Finite Group Databasebeta

← #37571564

Subgroups — #37571564

Order 24448.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#27133294C211yesmaximal, characteristic
2#27132999C212yesmaximal
3#27132602C211yesmaximal, characteristic
4#27132401C212yesmaximal
5#324×C191C211yesmaximal, characteristic
6#20259321—22no—
7#20259313—22no—
8#20259301—21no—
9#20259301C2212yes—
10#20259281—21no—
11C2×C4⋊Dic191C2211yescharacteristic
12#20259256—22no—
13#20259247—22no—
14C191⋊#95—21no—
15C191⋊#95—21no—
16C191⋊#95C2211yescharacteristic
17C2×C4⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yes—
19C2×Dic382—21no—
20C2×Dic382D412yes—
21C22×Dic191—21no—
22C22×Dic191—21no—
23C4⋊Dic191—21no—
24C4⋊Dic191—21no—
25C4⋊Dic191—21no—
26C4⋊Dic191—22no—
27C4⋊Dic191D412yes—
28Dic191⋊C4—22no—
29Dic191⋊C4—22no—
30C22⋊Dic191—22no—
31C4×Dic191—22no—
32C22×C4×C191D411yescharacteristic
33C22×C4×C191D411yescharacteristic
34C22×C4×C191C2311yescharacteristic
35C2×C8×C191—22no—
36C4⋊C4×C191—22no—
37Dic382—42no—
38Dic382—81no—
39C2×Dic191—22no—
40C2×Dic191—22no—
41C2×Dic191—41no—
42C2×Dic191—41no—
43C2×Dic191—42no—
44C2×Dic191—41no—
45C2×Dic191—41no—
46C23×C191C2×D411yescharacteristic
47C2×C4×C191—21no—
48C2×C4×C191—21no—
49C2×C4×C191—21no—
50C2×C4×C191—41no—
51C2×C4×C191—41no—
52C2×C4×C191Q1612yes—
53C2×C4×C191C2×D412yes—
54C8×C191—42no—
55C22×C191—21no—
56C22×C191—21no—
57C22×C191#12011yescharacteristic
58C22×C191C2×Q1611yescharacteristic
59C22×C191#13711yescharacteristic
60C4×C191—22no—
61C4×C191—22no—
62C4×C191—41no—
63Dic191—42no—
64Dic191—42no—
65Dic191—81no—
66Dic191—81no—
67C2×C191—21no—
68C2×C191—21no—
69C2×C191#45111yescharacteristic
70C2×C191#45411yescharacteristic
71C2×C191#45811yescharacteristic
72C191#161711yescharacteristic, complemented, Sylow
73#1617—1911nomaximal, Sylow
74#544—1911no—
75#484—1912no—
76#400—1911no—
77#328—1912no—
78#324D19111yescharacteristic
79C4⋊Q8—3822no—
80#125—3822no—
81C22⋊Q8—3821no—
82C22⋊Q8—1912no—
83#117—3821no—
84C2×C4⋊C4—1911no—
85C2×C4⋊C4C2×D19111yescharacteristic
86#107—3822no—
87#103—3822no—
88C22⋊C8C2×D19112yes—
89#95—3821no—
90#95—3821no—
91#95—1911no—
92C2×Q8—3821no—
93C2×Q8—1912no—
94C22×C4—3821no—
95C22×C4—3821no—
96C22×C4D76411yescharacteristic
97C22×C4D76411yescharacteristic
98C22×C4C22×D19111yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—3822no—
102C4⋊C4—3821no—
103C4⋊C4—3821no—
104C4⋊C4—3821no—
105C4⋊C4—3822no—
106C4⋊C4—3822no—
107C4⋊C4—1912no—
108C22⋊C4—3822no—
109C42—3822no—
110C23C2×D76411yescharacteristic
111Q8—15281no—
112Q8—7642no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—3822no—
119C2×C4—3822no—
120C2×C4—7641no—
121C2×C4—7641no—
122C2×C4—7642no—
123C2×C4—7641no—
124C2×C4—7641no—
125C2×C4Dic76412yes—
126C2×C4D4×D19112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2025929211yescharacteristic
131C22C2×Dic76411yescharacteristic
132C22#2025935511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—15281no—
137C4—15281no—
138C4—7642no—
139C4—7642no—
140C2—21no—
141C2—21no—
142C2#2713282111yescharacteristic
143C2#2713283811yescharacteristic
144C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#324×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
hypercenter#324D191
hypocenterC191#1617
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C191#1617semidirect

Maximal subgroups

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

subgroupindex
#271332942
#271329992
#271326022
#271324012
#324×C1912
#1617191