Finite Group Databasebeta

← #37582919

Subgroups — #37582919

Order 24448.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#27133211C211yesmaximal, characteristic
2#125×D191C211yesmaximal, characteristic, complemented
3#27133033C211yesmaximal, characteristic, complemented
4#27133032C211yesmaximal, characteristic, complemented
5#27133027C211yesmaximal, characteristic, complemented
6#27133016C214yesmaximal, complemented
7#27132661C214yesmaximal, complemented
8#27132615C211yesmaximal, characteristic, complemented
9#490×C191C211yesmaximal, characteristic, complemented
10C2×#15690286C2212yes—
11C2×#15690270C2212yes—
12#20259322C2211yescharacteristic
13#20259314C2211yescharacteristic
14#20259313C2212yes—
15#20259312—22no—
16#20259309C2212yes—
17#20259293—22no—
18D4×Dic191—22no—
19C4⋊C4×D191—22no—
20C4⋊C4×D191C2212yes—
21C42×D191C2211yescharacteristic
22#20259247C2214yes—
23#20259245C2214yes—
24#20259243C2214yes—
25#20259233C2211yescharacteristic
26C8×Dic191C2212yes—
27#127×C191C2211yescharacteristic
28#125×C191C2211yescharacteristic
29#102×C191C2214yes—
30#97×C191C2211yescharacteristic
31#15690286—28no—
32C2×Dic382C2312yes—
33C2×C22⋊D191—22no—
34C22×Dic191—22no—
35C2×C4×D191—22no—
36C2×C4×D191D412yes—
37C2×C4×D191C2311yescharacteristic
38#15690270—24no—
39C2×C191⋊C8C2312yes—
40C4⋊Dic191—22no—
41C4⋊Dic191—22no—
42C4⋊Dic191C2312yes—
43Dic191⋊C4—22no—
44Dic191⋊C4—22no—
45Dic191⋊C4—22no—
46C22⋊Dic191—24no—
47C4×Dic191D412yes—
48C4×Dic191C2311yescharacteristic
49C2×D4×C191—22no—
50C2×D4×C191C2312yes—
51C2×C8×C191C2312yes—
52C4⋊C4×C191—22no—
53C4⋊C4×C191C2312yes—
54C42×C191C2311yescharacteristic
55C22×D191C2×D411yescharacteristic
56Dic382—24no—
57C22⋊D191—44no—
58C2×Dic191—22no—
59C2×Dic191—22no—
60C2×Dic191—44no—
61C2×Dic191C2×D412yes—
62C2×Dic191C2×D411yescharacteristic
63C4×D191—42no—
64C4×D191—44no—
65C4×D191#4114yes—
66C191⋊C8—22no—
67C23×C191—22no—
68D4×C191—24no—
69D4×C191—44no—
70C2×C4×C191—22no—
71C2×C4×C191C2×D412yes—
72C2×C4×C191C2411yescharacteristic
73C8×C191—22no—
74C22×C191—42no—
75C22×C191—44no—
76C22×C191C22×D411yescharacteristic
77C2×D191—22no—
78C2×D191#12412yes—
79C4×C191—22no—
80C4×C191—42no—
81C4×C191C2×#4112yes—
82Dic191—22no—
83Dic191—42no—
84Dic191—42no—
85Dic191#12412yes—
86C2×C191—82no—
87C2×C191C2×#12411yescharacteristic
88C2×C191#57512yes—
89D191—22no—
90C191#314211yescharacteristic, complemented, Sylow
91#3142—1911nomaximal, Sylow
92#532—1911no—
93C2×#125—1911no—
94#491—1911no—
95#491—1911no—
96#490—1911no—
97#490D19111yescharacteristic, complemented
98#488—1914no—
99#417—1914no—
100C4×M16—1911no—
101C2×#41—1912no—
102C2×M16—1912no—
103C4⋊Q8—1911no—
104#127C2×D19111yescharacteristic
105#125—3822no—
106#125—1912no—
107#125—1911no—
108#125C2×D19111yescharacteristic
109#124—1912no—
110#121—3822no—
111C4×D4—3822no—
112C2×C4⋊C4—3822no—
113C2×C4⋊C4—1912no—
114C2×C42—1911no—
115#103—1914no—
116#103—1914no—
117#102—1914no—
118#102C2×D19114yes—
119#97—1911no—
120#97C2×D19111yescharacteristic
121C4×C8—1912no—
122#41—3828no—
123C2×Q8—1912no—
124C2×D4—22no—
125C2×D4—3822no—
126C2×D4C22×D19112yes—
127C22×C4—3822no—
128C22×C4—3822no—
129C22×C4—1911no—
130C22×C4—1912no—
131M16—3824no—
132C2×C8—1912no—
133C2×C8C22×D19112yes—
134C4⋊C4—22no—
135C4⋊C4—3822no—
136C4⋊C4—3822no—
137C4⋊C4—3822no—
138C4⋊C4—3822no—
139C4⋊C4—3822no—
140C4⋊C4—1912no—
141C4⋊C4C22×D19112yes—
142C22⋊C4—3824no—
143C42—1912no—
144C42—1911no—
145C42C22×D19111yescharacteristic
146C23—22no—
147C23—1911no—
148Q8—3824no—
149D4—24no—
150D4—44no—
151D4—7644no—
152C2×C4—22no—
153C2×C4—3822no—
154C2×C4—3822no—
155C2×C4—1912no—
156C2×C4—1911no—
157C2×C4—1914no—
158C2×C4—7642no—
159C2×C4—7644no—
160C2×C4—7644no—
161C2×C4D4×D19112yes—
162C2×C4C23×D19111yescharacteristic
163C8—22no—
164C8—3822no—
165C22—44no—
166C22—42no—
167C22—3822no—
168C22—1912no—
169C22C2×D4×D19111yescharacteristic
170C4—22no—
171C4—42no—
172C4—3822no—
173C4—1912no—
174C4—7642no—
175C4—7642no—
176C4#41×D19112yes—
177C2—82no—
178C2—3822no—
179C2#124×D19111yescharacteristic
180C2#2713345912yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#490×C191C2
socleC22×C191C22×D4
prime radical#27133211C2
hypercenter#490D191
hypocenterC191#3142
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
2. #125×D191C2semidirect
3. #27133033C2semidirect
4. #27133032C2semidirect
5. #27133027C2semidirect
6. #27133016C2semidirect
7. #27132661C2semidirect
8. #27132615C2semidirect
9. #490×C191C2semidirect
90. C191#3142semidirect
97. #490D191semidirect

Maximal subgroups

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

subgroupindex
#271332112
#125×D1912
#271330332
#271330322
#271330272
#271330162
#271326612
#271326152
#490×C1912
#3142191