C2×#10593805 #11858243

Order 1152.

1074 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 242 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
3#10593805C218yesmaximal, direct product factor
4C2×#63779C212yesmaximal, complemented
5C2×C4⋊#622C212yesmaximal, complemented
6C23×C32×C4C411yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C2×#3792—28no—
10C2×#3792C2218yes—
11C22×#622C2214yes—
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C414yes—
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2214yes—
18#63779C2218yescomplemented
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×C411yescharacteristic
32C22×C3⋊Dic3D414yes—
33C22×C3⋊Dic3Q814yes—
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36#3792—216no—
37C2×#622—28no—
38C2×#622C2318yes—
39C4×C3⋊Dic3C2×C414yes—
40C4×C3⋊Dic3C2×C412yes—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3C2×C414yes—
43C4×C3⋊Dic3C2312yes—
44C4×C3⋊Dic3C2312yes—
45C2×#423—91nomaximal, Sylow
46C23×C3×C4—22no—
47C23×Dic3—62no—
48C23×Dic3—62no—
49C2×C4×Dic3—68no—
50C2×C4×Dic3—62no—
51C2×C4×Dic3—62no—
52C2×C4×Dic3—62no—
53C2×C4×Dic3—62no—
54C2×C4×Dic3—68no—
55C23×C32—22no—
56C23×C32—22no—
57C23×C32C4⋊C414yes—
58C23×C32C22×C412yes—
59C23×C32C22×C411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4—28no—
62C2×C32×C4M1614yescomplemented
63C2×C32×C4C22×C412yes—
64C2×C32×C4C22×C412yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—28no—
67C2×C3⋊Dic3C4⋊C418yes—
68C2×C3⋊Dic3C4⋊C414yes—
69C2×C3⋊Dic3M1614yescomplemented
70C2×C3⋊Dic3C22×C412yes—
71C2×C3⋊Dic3C22×C411yescharacteristic
72C2×C3⋊Dic3C22×C412yes—
73C2×C3⋊Dic3C22×C412yes—
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D414yes—
76C2×C3⋊Dic3C2×Q814yes—
77C2×C3⋊Dic3C2×Q812yes—
78C2×C3⋊Dic3C2411yescharacteristic
79#622—28no—
80C22×M16—92no—
81C22×C42—91no—
82#423—98no—
83C2×C4⋊C8—92no—
84C2×C4⋊C8—92no—
85C24×C3—22no—
86C22×C3×C4—216no—
87C22×C3×C4—28no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×Dic3—64no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C22×Dic3—68no—
94C22×Dic3—62no—
95C22×Dic3—64no—
96C22×Dic3—62no—
97C22×Dic3—68no—
98C22×Dic3—68no—
99C22×Dic3—616no—
100C4×Dic3—64no—
101C4×Dic3—68no—
102C4×Dic3—68no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C22×C32—22no—
107C22×C32—22no—
108C22×C32—28no—
109C22×C32C2×C4⋊C414yes—
110C22×C32C2×C4⋊C412yes—
111C22×C32C2×M1612yes—
112C22×C32C2×M1612yes—
113C22×C32C23×C411yescharacteristic
114C32×C4—22no—
115C32×C4C2×M1614yescomplemented
116C3⋊Dic3—22no—
117C3⋊Dic3C2×C4⋊C412yes—
118C3⋊Dic3C2×C4⋊C414yes—
119C3⋊Dic3C2×M1614yescomplemented
120C3⋊Dic3C22×D411yescharacteristic
121C3⋊Dic3C22×Q811yescharacteristic
122C23×C4—91no—
123C23×C4—91no—
124C23×C4#15711yescharacteristic
125C2×M16—98no—
126C2×M16—188no—
127C22×C8—94no—
128C2×C42—91no—
129C2×C42—91no—
130C2×C42—94no—
131C2×C42—94no—
