Finite Group Databasebeta

← C22⋊C4×#622 #11783643

Subgroups — C22⋊C4×#622 #11783643

Order 1152.

642 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 146 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×#622C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3C2×C4×#622C212yesmaximal, complemented
4C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
5#10590207C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C22×#622—24no—
8C22×#622C414yescomplemented
9C22×#622C2212yes—
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×C32×C22⋊C4C411yescharacteristic
13C2×#3757C411yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C22⋊#622C414yescomplemented
16C4×#622—24no—
17#63658C412yes—
18Dic3×C22⋊C4—62no—
19C24×C32C2×C411yescharacteristic
20C22×C32×C4C2×C412yes—
21C22×C3⋊Dic3—22no—
22C22×C3⋊Dic3—22no—
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2311yescharacteristic
28C2×#622—22no—
29C2×#622—22no—
30C2×#622—22no—
31C2×#622—28no—
32C2×#622C2×C412yes—
33C2×#622C2×C414yes—
34C2×#622C2×C412yes—
35C2×#622D414yes—
36C32×C22⋊C4C814yescomplemented
37#3757C814yescomplemented
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3—22no—
40C8×C22⋊C4—91nomaximal, Sylow
41C23×Dic3—62no—
42C2×C3×C22⋊C4—22no—
43C2×#217—62no—
44C2×C4×Dic3—64no—
45C3⋊#95—64no—
46C23×C32—22no—
47C23×C32—22no—
48C23×C32C4212yes—
49C23×C32C2×C812yes—
50C23×C32C2×C812yes—
51C23×C32C22×C411yescharacteristic
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4C2×C814yescomplemented
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—24no—
61C2×C3⋊Dic3C4212yes—
62C2×C3⋊Dic3C2×C814yescomplemented
63C2×C3⋊Dic3C22×C411yescharacteristic
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3#4112yes—
67#622—22no—
68#622—24no—
69#622C22⋊C414yesdirect product factor
70C23×C8—91no—
71C2×C22⋊C8—91no—
72C2×C4×C8—92no—
73C4×C22⋊C4—91no—
74#336—92no—
75C24×C3—22no—
76C22×C3×C4—24no—
77C22×Dic3—62no—
78C22×Dic3—62no—
79C22×Dic3—64no—
80C22×Dic3—64no—
81C22×Dic3—64no—
82C22×Dic3—124no—
83C22×Dic3—124no—
84C3×C22⋊C4—28no—
85#217—68no—
86C4×Dic3—124no—
87C4×Dic3—124no—
88C22×C32—22no—
89C22×C32—22no—
90C22×C32—24no—
91C22×C32—24no—
92C22×C32C4×C814yescomplemented
93C22×C32C2×C4211yescharacteristic
94C22×C32C4×D412yes—
95C22×C32C22×C811yescharacteristic
96C22×C32C22×C811yescharacteristic
97C22×C32#13112yes—
98C32×C4—24no—
99C3⋊Dic3—22no—
100C3⋊Dic3—24no—
101C3⋊Dic3C2×C22⋊C411yescharacteristic
102C3⋊Dic3#11711yescharacteristic
103C3⋊Dic3C4×D412yes—
104C23×C4—91no—
105C22×C8—91no—
106C22×C8—94no—
107C22×C8—91no—
108C22×C8—92no—
109C22×C8—184no—
110C2×C22⋊C4—91no—
111C2×C22⋊C4#15711yescharacteristic
112C2×C42—92no—
113C22⋊C8—94no—
114C4×C8—184no—
115#95—92no—
116C23×C3—22no—
117C23×C3—24no—
118C23×C3—24no—
119C23×C3—24no—
120C23×C3—44no—
121C23×C3—44no—
122C2×C3×C4—28no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—68no—
131C2×Dic3—124no—
132C2×Dic3—124no—
133C2×Dic3—128no—
134C2×Dic3—124no—
135C2×Dic3—124no—
136C2×Dic3—124no—
137C2×C32—24no—
138C2×C32C4×C22⋊C411yescharacteristic
139C2×C32C2×C4×C811yescharacteristic
140C2×C32#40511yescharacteristic
141C2×C32C8×D412yes—
142C2×C32C8×D412yes—
143C24C2×#15711yescharacteristic
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—92no—
147C22×C4—92no—
148C22×C4—92no—
149C22×C4—182no—
150C22×C4—182no—
151C22×C4C2×#15712yes—
152C2×C8—94no—
153C2×C8—92no—
154C2×C8—94no—
155C2×C8—92no—
156C2×C8—188no—
157C2×C8—182no—
158C2×C8—182no—
159C2×C8—182no—
160C22⋊C4—94no—
161C22⋊C4#62214yesdirect product factor
162C42—182no—
163C42—182no—
164C22×C3—22no—
165C22×C3—22no—
166C22×C3—28no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3—22no—
170C22×C3—44no—
171C22×C3—48no—
172C22×C3—44no—
173C22×C3—48no—
174C3×C4—48no—
175Dic3—62no—
176Dic3—62no—
177Dic3—64no—
178Dic3—124no—
179Dic3—128no—
180C32C8×C22⋊C411yescharacteristic, complemented, Sylow
181C23—22no—
182C23—22no—
183C23#378712yes—
184C23C4×#15712yes—
185C23C2×#62212yes—
186C23C22×#15711yescharacteristic
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—94no—
194C2×C4—92no—
195C2×C4—182no—
196C2×C4—184no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—182no—
200C2×C4—182no—
201C2×C4C2×#62214yescomplemented
202C8—94no—
203C8—182no—
204C8—184no—
205C2×C3—22no—
206C2×C3—24no—
207C2×C3—22no—
208C2×C3—24no—
209C2×C3—22no—
210C2×C3—48no—
211C22—24no—
212C22—22no—
213C22—24no—
214C22—22no—
215C22C4×#62214yescomplemented
216C22C2×#378711yescharacteristic
217C22C2×C4×#15711yescharacteristic
218C22#6428712yes—
219C22D4×#15712yes—
220C22C22×#62211yescharacteristic
221C4—24no—
222C4—91no—
223C4—92no—
224C4—91no—
225C4—184no—
226C4—182no—
227C3—22no—
228C2—24no—
229C2#1059373811yescharacteristic
230C2#1059373912yes—
231C2C22⋊C4×#15711yescharacteristic
232C2C2×C4×#62211yescharacteristic
233C2D4×#62212yes—
subgroupG/H
center, FrattiniC23C22×#157
commutatorC2×C32C2×C4×C8
FittingC2×C32×C22⋊C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#622C2semidirect
5. #10590207C2semidirect
8. C22×#622C4semidirect
15. C22⋊#622C4semidirect
36. C32×C22⋊C4C8semidirect
37. #3757C8semidirect
54. C2×C32×C4C2×C8semidirect
62. C2×C3⋊Dic3C2×C8semidirect
69. #622C22⋊C4direct (N × H)
92. C22×C32C4×C8semidirect
161. C22⋊C4#622direct (N × H)
180. C32C8×C22⋊C4semidirect
201. C2×C4C2×#622semidirect
215. C22C4×#622semidirect

Maximal subgroups

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

subgroupindex
C23×#6222
C2×C22⋊#6222
C2×C4×#6222
C22⋊C4×C3⋊Dic32
#105902072
C8×C22⋊C49