Finite Group Databasebeta

← C2×#10593845 #11857356

Subgroups — C2×#10593845 #11857356

Order 1152.

2370 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 2370 conjugacy classes of subgroups — too many to draw. Only its 250 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
1C24×C3⋊Dic3C211yesmaximal, characteristic
2C22×#3792C212yesmaximal, complemented
3#10593845C218yesmaximal, direct product factor
4C2×C22⋊#622C214yesmaximal, complemented
5C25×C32C411yescharacteristic
6C23×C3⋊Dic3—28no—
7C23×C3⋊Dic3C414yes—
8C23×C3⋊Dic3C411yescharacteristic
9C23×C3⋊Dic3C412yes—
10C23×C3⋊Dic3C2212yes—
11C23×C3⋊Dic3C2214yes—
12C23×C3⋊Dic3C2211yescharacteristic
13C2×#3792—28no—
14C2×#3792C2218yescomplemented
15C22×#622C2214yescomplemented
16C22⋊#622C22116yescomplemented
17C24×Dic3—62no—
18C24×C32—24no—
19C24×C32—28no—
20C24×C32C2×C414yes—
21C24×C32C2×C411yescharacteristic
22C24×C32C2×C412yes—
23C22×C3⋊Dic3—24no—
24C22×C3⋊Dic3—216no—
25C22×C3⋊Dic3—28no—
26C22×C3⋊Dic3—28no—
27C22×C3⋊Dic3—216no—
28C22×C3⋊Dic3C2×C414yes—
29C22×C3⋊Dic3C2×C412yes—
30C22×C3⋊Dic3C2×C414yes—
31C22×C3⋊Dic3C2×C418yes—
32C22×C3⋊Dic3C2×C412yes—
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3D418yes—
35C22×C3⋊Dic3C2314yes—
36C22×C3⋊Dic3C2311yescharacteristic
37C22×C3⋊Dic3C2312yes—
38#3792—216no—
39C2×#622—28no—
40C2×#622C2318yescomplemented
41C2×#407—91nomaximal, Sylow
42C25×C3—22no—
43C23×Dic3—68no—
44C23×Dic3—64no—
45C23×Dic3—62no—
46C23×Dic3—62no—
47C23×Dic3—64no—
48C23×Dic3—68no—
49C23×Dic3—632no—
50C23×C32—232no—
51C23×C32—28no—
52C23×C32—24no—
53C23×C32—24no—
54C23×C32—24no—
55C23×C32—216no—
56C23×C32C22⋊C414yes—
57C23×C32M1618yescomplemented
58C23×C32C22×C412yes—
59C23×C32C22×C414yes—
60C23×C32C22×C411yescharacteristic
61C2×C3⋊Dic3—28no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3—28no—
64C2×C3⋊Dic3—216no—
65C2×C3⋊Dic3—28no—
66C2×C3⋊Dic3C22⋊C418yes—
67C2×C3⋊Dic3C22⋊C414yes—
68C2×C3⋊Dic3C22×C414yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C22×C412yes—
71C2×C3⋊Dic3C2×D414yes—
72C2×C3⋊Dic3C2×D418yes—
73C2×C3⋊Dic3C2411yescharacteristic
74#622—28no—
75C24×C4—91no—
76C22×M16—92no—
77#407—98no—
78C2×C22⋊C8—94no—
79C24×C3—232no—
80C24×C3—216no—
81C24×C3—28no—
82C24×C3—24no—
83C24×C3—22no—
84C22×Dic3—64no—
85C22×Dic3—62no—
86C22×Dic3—68no—
87C22×Dic3—616no—
88C22×Dic3—68no—
89C22×Dic3—64no—
90C22×Dic3—616no—
91C22×Dic3—64no—
92C22×Dic3—62no—
93C22×Dic3—68no—
94C22×Dic3—664no—
95C22×Dic3—632no—
96C22×Dic3—632no—
97C22×Dic3—664no—
98C22×Dic3—616no—
99C22×C32—232no—
100C22×C32—24no—
101C22×C32—24no—
102C22×C32—24no—
103C22×C32—28no—
104C22×C32—216no—
105C22×C32C2×C22⋊C414yes—
106C22×C32C2×C22⋊C412yes—
107C22×C32C2×M1614yes—
108C22×C32C2×M1618yescomplemented
109C22×C32C23×C411yescharacteristic
110C3⋊Dic3—24no—
111C3⋊Dic3C2×C22⋊C412yes—
112C3⋊Dic3C2×C22⋊C414yes—
113C3⋊Dic3C22×D412yes—
114C25#15711yescharacteristic
115C23×C4—91no—
116C23×C4—92no—
117C23×C4—94no—
