Finite Group Databasebeta

← C2×#27132906 #37582105

Subgroups — C2×#27132906 #37582105

Order 24448.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690270C211yesmaximal, characteristic, complemented
2C2×#20259298C211yesmaximal, characteristic, complemented
3C2×#20259293C211yesmaximal, characteristic
4#27132906C218yesmaximal, direct product factor
5C2×#20259256C211yesmaximal, characteristic, complemented
6C2×#20259246C211yesmaximal, characteristic, complemented
7C2×#20259243C211yesmaximal, characteristic, complemented
8C22×SD16×C191C211yesmaximal, characteristic, complemented
9C22×C22⋊D191—21no—
10C22×C4×D191C2211yescharacteristic
11C2×#15690270—24no—
12C2×#15690270C2214yescomplemented
13C22×C191⋊C8C2211yescharacteristic
14#20259298—22no—
15#20259298C2214yescomplemented
16#20259293—22no—
17#20259293C2214yes—
18C2×C4⋊Dic191C2211yescharacteristic
19C2×C4⋊Dic191C2211yescharacteristic
20C2×Dic191⋊C4—21no—
21C2×C22⋊Dic191—21no—
22C2×(C2×D191)⋊C4—21no—
23#20259256C2214yescomplemented
24#20259246C2214yescomplemented
25#20259243C2214yescomplemented
26C22×Q8×C191C2211yescharacteristic
27C22×D4×C191C2211yescharacteristic
28C2×SD16×C191—24no—
29C2×SD16×C191C2214yescomplemented
30C22×C8×C191C2211yescharacteristic
31C23×D191D411yescharacteristic
32C2×C22⋊D191—24no—
33C2×C22⋊D191—44no—
34C22×Dic191—21no—
35C22×Dic191—21no—
36C22×Dic191D411yescharacteristic
37C2×C4×D191—22no—
38C2×C4×D191—22no—
39C2×C4×D191D412yes—
40C2×C4×D191C2312yes—
41#15690270—28no—
42C2×C191⋊C8—22no—
43C2×C191⋊C8C2312yes—
44C4⋊Dic191—21no—
45C4⋊Dic191—21no—
46C4⋊Dic191C2312yes—
47C4⋊Dic191C2312yes—
48Dic191⋊C4—24no—
49C22⋊Dic191—24no—
50(C2×D191)⋊C4—24no—
51C24×C191—21no—
52C2×Q8×C191—21no—
53C2×Q8×C191—22no—
54C2×Q8×C191—22no—
55C2×Q8×C191C2312yes—
56C2×D4×C191—22no—
57C2×D4×C191—21no—
58C2×D4×C191—22no—
59C2×D4×C191C2312yes—
60C22×C4×C191—21no—
61C22×C4×C191C2311yescharacteristic
62SD16×C191—28no—
63C2×C8×C191D414yescomplemented
64C2×C8×C191C2312yes—
65C22×D191—22no—
66C22×D191—22no—
67C22×D191—22no—
68C22×D191C2×D412yes—
69C22⋊D191—48no—
70C2×Dic191—22no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C2×Dic191—42no—
74C2×Dic191—42no—
75C2×Dic191C2×D412yes—
76C4×D191—24no—
77C4×D191—22no—
78C4×D191—22no—
79C191⋊C8—22no—
80C23×C191—22no—
81C23×C191—42no—
82C23×C191—42no—
83C23×C191—42no—
84C23×C191C2×D411yescharacteristic
85Q8×C191—22no—
86Q8×C191—22no—
87Q8×C191—42no—
88D4×C191—22no—
89D4×C191—22no—
90D4×C191—42no—
91C2×C4×C191—22no—
92C2×C4×C191—42no—
93C2×C4×C191C2×D411yescharacteristic
94C2×C4×C191C2×D412yes—
95C2×C4×C191#4112yes—
96C2×C4×C191C2411yescharacteristic
97C8×C191C2×D414yescomplemented
98C22×C191—42no—
99C22×C191—42no—
100C22×C191—42no—
101C22×C191—84no—
102C22×C191#12112yes—
103C22×C191AGL(1,ℤ/8)12yes—
104C22×C191#13712yes—
105C22×C191C22×D411yescharacteristic
106C2×D191—22no—
107C2×D191—22no—
108C2×D191—22no—
109C2×D191—44no—
110C4×C191—42no—
111C4×C191#12112yes—
112C4×C191C22×D411yescharacteristic
113C4×C191C2×#4111yescharacteristic
114Dic191—22no—
115Dic191—42no—
116Dic191—42no—
117C2×C191—82no—
118C2×C191#46814yescomplemented
119C2×C191C2×#12111yescharacteristic
120C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C191C2×#13711yescharacteristic
