Finite Group Databasebeta

← C2×#27132892 #37582080

Subgroups — C2×#27132892 #37582080

Order 24448.

564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15690276C211yesmaximal, characteristic, complemented
2C2×#20259301C211yesmaximal, characteristic, complemented
3C2×#20259296C211yesmaximal, characteristic
4#27132892C218yesmaximal, direct product factor
5C2×#20259254C211yesmaximal, characteristic, complemented
6C2×#20259247C211yesmaximal, characteristic, complemented
7C2×#20259244C211yesmaximal, characteristic, complemented
8C23×C8×C191C211yesmaximal, characteristic, complemented
9C22×Dic382C2211yescharacteristic
10C22×D764C2211yescharacteristic
11C22×C22⋊D191—21no—
12C2×#15690276—24no—
13C2×#15690276C2214yescomplemented
14#20259301—22no—
15#20259301C2214yescomplemented
16#20259296—22no—
17#20259296C2214yes—
18C2×C4⋊Dic191C2211yescharacteristic
19C2×C4⋊Dic191C2211yescharacteristic
20C2×Dic191⋊C4—21no—
21C2×C22⋊Dic191—21no—
22C2×(C2×D191)⋊C4—21no—
23#20259254C2214yescomplemented
24#20259247C2214yescomplemented
25#20259244C2214yescomplemented
26C23×C4×C191C2211yescharacteristic
27C22×C8×C191—24no—
28C22×C8×C191C2211yescharacteristic
29C22×C8×C191C2211yescharacteristic
30C22×C8×C191C2214yescomplemented
31C23×D191—21no—
32C2×Dic382—21no—
33C2×Dic382—22no—
34C2×Dic382—22no—
35C2×Dic382C2312yes—
36C2×D764—22no—
37C2×D764—21no—
38C2×D764—22no—
39C2×D764C2312yes—
40C2×C22⋊D191—24no—
41C2×C22⋊D191—44no—
42C22×Dic191—21no—
43C22×Dic191—21no—
44C22×Dic191—21no—
45#15690276—28no—
46C4⋊Dic191—21no—
47C4⋊Dic191—21no—
48C4⋊Dic191C2312yes—
49C4⋊Dic191C2312yes—
50Dic191⋊C4—24no—
51C22⋊Dic191—24no—
52(C2×D191)⋊C4—24no—
53C24×C191D411yescharacteristic
54C22×C4×C191—22no—
55C22×C4×C191—22no—
56C22×C4×C191D411yescharacteristic
57C22×C4×C191D412yes—
58C22×C4×C191C2312yes—
59C22×C4×C191C2311yescharacteristic
60C2×C8×C191—22no—
61C2×C8×C191—28no—
62C2×C8×C191D414yescomplemented
63C2×C8×C191C2312yes—
64C2×C8×C191C2312yes—
65C22×D191—22no—
66C22×D191—42no—
67C22×D191—42no—
68C22×D191—42no—
69Dic382—22no—
70Dic382—22no—
71Dic382—42no—
72D764—22no—
73D764—22no—
74D764—42no—
75C22⋊D191—48no—
76C2×Dic191—22no—
77C2×Dic191—22no—
78C2×Dic191—22no—
79C2×Dic191—42no—
80C2×Dic191—42no—
81C2×Dic191—42no—
82C23×C191—22no—
83C23×C191—22no—
84C23×C191SD1614yescomplemented
85C23×C191C2×D412yes—
86C23×C191C2×D411yescharacteristic
87C2×C4×C191—22no—
88C2×C4×C191—24no—
89C2×C4×C191—22no—
90C2×C4×C191—22no—
91C2×C4×C191C2×D412yes—
92C2×C4×C191C2×D412yes—
93C2×C4×C191C2×D411yescharacteristic
94C2×C4×C191#4112yes—
95C2×C4×C191C2411yescharacteristic
96C8×C191—22no—
97C8×C191C2×D414yescomplemented
98C22×C191—22no—
99C22×C191—22no—
100C22×C191—28no—
101C22×C191#12112yes—
102C22×C191C2×SD1612yes—
103C22×C191C2×SD1614yescomplemented
104C22×C191#13512yes—
105C22×C191C22×D411yescharacteristic
106C2×D191—42no—
107C2×D191—42no—
108C2×D191—42no—
109C2×D191—84no—
110C4×C191—22no—
111C4×C191#12112yes—
112C4×C191C22×D411yescharacteristic
113C4×C191C2×#4111yescharacteristic
114Dic191—42no—
115Dic191—42no—
116Dic191—42no—
117C2×C191—24no—
118C2×C191#46514yescomplemented
119C2×C191C2×#12111yescharacteristic
120C2×C191C22×SD1611yescharacteristic
121C2×C191C2×#13511yescharacteristic
122D191—82no—
123C191C2×#46511yescharacteristic, complemented, Sylow
124C2×#465—1911nomaximal, Sylow
125C22×SD16—1911no—
126C23×C8D19111yescharacteristic, complemented
127C2×C22⋊Q8—1911no—
128C2×#121—1911no—
129#465—1918no—
130C2×#106—1911no—
131C2×#103—1911no—
