Finite Group Databasebeta

← C4×#63737 #11773148

Subgroups — C4×#63737 #11773148

Order 1152.

1250 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 247 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×C4×#157C211yesmaximal, characteristic
2C2×C4×#624C212yesmaximal
3C2×#63737C214yesmaximal
4C23×#157C2212yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C2214yes—
7C2×C4×#157—24no—
8C2×C4×#157C414yescomplemented
9C2×C3×C4×Dic3—22no—
10C2×Dic32—22no—
11C4×#624—24no—
12C4×#624C418yescomplemented
13#63737C4116yesdirect product factor
14C2×C42×D3—62no—
15C23×C3⋊D3C2311yescharacteristic
16C22×#157—24no—
17C22×#157—24no—
18C22×#157C2×C414yes—
19C22×#157C2×C418yes—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C2×C4×C3⋊D3C2×C412yes—
23C2×C4×C3⋊D3C2×C414yes—
24C2×C4×C3⋊D3D414yes—
25C2×C4×C3⋊D3Q812yes—
26C22×C3×Dic3—24no—
27C2×#624—24no—
28C2×#624—28no—
29C2×#624C2×C418yes—
30C2×#624C2×C4116yes—
31C4×#157—28no—
32C3×C4×Dic3—28no—
33Dic32—28no—
34C4×#95—91nomaximal, Sylow
35C22×C4×D3—64no—
36C22×C4×D3—62no—
37C2×C3×C42—62no—
38C2×C4×Dic3—22no—
39C2×C4×Dic3—64no—
40C42×D3—68no—
41C42×D3—68no—
42C23×C32C2×D411yescharacteristic
43C22×C3⋊D3C22×C411yescharacteristic
44C22×C3⋊D3C22×C412yes—
45C22×C3⋊D3C22×C414yes—
46C22×C3⋊D3C2×D412yes—
47C22×C3⋊D3C2×Q811yescharacteristic
48C22×C3⋊D3#4114yes—
49C2×#157—24no—
50C2×#157—24no—
51C2×#157—216no—
52C2×#157C4218yescomplemented
53C2×C32×C4C22⋊C414yes—
54C2×C32×C4C4⋊C412yes—
55C2×C3⋊Dic3C22⋊C414yes—
56C2×C3⋊Dic3C4⋊C412yes—
57C4×C3⋊D3C4214yes—
58C4×C3⋊D3C22⋊C414yes—
59C4×C3⋊D3C4⋊C418yes—
60C2×C3×Dic3—28no—
61C2×C3×Dic3—216no—
62#624—28no—
63#624—216no—
64#624C42116yescomplemented
65C22×C42—92no—
66C22×C42—91no—
67C2×#95—94no—
68C23×D3—62no—
69C22×C3×C4—22no—
70C22×C3×C4—64no—
71C22×Dic3—24no—
72C22×Dic3—62no—
73C2×C4×D3—68no—
74C2×C4×D3—616no—
75C2×C4×D3—64no—
76C2×C4×D3—64no—
77C2×C4×D3—64no—
78C2×C4×D3—64no—
79C2×C4×D3—64no—
80C2×C4×D3—64no—
81C2×C4×D3—68no—
82C2×C4×D3—616no—
83C3×C42—68no—
84C4×Dic3—28no—
85C4×Dic3—616no—
86C22×C32C2×C22⋊C412yes—
87C22×C32C2×C4⋊C411yescharacteristic
88C22×C32C4×D414yes—
89C2×C3⋊D3C2×C4211yescharacteristic
90C2×C3⋊D3C2×C4212yes—
91C2×C3⋊D3C2×C4214yes—
92C2×C3⋊D3C2×C22⋊C411yescharacteristic
93C2×C3⋊D3C2×C4⋊C412yes—
94C2×C3⋊D3#11712yes—
95C2×C3⋊D3#11714yes—
96C2×C3⋊D3C4×D418yes—
97C2×C3⋊D3C4×Q814yes—
98#157—28no—
99C32×C4#9514yescomplemented
100C3⋊Dic3#9514yescomplemented
101C3×Dic3—216no—
102C23×C4—94no—
103C23×C4—91no—
104C23×C4—92no—
105C2×C42—62no—
106C2×C42—98no—
107C2×C42—94no—
108C2×C42—184no—
109C2×C42—182no—
110C2×C42—184no—
111#95—916no—
112C23×C3—22no—
113C22×D3—62no—
114C22×D3—68no—
115C22×D3—62no—
116C22×D3—62no—
