Finite Group Databasebeta

← #37571693

Subgroups — #37571693

Order 24448.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#27133387C211yesmaximal, characteristic
2#27133015C211yesmaximal, characteristic, complemented
3#27132959C211yesmaximal, characteristic, complemented
4#27132954C211yesmaximal, characteristic
5#27132393C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic
7#332×C191C211yesmaximal, characteristic, complemented
8#20259322C2211yescharacteristic
9#20259317—22no—
10#20259311—21no—
11#20259302—21no—
12Q8×Dic191—21no—
13C4×Dic382C2211yescharacteristic
14C4×D764C2211yescharacteristic
15#20259280—21no—
16#20259256—21no—
17#20259254—21no—
18#20259247—21no—
19#20259245—22no—
20#20259244—21no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25C2×Dic382—21no—
26C2×Dic382D411yescharacteristic
27C2×D764D411yescharacteristic
28C2×C4×D191—21no—
29C2×C191⋊C8—21no—
30C4⋊Dic191—22no—
31C4⋊Dic191—21no—
32C4⋊Dic191—21no—
33C4⋊Dic191D411yescharacteristic
34C4⋊Dic191D411yescharacteristic
35Dic191⋊C4—21no—
36(C2×D191)⋊C4—22no—
37(C2×D191)⋊C4—22no—
38(C2×D191)⋊C4—21no—
39C4×Dic191—22no—
40C4×Dic191—21no—
41C2×Q8×C191—21no—
42C2×C8×C191—21no—
43C2×C8×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191D412yes—
46C42×C191C2311yescharacteristic
47C22×D191—21no—
48Dic382—21no—
49Dic382—21no—
50Dic382—42no—
51D764—21no—
52D764—21no—
53C2×Dic191—21no—
54C2×Dic191—21no—
55C2×Dic191—21no—
56C2×Dic191—41no—
57C4×D191—41no—
58C4×D191—41no—
59C191⋊C8—41no—
60Q8×C191—41no—
61Q8×C191—41no—
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
69C2×D191—41no—
70C2×D191—41no—
71C2×D191—41no—
72C4×C191—21no—
73C4×C191—42no—
74C4×C191#13511yescharacteristic
75C4×C191#13511yescharacteristic
76C4×C191#13711yescharacteristic
77C4×C191#13711yescharacteristic
78Dic191—41no—
79Dic191—41no—
80Dic191—41no—
81Dic191—81no—
82C2×C191#45211yescharacteristic
83C2×C191#45211yescharacteristic
84C2×C191#45411yescharacteristic
85D191—81no—
86C191#163811yescharacteristic, complemented, Sylow
87#1638—1911nomaximal, Sylow
88#556—1911no—
89#487—1911no—
90#477—1911no—
91#476—1911no—
92#332D19111yescharacteristic, complemented
93Q8⋊C8—1911no—
94D4⋊C8—1911no—
95C4⋊Q8—1911no—
96C4⋊Q8C2×D19111yescharacteristic
97#126—3822no—
98#124—3821no—
99C22⋊Q8—3821no—
100C4×Q8—3821no—
101C4×Q8—1911no—
102C4×D4—1911no—
103#117—3821no—
104#107—3821no—
105#106—3821no—
106C4⋊C8C2×D19111yescharacteristic
107C4⋊C8C2×D19111yescharacteristic
108#103—3821no—
109#103—3822no—
110#102—3821no—
111C4×C8—1911no—
112C2×Q8—21no—
113C2×Q8—3821no—
114C2×Q8—1911no—
115C2×D4—1911no—
116C22×C4—3821no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—3821no—
120C4⋊C4—21no—
121C4⋊C4—3822no—
122C4⋊C4—3821no—
123C4⋊C4—3821no—
124C4⋊C4—3821no—
125C4⋊C4—1911no—
126C4⋊C4—1911no—
127C4⋊C4D76412yes—
128C22⋊C4—3822no—
129C22⋊C4—3822no—
130C22⋊C4—3821no—
131C42—3822no—
132C42—3821no—
133C42C22×D19111yescharacteristic
134C23—3821no—
135Q8—41no—
136Q8—41no—
137Q8—3821no—
138Q8—3821no—
139Q8—7642no—
140D4—3821no—
141D4—3821no—
142C2×C4—22no—
143C2×C4—3821no—
144C2×C4—3821no—
145C2×C4—3821no—
146C2×C4—7641no—
147C2×C4—7641no—
148C2×C4—7641no—
149C2×C4D4×D19111yescharacteristic
150C2×C4D4×D19111yescharacteristic
151C2×C4C2×D76411yescharacteristic
152C8—41no—
153C8—41no—
154C8—7641no—
155C22—7641no—
156C22—7641no—
157C22—7641no—
158C22#2025929211yescharacteristic
159C4—21no—
160C4—42no—
161C4—15281no—
162C4—7641no—
163C4—7641no—
164C4—7641no—
165C4#2025934111yescharacteristic
166C4#2025934311yescharacteristic
167C4#2025935111yescharacteristic
168C4#2025935411yescharacteristic
169C2—15281no—
170C2#2713282611yescharacteristic
171C2#2713282811yescharacteristic
172C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#332×C191C2
socleC22×C191#120
prime radicalC2×D764D4
hypercenter#332D191
hypocenterC191#1638
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #27133015C2semidirect
3. #27132959C2semidirect
5. #27132393C2semidirect
7. #332×C191C2semidirect
86. C191#1638semidirect
92. #332D191semidirect

Maximal subgroups

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

subgroupindex
#271333872
#271330152
#271329592
#271329542
#271323932
#271323902
#332×C1912
#1638191