Finite Group Databasebeta

← C2×#27132856 #37581930

Subgroups — C2×#27132856 #37581930

Order 24448.

648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C2×#20259318C211yesmaximal, characteristic, complemented
3C2×D4×Dic191C211yesmaximal, characteristic, complemented
4#27132856C218yesmaximal, direct product factor
5C2×Dic191⋊C8C211yesmaximal, characteristic, complemented
6C2×#20259244C211yesmaximal, characteristic, complemented
7C2×#20259243C211yesmaximal, characteristic, complemented
8C22×D8×C191C211yesmaximal, characteristic, complemented
9C22×D764C2211yescharacteristic
10C22×C22⋊D191—21no—
11C22×C22⋊D191—21no—
12C23×Dic191—21no—
13C2×#15690272—24no—
14C2×#15690272C2214yescomplemented
15C22×C191⋊C8C2211yescharacteristic
16#20259318—22no—
17#20259318C2214yescomplemented
18D4×Dic191—22no—
19D4×Dic191C2214yescomplemented
20C2×C4⋊Dic191C2211yescharacteristic
21C2×C22⋊Dic191—21no—
22C2×C4×Dic191C2211yescharacteristic
23Dic191⋊C8C2214yescomplemented
24#20259244C2214yescomplemented
25#20259243C2214yescomplemented
26C22×D4×C191C2211yescharacteristic
27C22×D4×C191C2211yescharacteristic
28C2×D8×C191—24no—
29C2×D8×C191C2214yescomplemented
30C22×C8×C191C2211yescharacteristic
31C23×D191—21no—
32C2×D764—22no—
33C2×D764—21no—
34C2×D764—22no—
35C2×D764C2312yes—
36C2×C22⋊D191—24no—
37C2×C22⋊D191—24no—
38C2×C22⋊D191—44no—
39C2×C22⋊D191—44no—
40C22×Dic191—24no—
41C22×Dic191—21no—
42C22×Dic191—44no—
43C22×Dic191D411yescharacteristic
44C22×Dic191D411yescharacteristic
45#15690272—28no—
46C2×C191⋊C8—22no—
47C2×C191⋊C8C2312yes—
48C4⋊Dic191—21no—
49C4⋊Dic191C2312yes—
50C22⋊Dic191—24no—
51C4×Dic191D412yes—
52C4×Dic191C2312yes—
53C24×C191—21no—
54C24×C191—21no—
55C2×D4×C191—21no—
56C2×D4×C191—22no—
57C2×D4×C191—21no—
58C2×D4×C191—22no—
59C2×D4×C191—22no—
60C2×D4×C191D414yescomplemented
61C2×D4×C191C2312yes—
62C2×D4×C191C2312yes—
63C22×C4×C191C2311yescharacteristic
64D8×C191—28no—
65C2×C8×C191—22no—
66C2×C8×C191C2312yes—
67C22×D191—22no—
68C22×D191—42no—
69C22×D191—42no—
70C22×D191—42no—
71D764—22no—
72D764—22no—
73D764—42no—
74C22⋊D191—48no—
75C22⋊D191—48no—
76C2×Dic191—22no—
77C2×Dic191—22no—
78C2×Dic191—42no—
79C2×Dic191—48no—
80C2×Dic191D814yescomplemented
81C2×Dic191C2×D412yes—
82C2×Dic191C2×D412yes—
83C191⋊C8—22no—
84C23×C191—24no—
85C23×C191—22no—
86C23×C191—22no—
87C23×C191—42no—
88C23×C191—42no—
89C23×C191—42no—
90C23×C191—42no—
91C23×C191—42no—
92C23×C191C2×D411yescharacteristic
93D4×C191—24no—
94D4×C191—22no—
95D4×C191—22no—
96D4×C191—22no—
97D4×C191—42no—
98D4×C191C2×D414yescomplemented
99C2×C4×C191C2×D411yescharacteristic
100C2×C4×C191C2×D412yes—
101C2×C4×C191#4112yes—
102C2×C4×C191C2411yescharacteristic
103C8×C191—22no—
104C22×C191—24no—
105C22×C191—42no—
106C22×C191—42no—
107C22×C191—48no—
108C22×C191—42no—
109C22×C191—42no—
110C22×C191—42no—
111C22×C191—84no—
112C22×C191#12112yes—
113C22×C191C2×D812yes—
114C22×C191AGL(1,ℤ/8)12yes—
115C22×C191C22×D411yescharacteristic
116C2×D191—42no—
117C2×D191—42no—
118C2×D191—42no—
119C2×D191—84no—
120C4×C191#12112yes—
121C4×C191C22×D411yescharacteristic
122C4×C191C2×#4111yescharacteristic
123Dic191—22no—
124Dic191—42no—
125Dic191C2×D814yescomplemented
126C2×C191—44no—
127C2×C191—82no—
128C2×C191#45914yescomplemented
129C2×C191C2×#12111yescharacteristic
130C2×C191C22×D811yescharacteristic
131C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
132D191—82no—
133C191C2×#45911yescharacteristic, complemented, Sylow
134C2×#459—1911nomaximal, Sylow
135C22×D8—1911no—
