Finite Group Databasebeta

← #1656×C191 #37568398

Subgroups — #1656×C191 #37568398

Order 24448.

230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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#562×C191C211yesmaximal, characteristic, complemented
2#496×C191C212yesmaximal, complemented
3#490×C191C211yesmaximal, characteristic, complemented
4#330×C191C211yesmaximal, characteristic, complemented
5#329×C191C212yesmaximal, complemented
6C2×SD16×C191—22no—
7C2×D8×C191—22no—
8#127×C191C2211yescharacteristic
9#125×C191C2211yescharacteristic
10#124×C191C2212yes—
11#123×C191—22no—
12C22⋊Q8×C191—22no—
13#121×C191—22no—
14#102×C191—22no—
15#97×C191C2211yescharacteristic
16#97×C191C2212yes—
17C2×Q8×C191D412yes—
18C2×D4×C191—22no—
19C2×D4×C191—21no—
20C2×D4×C191—22no—
21C2×D4×C191D412yes—
22C22×C4×C191—22no—
23SD16×C191—44no—
24D8×C191—44no—
25C2×C8×C191—22no—
26C2×C8×C191—21no—
27C4⋊C4×C191—22no—
28C4⋊C4×C191—22no—
29C4⋊C4×C191D412yes—
30C22⋊C4×C191—22no—
31C22⋊C4×C191—22no—
32C22⋊C4×C191—22no—
33C42×C191C2311yescharacteristic
34C23×C191—22no—
35C23×C191—41no—
36Q8×C191—42no—
37D4×C191—42no—
38D4×C191—42no—
39D4×C191—42no—
40D4×C191—42no—
41D4×C191—82no—
42C2×C4×C191—22no—
43C2×C4×C191—22no—
44C2×C4×C191—82no—
45C2×C4×C191C2×D411yescharacteristic
46C2×C4×C191C2×D412yes—
47C8×C191—24no—
48C8×C191—41no—
49C22×C191—42no—
50C22×C191—42no—
51C22×C191—42no—
52C22×C191—82no—
53C22×C191—81no—
54C22×C191#12011yescharacteristic
55C4×C191—22no—
56C4×C191—21no—
57C4×C191—42no—
58C4×C191—42no—
59C2×C191—82no—
60C2×C191—161no—
61C2×C191#45312yes—
62C2×C191#45411yescharacteristic
63C191#165611yescharacteristic, direct product factor, Sylow
64#1656C19111yesmaximal, characteristic, direct product factor, Sylow
65#562C2×C19111yescharacteristic, complemented
66#496C2×C19112yescomplemented
67#490C2×C19111yescharacteristic, complemented
68#330C2×C19111yescharacteristic, complemented
69#329C2×C19112yescomplemented
70C2×SD16—22no—
71C2×D8—22no—
72#127C22×C19111yescharacteristic
73#125C22×C19111yescharacteristic
74#124C22×C19112yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—22no—
79#97C22×C19111yescharacteristic
80#97C22×C19112yes—
81C2×Q8D4×C19112yes—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—22no—
85C2×D4D4×C19112yes—
86C22×C4—22no—
87SD16—44no—
88D8—44no—
89C2×C8—22no—
90C2×C8—21no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4D4×C19112yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C23×C19111yescharacteristic
98C23—22no—
99C23—41no—
100Q8—42no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×D4×C19111yescharacteristic
110C2×C4C2×D4×C19112yes—
111C8—24no—
112C8—41no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—82no—
117C22—81no—
118C22#120×C19111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—161no—
125C2#453×C19112yes—
126C2#454×C19111yescharacteristic
subgroupG/H
center, socleC22×C191#120
commutator, Frattini, cosocleC42C23×C191
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C191 ◁ C42×C191 ◁ G

Complements

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

NH ≅ G/Ntype
1. #562×C191C2semidirect
2. #496×C191C2semidirect
3. #490×C191C2semidirect
4. #330×C191C2semidirect
5. #329×C191C2semidirect
63. C191#1656direct (N × H)
64. #1656C191direct (N × H)
65. #562C2×C191semidirect
66. #496C2×C191semidirect
67. #490C2×C191semidirect
68. #330C2×C191semidirect
69. #329C2×C191semidirect

Maximal subgroups

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

subgroupindex
#562×C1912
#496×C1912
#490×C1912
#330×C1912
#329×C1912
#1656191