Finite Group Databasebeta

← #1354×C191 #37568096

Subgroups — #1354×C191 #37568096

Order 24448.

140 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 40 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#395×C191C211yesmaximal, characteristic
2#343×C191C211yesmaximal, characteristic
3#324×C191C211yesmaximal, characteristic
4C22×Q8×C191C411yescharacteristic
5C2×M16×C191—21no—
6C2×C4⋊C4×C191—21no—
7C2×C4⋊C4×C191C2211yescharacteristic
8C22⋊C8×C191—21no—
9#95×C191—21no—
10#95×C191C411yescharacteristic
11C2×Q8×C191—42no—
12C2×Q8×C191—41no—
13C22×C4×C191—21no—
14C22×C4×C191—21no—
15C22×C4×C191C2×C411yescharacteristic
16C22×C4×C191D411yescharacteristic
17C22×C4×C191D411yescharacteristic
18M16×C191—22no—
19M16×C191—41no—
20C2×C8×C191—41no—
21C2×C8×C191—41no—
22C4⋊C4×C191—41no—
23C4⋊C4×C191—42no—
24C23×C191C22⋊C411yescharacteristic
25Q8×C191—42no—
26Q8×C191—42no—
27C2×C4×C191—21no—
28C2×C4×C191—21no—
29C2×C4×C191—22no—
30C2×C4×C191—22no—
31C2×C4×C191—21no—
32C2×C4×C191—21no—
33C2×C4×C191—41no—
34C2×C4×C191—41no—
35C2×C4×C191—41no—
36C2×C4×C191—41no—
37C2×C4×C191—41no—
38C2×C4×C191—41no—
39C2×C4×C191SD1611yescharacteristic
40C2×C4×C191Q1611yescharacteristic
41C8×C191—42no—
42C8×C191—81no—
43C22×C191—21no—
44C22×C191—21no—
45C22×C191#9911yescharacteristic
46C22×C191#10311yescharacteristic
47C22×C191#10411yescharacteristic
48C4×C191—21no—
49C4×C191—21no—
50C4×C191—42no—
51C4×C191—41no—
52C4×C191—42no—
53C4×C191—41no—
54C2×C191—21no—
55C2×C191—21no—
56C2×C191#32811yescharacteristic
57C2×C191AΣL(1,𝔽16)11yescharacteristic
58C2×C191#35611yescharacteristic
59C191#135411yescharacteristic, direct product factor, Sylow
60#1354C19111yesmaximal, characteristic, direct product factor, Sylow
61#395C2×C19111yescharacteristic
62#343C2×C19111yescharacteristic
63#324C2×C19111yescharacteristic
64C22×Q8C4×C19111yescharacteristic
65C2×M16—21no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C22×C19111yescharacteristic
68C22⋊C8—21no—
69#95—21no—
70#95C4×C19111yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×C4×C19111yescharacteristic
76C22×C4D4×C19111yescharacteristic
77C22×C4D4×C19111yescharacteristic
78M16—22no—
79M16—41no—
80C2×C8—41no—
81C2×C8—41no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊C4×C19111yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4SD16×C19111yescharacteristic
100C2×C4Q16×C19111yescharacteristic
101C8—42no—
102C8—81no—
103C22—21no—
104C22—21no—
105C22#99×C19111yescharacteristic
106C22#103×C19111yescharacteristic
107C22#104×C19111yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#328×C19111yescharacteristic
117C2AΣL(1,𝔽16)×C19111yescharacteristic
118C2#356×C19111yescharacteristic
subgroupG/H
center, socleC22×C191#99
commutatorC22×C4C2×C4×C191
Frattini, cosocleC2×C4⋊C4C22×C191
prime radicalC23×C191C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C191 ◁ C23×C191 ◁ C2×C4⋊C4×C191 ◁ G

Complements

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

NH ≅ G/Ntype
59. C191#1354direct (N × H)
60. #1354C191direct (N × H)

Maximal subgroups

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

subgroupindex
#395×C1912
#343×C1912
#324×C1912
#1354191