132C2×#102—1911no—
133C22×Q8—1911no—
134C22×D4—3821no—
135C22×D4—1911no—
136C23×C4C2×D19111yescharacteristic
137C2×SD16—3824no—
138C2×SD16—1914no—
139C22×C8—24no—
140C22×C8C2×D19111yescharacteristic
141C22×C8C2×D19111yescharacteristic
142C22×C8C2×D19114yescomplemented
143C22⋊Q8—3822no—
144C22⋊Q8—1914no—
145#121—3822no—
146#121—1914no—
147C2×C4⋊C4—3821no—
148C2×C4⋊C4—1911no—
149C2×C4⋊C4—1911no—
150C2×C22⋊C4—3821no—
151C2×C22⋊C4—3821no—
152#106—1914no—
153#103—1914no—
154#102—1914no—
155C24—3821no—
156C24D76411yescharacteristic
157C2×Q8—3821no—
158C2×Q8—3822no—
159C2×Q8—3822no—
160C2×Q8—1912no—
161C2×D4—3824no—
162C2×D4—3822no—
163C2×D4—3821no—
164C2×D4—3822no—
165C2×D4—1912no—
166C2×D4—7644no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—3821no—
170C22×C4—3821no—
171C22×C4—3821no—
172C22×C4D76412yes—
173C22×C4D76411yescharacteristic
174C22×C4C22×D19112yes—
175C22×C4C22×D19111yescharacteristic
176SD16—3828no—
177C2×C8—22no—
178C2×C8—28no—
179C2×C8C22⋊D19114yescomplemented
180C2×C8C22×D19112yes—
181C2×C8C22×D19112yes—
182C4⋊C4—3824no—
183C4⋊C4—3821no—
184C4⋊C4—3821no—
185C4⋊C4—1912no—
186C4⋊C4—1912no—
187C22⋊C4—3824no—
188C22⋊C4—3824no—
189C23—22no—
190C23—22no—
191C23—3822no—
192C23—7642no—
193C23—7642no—
194C23—7642no—
195C23#1569027614yescomplemented
196C23C2×D76412yes—
197C23C2×D76411yescharacteristic
198Q8—3822no—
199Q8—3822no—
200Q8—7642no—
201D4—3822no—
202D4—3822no—
203D4—7648no—
204D4—7642no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—3822no—
210C2×C4—3822no—
211C2×C4—3822no—
212C2×C4—7642no—
213C2×C4—7642no—
214C2×C4—7642no—
215C2×C4C2×C22⋊D19112yes—
216C2×C4C2×D76412yes—
217C2×C4C2×D76411yescharacteristic
218C2×C4#1569028712yes—
219C2×C4C23×D19111yescharacteristic
220C8—22no—
221C8C2×C22⋊D19114yescomplemented
222C22—22no—
223C22—28no—
224C22—22no—
225C22—15284no—
226C22—7642no—
227C22—7642no—
228C22—7642no—
229C22#2025929612yes—
230C22C2×#1569027612yes—
231C22C2×#1569027614yescomplemented
232C22#2025934412yes—
233C22C22×D76411yescharacteristic
234C4—22no—
235C4—7642no—
236C4—7642no—
237C4—7642no—
238C4#2025929612yes—
239C4C22×C22⋊D19111yescharacteristic
240C4C2×#1569028711yescharacteristic
241C2—24no—
242C2—15282no—
243C2#2713289214yesdirect product factor
244C2C2×#2025929611yescharacteristic
245C2C22×#1569027611yescharacteristic
246C2C2×#2025934411yescharacteristic
subgroupG/H
centerC23C2×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC23×C8×C191C2
socleC23×C191C2×D4
prime radicalC2×#20259296C2
hypercenterC23×C8D191
hypocenterC191C2×#465
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C22×#15690276C2semidirect
2. C2×#20259301C2semidirect
4. #27132892C2direct (N × H)
5. C2×#20259254C2semidirect
6. C2×#20259247C2semidirect
7. C2×#20259244C2semidirect
8. C23×C8×C191C2semidirect
13. C2×#15690276C22semidirect
15. #20259301C22semidirect
23. #20259254C22semidirect
24. #20259247C22semidirect
25. #20259244C22semidirect
30. C22×C8×C191C22semidirect
62. C2×C8×C191D4semidirect
84. C23×C191SD16semidirect
97. C8×C191C2×D4semidirect
103. C22×C191C2×SD16semidirect
118. C2×C191#465semidirect
123. C191C2×#465semidirect
126. C23×C8D191semidirect
142. C22×C8C2×D191semidirect
179. C2×C8C22⋊D191semidirect
195. C23#15690276semidirect
221. C8C2×C22⋊D191semidirect
231. C22C2×#15690276semidirect
243. C2#27132892direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902762
C2×#202593012
C2×#202592962
#271328922
C2×#202592542
C2×#202592472
C2×#202592442
C23×C8×C1912
C2×#465191