Finite Group Databasebeta

← #37571832

Subgroups — #37571832

Order 24448.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#27133413C211yesmaximal, characteristic
2#27133072C212yesmaximal, complemented
3#27133058C211yesmaximal, characteristic
4#27132404C212yesmaximal, complemented
5#329×C191C211yesmaximal, characteristic
6C2×#15690277—21no—
7C2×#15690275—21no—
8#20259322C2211yescharacteristic
9#20259320—21no—
10#20259315—22no—
11#20259314C2212yes—
12#20259303—21no—
13#20259299—22no—
14#20259256—22no—
15#20259254—22no—
16#20259233C2211yescharacteristic
17#124×C191C2211yescharacteristic
18#97×C191C2212yes—
19C2×Dic382—21no—
20C2×Dic382—21no—
21C22×Dic191—21no—
22#15690277—42no—
23#15690275—42no—
24C2×C191⋊C8—21no—
25C4⋊Dic191—22no—
26C4⋊Dic191D412yes—
27C4⋊Dic191D412yes—
28Dic191⋊C4—22no—
29Dic191⋊C4—22no—
30Dic191⋊C4—22no—
31C22⋊Dic191—22no—
32C22⋊Dic191—21no—
33C4×Dic191—21no—
34C2×Q8×C191D411yescharacteristic
35C2×D4×C191D411yescharacteristic
36C2×C8×C191—22no—
37C22⋊C4×C191—22no—
38C42×C191C2311yescharacteristic
39Dic382—41no—
40Dic382—41no—
41Dic382—81no—
42C2×Dic191—22no—
43C2×Dic191—22no—
44C2×Dic191—41no—
45C2×Dic191—81no—
46C191⋊C8—22no—
47C23×C191—21no—
48Q8×C191—41no—
49D4×C191—41no—
50C2×C4×C191—21no—
51C2×C4×C191C2×D412yes—
52C2×C4×C191C2×D411yescharacteristic
53C8×C191—24no—
54C22×C191—41no—
55C22×C191—42no—
56C22×C191#12011yescharacteristic
57C4×C191—21no—
58C4×C191—22no—
59C4×C191—41no—
60Dic191—42no—
61Dic191—42no—
62Dic191—81no—
63C2×C191—81no—
64C2×C191#45311yescharacteristic
65C2×C191#45612yes—
66C191#166011yescharacteristic, complemented, Sylow
67#1660—1911nomaximal, Sylow
68#563—1911no—
69#501—1912no—
70#497—1911no—
71#330—1912no—
72#329D19111yescharacteristic
73C2×Q16—3821no—
74C2×SD16—3821no—
75C4⋊Q8—3821no—
76C4⋊Q8—1911no—
77#126—3822no—
78#125—1912no—
79#124C2×D19111yescharacteristic
80#123—3821no—
81C22⋊Q8—3822no—
82#107—3822no—
83#106—3822no—
84#97—1911no—
85#97C2×D19112yes—
86C2×Q8—3821no—
87C2×Q8—3821no—
88C2×Q8D76411yescharacteristic
89C2×D4D76411yescharacteristic
90C22×C4—3821no—
91Q16—7642no—
92SD16—7642no—
93C2×C8—22no—
94C2×C8—3821no—
95C4⋊C4—3822no—
96C4⋊C4—3822no—
97C4⋊C4—3822no—
98C4⋊C4—3822no—
99C4⋊C4—1912no—
100C4⋊C4—1912no—
101C22⋊C4—22no—
102C22⋊C4—3822no—
103C22⋊C4—3821no—
104C42—3821no—
105C42C22×D19111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—15281no—
109Q8—7641no—
110Q8—7641no—
111D4—41no—
112C2×C4—21no—
113C2×C4—3822no—
114C2×C4—3822no—
115C2×C4—15281no—
116C2×C4—7641no—
117C2×C4D4×D19112yes—
118C2×C4C2×D76411yescharacteristic
119C8—24no—
120C8—3822no—
121C22—41no—
122C22—42no—
123C22#2025929211yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—15281no—
128C4—7642no—
129C4—7642no—
130C2—81no—
131C2#2713283311yescharacteristic
132C2#2713284712yes—
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#329×C191C2
socleC22×C191#120
prime radicalC2×D4×C191D4
hypercenter#329D191
hypocenterC191#1660
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #27133072C2semidirect
4. #27132404C2semidirect
66. C191#1660semidirect

Maximal subgroups

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

subgroupindex
#271334132
#271330722
#271330582
#271324042
#329×C1912
#1660191