Finite Group Databasebeta

← C2×#27132990 #37582407

Subgroups — C2×#27132990 #37582407

Order 24448.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259297C211yesmaximal, characteristic
2C2×#20259280C211yesmaximal, characteristic, complemented
3#27132990C218yesmaximal, direct product factor
4C2×#20259253C211yesmaximal, characteristic, complemented
5C2×#20259244C211yesmaximal, characteristic, complemented
6C2×#20259242C211yesmaximal, characteristic, complemented
7C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
8C2×#107×C191C211yesmaximal, characteristic, complemented
9C22×D764—21no—
10C22×D764C2211yescharacteristic
11C22×C4×D191C2211yescharacteristic
12C22×C191⋊C8C2211yescharacteristic
13#20259297—22no—
14#20259297C2214yes—
15#20259280—22no—
16#20259280C2214yescomplemented
17C2×C4⋊Dic191C2211yescharacteristic
18C2×(C2×D191)⋊C4—21no—
19C2×(C2×D191)⋊C4—21no—
20C2×C4×Dic191—21no—
21#20259253C2214yescomplemented
22#20259244C2214yescomplemented
23#20259242C2214yescomplemented
24(C2×D191)⋊C8C2214yescomplemented
25C22×C8×C191C2211yescharacteristic
26C2×C4⋊C4×C191C2211yescharacteristic
27C2×C4⋊C4×C191C2211yescharacteristic
28#107×C191C2214yescomplemented
29C23×D191—21no—
30C23×D191D411yescharacteristic
31C2×D764—24no—
32C2×D764—21no—
33C2×D764—22no—
34C2×D764—22no—
35C2×D764—44no—
36C2×D764C2312yes—
37C22×Dic191—21no—
38C22×Dic191D411yescharacteristic
39C2×C4×D191—22no—
40C2×C4×D191—22no—
41C2×C4×D191D412yes—
42C2×C4×D191C2312yes—
43C2×C191⋊C8—22no—
44C2×C191⋊C8C2312yes—
45C4⋊Dic191—21no—
46C4⋊Dic191C2312yes—
47(C2×D191)⋊C4—24no—
48(C2×D191)⋊C4—24no—
49C4×Dic191—24no—
50C22×C4×C191—21no—
51C22×C4×C191—21no—
52C22×C4×C191C2311yescharacteristic
53C2×C8×C191—22no—
54C2×C8×C191C2312yes—
55C4⋊C4×C191—21no—
56C4⋊C4×C191—21no—
57C4⋊C4×C191C2312yes—
58C4⋊C4×C191C2312yes—
59C22×D191—22no—
60C22×D191—22no—
61C22×D191—22no—
62C22×D191—22no—
63C22×D191—42no—
64C22×D191—42no—
65C22×D191—42no—
66C22×D191C2×D412yes—
67D764—22no—
68D764—22no—
69D764—48no—
70D764—42no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C2×Dic191—42no—
74C2×Dic191C2×D412yes—
75C4×D191—24no—
76C4×D191—22no—
77C4×D191—22no—
78C191⋊C8—22no—
79C23×C191C2×D411yescharacteristic
80C2×C4×C191—22no—
81C2×C4×C191—22no—
82C2×C4×C191—42no—
83C2×C4×C191—42no—
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191#4112yes—
86C2×C4×C191#4112yes—
87C2×C4×C191C2411yescharacteristic
88C8×C191—22no—
89C22×C191#12312yes—
90C22×C191#13512yes—
91C22×C191AGL(1,ℤ/8)12yes—
92C22×C191C22×D411yescharacteristic
93C2×D191—22no—
94C2×D191—22no—
95C2×D191—22no—
96C2×D191—44no—
97C2×D191—42no—
98C2×D191—42no—
99C2×D191—42no—
100C2×D191—84no—
101C4×C191—42no—
102C4×C191—42no—
103C4×C191#12312yes—
104C4×C191C2×#4111yescharacteristic
105C4×C191C2×#4111yescharacteristic
106Dic191—22no—
107Dic191—42no—
108C2×C191#48214yescomplemented
109C2×C191C2×#12311yescharacteristic
110C2×C191C2×#13511yescharacteristic
111C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
112D191—42no—
113D191—82no—
114C191C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—1911nomaximal, Sylow
116C2×#121—1911no—
