Finite Group Databasebeta

← #1617×C191 #37568359

Subgroups — #1617×C191 #37568359

Order 24448.

202 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 68 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#544×C191C211yesmaximal, characteristic
2#484×C191C212yesmaximal
3#400×C191C211yesmaximal, characteristic
4#328×C191C212yesmaximal
5#324×C191C211yesmaximal, characteristic
6C4⋊Q8×C191—22no—
7#125×C191—22no—
8C22⋊Q8×C191—21no—
9C22⋊Q8×C191C2212yes—
10#117×C191—21no—
11C2×C4⋊C4×C191C2211yescharacteristic
12C2×C4⋊C4×C191C2211yescharacteristic
13#107×C191—22no—
14#103×C191—22no—
15C22⋊C8×C191C2212yes—
16#95×C191—21no—
17#95×C191—21no—
18#95×C191C2211yescharacteristic
19C2×Q8×C191—21no—
20C2×Q8×C191D412yes—
21C22×C4×C191—21no—
22C22×C4×C191—21no—
23C22×C4×C191D411yescharacteristic
24C22×C4×C191D411yescharacteristic
25C22×C4×C191C2311yescharacteristic
26C2×C8×C191—22no—
27C4⋊C4×C191—21no—
28C4⋊C4×C191—21no—
29C4⋊C4×C191—21no—
30C4⋊C4×C191—22no—
31C4⋊C4×C191—22no—
32C4⋊C4×C191—22no—
33C4⋊C4×C191—22no—
34C4⋊C4×C191D412yes—
35C22⋊C4×C191—22no—
36C42×C191—22no—
37C23×C191C2×D411yescharacteristic
38Q8×C191—42no—
39Q8×C191—81no—
40C2×C4×C191—21no—
41C2×C4×C191—21no—
42C2×C4×C191—22no—
43C2×C4×C191—22no—
44C2×C4×C191—21no—
45C2×C4×C191—41no—
46C2×C4×C191—41no—
47C2×C4×C191—41no—
48C2×C4×C191—41no—
49C2×C4×C191—42no—
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—42no—
63C4×C191—41no—
64C4×C191—42no—
65C4×C191—81no—
66C4×C191—81no—
67C2×C191—21no—
68C2×C191—21no—
69C2×C191#45111yescharacteristic
70C2×C191#45411yescharacteristic
71C2×C191#45811yescharacteristic
72C191#161711yescharacteristic, direct product factor, Sylow
73#1617C19111yesmaximal, characteristic, direct product factor, Sylow
74#544C2×C19111yescharacteristic
75#484C2×C19112yes—
76#400C2×C19111yescharacteristic
77#328C2×C19112yes—
78#324C2×C19111yescharacteristic
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C22×C19112yes—
83#117—21no—
84C2×C4⋊C4C22×C19111yescharacteristic
85C2×C4⋊C4C22×C19111yescharacteristic
86#107—22no—
87#103—22no—
88C22⋊C8C22×C19112yes—
89#95—21no—
90#95—21no—
91#95C22×C19111yescharacteristic
92C2×Q8—21no—
93C2×Q8D4×C19112yes—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4D4×C19111yescharacteristic
97C22×C4D4×C19111yescharacteristic
98C22×C4C23×C19111yescharacteristic
99C2×C8—22no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4D4×C19112yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×D4×C19111yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4Q16×C19112yes—
126C2×C4C2×D4×C19112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#120×C19111yescharacteristic
131C22C2×Q16×C19111yescharacteristic
132C22#137×C19111yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—81no—
139C4—81no—
140C2—21no—
141C2—21no—
142C2#451×C19111yescharacteristic
143C2#454×C19111yescharacteristic
144C2#458×C19111yescharacteristic
subgroupG/H
center, socleC22×C191#120
commutator, Frattini, cosocleC22×C4C23×C191
prime radicalC23×C191C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C191 ◁ C22×C4×C191 ◁ G

Complements

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

NH ≅ G/Ntype
72. C191#1617direct (N × H)
73. #1617C191direct (N × H)

Maximal subgroups

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

subgroupindex
#544×C1912
#484×C1912
#400×C1912
#328×C1912
#324×C1912
#1617191