117C22×D3—62no—
118C22×D3—62no—
119C22×D3—62no—
120C22×D3—68no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—24no—
124C2×C3×C4—68no—
125C2×C3×C4—616no—
126C2×Dic3—28no—
127C2×Dic3—216no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—64no—
131C4×D3—616no—
132C4×D3—68no—
133C4×D3—68no—
134C4×D3—68no—
135C4×D3—68no—
136C4×D3—616no—
137C4×D3—632no—
138C2×C32C2×#9511yescharacteristic
139C2×C32C4×C22⋊C414yes—
140C2×C32C4×C4⋊C412yes—
141C3⋊D3C4311yescharacteristic
142C3⋊D3#37611yescharacteristic
143C3⋊D3C4×C22⋊C412yes—
144C3⋊D3C4×C4⋊C414yes—
145C24—91no—
146C22×C4—64no—
147C22×C4—916no—
148C22×C4—98no—
149C22×C4—91no—
150C22×C4—94no—
151C22×C4—94no—
152C22×C4—92no—
153C22×C4—92no—
154C22×C4—98no—
155C22×C4—94no—
156C22×C4—184no—
157C22×C4—188no—
158C22×C4—184no—
159C22×C4—184no—
160C22×C4GO+(4,𝔽2)11yescharacteristic
161C42—68no—
162C42—188no—
163C42—188no—
164C22×C3—28no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3—22no—
168C2×D3—64no—
169C2×D3—62no—
170C2×D3—62no—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—64no—
174C2×D3—68no—
175C2×D3—64no—
176C2×D3—64no—
177C2×D3—64no—
178C2×D3—64no—
179C2×D3—68no—
180C2×D3—68no—
181C3×C4—28no—
182C3×C4—616no—
183Dic3—216no—
184Dic3—68no—
185C32C4×#9511yescharacteristic, complemented, Sylow
186C23—94no—
187C23—94no—
188C23—92no—
189C23—92no—
190C23—91no—
191C23—91no—
192C23C2×GO+(4,𝔽2)11yescharacteristic
193C2×C4—616no—
194C2×C4—68no—
195C2×C4—916no—
196C2×C4—94no—
197C2×C4—92no—
198C2×C4—94no—
199C2×C4—94no—
200C2×C4—98no—
201C2×C4—98no—
202C2×C4—1816no—
203C2×C4—188no—
204C2×C4—184no—
205C2×C4—1816no—
206C2×C4—184no—
207C2×C4D32⋊C414yes—
208C2×C4#377312yes—
209C2×C3—24no—
210C2×C3—24no—
211C2×C3—24no—
212C2×C3—22no—
213D3—62no—
214D3—62no—
215D3—64no—
216D3—64no—
217D3—64no—
218C22—94no—
219C22—98no—
220C22—94no—
221C22—92no—
222C22—92no—
223C22—94no—
224C22—91no—
225C22—91no—
226C22—92no—
227C22C4×GO+(4,𝔽2)14yes—
228C22C2×D32⋊C412yes—
229C22C2×#377311yescharacteristic
230C4—616no—
231C4—94no—
232C4—188no—
233C4#6373714yesdirect product factor
234C3—22no—
235C2—92no—
236C2—91no—
237C2—94no—
238C2—91no—
239C2C4×D32⋊C414yes—
240C2C4×#377312yes—
241C2C2×#6373711yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊D3C43
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypocenterC32C4×#95
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×C4×#157C4semidirect
12. C4×#624C4semidirect
13. #63737C4direct (N × H)
52. C2×#157C42semidirect
64. #624C42semidirect
99. C32×C4#95semidirect
100. C3⋊Dic3#95semidirect
185. C32C4×#95semidirect
233. C4#63737direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×C4×#6242
C2×#637372
C4×#959