Finite Group Databasebeta

← C4×C22⋊#622 #11783554

Subgroups — C4×C22⋊#622 #11783554

Order 1152.

934 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 166 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×C3⋊Dic3C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal
3C2×C4×#622C212yesmaximal, complemented
4#10590207C212yesmaximal, complemented
5C23×C32×C4C411yescharacteristic
6C23×C3⋊Dic3C411yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C22×#622C2214yes—
9C2×C4×C3⋊Dic3—24no—
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622C418yesdirect product factor
15C4×#622—24no—
16C22×C4×Dic3—62no—
17C24×C32C2×C411yescharacteristic
18C22×C32×C4—22no—
19C22×C32×C4—22no—
20C22×C32×C4C814yescomplemented
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—22no—
24C22×C3⋊Dic3—22no—
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3—22no—
27C22×C3⋊Dic3C814yescomplemented
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C414yes—
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C2×#622—24no—
34C2×#622—24no—
35C2×#622C2×C418yescomplemented
36C4×C3⋊Dic3—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3D414yes—
40C4×C22⋊C8—91nomaximal, Sylow
41C23×C3×C4—22no—
42C23×Dic3—62no—
43C23×Dic3—62no—
44C2×C4×Dic3—62no—
45C2×C4×Dic3—62no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—62no—
48C2×C4×Dic3—616no—
49C23×C32—21no—
50C23×C32—21no—
51C23×C32—21no—
52C23×C32—21no—
53C23×C32C4212yes—
54C23×C32C2×C812yes—
55C23×C32C2×C812yes—
56C23×C32C22×C411yescharacteristic
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—28no—
60C2×C32×C4C22⋊C412yes—
61C2×C32×C4C2×C812yes—
62C2×C32×C4C2×C812yes—
63C2×C32×C4M1612yes—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—28no—
69C2×C3⋊Dic3—28no—
70C2×C3⋊Dic3C4212yes—
71C2×C3⋊Dic3C22⋊C412yes—
72C2×C3⋊Dic3C2×C812yes—
73C2×C3⋊Dic3C2×C812yes—
74C2×C3⋊Dic3M1612yes—
75C2×C3⋊Dic3C22×C412yes—
76C2×C3⋊Dic3C2×D412yes—
77C2×C3⋊Dic3#4112yes—
78#622—28no—
79C22×C42—91no—
80C2×C22⋊C8—92no—
81C2×C4×C8—92no—
82#336—92no—
83C24×C3—22no—
84C22×C3×C4—28no—
85C22×C3×C4—28no—
86C22×C3×C4—28no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C22×Dic3—68no—
94C22×Dic3—68no—
95C22×Dic3—68no—
96C22×Dic3—68no—
97C22×Dic3—68no—
98C22×Dic3—68no—
99C4×Dic3—68no—
100C4×Dic3—68no—
101C4×Dic3—68no—
102C4×Dic3—68no—
103C22×C32—22no—
104C22×C32—22no—
105C22×C32—22no—
106C22×C32—22no—
107C22×C32—22no—
108C22×C32—22no—
109C22×C32C4×C814yescomplemented
110C22×C32C2×C4211yescharacteristic
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32#11711yescharacteristic
113C22×C32C22×C811yescharacteristic
114C22×C32C22×C811yescharacteristic
115C22×C32C2×M1611yescharacteristic
116C22×C32C2×M1611yescharacteristic
117C32×C4—22no—
118C32×C4C22⋊C814yescomplemented
119C3⋊Dic3—22no—
120C3⋊Dic3—22no—
121C3⋊Dic3C22⋊C814yescomplemented
122C3⋊Dic3C4×D414yes—
123C23×C4—91no—
124C23×C4—91no—
125C23×C4#15711yescharacteristic
126C22×C8—94no—
127C2×C42—91no—
128C2×C42—91no—
129C2×C42—91no—
130C2×C42—91no—
131C2×C42—184no—
132C22⋊C8—98no—
133C4×C8—184no—
134C23×C3—24no—
135C23×C3—24no—
136C23×C3—24no—
137C23×C3—24no—
138C23×C3—22no—
139C23×C3—24no—
140C23×C3—24no—
141C23×C3—24no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—232no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—632no—
160C2×Dic3—632no—
161C2×Dic3—64no—
162C2×Dic3—64no—
163C2×C32—24no—
164C2×C32C4×C22⋊C411yescharacteristic
165C2×C32C2×C4×C811yescharacteristic
166C2×C32C4×M1611yescharacteristic
167C2×C32C2×C22⋊C811yescharacteristic
168C2×C32C2×C22⋊C811yescharacteristic
169C2×C32#43111yescharacteristic
170C2×C32#43111yescharacteristic
171C24C2×#15711yescharacteristic
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—94no—
179C22×C4—94no—
180C22×C4—182no—
181C22×C4—182no—
182C22×C4—182no—
183C22×C4—182no—
184C22×C4#62214yescomplemented
185C22×C4C2×#15711yescharacteristic
186C22×C4C2×#15711yescharacteristic
187C2×C8—98no—
188C2×C8—184no—
189C2×C8—184no—
190C42—94no—
191C42—182no—
192C42—182no—
193C42—182no—
194C22×C3—28no—
195C22×C3—28no—
196C22×C3—28no—
197C22×C3—28no—
198C22×C3—28no—
199C22×C3—28no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—28no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C3×C4—28no—
209C3×C4—28no—
210Dic3—68no—
211Dic3—68no—
212Dic3—68no—
213Dic3—68no—
214C32C4×C22⋊C811yescharacteristic, complemented, Sylow
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23#378712yes—
220C23C4×#15712yes—
221C23C2×#62212yes—
222C23C22×#15711yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—28no—
226C2×C4—92no—
227C2×C4—92no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—92no—
234C2×C4—188no—
235C2×C4—188no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4C2×#62212yes—
241C2×C4C2×#62212yes—
242C2×C4#379212yes—
243C2×C4C22⋊#15712yes—
244C8—188no—
245C2×C3—216no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22C4×#62214yescomplemented
260C22C2×#378711yescharacteristic
261C22#6428311yescharacteristic
262C22C2×C4×#15711yescharacteristic
263C22#6428611yescharacteristic
264C22C22×#62211yescharacteristic
265C22C2×#379211yescharacteristic
266C22C2×C22⋊#15711yescharacteristic
267C4—22no—
268C4—94no—
269C4—94no—
270C4—182no—
271C4—182no—
272C4C22⋊#62214yesdirect product factor
273C3—22no—
274C2—24no—
275C2C2×C4×#62211yescharacteristic
276C2#1059379511yescharacteristic
277C2C4×#379211yescharacteristic
278C2#1059380011yescharacteristic
279C2#1059380111yescharacteristic
280C2C4×C22⋊#15711yescharacteristic
281C2C2×C22⋊#62211yescharacteristic
subgroupG/H
centerC22×C4C2×#157
commutatorC2×C32C2×C4×C8
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32C4×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#622C2semidirect
4. #10590207C2semidirect
14. C22⋊#622C4direct (N × H)
20. C22×C32×C4C8semidirect
27. C22×C3⋊Dic3C8semidirect
35. C2×#622C2×C4semidirect
109. C22×C32C4×C8semidirect
118. C32×C4C22⋊C8semidirect
121. C3⋊Dic3C22⋊C8semidirect
184. C22×C4#622semidirect
214. C32C4×C22⋊C8semidirect
259. C22C4×#622semidirect
272. C4C22⋊#622direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×C22⋊#6222
C2×C4×#6222
#105902072
C4×C22⋊C89