Finite Group Databasebeta

← #37582892

Subgroups — #37582892

Order 24448.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#27133216C211yesmaximal, characteristic, complemented
2C2×#20259318C211yesmaximal, characteristic
3#27133026C214yesmaximal, complemented
4#27133008C214yesmaximal, complemented
5#27132669C211yesmaximal, characteristic, complemented
6#27132668C211yesmaximal, characteristic, complemented
7#27132667C211yesmaximal, characteristic, complemented
8M16×Dic191C211yesmaximal, characteristic, complemented
9#418×C191C211yesmaximal, characteristic, complemented
10C22×D764C2211yescharacteristic
11C22×C22⋊D191—22no—
12C2×#15690271C2211yescharacteristic
13#20259321C2212yescomplemented
14#20259318—22no—
15#20259318C2212yes—
16#20259318C2212yes—
17#20259313C2212yescomplemented
18#20259299—22no—
19C4×Dic382—22no—
20#20259281C2211yescharacteristic
21C2×C4×Dic191C2211yescharacteristic
22#20259244C2214yescomplemented
23#20259243C2214yescomplemented
24#20259242C2214yescomplemented
25#20259232C2212yescomplemented
26C8×Dic191C2212yescomplemented
27C22×D4×C191C2211yescharacteristic
28C2×M16×C191C2211yescharacteristic
29#117×C191C2211yescharacteristic
30#102×C191C2214yescomplemented
31C23×D191—21no—
32C2×Dic382—22no—
33C2×D764—21no—
34C2×D764—22no—
35C2×D764—22no—
36C2×D764C2312yes—
37C2×C22⋊D191—24no—
38C2×C22⋊D191—24no—
39C2×C22⋊D191—48no—
40C22×Dic191D412yes—
41#15690271—22no—
42C2×C191⋊C8C2312yes—
43C4⋊Dic191—22no—
44C4⋊Dic191C2312yes—
45Dic191⋊C4—22no—
46Dic191⋊C4—22no—
47C22⋊Dic191—21no—
48C4×Dic191—21no—
49C4×Dic191D412yes—
50C4×Dic191C2311yescharacteristic
51C4×Dic191C2311yescharacteristic
52C24×C191—21no—
53C2×D4×C191—21no—
54C2×D4×C191—22no—
55C2×D4×C191—22no—
56C2×D4×C191C2312yes—
57C22×C4×C191C2311yescharacteristic
58M16×C191—22no—
59C2×C8×C191C2312yes—
60C4⋊C4×C191C2312yes—
61C22⋊C4×C191—21no—
62C42×C191—21no—
63C22×D191—22no—
64C22×D191—44no—
65C22×D191—42no—
66Dic382—44no—
67D764—22no—
68D764—22no—
69D764—42no—
70C22⋊D191—48no—
71C22⋊D191—48no—
72C2×Dic191—24no—
73C2×Dic191—22no—
74C2×Dic191C2×D412yes—
75C2×Dic191C2×D412yes—
76C191⋊C8—22no—
77C23×C191—22no—
78C23×C191—44no—
79C23×C191—42no—
80C23×C191C2×D411yescharacteristic
81D4×C191—22no—
82D4×C191—22no—
83D4×C191—42no—
84C2×C4×C191—22no—
85C2×C4×C191C2×D411yescharacteristic
86C2×C4×C191#4112yes—
87C2×C4×C191#4112yes—
88C2×C4×C191C2411yescharacteristic
89C8×C191—22no—
90C22×C191—22no—
91C22×C191—42no—
92C22×C191—44no—
93C22×C191—84no—
94C22×C191#12412yes—
95C22×C191C22×D411yescharacteristic
96C2×D191—42no—
97C2×D191—44no—
98C2×D191—84no—
99C4×C191—42no—
100C4×C191#12412yes—
101C4×C191C2×#4111yescharacteristic
102C4×C191C2×#4111yescharacteristic
103Dic191—22no—
104Dic191—42no—
105Dic191AGL(1,ℤ/8)14yes—
106C2×C191—22no—
107C2×C191—82no—
108C2×C191C2×#12411yescharacteristic
109C2×C191C2×AGL(1,ℤ/8)12yes—
110D191—82no—
111C191#313811yescharacteristic, complemented, Sylow
