Finite Group Databasebeta

← C2×#10593802 #11857357

Subgroups — C2×#10593802 #11857357

Order 1152.

2370 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 2370 conjugacy classes of subgroups — too many to draw. Only its 234 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
2C22×#3792C212yesmaximal, complemented
3#10593802C218yesmaximal, direct product factor
4C2×#63778C214yesmaximal, complemented
5C24×C3⋊D3C411yescharacteristic
6C23×C32×C4C411yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C4×C3⋊D3—28no—
9C22×C4×C3⋊D3C414yes—
10C22×C4×C3⋊D3C412yes—
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2214yes—
13C2×#3792—28no—
14C2×#3792C2218yescomplemented
15C22×#622C2214yescomplemented
16#63778C22116yescomplemented
17C23×C4×D3—62no—
18C24×C32C2×C411yescharacteristic
19C23×C3⋊D3—24no—
20C23×C3⋊D3—28no—
21C23×C3⋊D3C2×C414yes—
22C23×C3⋊D3C2×C412yes—
23C22×C32×C4—24no—
24C22×C32×C4C2×C414yes—
25C22×C32×C4C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3D418yes—
29C22×C3⋊Dic3C2311yescharacteristic
30C22×C3⋊Dic3C2312yes—
31C2×C4×C3⋊D3—216no—
32C2×C4×C3⋊D3—28no—
33C2×C4×C3⋊D3—28no—
34C2×C4×C3⋊D3—216no—
35C2×C4×C3⋊D3C2×C414yes—
36C2×C4×C3⋊D3C2×C418yes—
37C2×C4×C3⋊D3C2314yes—
38#3792—216no—
39C2×#622—28no—
40C2×#622C2318yescomplemented
41C2×#407—91nomaximal, Sylow
42C24×D3—62no—
43C23×C3×C4—22no—
44C23×Dic3—62no—
45C22×C4×D3—68no—
46C22×C4×D3—64no—
47C22×C4×D3—64no—
48C22×C4×D3—68no—
49C22×C4×D3—632no—
50C23×C32—24no—
51C23×C32C22⋊C414yes—
52C23×C32C22×C412yes—
53C23×C32C22×C411yescharacteristic
54C22×C3⋊D3—232no—
55C22×C3⋊D3—28no—
56C22×C3⋊D3—24no—
57C22×C3⋊D3—24no—
58C22×C3⋊D3—216no—
59C22×C3⋊D3M1618yescomplemented
60C22×C3⋊D3C22×C414yes—
61C2×C32×C4—28no—
62C2×C32×C4—24no—
63C2×C32×C4C22×C414yes—
64C2×C3⋊Dic3C22⋊C418yes—
65C2×C3⋊Dic3C22⋊C414yes—
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C22×C412yes—
68C2×C3⋊Dic3C2×D414yes—
69C2×C3⋊Dic3C2×D418yes—
70C2×C3⋊Dic3C2411yescharacteristic
71C4×C3⋊D3—28no—
72C4×C3⋊D3—216no—
73C4×C3⋊D3—28no—
74#622—28no—
75C24×C4—91no—
76C22×M16—92no—
77#407—98no—
78C2×C22⋊C8—94no—
79C24×C3—22no—
80C23×D3—64no—
81C23×D3—68no—
82C23×D3—616no—
83C23×D3—632no—
84C22×C3×C4—216no—
85C22×C3×C4—28no—
86C22×C3×C4—24no—
87C22×Dic3—64no—
88C22×Dic3—62no—
89C22×Dic3—616no—
90C22×Dic3—64no—
91C22×Dic3—62no—
92C2×C4×D3—68no—
93C2×C4×D3—616no—
94C2×C4×D3—68no—
95C2×C4×D3—664no—
96C2×C4×D3—632no—
97C2×C4×D3—632no—
98C2×C4×D3—664no—
99C22×C32—24no—
100C22×C32—28no—
101C22×C32C2×C22⋊C414yes—
102C22×C32C2×C22⋊C412yes—
103C22×C32C2×M1614yes—
104C22×C32C23×C411yescharacteristic
105C2×C3⋊D3—232no—
106C2×C3⋊D3—24no—
107C2×C3⋊D3—24no—
108C2×C3⋊D3—216no—
109C2×C3⋊D3C2×M1618yescomplemented
110C32×C4—24no—
111C3⋊Dic3C2×C22⋊C412yes—
112C3⋊Dic3C2×C22⋊C414yes—
113C3⋊Dic3C22×D412yes—
114C25—91no—