122D191—42no—
123C191C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1911nomaximal, Sylow
125C22×SD16D19111yescharacteristic, complemented
126C22×M16—1911no—
127C2×C22⋊Q8—1911no—
128C2×#121—1911no—
129#468—1918no—
130C2×#107—1911no—
131C2×#103—1911no—
132C2×#102—1911no—
133C22×Q8C2×D19111yescharacteristic
134C22×D4—3821no—
135C22×D4C2×D19111yescharacteristic
136C23×C4—1911no—
137C2×SD16—24no—
138C2×SD16C2×D19114yescomplemented
139C2×M16—3824no—
140C2×M16—1914no—
141C22×C8—1911no—
142C22×C8C2×D19111yescharacteristic
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#107—1914no—
153#103—1914no—
154#102—1914no—
155C24—21no—
156C24—1911no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D19112yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—3824no—
165C2×D4—7644no—
166C2×D4C22×D19112yes—
167C22×C4—21no—
168C22×C4—3822no—
169C22×C4—3822no—
170C22×C4—3821no—
171C22×C4—3821no—
172C22×C4—1911no—
173C22×C4—1912no—
174C22×C4—1912no—
175C22×C4C22×D19111yescharacteristic
176SD16—28no—
177M16—3828no—
178C2×C8—3822no—
179C2×C8—1912no—
180C2×C8C22⋊D19114yescomplemented
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—42no—
191C23—42no—
192C23—42no—
193C23—3822no—
194C23—3822no—
195C23—3822no—
196C23—1912no—
197C23D4×D19111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—7648no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—3822no—
208C2×C4—3822no—
209C2×C4—3822no—
210C2×C4—3824no—
211C2×C4—3822no—
212C2×C4—3822no—
213C2×C4—1912no—
214C2×C4—7642no—
215C2×C4—7642no—
216C2×C4D4×D19111yescharacteristic
217C2×C4C2×C22⋊D19112yes—
218C2×C4#1569028612yes—
219C2×C4C23×D19111yescharacteristic
220C8—3822no—
221C8C2×C22⋊D19114yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—3822no—
227C22—3822no—
228C22—3822no—
229C22—7644no—
230C22#2025929312yes—
231C22#2025934912yes—
232C22#2025935112yes—
233C22C2×D4×D19111yescharacteristic
234C4—42no—
235C4—3822no—
236C4—7642no—
237C4—7642no—
238C4#2025929312yes—
239C4C22×C22⋊D19111yescharacteristic
240C4C2×#1569028611yescharacteristic
241C2—82no—
242C2—7642no—
243C2#2713290614yesdirect product factor
244C2C2×#2025929311yescharacteristic
245C2C2×#2025934911yescharacteristic
246C2C2×#2025935111yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×SD16×C191C2
socleC23×C191C2×D4
prime radicalC2×#20259293C2
hypercenterC22×SD16D191
hypocenterC191C2×#468
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#15690270C2semidirect
2. C2×#20259298C2semidirect
4. #27132906C2direct (N × H)
5. C2×#20259256C2semidirect
6. C2×#20259246C2semidirect
7. C2×#20259243C2semidirect
8. C22×SD16×C191C2semidirect
12. C2×#15690270C22semidirect
15. #20259298C22semidirect
23. #20259256C22semidirect
24. #20259246C22semidirect
25. #20259243C22semidirect
29. C2×SD16×C191C22semidirect
63. C2×C8×C191D4semidirect
97. C8×C191C2×D4semidirect
118. C2×C191#468semidirect
123. C191C2×#468semidirect
125. C22×SD16D191semidirect
138. C2×SD16C2×D191semidirect
180. C2×C8C22⋊D191semidirect
221. C8C2×C22⋊D191semidirect
243. C2#27132906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902702
C2×#202592982
C2×#202592932
#271329062
C2×#202592562
C2×#202592462
C2×#202592432
C22×SD16×C1912
C2×#468191