Finite Group Databasebeta

← C4×#64228 #11859959

Subgroups — C4×#64228 #11859959

Order 1152.

786 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 169 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×#64228C211yesmaximal, characteristic
2C4×#3797C212yesmaximal
3C4×#3787C211yesmaximal, characteristic
4#10593445C214yesmaximal, complemented
5C4×#3776C214yesmaximal, complemented
6#10593396C211yesmaximal, characteristic
7#10593375C212yesmaximal
8C2×#3797C2212yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×#3776C2214yes—
12#64228C418yesdirect product factor
13C42×C3⋊D3C2211yescharacteristic
14C3×C4×Dic6—22no—
15C4×#627C2214yes—
16#63900C2212yes—
17#63883—22no—
18C4×#624—22no—
19#63843—22no—
20#63838C2214yes—
21C4×#622C2212yes—
22C4×#622C2212yes—
23#63743C2214yes—
24#63740C2218yes—
25C4×D3×Q8—62no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×Dic6—22no—
30C2×#627C2314yes—
31C2×#624—22no—
32C2×#624—22no—
33#3797—24no—
34#3797C2×C418yes—
35C2×#622C2312yes—
36C2×#622C2312yes—
37#3787—22no—
38#3787C2×C414yes—
39#3776C2×C4116yescomplemented
40C32×C42D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43C4×C3⋊Dic3C2311yescharacteristic
44C3×C4⋊Dic3—22no—
45C3×Dic3⋊C4—24no—
46C3×C4×Dic3—24no—
47#3724C2314yes—
48Dic3⋊Dic3—24no—
49Dic32—24no—
50C2×C4×Q16—91nomaximal, Sylow
51C2×D3×Q8—62no—
52C3×C4×Q8—62no—
53Q8×Dic3—62no—
54D3×C4⋊C4—62no—
55D3×C4⋊C4—64no—
56#887—64no—
57#887—62no—
58C42×D3—62no—
59C42×D3—64no—
60C4×Dic6—22no—
61C4×Dic6—64no—
62C22×C3⋊D3C2×D411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3C2411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3Q1614yescomplemented
71C4×C3⋊D3C22×C412yes—
72C4×C3⋊D3#4112yes—
73C2×C3×Dic3—24no—
74C2×C3×Dic3—24no—
75C3×Dic6—28no—
76#627—24no—
77#627C22×C418yes—
78#624—28no—
79#624—44no—
80#622—22no—
81#622C22×C414yes—
82C22×Q16—91no—
83C2×C4×Q8—92no—
84C4×Q16—94no—
85C4×Q16—94no—
86C2×#107—91no—
87C2×#103—92no—
88C2×C4×C8—91no—
89C2×C3×Q8—62no—
90D3×Q8—68no—
91D3×Q8—68no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—64no—
96C2×C4×D3—64no—
97C2×Dic6—22no—
98C2×Dic6—64no—
99C3×C4⋊C4—64no—
100C3×C4⋊C4—62no—
101C3×C42—22no—
102C3×C42—64no—
103C4⋊Dic3—22no—
104C4⋊Dic3—64no—
105Dic3⋊C4—24no—
106Dic3⋊C4—64no—
107Dic3⋊C4—64no—
108C4×Dic3—24no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—64no—
113C4×Dic3—64no—
114C22×C32C22×D411yescharacteristic
115C2×C3⋊D3C4×D412yes—
116C2×C3⋊D3C2×Q1612yes—
117C2×C3⋊D3#13512yes—
118C32×C4—21no—
119C32×C4C4×D412yes—
120C32×C4C2×Q1612yescomplemented
121C3⋊Dic3—21no—
122C3⋊Dic3C2×Q1612yescomplemented
123C3⋊Dic3C23×C411yescharacteristic
124C3⋊Dic3C2×#4111yescharacteristic
125C3×Dic3—28no—
126C3×Dic3—44no—
127C22×Q8—92no—
128C2×Q16—94no—
129C2×Q16—98no—
130C22×C8—91no—
131C22×C8—91no—
132C4×Q8—62no—
133C4×Q8—94no—
134C4×Q8—94no—
135C4×Q8—182no—
136C2×C4⋊C4—92no—
137C2×C4⋊C4—182no—
138C2×C42—91no—
139C2×C42—182no—
140#107—94no—
141#103—98no—
142C4×C8—92no—
143C4×C8—92no—
144C22×D3—62no—
145C3×Q8—68no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—64no—
150C2×C3×C4—64no—
151C2×Dic3—24no—
152C2×Dic3—24no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C4×D3—68no—
157C4×D3—64no—
158C4×D3—64no—
159C4×D3—616no—
160C4×D3—124no—
161C4×D3—128no—
162Dic6—28no—
163Dic6—68no—
164Dic6—68no—
165C2×C32C2×C4×D411yescharacteristic
166C2×C32C22×Q1611yescharacteristic
167C2×C32C2×#13511yescharacteristic
168C3⋊D3C4×Q1614yescomplemented
169C2×Q8—62no—
170C2×Q8—94no—
171C2×Q8—98no—
172C2×Q8—184no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—182no—
177C22×C4—182no—
178Q16—916no—
179C2×C8—92no—
180C2×C8—94no—
181C2×C8—92no—
182C2×C8—182no—
183C4⋊C4—62no—
184C4⋊C4—64no—
185C4⋊C4—94no—
186C4⋊C4—184no—
187C42—64no—
188C42—91no—
189C42—91no—
190C42—91no—
191C42—184no—
192C42GO+(4,𝔽2)11yescharacteristic
193C22×C3—22no—
194C2×D3—64no—
195C2×D3—64no—
196C2×D3—64no—
197C3×C4—24no—
198C3×C4—24no—
199C3×C4—42no—
200C3×C4—68no—
201C3×C4—124no—
202Dic3—28no—
203Dic3—44no—
204Dic3—62no—
205Dic3—62no—
206Dic3—64no—
207Dic3—122no—
208C32C2×C4×Q1611yescharacteristic, complemented, Sylow
209C23—91no—
210Q8—68no—
211Q8—98no—
212Q8—184no—
213C2×C4—64no—
214C2×C4—64no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—94no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—91no—
221C2×C4—182no—
222C2×C4—188no—
223C2×C4—364no—
224C2×C4C2×GO+(4,𝔽2)11yescharacteristic
225C2×C4C2×GO+(4,𝔽2)11yescharacteristic
226C2×C4C2×GO+(4,𝔽2)11yescharacteristic
227C8—94no—
228C8—182no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232D3—68no—
233C22—92no—
234C22—92no—
235C22—92no—
236C22C22×GO+(4,𝔽2)11yescharacteristic
237C4—21no—
238C4—68no—
239C4—92no—
240C4—91no—
241C4—91no—
242C4—124no—
243C4—181no—
244C4#6422812yesdirect product factor
245C4C4×GO+(4,𝔽2)12yes—
246C3—22no—
247C2—94no—
248C2#1059650011yescharacteristic
249C2C2×#6422811yescharacteristic
250C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×C4×Q16
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593445C2semidirect
5. C4×#3776C2semidirect
12. #64228C4direct (N × H)
39. #3776C2×C4semidirect
70. C4×C3⋊D3Q16semidirect
120. C32×C4C2×Q16semidirect
122. C3⋊Dic3C2×Q16semidirect
168. C3⋊D3C4×Q16semidirect
208. C32C2×C4×Q16semidirect
244. C4#64228direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642282
C4×#37972
C4×#37872
#105934452
C4×#37762
#105933962
#105933752
C2×C4×Q169