136C22×D8D19111yescharacteristic, complemented
137C2×#127—1911no—
138C2×C4×D4—1911no—
139#459—1918no—
140C2×C4⋊C8—1911no—
141C2×#102—1911no—
142C2×#102—1911no—
143C22×D4—3821no—
144C22×D4—3821no—
145C22×D4—1911no—
146C22×D4C2×D19111yescharacteristic
147C22×D4C2×D19111yescharacteristic
148C23×C4—3821no—
149C2×D8—24no—
150C2×D8—3824no—
151C2×D8—1914no—
152C2×D8C2×D19114yescomplemented
153C22×C8—1911no—
154C22×C8C2×D19111yescharacteristic
155#127—3822no—
156#127—1914no—
157C4×D4—3822no—
158C4×D4—1914no—
159C2×C4⋊C4—1911no—
160C2×C22⋊C4—3821no—
161C2×C42—1911no—
162C4⋊C8—1914no—
163#102—1914no—
164#102—1914no—
165C24—21no—
166C24—21no—
167C24—3821no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—3824no—
174C2×D4—3824no—
175C2×D4—3821no—
176C2×D4—3822no—
177C2×D4—3822no—
178C2×D4—1912no—
179C2×D4—7644no—
180C2×D4—7644no—
181C2×D4C22⋊D19114yescomplemented
182C2×D4C22×D19112yes—
183C2×D4C22×D19112yes—
184C22×C4—3821no—
185C22×C4—3824no—
186C22×C4—1911no—
187C22×C4—1911no—
188C22×C4—7644no—
189C22×C4C22×D19111yescharacteristic
190D8—28no—
191D8—3828no—
192C2×C8—22no—
193C2×C8—3822no—
194C2×C8—1912no—
195C2×C8C22×D19112yes—
196C4⋊C4—3821no—
197C4⋊C4—1912no—
198C22⋊C4—3824no—
199C42—1912no—
200C42—1912no—
201C23—22no—
202C23—24no—
203C23—22no—
204C23—42no—
205C23—42no—
206C23—42no—
207C23—42no—
208C23—42no—
209C23—3822no—
210C23—7642no—
211C23—7642no—
212C23—7642no—
213C23D4×D19111yescharacteristic
214D4—22no—
215D4—22no—
216D4—22no—
217D4—24no—
218D4—42no—
219D4—3822no—
220D4—3822no—
221D4—7648no—
222D4—7648no—
223D4—7642no—
224D4C2×C22⋊D19114yescomplemented
225C2×C4—3822no—
226C2×C4—3822no—
227C2×C4—1912no—
228C2×C4—1914no—
229C2×C4—1912no—
230C2×C4—7648no—
231C2×C4—7642no—
232C2×C4D4×D19111yescharacteristic
233C2×C4C2×C22⋊D19112yes—
234C2×C4#1569028612yes—
235C2×C4C23×D19111yescharacteristic
236C8—22no—
237C8—3822no—
238C22—24no—
239C22—42no—
240C22—48no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—84no—
246C22—15284no—
247C22—7642no—
248C22—7642no—
249C22—7642no—
250C22#2025929412yes—
251C22D8×D19112yes—
252C22#2025934612yes—
253C22C2×D4×D19111yescharacteristic
254C4—3822no—
255C4—1914no—
256C4—7642no—
257C4#2025929412yes—
258C4C22×C22⋊D19111yescharacteristic
259C4C2×#1569028611yescharacteristic
260C2—44no—
261C2—82no—
262C2—15282no—
263C2#2713285614yesdirect product factor
264C2C2×#2025929411yescharacteristic
265C2C2×D8×D19111yescharacteristic
266C2C2×#2025934611yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×D8×C191C2
socleC23×C191C2×D4
hypercenterC22×D8D191
hypocenterC191C2×#459
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#15690272C2semidirect
2. C2×#20259318C2semidirect
3. C2×D4×Dic191C2semidirect
4. #27132856C2direct (N × H)
5. C2×Dic191⋊C8C2semidirect
6. C2×#20259244C2semidirect
7. C2×#20259243C2semidirect
8. C22×D8×C191C2semidirect
14. C2×#15690272C22semidirect
17. #20259318C22semidirect
19. D4×Dic191C22semidirect
23. Dic191⋊C8C22semidirect
24. #20259244C22semidirect
25. #20259243C22semidirect
29. C2×D8×C191C22semidirect
60. C2×D4×C191D4semidirect
80. C2×Dic191D8semidirect
98. D4×C191C2×D4semidirect
125. Dic191C2×D8semidirect
128. C2×C191#459semidirect
133. C191C2×#459semidirect
136. C22×D8D191semidirect
152. C2×D8C2×D191semidirect
181. C2×D4C22⋊D191semidirect
224. D4C2×C22⋊D191semidirect
263. C2#27132856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902722
C2×#202593182
C2×D4×Dic1912
#271328562
C2×Dic191⋊C82
C2×#202592442
C2×#202592432
C22×D8×C1912
C2×#459191