Finite Group Databasebeta

← C2×#27132898 #37582087

Subgroups — C2×#27132898 #37582087

Order 24448.

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

normal subgroups only

This group has 616 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×#15690272C211yesmaximal, characteristic, complemented
2C22×C8×D191C211yesmaximal, characteristic, complemented
3C2×#20259297C211yesmaximal, characteristic, complemented
4C2×#20259293C211yesmaximal, characteristic, complemented
5#27132898C218yesmaximal, direct product factor
6C2×#20259255C211yesmaximal, characteristic, complemented
7C2×#20259244C211yesmaximal, characteristic, complemented
8C2×#102×C191C211yesmaximal, characteristic, complemented
9C22×D764—21no—
10C22×D764C2211yescharacteristic
11C22×C22⋊D191—21no—
12C22×C4×D191C2211yescharacteristic
13C2×#15690272—24no—
14C2×#15690272C2214yescomplemented
15C22×C191⋊C8C2211yescharacteristic
16C2×C8×D191—24no—
17C2×C8×D191C2214yescomplemented
18#20259297—22no—
19#20259297C2214yescomplemented
20#20259293—22no—
21#20259293C2214yescomplemented
22C2×C4⋊Dic191C2211yescharacteristic
23C2×C22⋊Dic191—21no—
24C2×(C2×D191)⋊C4—21no—
25#20259255C2214yescomplemented
26#20259244C2214yescomplemented
27C22×D4×C191C2211yescharacteristic
28C22×C8×C191C2211yescharacteristic
29C2×C4⋊C4×C191C2211yescharacteristic
30#102×C191C2214yescomplemented
31C23×D191—21no—
32C23×D191D411yescharacteristic
33C2×D764—24no—
34C2×D764—22no—
35C2×D764—21no—
36C2×D764—22no—
37C2×D764—44no—
38C2×D764C2312yes—
39C2×C22⋊D191—24no—
40C2×C22⋊D191—44no—
41C22×Dic191—21no—
42C22×Dic191D411yescharacteristic
43C2×C4×D191—22no—
44C2×C4×D191—22no—
45C2×C4×D191D412yes—
46C2×C4×D191C2312yes—
47#15690272—28no—
48C2×C191⋊C8D414yescomplemented
49C2×C191⋊C8C2312yes—
50C8×D191—28no—
51C4⋊Dic191—21no—
52C4⋊Dic191C2312yes—
53C22⋊Dic191—24no—
54(C2×D191)⋊C4—24no—
55C24×C191—21no—
56C2×D4×C191—22no—
57C2×D4×C191—21no—
58C2×D4×C191—22no—
59C2×D4×C191C2312yes—
60C22×C4×C191—21no—
61C22×C4×C191C2311yescharacteristic
62C2×C8×C191—22no—
63C2×C8×C191C2312yes—
64C4⋊C4×C191—21no—
65C4⋊C4×C191C2312yes—
66C22×D191—22no—
67C22×D191—22no—
68C22×D191—22no—
69C22×D191—42no—
70C22×D191—42no—
71C22×D191—42no—
72C22×D191D814yescomplemented
73C22×D191C2×D412yes—
74D764—22no—
75D764—22no—
76D764—48no—
77D764—42no—
78C22⋊D191—48no—
79C2×Dic191—22no—
80C2×Dic191—22no—
81C2×Dic191—42no—
82C2×Dic191C2×D412yes—
83C4×D191—24no—
84C4×D191—22no—
85C4×D191—22no—
86C191⋊C8C2×D414yescomplemented
87C23×C191—22no—
88C23×C191—42no—
89C23×C191—42no—
90C23×C191—42no—
91C23×C191C2×D411yescharacteristic
92D4×C191—22no—
93D4×C191—22no—
94D4×C191—42no—
95C2×C4×C191—22no—
96C2×C4×C191—42no—
97C2×C4×C191C2×D411yescharacteristic
98C2×C4×C191C2×D412yes—
99C2×C4×C191#4112yes—
100C2×C4×C191C2411yescharacteristic
101C8×C191—22no—
102C22×C191—42no—
103C22×C191—42no—
104C22×C191—42no—
105C22×C191—84no—
106C22×C191#12112yes—
107C22×C191C2×D812yes—
108C22×C191#13512yes—
109C22×C191C22×D411yescharacteristic
110C2×D191—22no—
111C2×D191—22no—
112C2×D191—28no—
113C2×D191—42no—
114C2×D191—42no—
115C2×D191—42no—
116C2×D191—84no—
117C2×D191C2×D814yescomplemented
118C4×C191—42no—
119C4×C191#12112yes—
120C4×C191C22×D411yescharacteristic
121C4×C191C2×#4111yescharacteristic
122Dic191—22no—
123Dic191—42no—
124C2×C191—82no—
125C2×C191#46614yescomplemented
126C2×C191C2×#12111yescharacteristic
127C2×C191C22×D811yescharacteristic
128C2×C191C2×#13511yescharacteristic
129D191—24no—
130D191—82no—
131C191C2×#46611yescharacteristic, complemented, Sylow