132C2×C42—91no—
133C2×C42—91no—
134C4⋊C8—98no—
135C4⋊C8—98no—
136C23×C3—28no—
137C23×C3—28no—
138C23×C3—24no—
139C23×C3—22no—
140C23×C3—28no—
141C2×C3×C4—28no—
142C2×C3×C4—232no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—28no—
146C2×Dic3—616no—
147C2×Dic3—68no—
148C2×Dic3—68no—
149C2×Dic3—64no—
150C2×Dic3—62no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—68no—
155C2×Dic3—68no—
156C2×Dic3—64no—
157C2×Dic3—62no—
158C2×Dic3—632no—
159C2×Dic3—68no—
160C2×C32—24no—
161C2×C32#42314yescomplemented
162C2×C32C22×C4⋊C411yescharacteristic
163C2×C32C22×M1611yescharacteristic
164C2×C32C22×M1611yescharacteristic
165C24C2×#15711yescharacteristic
166C22×C4—24no—
167C22×C4—92no—
168C22×C4—92no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—94no—
173C22×C4—94no—
174C22×C4—94no—
175C22×C4—91no—
176C22×C4—184no—
177C22×C4C2×#15714yes—
178C22×C4C2×#15711yescharacteristic
179C22×C4C2×#15711yescharacteristic
180M16—1816no—
181C2×C8—98no—
182C2×C8—188no—
183C42—92no—
184C42—92no—
185C42—92no—
186C42—94no—
187C42—94no—
188C42—92no—
189C22×C3—28no—
190C22×C3—28no—
191C22×C3—232no—
192C22×C3—24no—
193C22×C3—28no—
194C22×C3—24no—
195C22×C3—24no—
196C22×C3—22no—
197C3×C4—28no—
198C3×C4—28no—
199Dic3—64no—
200Dic3—68no—
201Dic3—68no—
202Dic3—62no—
203Dic3—62no—
204Dic3—68no—
205C32C2×#42311yescharacteristic, complemented, Sylow
206C23—22no—
207C23—22no—
208C23C4⋊#15714yes—
209C23C22×#15712yes—
210C23C22×#15711yescharacteristic
211C2×C4—22no—
212C2×C4—28no—
213C2×C4—94no—
214C2×C4—92no—
215C2×C4—94no—
216C2×C4—94no—
217C2×C4—98no—
218C2×C4—92no—
219C2×C4—94no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—188no—
226C2×C4—182no—
227C2×C4#379214yescomplemented
228C2×C4C22×#15712yes—
229C2×C4C22×#15712yes—
230C8—188no—
231C2×C3—216no—
232C2×C3—28no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C22—28no—
237C22—22no—
238C22—22no—
239C22#6428312yes—
240C22C2×C4⋊#15714yes—
241C22C2×C4⋊#15712yes—
242C22C2×#379212yes—
243C22C23×#15711yescharacteristic
244C4—22no—
245C4—94no—
246C4—91no—
247C4—92no—
248C4—94no—
249C4—91no—
250C4—182no—
251C4C2×#379214yescomplemented
252C3—22no—
253C2—24no—
254C2#1059380514yesdirect product factor
255C2C2×#6428311yescharacteristic
256C2C22×C4⋊#15711yescharacteristic
257C2C22×#379211yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×#423
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10593805C2direct (N × H)
4. C2×#63779C2semidirect
5. C2×C4⋊#622C2semidirect
18. #63779C22semidirect
19. C4⋊#622C22semidirect
62. C2×C32×C4M16semidirect
69. C2×C3⋊Dic3M16semidirect
115. C32×C4C2×M16semidirect
119. C3⋊Dic3C2×M16semidirect
161. C2×C32#423semidirect
205. C32C2×#423semidirect
227. C2×C4#3792semidirect
251. C4C2×#3792semidirect
254. C2#10593805direct (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
#105938052
C2×#637792
C2×C4⋊#6222
C2×#4239