Finite Group Databasebeta

← C2×#88964 #11724436

Subgroups — C2×#88964 #11724436

Order 864.

834 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C2×#6295C211yesmaximal, characteristic, complemented
2C2×Dic3×C3⋊D3C212yesmaximal, complemented
3C2×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#627C211yesmaximal, characteristic, complemented
5C2×C3×#626C212yesmaximal, complemented
6#88964C218yesmaximal, direct product factor
7C2×#3805—31nomaximal
8C2×#3796—32nomaximal
9C22×C3×C3⋊D3C2212yes—
10C22×C32×D3C2211yescharacteristic
11C2×C3⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C3×C3⋊Dic3C2211yescharacteristic
13C2×C32×Dic3C2212yes—
14#6295C2214yescomplemented
15Dic3×C3⋊D3C2218yescomplemented
16D3×C3⋊Dic3C2214yescomplemented
17C3×#627C2214yescomplemented
18C3×#626C2218yescomplemented
19C22×C3⋊Dic3—31no—
20C2×C4×C3⋊D3—32no—
21C2×C3×#67—32no—
22C2×C3×D12—32no—
23C2×C3×Dic6—32no—
24C2×#627D311yescharacteristic, complemented
25C2×#626—32no—
26C2×#626D312yescomplemented
27C2×#625—31no—
28#3805—38no—
29C2×D3×Dic3—32no—
30C2×D3×Dic3—32no—
31C2×D3×Dic3—32no—
32C2×D3×Dic3—62no—
33C2×D3×Dic3—61no—
34#3796—316no—
35C22×C33C2311yescharacteristic
36C2×C3×C3⋊D3—24no—
37C2×C3×C3⋊D3C2314yes—
38C2×C32×D3—22no—
39C2×C32×D3C2312yes—
40C3⋊(C3⋊Dic3)C2312yes—
41C3×C3⋊Dic3C2312yes—
42C32×Dic3C2314yes—
43C2×#239—91no—
44C2×#237—92no—
45C23×C32—31no—
46C22×C3⋊D3C2×D312yes—
47C22×C3×D3—21no—
48C22×C3×D3—32no—
49C22×C3×D3—32no—
50C22×C3×D3—62no—
51C22×C3×D3C2×D312yes—
52C2×C32×C4—32no—
53C2×C3⋊Dic3—32no—
54C2×C3⋊Dic3—31no—
55C2×C3⋊Dic3—34no—
56C2×C3⋊Dic3—61no—
57C2×C3⋊Dic3—62no—
58C2×C3⋊Dic3—121no—
59C2×C3⋊Dic3C2×D311yescharacteristic
60C4×C3⋊D3—38no—
61C3×#67—38no—
62C2×C3×Dic3—22no—
63C2×C3×Dic3—32no—
64C2×C3×Dic3—61no—
65C2×C3×Dic3C2×D312yes—
66C2×C3×Dic3C2×D312yes—
67C3×D12—38no—
68C3×Dic6—38no—
69#627C2×D314yescomplemented
70#626—38no—
71#626C2×D318yescomplemented
72#625—34no—
73D3×Dic3—38no—
74D3×Dic3—38no—
75D3×Dic3—38no—
76D3×Dic3—64no—
77D3×Dic3—68no—
78C2×C33#4112yescomplemented
79C2×C33C2411yescharacteristic
80C3×C3⋊D3—24no—
81C32×D3—22no—
82C2×C3×Q8—91no—
83C2×C3×D4—92no—
84C2×#67—32no—
85C2×#67—92no—
86C22×Dic3—92no—
87C22×Dic3—92no—
88C22×Dic3—181no—
89#239—98no—
90#237—916no—
91C2×D12—32no—
92C2×D12—91no—
93C2×C4×D3—92no—
94C2×C4×D3—92no—
95C2×C4×D3—91no—
96C2×C4×D3—182no—
97C2×Dic6—32no—
98C22×C32—22no—
99C22×C32—21no—
100C22×C32—32no—
101C22×C32—41no—
102C22×C32—62no—
103C22×C32C22×D312yes—
104C22×C32C22×D311yescharacteristic
105C2×C3⋊D3—24no—
106C2×C3⋊D3C22×D314yes—
107C2×C3×D3—24no—
108C2×C3×D3—24no—
109C2×C3×D3—22no—
110C2×C3×D3—34no—
111C2×C3×D3—34no—
112C2×C3×D3—64no—
113C2×C3×D3—68no—
114C2×C3×D3—64no—
115C2×C3×D3—64no—
116C2×C3×D3C22×D314yes—
117C32×C4—34no—
118C3⋊Dic3—34no—
119C3⋊Dic3—32no—
120C3⋊Dic3—62no—
121C3⋊Dic3—64no—
122C3⋊Dic3—122no—
123C3⋊Dic3C22×D312yes—
124C3×Dic3—24no—
125C3×Dic3—34no—
126C3×Dic3—62no—
127C3×Dic3C22×D314yes—
128C3×Dic3C22×D314yes—
129C2×#41—271noSylow
130C33C2×#4111yescharacteristic, complemented, Sylow
131C23×C3—32no—
132C23×C3—61no—
133C23×C3—92no—
134C22×D3—32no—
135C22×D3—32no—
136C22×D3—62no—
137C22×D3D3211yescharacteristic
138C3×Q8—94no—
139C3×D4—98no—