115C23×C4—91no—
116C23×C4—92no—
117C23×C4—94no—
118C23×C4—94no—
119C23×C4—92no—
120C23×C4—188no—
121C23×C4#15711yescharacteristic
122C2×M16—98no—
123C2×M16—188no—
124C22×C8—94no—
125C22⋊C8—916no—
126C23×C3—216no—
127C23×C3—24no—
128C23×C3—22no—
129C23×C3—28no—
130C22×D3—616no—
131C22×D3—68no—
132C22×D3—632no—
133C22×D3—616no—
134C22×D3—664no—
135C22×D3—6128no—
136C22×D3—616no—
137C2×C3×C4—232no—
138C2×C3×C4—216no—
139C2×C3×C4—28no—
140C2×Dic3—616no—
141C2×Dic3—68no—
142C2×Dic3—64no—
143C2×Dic3—62no—
144C2×Dic3—68no—
145C2×Dic3—616no—
146C2×Dic3—62no—
147C4×D3—632no—
148C4×D3—664no—
149C4×D3—632no—
150C2×C32—24no—
151C2×C32#40714yescomplemented
152C2×C32C22×C22⋊C411yescharacteristic
153C2×C32C22×M1612yes—
154C3⋊D3—28no—
155C24—92no—
156C24—94no—
157C24—188no—
158C24—184no—
159C24C2×#15711yescharacteristic
160C22×C4—24no—
161C22×C4—92no—
162C22×C4—92no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—98no—
166C22×C4—94no—
167C22×C4—94no—
168C22×C4—98no—
169C22×C4—188no—
170C22×C4—1816no—
171C22×C4—1816no—
172C22×C4—188no—
173C22×C4C2×#15714yes—
174C22×C4C2×#15712yes—
175M16—1816no—
176C2×C8—98no—
177C2×C8—188no—
178C22×C3—232no—
179C22×C3—216no—
180C22×C3—28no—
181C22×C3—28no—
182C22×C3—24no—
183C22×C3—22no—
184C2×D3—616no—
185C2×D3—616no—
186C2×D3—6128no—
187C2×D3—664no—
188C2×D3—616no—
189C3×C4—216no—
190Dic3—64no—
191Dic3—68no—
192Dic3—64no—
193C32C2×#40711yescharacteristic, complemented, Sylow
194C23—24no—
195C23—98no—
196C23—94no—
197C23—1816no—
198C23—1832no—
199C23—184no—
200C23—188no—
201C23—184no—
202C23C22⋊#15714yes—
203C23C22×#15712yes—
204C23C22×#15711yescharacteristic
205C2×C4—28no—
206C2×C4—24no—
207C2×C4—94no—
208C2×C4—98no—
209C2×C4—98no—
210C2×C4—94no—
211C2×C4—91no—
212C2×C4—92no—
213C2×C4—91no—
214C2×C4—188no—
215C2×C4—188no—
216C2×C4—1816no—
217C2×C4C22×#15714yes—
218C8—188no—
219C2×C3—216no—
220C2×C3—28no—
221C2×C3—24no—
222C2×C3—22no—
223D3—632no—
224C22—28no—
225C22—24no—
226C22—98no—
227C22—1832no—
228C22—1816no—
229C22—184no—
230C22—184no—
231C22#6428314yes—
232C22C2×C22⋊#15714yes—
233C22C2×C22⋊#15712yes—
234C22C23×#15711yescharacteristic
235C4—24no—
236C4—92no—
237C4—92no—
238C4—94no—
239C3—22no—
240C2—24no—
241C2—188no—
242C2#1059380214yesdirect product factor
243C2C2×#6428312yes—
244C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C3⋊D3C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3792C2semidirect
3. #10593802C2direct (N × H)
4. C2×#63778C2semidirect
14. C2×#3792C22semidirect
15. C22×#622C22semidirect
16. #63778C22semidirect
40. C2×#622C23semidirect
59. C22×C3⋊D3M16semidirect
109. C2×C3⋊D3C2×M16semidirect
151. C2×C32#407semidirect
193. C32C2×#407semidirect
242. C2#10593802direct (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
C22×#37922
#105938022
C2×#637782
C2×#4079