112#3138—1911nomaximal, Sylow
113#533—1911no—
114C2×#127—1911no—
115#490—1914no—
116#486—1914no—
117#418—1911no—
118#418—1911no—
119#418—1911no—
120#418D19111yescharacteristic, complemented
121C4×M16—1911no—
122C22×D4—3822no—
123C22×D4—1911no—
124C22×D4C2×D19111yescharacteristic
125C2×M16—1911no—
126C2×M16C2×D19111yescharacteristic
127C4⋊Q8—1912no—
128#127—3822no—
129#127—1912no—
130#127—1912no—
131#125—1912no—
132C22⋊Q8—3822no—
133C4×Q8—3822no—
134#117—1911no—
135#117C2×D19111yescharacteristic
136C2×C42—1911no—
137#102—1914no—
138#102—1914no—
139#102—1914no—
140#102C2×D19114yescomplemented
141#97—1912no—
142C4×C8—1912no—
143C24—21no—
144C24—3821no—
145C2×Q8—3822no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—3824no—
150C2×D4—3824no—
151C2×D4—3821no—
152C2×D4—3822no—
153C2×D4—3822no—
154C2×D4—1912no—
155C2×D4—7648no—
156C2×D4C22×D19112yes—
157C22×C4—1912no—
158C22×C4C22×D19111yescharacteristic
159M16—22no—
160M16—3822no—
161C2×C8—1912no—
162C2×C8C22×D19112yes—
163C4⋊C4—3822no—
164C4⋊C4—3822no—
165C4⋊C4—3822no—
166C4⋊C4—1912no—
167C4⋊C4C22×D19112yes—
168C22⋊C4—21no—
169C22⋊C4—3821no—
170C42—21no—
171C42—3821no—
172C42—1912no—
173C42—1911no—
174C42—1911no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—3822no—
179C23—7644no—
180C23—7642no—
181C23D4×D19111yescharacteristic
182Q8—7644no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—3822no—
187D4—3822no—
188D4—7648no—
189D4—7648no—
190D4—7642no—
191C2×C4—22no—
192C2×C4—3824no—
193C2×C4—3822no—
194C2×C4—1912no—
195C2×C4—1912no—
196C2×C4D4×D19111yescharacteristic
197C2×C4#1569028612yes—
198C2×C4#1569028712yes—
199C2×C4C23×D19111yescharacteristic
200C8—22no—
201C8—3822no—
202C22—22no—
203C22—44no—
204C22—42no—
205C22—84no—
206C22—15284no—
207C22—7644no—
208C22—7642no—
209C22#2025930812yes—
210C22C2×D4×D19111yescharacteristic
211C4—42no—
212C4—3822no—
213C4—1914no—
214C4—7642no—
215C4#2025930812yes—
216C4C2×#1569028611yescharacteristic
217C4C2×#1569028711yescharacteristic
218C2—22no—
219C2—82no—
220C2—15282no—
221C2C2×#2025930811yescharacteristic
222C2AGL(1,ℤ/8)×D19112yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#418×C191C2
socleC22×C191C22×D4
prime radicalC2×#20259318C2
hypercenter#418D191
hypocenterC191#3138
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #27133216C2semidirect
3. #27133026C2semidirect
4. #27133008C2semidirect
5. #27132669C2semidirect
6. #27132668C2semidirect
7. #27132667C2semidirect
8. M16×Dic191C2semidirect
9. #418×C191C2semidirect
13. #20259321C22semidirect
17. #20259313C22semidirect
22. #20259244C22semidirect
23. #20259243C22semidirect
24. #20259242C22semidirect
25. #20259232C22semidirect
26. C8×Dic191C22semidirect
30. #102×C191C22semidirect
111. C191#3138semidirect
120. #418D191semidirect
140. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332162
C2×#202593182
#271330262
#271330082
#271326692
#271326682
#271326672
M16×Dic1912
#418×C1912
#3138191