Finite Group Databasebeta

← #37571742

Subgroups — #37571742

Order 24448.

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

normal subgroups only

This group has 200 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#27133393C211yesmaximal, characteristic
2#27133013C211yesmaximal, characteristic
3#27132949C211yesmaximal, characteristic
4#27132874C211yesmaximal, characteristic
5#27132393C211yesmaximal, characteristic
6#27132393C211yesmaximal, characteristic
7#333×C191C211yesmaximal, characteristic
8C2×Dic764—21no—
9#20259322C2211yescharacteristic
10#20259321—21no—
11#20259321—21no—
12#20259320—22no—
13C4×Dic382C2211yescharacteristic
14C4×Dic382C2211yescharacteristic
15#20259287—21no—
16#20259287—21no—
17#20259254—21no—
18#20259247—21no—
19#20259247—21no—
20#20259246—22no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25C2×Dic382—22no—
26C2×Dic382—21no—
27C2×Dic382D411yescharacteristic
28C2×Dic382D411yescharacteristic
29Dic764—42no—
30C2×C191⋊C8—21no—
31C4⋊Dic191—21no—
32C4⋊Dic191—21no—
33C4⋊Dic191D411yescharacteristic
34C4⋊Dic191D411yescharacteristic
35Dic191⋊C4—22no—
36Dic191⋊C4—22no—
37Dic191⋊C4—21no—
38Dic191⋊C4—21no—
39C4×Dic191—22no—
40C4×Dic191—21no—
41C4×Dic191—21no—
42C2×Q8×C191D412yes—
43C2×C8×C191—21no—
44C2×C8×C191—21no—
45C4⋊C4×C191—21no—
46C4⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48Dic382—21no—
49Dic382—21no—
50Dic382—41no—
51Dic382—41no—
52Dic382—82no—
53Dic382SD1612yes—
54Dic382Q1612yescomplemented
55C2×Dic191—21no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—41no—
60C191⋊C8—41no—
61Q8×C191—42no—
62C2×C4×C191—22no—
63C2×C4×C191C2×D411yescharacteristic
64C2×C4×C191C2×D411yescharacteristic
65C2×C4×C191C2×D411yescharacteristic
66C8×C191—41no—
67C8×C191—41no—
68C22×C191#12011yescharacteristic
69C4×C191—21no—
70C4×C191—42no—
71C4×C191C2×SD1611yescharacteristic
72C4×C191C2×Q1611yescharacteristic
73C4×C191#13711yescharacteristic
74C4×C191#13711yescharacteristic
75Dic191—22no—
76Dic191—22no—
77Dic191—41no—
78Dic191—41no—
79Dic191—81no—
80C2×C191#44811yescharacteristic
81C2×C191#45111yescharacteristic
82C2×C191#45511yescharacteristic
83C191#164511yescharacteristic, complemented, Sylow
84#1645—1911nomaximal, Sylow
85Q82—1911no—
86#487—1911no—
87#475—1911no—
88#462—1911no—
89#333D19111yescharacteristic
90Q8⋊C8—1911no—
91Q8⋊C8—1911no—
92C2×Q16—3821no—
93C4⋊Q8—3821no—
94C4⋊Q8—3821no—
95C4⋊Q8—3822no—
96C4⋊Q8—1911no—
97C4⋊Q8C2×D19111yescharacteristic
98C4×Q8—3821no—
99C4×Q8—3821no—
100C4×Q8—1911no—
101C4×Q8—1911no—
102#106—3821no—
103C4⋊C8C2×D19111yescharacteristic
104C4⋊C8C2×D19111yescharacteristic
105#103—3821no—
106#103—3822no—
107#103—3821no—
108C4×C8—1911no—
109C2×Q8—3822no—
110C2×Q8—3821no—
111C2×Q8—1911no—
112C2×Q8—1911no—
113C2×Q8D76412yes—
114Q16—7642no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—3821no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—3822no—
121C4⋊C4—3822no—
122C4⋊C4—3821no—
123C4⋊C4—3821no—
124C4⋊C4—3821no—
125C4⋊C4—3821no—
126C4⋊C4—1911no—
127C4⋊C4—1911no—
128C42—3822no—
129C42—3821no—
130C42—3821no—
131C42C22×D19111yescharacteristic
132Q8—42no—
133Q8—3821no—
134Q8—3821no—
135Q8—1912no—
136Q8—1912no—
137Q8—15282no—
138Q8—7641no—
139Q8—7641no—
140C2×C4—22no—
141C2×C4—3821no—
142C2×C4—3821no—
143C2×C4—3821no—
144C2×C4—3821no—
145C2×C4—7641no—
146C2×C4D4×D19111yescharacteristic
147C2×C4D4×D19111yescharacteristic
148C2×C4C2×D76411yescharacteristic
149C8—41no—
150C8—41no—
151C8—7641no—
152C22#2025929211yescharacteristic
153C4—21no—
154C4—42no—
155C4—3822no—
156C4—3822no—
157C4—15281no—
158C4—7641no—
159C4—7641no—
160C4SD16×D19111yescharacteristic
161C4Q16×D19111yescharacteristic
162C4#2025935111yescharacteristic
163C4#2025935411yescharacteristic
164C2#2713280311yescharacteristic
165C2#2713282011yescharacteristic
166C2#2713284311yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#333×C191C2
socle, prime radicalC22×C191#120
hypercenter#333D191
hypocenterC191#1645
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
54. Dic382Q16semidirect
83. C191#1645semidirect

Maximal subgroups

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

subgroupindex
#271333932
#271330132
#271329492
#271328742
#271323932
#333×C1912
#1645191