Finite Group Databasebeta

← #37582893

Subgroups — #37582893

Order 24448.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#27133219C211yesmaximal, characteristic, complemented
2#127×D191C211yesmaximal, characteristic
3#27133029C211yesmaximal, characteristic, complemented
4#27133028C211yesmaximal, characteristic, complemented
5#27133027C211yesmaximal, characteristic, complemented
6#27133008C214yesmaximal, complemented
7#27132666C214yesmaximal, complemented
8#27132615C211yesmaximal, characteristic, complemented
9#490×C191C211yesmaximal, characteristic, complemented
10C2×D4×D191—22no—
11C2×D4×D191C2212yes—
12C2×#15690270C2212yes—
13#20259321C2212yescomplemented
14#20259319C2211yescharacteristic
15#20259318—22no—
16#20259318C2212yes—
17#20259314C2211yescharacteristic, complemented
18#20259300—22no—
19#20259287—22no—
20#20259280C2212yes—
21C42×D191C2211yescharacteristic
22#20259244C2214yescomplemented
23#20259243C2214yescomplemented
24#20259242C2214yescomplemented
25#20259233C2211yescharacteristic, complemented
26C8×Dic191C2212yescomplemented
27#127×C191C2211yescharacteristic
28#125×C191C2211yescharacteristic, complemented
29#102×C191C2214yescomplemented
30#97×C191C2211yescharacteristic, complemented
31C23×D191—22no—
32C2×Dic382—22no—
33C2×D764—22no—
34C2×D764C2312yes—
35C2×C22⋊D191—24no—
36C2×C22⋊D191—22no—
37D4×D191—28no—
38D4×D191—48no—
39C2×C4×D191D412yes—
40C2×C4×D191C2311yescharacteristic
41#15690270—24no—
42C2×C191⋊C8C2312yes—
43C4⋊Dic191C2312yes—
44Dic191⋊C4—22no—
45Dic191⋊C4—22no—
46(C2×D191)⋊C4—22no—
47C4×Dic191—22no—
48C4×Dic191D412yes—
49C4×Dic191C2311yescharacteristic
50C2×D4×C191—22no—
51C2×D4×C191C2312yes—
52C2×C8×C191C2312yes—
53C4⋊C4×C191—22no—
54C4⋊C4×C191C2312yes—
55C42×C191C2311yescharacteristic
56C22×D191—22no—
57C22×D191—48no—
58C22×D191—44no—
59C22×D191C2×D411yescharacteristic
60Dic382—44no—
61D764—24no—
62D764—44no—
63C22⋊D191—44no—
64C22⋊D191—48no—
65C2×Dic191—22no—
66C2×Dic191C2×D411yescharacteristic
67C2×Dic191C2×D412yes—
68C4×D191—24no—
69C4×D191#4114yes—
70C191⋊C8—22no—
71C23×C191—22no—
72D4×C191—24no—
73D4×C191—44no—
74C2×C4×C191—22no—
75C2×C4×C191C2×D412yes—
76C2×C4×C191C2411yescharacteristic
77C8×C191—22no—
78C22×C191—42no—
79C22×C191—44no—
80C22×C191C22×D411yescharacteristic
81C2×D191—22no—
82C2×D191—42no—
83C2×D191—44no—
84C2×D191—88no—
85C2×D191#12412yes—
86C4×C191—22no—
87C4×C191—42no—
88C4×C191C2×#4112yes—
89Dic191—42no—
90Dic191#12412yes—
91Dic191AGL(1,ℤ/8)14yes—
92C2×C191—82no—
93C2×C191C2×#12411yescharacteristic
94C2×C191C2×AGL(1,ℤ/8)12yes—
95D191—22no—
96D191—82no—
97C191#313811yescharacteristic, complemented, Sylow
98#3138—1911nomaximal, Sylow
99#533—1911no—
100C2×#127—1911no—
101#490—1911no—
102#490—1911no—
103#490—1911no—
104#490D19111yescharacteristic, complemented
105#486—1914no—
106#418—1914no—
107C4×M16—1911no—
108C22×D4—3822no—
109C22×D4—1912no—
110C2×M16—1912no—
111C4⋊Q8—1912no—
112#127—3822no—
113#127—1912no—
114#127—1911no—
115#127C2×D19111yescharacteristic
116#125—1911no—
117#125C2×D19111yescharacteristic, complemented
118C22⋊Q8—3822no—
119C4×Q8—3822no—
120#117—1912no—
121C2×C42—1911no—
122#102—1914no—
123#102—1914no—
124#102—1914no—
125#102C2×D19114yescomplemented
126#97—1911no—
127#97C2×D19111yescharacteristic, complemented
128C4×C8—1912no—
129C24—3822no—
130C2×Q8—3822no—
131C2×D4—22no—
132C2×D4—3828no—
133C2×D4—3822no—
134C2×D4—3824no—
135C2×D4—3822no—
136C2×D4—1912no—
137C2×D4—7648no—
138C2×D4C22×D19112yes—
139C22×C4—1912no—
140C22×C4—1911no—
141M16—3824no—
142C2×C8—1912no—
143C2×C8C22×D19112yes—
144C4⋊C4—22no—
145C4⋊C4—3822no—
146C4⋊C4—3822no—
147C4⋊C4—1912no—
148C4⋊C4C22×D19112yes—
149C22⋊C4—3822no—
150C42—3822no—
151C42—1912no—
152C42—1911no—
153C42C22×D19111yescharacteristic
154C23—22no—
155C23—3822no—
156C23—1911no—
157C23—7648no—
158C23—7644no—
159Q8—7644no—
160D4—24no—
161D4—44no—
162D4—3824no—
163D4—7644no—
164D4—7644no—
165D4—7648no—
166C2×C4—22no—
167C2×C4—3824no—
168C2×C4—3822no—
169C2×C4—1911no—
170C2×C4—1912no—
171C2×C4—1914no—
172C2×C4D4×D19112yes—
173C2×C4C23×D19111yescharacteristic
174C8—22no—
175C8—3822no—
176C22—44no—
177C22—42no—
178C22—3822no—
179C22—1912no—
180C22—15288no—
181C22—7644no—
182C22—7642no—
183C22C2×D4×D19111yescharacteristic
184C4—22no—
185C4—42no—
186C4—1914no—
187C4—1912no—
188C4—7642no—
189C4#41×D19112yes—
190C2—82no—
191C2—3822no—
192C2—15282no—
193C2#124×D19111yescharacteristic
194C2AGL(1,ℤ/8)×D19112yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#490×C191C2
socleC22×C191C22×D4
prime radical#127×D191C2
hypercenter#490D191
hypocenterC191#3138
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #27133219C2semidirect
3. #27133029C2semidirect
4. #27133028C2semidirect
5. #27133027C2semidirect
6. #27133008C2semidirect
7. #27132666C2semidirect
8. #27132615C2semidirect
9. #490×C191C2semidirect
13. #20259321C22semidirect
17. #20259314C22semidirect
22. #20259244C22semidirect
23. #20259243C22semidirect
24. #20259242C22semidirect
25. #20259233C22semidirect
26. C8×Dic191C22semidirect
28. #125×C191C22semidirect
29. #102×C191C22semidirect
30. #97×C191C22semidirect
97. C191#3138semidirect
104. #490D191semidirect
117. #125C2×D191semidirect
125. #102C2×D191semidirect
127. #97C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332192
#127×D1912
#271330292
#271330282
#271330272
#271330082
#271326662
#271326152
#490×C1912
#3138191