Finite Group Databasebeta

← #37571528

Subgroups — #37571528

Order 24448.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#27132991C212yesmaximal
2#27132593C211yesmaximal, characteristic
3#27132400C212yesmaximal
4#27132389C211yesmaximal, characteristic
5#544×C191C211yesmaximal, characteristic
6C2×C4⋊Dic191C2211yescharacteristic
7C2×Dic191⋊C4—21no—
8#20259253—22no—
9#20259246—22no—
10C22⋊(C191⋊C8)C2212yes—
11C191⋊#95—21no—
12C191⋊#95C2211yescharacteristic
13C4⋊Q8×C191—22no—
14#125×C191—22no—
15C22⋊Q8×C191—21no—
16C22⋊Q8×C191C2212yes—
17#117×C191—21no—
18C2×C4⋊C4×C191C2211yescharacteristic
19C22×Dic191—21no—
20C22×Dic191—21no—
21C2×C191⋊C8—22no—
22C4⋊Dic191—22no—
23Dic191⋊C4—42no—
24C2×Q8×C191—21no—
25C2×Q8×C191D412yes—
26C22×C4×C191D411yescharacteristic
27C22×C4×C191D411yescharacteristic
28C22×C4×C191C2311yescharacteristic
29C4⋊C4×C191—21no—
30C4⋊C4×C191—21no—
31C4⋊C4×C191—21no—
32C4⋊C4×C191—22no—
33C4⋊C4×C191—22no—
34C4⋊C4×C191—22no—
35C4⋊C4×C191D412yes—
36C22⋊C4×C191—22no—
37C42×C191—22no—
38C2×Dic191—22no—
39C2×Dic191—41no—
40C2×Dic191—41no—
41C2×Dic191—41no—
42C2×Dic191—41no—
43C2×Dic191—41no—
44C191⋊C8—42no—
45C23×C191C2×D411yescharacteristic
46Q8×C191—42no—
47Q8×C191—81no—
48C2×C4×C191—21no—
49C2×C4×C191—21no—
50C2×C4×C191—22no—
51C2×C4×C191—22no—
52C2×C4×C191—21no—
53C2×C4×C191—41no—
54C2×C4×C191—41no—
55C2×C4×C191SD1612yes—
56C2×C4×C191C2×D412yes—
57C22×C191—21no—
58C22×C191—21no—
59C22×C191#12011yescharacteristic
60C22×C191C2×SD1611yescharacteristic
61C22×C191#13711yescharacteristic
62C4×C191—22no—
63C4×C191—22no—
64C4×C191—42no—
65C4×C191—41no—
66C4×C191—42no—
67Dic191—42no—
68Dic191—81no—
69C2×C191—21no—
70C2×C191—21no—
71C2×C191#44811yescharacteristic
72C2×C191#45611yescharacteristic
73C2×C191#45811yescharacteristic
74C191#161111yescharacteristic, complemented, Sylow
75#1611—1911nomaximal, Sylow
76#544D19111yescharacteristic
77#483—1912no—
78#398—1911no—
79#328—1912no—
80#324—1911no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D19112yes—
85#117—21no—
86C2×C4⋊C4—3821no—
87C2×C4⋊C4—1911no—
88C2×C4⋊C4C2×D19111yescharacteristic
89#106—3822no—
90#103—3822no—
91C22⋊C8—1912no—
92#95—3821no—
93#95—1911no—
94C2×Q8—21no—
95C2×Q8C22⋊D19112yes—
96C22×C4—3821no—
97C22×C4—3821no—
98C22×C4C22⋊D19111yescharacteristic
99C22×C4C22⋊D19111yescharacteristic
100C22×C4C22×D19111yescharacteristic
101C2×C8—3822no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—3822no—
109C4⋊C4—7642no—
110C4⋊C4C22⋊D19112yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D19111yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—3822no—
124C2×C4—7641no—
125C2×C4—7641no—
126C2×C4—7641no—
127C2×C4—7641no—
128C2×C4—7641no—
129C2×C4#1569027412yes—
130C2×C4C2×C22⋊D19112yes—
131C8—7642no—
132C22—21no—
133C22—21no—
134C22#2025929111yescharacteristic
135C22C2×#1569027411yescharacteristic
136C22#2025935311yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—15281no—
143C4—7642no—
144C2—21no—
145C2—21no—
146C2#2713280211yescharacteristic
147C2#2713284611yescharacteristic
148C2#2713285311yescharacteristic
subgroupG/H
centerC22#20259291
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#544×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
hypercenter#544D191
hypocenterC191#1611
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
74. C191#1611semidirect

Maximal subgroups

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

subgroupindex
#271329912
#271325932
#271324002
#271323892
#544×C1912
#1611191