Finite Group Databasebeta

← C4×#63874 #11800790

Subgroups — C4×#63874 #11800790

Order 1152.

1753 conjugacy classes of subgroups; only the 492 normal subgroups are shown.

normal subgroups only

This group has 1753 conjugacy classes of subgroups — too many to draw. Only its 492 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×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63874C212yesmaximal
3C3×C42×Dic3C212yesmaximal, complemented
4C4×#3724C214yesmaximal, complemented
5C4×#3722C214yesmaximal
6#10591222C212yesmaximal, complemented
7C4×#872—32nomaximal
8C22×C4×C3⋊D3C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C42×C3⋊D3C418yescomplemented
14C2×C3×C4×Dic3C2218yes—
15C2×C3×C4×Dic3C2214yes—
16C2×#3724C2214yes—
17C2×#3722C2214yes—
18#63874C4116yesdirect product factor
19#63579C2218yes—
20C2×#872—34no—
21C2×C42×D3—32no—
22C2×C42×D3—61no—
23C3×C43—32no—
24C4×(C2×D3)⋊C4—38no—
25#4932—34no—
26C4×Dic3⋊C4—38no—
27C42×Dic3D312yescomplemented
28C23×C3⋊D3C2311yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C32×C4C2312yes—
31C22×C3⋊Dic3C2312yes—
32C22×C3⋊Dic3C2311yescharacteristic
33C2×C4×C3⋊D3—28no—
34C2×C4×C3⋊D3C2×C418yes—
35C2×C4×C3⋊D3C2×C414yes—
36C2×C4×C3⋊D3C2×C418yes—
37C22×C3×Dic3C2318yes—
38C32×C42C2×C414yes—
39C4×C3⋊Dic3C2×C414yes—
40C4×C3⋊Dic3C2×C418yes—
41C3×C4×Dic3—216no—
42C3×C4×Dic3C2×C4116yescomplemented
43#3724C2×C4116yescomplemented
44#3722C2×C4116yes—
45C4×#117—91noSylow
46C22×C4×D3—32no—
47C22×C4×D3—34no—
48C22×C4×D3—61no—
49C22×C4×D3—62no—
50C2×C3×C42—21no—
51C2×C3×C42—34no—
52C2×C3×C42—38no—
53C2×C3×C42C2×D312yes—
54C2×(C2×D3)⋊C4—38no—
55C2×Dic3⋊C4—38no—
56C2×C4×Dic3—34no—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—62no—
60C2×C4×Dic3C2×D318yes—
61C2×C4×Dic3C2×D314yes—
62#872—332no—
63C42×D3—316no—
64C42×D3—68no—
65C3⋊#95—316no—
66C23×C32C2411yescharacteristic
67C22×C3⋊D3—24no—
68C22×C3⋊D3C22×C414yes—
69C22×C3⋊D3C22×C412yes—
70C2×C32×C4C22×C414yes—
71C2×C32×C4C22×C412yes—
72C2×C32×C4C22×C414yes—
73C2×C32×C4#4118yes—
74C2×C3⋊Dic3—24no—
75C2×C3⋊Dic3C22×C414yes—
76C2×C3⋊Dic3C22×C414yes—
77C2×C3⋊Dic3C22×C412yes—
78C4×C3⋊D3—216no—
79C4×C3⋊D3C42116yescomplemented
80C2×C3×Dic3—216no—
81C2×C3×Dic3C22×C4116yes—
82C2×#117—92no—
83C22×C42—91no—
84C4×C4⋊C4—94no—
85C4×C22⋊C4—94no—
86#376—92no—
87C43—32no—
88C23×D3—32no—
89C23×D3—61no—
90C22×C3×C4—22no—
91C22×C3×C4—21no—
92C22×C3×C4—38no—
93C22×C3×C4C22×D312yes—
94C22×C3×C4C22×D314yes—
95C22×Dic3—32no—
96C22×Dic3—34no—
97C22×Dic3—61no—
98C22×Dic3—62no—
99C22×Dic3C22×D318yes—
100C2×C4×D3—38no—
101C2×C4×D3—316no—
102C2×C4×D3—316no—
103C2×C4×D3—64no—
104C2×C4×D3—68no—
105C2×C4×D3—68no—
106C2×C4×D3—616no—
107C2×C4×D3—616no—
108C3×C42—24no—
109C3×C42—316no—
110C3×C42—616no—
111C3×C42C4×D318yes—
112(C2×D3)⋊C4—332no—
113Dic3⋊C4—332no—
114C4×Dic3—216no—
115C4×Dic3—316no—
116C4×Dic3—38no—
117C4×Dic3—68no—
118C4×Dic3—64no—
119C4×Dic3C4×D3116yescomplemented
120C22×C32C23×C411yescharacteristic
121C22×C32C23×C412yes—
122C22×C32C2×#4114yes—
123C2×C3⋊D3—24no—
124C2×C3⋊D3—28no—
125C2×C3⋊D3C2×C4214yes—
126C32×C4C2×C4214yes—