140C2×C3×C4—32no—
141C2×C3×C4—32no—
142C2×C3×C4—62no—
143C2×C3×C4—91no—
144#67—38no—
145#67—98no—
146C2×Dic3—32no—
147C2×Dic3—61no—
148C2×Dic3—98no—
149C2×Dic3—91no—
150C2×Dic3—92no—
151C2×Dic3—98no—
152C2×Dic3—184no—
153C2×Dic3—182no—
154C2×Dic3—181no—
155C2×Dic3—361no—
156C2×Dic3D3212yes—
157D12—38no—
158D12—94no—
159C4×D3—98no—
160C4×D3—98no—
161C4×D3—94no—
162C4×D3—188no—
163Dic6—38no—
164C2×C32—22no—
165C2×C32—21no—
166C2×C32—24no—
167C2×C32—22no—
168C2×C32—42no—
169C2×C32—41no—
170C2×C32—62no—
171C2×C32#23714yescomplemented
172C2×C32#23912yescomplemented
173C2×C32C23×D312yes—
174C2×C32C23×D311yescharacteristic
175C3⋊D3—24no—
176C3×D3—24no—
177C3×D3—24no—
178C3×D3—68no—
179C3×D3—64no—
180C3×D3—64no—
181#41—278no—
182C2×Q8—91no—
183C2×D4—92no—
184C2×D4—271no—
185C22×C4—272no—
186C22×C4—271no—
187C22×C3—21no—
188C22×C3—22no—
189C22×C3—34no—
190C22×C3—41no—
191C22×C3—62no—
192C22×C3—64no—
193C22×C3—64no—
194C22×C3—94no—
195C22×C3—184no—
196C22×C3C2×D3212yes—
197C22×C3C2×D3211yescharacteristic
198C2×D3—22no—
199C2×D3—34no—
200C2×D3—34no—
201C2×D3—64no—
202C2×D3—68no—
203C2×D3—64no—
204C2×D3—64no—
205C2×D3C2×D3212yes—
206C3×C4—34no—
207C3×C4—34no—
208C3×C4—64no—
209C3×C4—92no—
210Dic3—34no—
211Dic3—62no—
212Dic3—92no—
213Dic3—94no—
214Dic3—184no—
215Dic3—182no—
216Dic3—362no—
217Dic3C2×D3214yes—
218C32—22no—
219C32—21no—
220C32—41no—
221C32C2×#23712yescomplemented
222C32C2×#23911yescharacteristic, complemented
223C23—31no—
224C23—92no—
225Q8—94no—
226D4—98no—
227D4—274no—
228C2×C4—32no—
229C2×C4—91no—
230C2×C4—278no—
231C2×C4—274no—
232C2×C4—271no—
233C2×C3—21no—
234C2×C3—22no—
235C2×C3—24no—
236C2×C3—22no—
237C2×C3—41no—
238C2×C3—42no—
239C2×C3—64no—
240C2×C3—64no—
241C2×C3—184no—
242C2×C3#379614yescomplemented
243C2×C3#380512yescomplemented
244C2×C3C22×D3212yes—
245C2×C3C22×D3211yescharacteristic
246D3—22no—
247D3—68no—
248D3—64no—
249D3—64no—
250C22—32no—
251C22—62no—
252C22—94no—
253C22—184no—
254C22D3311yescharacteristic
255C4—34no—
256C4—92no—
257C4—272no—
258C3—22no—
259C3—21no—
260C3—41no—
261C3C2×#379612yescomplemented
262C3C2×#380511yescharacteristic, complemented
263C2—62no—
264C2—184no—
265C2#8896412yesdirect product factor
266C2C2×D3311yescharacteristic
subgroupG/H
center, hypercenterC22D33
commutator, cosocleC2×C33C24
FrattiniC2C2×D33
Fitting, socleC22×C33C23
hypocenterC33C2×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#6295C2semidirect
2. C2×Dic3×C3⋊D3C2semidirect
3. C2×D3×C3⋊Dic3C2semidirect
4. C2×C3×#627C2semidirect
5. C2×C3×#626C2semidirect
6. #88964C2direct (N × H)
14. #6295C22semidirect
15. Dic3×C3⋊D3C22semidirect
16. D3×C3⋊Dic3C22semidirect
17. C3×#627C22semidirect
18. C3×#626C22semidirect
24. C2×#627D3semidirect
26. C2×#626D3semidirect
69. #627C2×D3semidirect
71. #626C2×D3semidirect
78. C2×C33#41semidirect
130. C33C2×#41semidirect
171. C2×C32#237semidirect
172. C2×C32#239semidirect
221. C32C2×#237semidirect
222. C32C2×#239semidirect
242. C2×C3#3796semidirect
243. C2×C3#3805semidirect
261. C3C2×#3796semidirect
262. C3C2×#3805semidirect
265. C2#88964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#62952
C2×Dic3×C3⋊D32
C2×D3×C3⋊Dic32
C2×C3×#6272
C2×C3×#6262
#889642
C2×#38053
C2×#37963