132C2×#466—1911nomaximal, Sylow
133C22×D8—1911no—
134C23×C8—1911no—
135C2×#121—1911no—
136C2×#121—1911no—
137#466—1918no—
138C2×#107—1911no—
139C2×#102—1911no—
140C2×#102D19111yescharacteristic, complemented
141C22×D4—3821no—
142C22×D4—3821no—
143C22×D4—1911no—
144C22×D4C2×D19111yescharacteristic
145C23×C4—1911no—
146C2×D8—3824no—
147C2×D8—1914no—
148C22×C8—3824no—
149C22×C8—1914no—
150C22×C8—1911no—
151C22×C8C2×D19111yescharacteristic
152#121—3822no—
153#121—3822no—
154#121—1914no—
155#121—1914no—
156C2×C4⋊C4—1911no—
157C2×C4⋊C4C2×D19111yescharacteristic
158C2×C22⋊C4—3821no—
159C2×C22⋊C4—3821no—
160#107—1914no—
161#102—1914no—
162#102C2×D19114yescomplemented
163C24—21no—
164C24—3821no—
165C24—1911no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—3824no—
170C2×D4—3824no—
171C2×D4—3822no—
172C2×D4—3821no—
173C2×D4—3822no—
174C2×D4—1912no—
175C2×D4—7644no—
176C2×D4—7644no—
177C2×D4C22×D19112yes—
178C22×C4—21no—
179C22×C4—3822no—
180C22×C4—3822no—
181C22×C4—3821no—
182C22×C4—1911no—
183C22×C4—1912no—
184C22×C4—1912no—
185C22×C4C22×D19111yescharacteristic
186D8—3828no—
187C2×C8—22no—
188C2×C8—3828no—
189C2×C8—1914no—
190C2×C8—1912no—
191C2×C8C22×D19112yes—
192C4⋊C4—21no—
193C4⋊C4—3821no—
194C4⋊C4—1912no—
195C4⋊C4C22×D19112yes—
196C22⋊C4—3824no—
197C22⋊C4—3824no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—3822no—
203C23—3822no—
204C23—3822no—
205C23—1914no—
206C23—1912no—
207C23—7642no—
208C23—7642no—
209C23—7642no—
210C23D4×D19111yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—3822no—
215D4—3822no—
216D4—7648no—
217D4—7648no—
218D4—7642no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—3822no—
222C2×C4—3822no—
223C2×C4—3822no—
224C2×C4—3824no—
225C2×C4—3822no—
226C2×C4—1912no—
227C2×C4—7642no—
228C2×C4D4×D19112yes—
229C2×C4D4×D19111yescharacteristic
230C2×C4#1569028712yes—
231C2×C4C23×D19111yescharacteristic
232C8—22no—
233C8—1914no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—3822no—
239C22—3828no—
240C22—3822no—
241C22—1914no—
242C22—15284no—
243C22—7642no—
244C22—7642no—
245C22—7642no—
246C22#2025929512yes—
247C22D8×D19112yes—
248C22#2025934312yes—
249C22C2×D4×D19111yescharacteristic
250C4—42no—
251C4—3822no—
252C4—7642no—
253C4#2025929512yes—
254C4C2×D4×D19111yescharacteristic
255C4C2×#1569028711yescharacteristic
256C2—82no—
257C2—3824no—
258C2—15282no—
259C2#2713289814yesdirect product factor
260C2C2×#2025929511yescharacteristic
261C2C2×D8×D19111yescharacteristic
262C2C2×#2025934311yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#102×C191C2
socleC23×C191C2×D4
hypercenterC2×#102D191
hypocenterC191C2×#466
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#15690272C2semidirect
2. C22×C8×D191C2semidirect
3. C2×#20259297C2semidirect
4. C2×#20259293C2semidirect
5. #27132898C2direct (N × H)
6. C2×#20259255C2semidirect
7. C2×#20259244C2semidirect
8. C2×#102×C191C2semidirect
14. C2×#15690272C22semidirect
17. C2×C8×D191C22semidirect
19. #20259297C22semidirect
21. #20259293C22semidirect
25. #20259255C22semidirect
26. #20259244C22semidirect
30. #102×C191C22semidirect
48. C2×C191⋊C8D4semidirect
72. C22×D191D8semidirect
86. C191⋊C8C2×D4semidirect
117. C2×D191C2×D8semidirect
125. C2×C191#466semidirect
131. C191C2×#466semidirect
140. C2×#102D191semidirect
162. #102C2×D191semidirect
259. C2#27132898direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902722
C22×C8×D1912
C2×#202592972
C2×#202592932
#271328982
C2×#202592552
C2×#202592442
C2×#102×C1912
C2×#466191