127C32×C4#11718yescomplemented
128C3⋊Dic3—24no—
129C3⋊Dic3C2×C4214yes—
130C3×Dic3—216no—
131C23×C4—91no—
132C23×C4—92no—
133#117—916no—
134C2×C4⋊C4—94no—
135C2×C22⋊C4—94no—
136C2×C42—34no—
137C2×C42—38no—
138C2×C42—91no—
139C2×C42—92no—
140C2×C42—98no—
141C2×C42D3211yescharacteristic
142#95—98no—
143C23×C3—21no—
144C23×C3C23×D312yes—
145C22×D3—38no—
146C22×D3—34no—
147C22×D3—62no—
148C22×D3—64no—
149C22×D3—68no—
150C22×D3—68no—
151C2×C3×C4—28no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—316no—
156C2×C3×C4—616no—
157C2×C3×C4C2×C4×D318yes—
158C2×C3×C4C2×C4×D314yes—
159C2×C3×C4C2×C4×D318yes—
160C2×C3×C4#235116yes—
161C2×Dic3—216no—
162C2×Dic3—34no—
163C2×Dic3—38no—
164C2×Dic3—38no—
165C2×Dic3—62no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—68no—
169C2×Dic3—68no—
170C2×Dic3C2×C4×D3116yes—
171C4×D3—332no—
172C4×D3—616no—
173C4×D3—632no—
174C4×D3—632no—
175C2×C32C22×C4211yescharacteristic
176C2×C32C2×#11712yes—
177C2×C32C4×#4114yes—
178C3⋊D3—24no—
179C24—91no—
180C22×C4—38no—
181C22×C4—91no—
182C22×C4—98no—
183C22×C4—94no—
184C22×C4—92no—
185C22×C4—98no—
186C22×C4—188no—
187C22×C4C2×D3212yes—
188C22×C4C2×D3211yescharacteristic
189C4⋊C4—916no—
190C22⋊C4—916no—
191C42—316no—
192C42—616no—
193C42—98no—
194C42—94no—
195C42#62414yes—
196C22×C3—24no—
197C22×C3—22no—
198C22×C3—21no—
199C22×C3C22×C4×D314yes—
200C22×C3C22×C4×D312yes—
201C22×C3C2×#23518yes—
202C2×D3—38no—
203C2×D3—64no—
204C2×D3—68no—
205C2×D3—616no—
206C2×D3—68no—
207C2×D3—616no—
208C3×C4—28no—
209C3×C4—24no—
210C3×C4—616no—
211C3×C4C42×D318yes—
212C3×C4#872116yescomplemented
213Dic3—216no—
214Dic3—38no—
215Dic3—64no—
216Dic3—68no—
217Dic3—68no—
218C32C4×#11711yescharacteristic, complemented, Sylow
219C23—94no—
220C23—92no—
221C23—184no—
222C23C22×D3211yescharacteristic
223C2×C4—316no—
224C2×C4—616no—
225C2×C4—94no—
226C2×C4—92no—
227C2×C4—916no—
228C2×C4—94no—
229C2×C4—184no—
230C2×C4—1816no—
231C2×C4#379818yes—
232C2×C4C4×D3214yes—
233C2×C4C2×#62414yes—
234C2×C4C2×#62412yes—
235C2×C3—22no—
236C2×C3—21no—
237C2×C3—24no—
238C2×C3C2×C42×D312yes—
239C2×C3C2×#87214yes—
240C2×C3C4×#23518yes—
241D3—68no—
242D3—68no—
243C22—94no—
244C22—184no—
245C22—188no—
246C22C2×#379814yes—
247C22C2×C4×D3212yes—
248C22C22×#62411yescharacteristic
249C4—616no—
250C4—94no—
251C4—184no—
252C4#6387418yesdirect product factor
253C4C4×#62414yes—
254C3—21no—
255C3C4×#87212yescomplemented
256C2—184no—
257C2C4×#379814yes—
258C2C2×#6387412yes—
259C2C2×C4×#62411yescharacteristic
subgroupG/H
center, hypercenterC2×C42D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C42×Dic3C2semidirect
4. C4×#3724C2semidirect
6. #10591222C2semidirect
13. C42×C3⋊D3C4semidirect
18. #63874C4direct (N × H)
27. C42×Dic3D3semidirect
42. C3×C4×Dic3C2×C4semidirect
43. #3724C2×C4semidirect
79. C4×C3⋊D3C42semidirect
119. C4×Dic3C4×D3semidirect
127. C32×C4#117semidirect
212. C3×C4#872semidirect
218. C32C4×#117semidirect
252. C4#63874direct (N × H)
255. C3C4×#872semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#638742
C3×C42×Dic32
C4×#37242
C4×#37222
#105912222
C4×#8723