118C23×C4—94no—
119C23×C4—92no—
120C23×C4—91no—
121C23×C4—188no—
122C2×M16—98no—
123C2×M16—188no—
124C22×C8—94no—
125C22⋊C8—916no—
126C23×C3—232no—
127C23×C3—216no—
128C23×C3—2128no—
129C23×C3—216no—
130C23×C3—216no—
131C23×C3—264no—
132C23×C3—28no—
133C23×C3—24no—
134C23×C3—22no—
135C23×C3—216no—
136C23×C3—28no—
137C2×Dic3—616no—
138C2×Dic3—68no—
139C2×Dic3—64no—
140C2×Dic3—62no—
141C2×Dic3—68no—
142C2×Dic3—68no—
143C2×Dic3—616no—
144C2×Dic3—62no—
145C2×Dic3—632no—
146C2×Dic3—664no—
147C2×Dic3—632no—
148C2×Dic3—632no—
149C2×Dic3—616no—
150C2×C32—24no—
151C2×C32—28no—
152C2×C32#40714yescomplemented
153C2×C32C22×C22⋊C411yescharacteristic
154C2×C32C22×M1612yes—
155C24—28no—
156C24—24no—
157C24C2×#15714yes—
158C24C2×#15712yes—
159C24C2×#15711yescharacteristic
160C22×C4—92no—
161C22×C4—92no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—98no—
165C22×C4—94no—
166C22×C4—94no—
167C22×C4—98no—
168C22×C4—94no—
169C22×C4—92no—
170C22×C4—188no—
171C22×C4—1816no—
172C22×C4—1816no—
173C22×C4—188no—
174C22×C4—184no—
175M16—1816no—
176C2×C8—98no—
177C2×C8—188no—
178C22×C3—216no—
179C22×C3—2128no—
180C22×C3—216no—
181C22×C3—216no—
182C22×C3—264no—
183C22×C3—232no—
184C22×C3—28no—
185C22×C3—216no—
186C22×C3—28no—
187C22×C3—24no—
188C22×C3—22no—
189Dic3—64no—
190Dic3—68no—
191Dic3—64no—
192Dic3—616no—
193C32C2×#40711yescharacteristic, complemented, Sylow
194C23—232no—
195C23—24no—
196C23—24no—
197C23—216no—
198C23—28no—
199C23—24no—
200C23#379218yescomplemented
201C23C22⋊#15714yes—
202C23C22×#15714yes—
203C23C22×#15712yes—
204C23C22×#15711yescharacteristic
205C2×C4—94no—
206C2×C4—98no—
207C2×C4—98no—
208C2×C4—94no—
209C2×C4—91no—
210C2×C4—92no—
211C2×C4—91no—
212C2×C4—94no—
213C2×C4—188no—
214C2×C4—188no—
215C2×C4—1816no—
216C2×C4—188no—
217C2×C4—184no—
218C8—188no—
219C2×C3—232no—
220C2×C3—216no—
221C2×C3—24no—
222C2×C3—22no—
223C2×C3—28no—
224C22—232no—
225C22—24no—
226C22—24no—
227C22—24no—
228C22—216no—
229C22—28no—
230C22C2×#379214yes—
231C22C2×#379218yescomplemented
232C22C2×C22⋊#15714yes—
233C22C2×C22⋊#15712yes—
234C22C23×#15711yescharacteristic
235C4—92no—
236C4—92no—
237C4—94no—
238C4—184no—
239C3—22no—
240C2—28no—
241C2—24no—
242C2#1059384514yesdirect product factor
243C2C22×#379212yes—
244C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
Fitting, prime radicalC25×C32C4
socleC23×C32C22×C4
cosocleC2×C3⋊Dic3C24
hypercenterC25#157
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×#3792C2semidirect
3. #10593845C2direct (N × H)
4. C2×C22⋊#622C2semidirect
14. C2×#3792C22semidirect
15. C22×#622C22semidirect
16. C22⋊#622C22semidirect
40. C2×#622C23semidirect
57. C23×C32M16semidirect
108. C22×C32C2×M16semidirect
152. C2×C32#407semidirect
193. C32C2×#407semidirect
200. C23#3792semidirect
231. C22C2×#3792semidirect
242. C2#10593845direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3⋊Dic32
C22×#37922
#105938452
C2×C22⋊#6222
C2×#4079