117C2×#117—1911no—
118#482—1918no—
119C2×#107D19111yescharacteristic, complemented
120C2×#106—1911no—
121C2×#102—1911no—
122C2×#102—1911no—
123C2×C22⋊C8—1911no—
124C22×D4—3821no—
125C22×D4—1911no—
126C23×C4—1911no—
127C22×C8—1911no—
128C22×C8C2×D19111yescharacteristic
129#121—3822no—
130#121—1914no—
131#117—3822no—
132#117—1914no—
133C2×C4⋊C4—1911no—
134C2×C4⋊C4C2×D19111yescharacteristic
135C2×C4⋊C4C2×D19111yescharacteristic
136C2×C22⋊C4—3821no—
137C2×C22⋊C4—3821no—
138C2×C42—3821no—
139#107C2×D19114yescomplemented
140#106—1914no—
141#102—1914no—
142#102—1914no—
143C22⋊C8—1914no—
144C24—3821no—
145C24—1911no—
146C2×D4—3824no—
147C2×D4—3821no—
148C2×D4—3822no—
149C2×D4—3822no—
150C2×D4—1912no—
151C2×D4—7644no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—3822no—
155C22×C4—3822no—
156C22×C4—3821no—
157C22×C4—1911no—
158C22×C4—1912no—
159C22×C4—1912no—
160C22×C4C22×D19111yescharacteristic
161C2×C8—22no—
162C2×C8—3822no—
163C2×C8—1912no—
164C2×C8C22×D19112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—3821no—
168C4⋊C4—1912no—
169C4⋊C4C22×D19112yes—
170C4⋊C4C22×D19112yes—
171C22⋊C4—3824no—
172C22⋊C4—3824no—
173C42—3824no—
174C23—3822no—
175C23—3822no—
176C23—3822no—
177C23—3822no—
178C23—1912no—
179C23—7642no—
180C23—7642no—
181C23—7642no—
182C23D4×D19111yescharacteristic
183D4—3822no—
184D4—3822no—
185D4—7648no—
186D4—7642no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—3822no—
192C2×C4—3822no—
193C2×C4—3822no—
194C2×C4—3824no—
195C2×C4—3822no—
196C2×C4—1912no—
197C2×C4—7642no—
198C2×C4D4×D19111yescharacteristic
199C2×C4#1569028712yes—
200C2×C4#1569028812yes—
201C2×C4C23×D19111yescharacteristic
202C8—22no—
203C8—3822no—
204C22—3822no—
205C22—3822no—
206C22—3822no—
207C22—15284no—
208C22—7642no—
209C22—7642no—
210C22—7642no—
211C22—7644no—
212C22#2025930712yes—
213C22#2025934512yes—
214C22#2025934612yes—
215C22C2×D4×D19111yescharacteristic
216C4—42no—
217C4—42no—
218C4—3822no—
219C4—7642no—
220C4#2025930712yes—
221C4C2×#1569028711yescharacteristic
222C4C2×#1569028811yescharacteristic
223C2—15282no—
224C2—7642no—
225C2#2713299014yesdirect product factor
226C2C2×#2025930711yescharacteristic
227C2C2×#2025934511yescharacteristic
228C2C2×#2025934611yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#107×C191C2
socleC23×C191C2×D4
prime radicalC2×#20259297C2
hypercenterC2×#107D191
hypocenterC191C2×#482
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#20259280C2semidirect
3. #27132990C2direct (N × H)
4. C2×#20259253C2semidirect
5. C2×#20259244C2semidirect
6. C2×#20259242C2semidirect
7. C2×(C2×D191)⋊C8C2semidirect
8. C2×#107×C191C2semidirect
16. #20259280C22semidirect
21. #20259253C22semidirect
22. #20259244C22semidirect
23. #20259242C22semidirect
24. (C2×D191)⋊C8C22semidirect
28. #107×C191C22semidirect
108. C2×C191#482semidirect
114. C191C2×#482semidirect
119. C2×#107D191semidirect
139. #107C2×D191semidirect
225. C2#27132990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202592972
C2×#202592802
#271329902
C2×#202592532
C2×#202592442
C2×#202592422
C2×(C2×D191)⋊C82
C2×#107×C1912
C2×#482191