Finite Group Databasebeta

← #37571737

Subgroups — #37571737

Order 24448.

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

normal subgroups only

This group has 208 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#27133370C211yesmaximal, characteristic
2#27133014C211yesmaximal, characteristic, complemented
3#27132943C211yesmaximal, characteristic
4#27132874C211yesmaximal, characteristic, complemented
5#27132411C211yesmaximal, characteristic, complemented
6#27132395C211yesmaximal, characteristic, complemented
7D4⋊C8×C191C211yesmaximal, characteristic
8C2×Dic764—21no—
9#20259322C2211yescharacteristic
10#20259322C2211yescharacteristic
11#20259313—21no—
12#20259301—21no—
13#20259299—22no—
14C4×Dic382C2211yescharacteristic
15D4×Dic191—21no—
16C2×C4⋊Dic191—21no—
17#20259255—21no—
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259247—22no—
20#20259247—21no—
21#20259243—21no—
22C4×D4×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4×C8×C191C2211yescharacteristic
25C2×Dic382—21no—
26C2×Dic382D411yescharacteristic
27C2×Dic382D412yes—
28C22×Dic191—22no—
29Dic764—42no—
30C2×C191⋊C8—21no—
31C4⋊Dic191—22no—
32C4⋊Dic191—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37Dic191⋊C4—22no—
38Dic191⋊C4—21no—
39C22⋊Dic191—22no—
40C4×Dic191—21no—
41C2×D4×C191D411yescharacteristic
42C22×C4×C191—21no—
43C2×C8×C191—21no—
44C2×C8×C191—21no—
45C4⋊C4×C191D411yescharacteristic
46C22⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48Dic382—21no—
49Dic382—21no—
50Dic382—42no—
51Dic382—41no—
52Dic382—41no—
53C2×Dic191—21no—
54C2×Dic191—21no—
55C2×Dic191—22no—
56C2×Dic191—41no—
57C2×Dic191—82no—
58C191⋊C8—41no—
59C23×C191—21no—
60D4×C191—21no—
61D4×C191Q1612yescomplemented
62C2×C4×C191—21no—
63C2×C4×C191—41no—
64C2×C4×C191—41no—
65C2×C4×C191C2×D411yescharacteristic
66C2×C4×C191C2×D411yescharacteristic
67C2×C4×C191C2×D411yescharacteristic
68C8×C191—41no—
69C8×C191—41no—
70C22×C191—22no—
71C22×C191—41no—
72C22×C191—41no—
73C22×C191#12011yescharacteristic
74C4×C191—21no—
75C4×C191—41no—
76C4×C191C2×Q1611yescharacteristic
77C4×C191#13511yescharacteristic
78C4×C191AGL(1,ℤ/8)11yescharacteristic
79C4×C191#13711yescharacteristic
80Dic191—41no—
81Dic191—41no—
82Dic191—42no—
83Dic191—81no—
84C2×C191—42no—
85C2×C191#44911yescharacteristic
86C2×C191#45111yescharacteristic
87C2×C191#45511yescharacteristic
88C191#164411yescharacteristic, complemented, Sylow
89#1644—1911nomaximal, Sylow
90#554—1911no—
91#487—1911no—
92#474—1911no—
93#462—1911no—
94#333—1911no—
95Q8⋊C8—1911no—
96D4⋊C8D19111yescharacteristic
97C2×Q16—3821no—
98C4⋊Q8—1911no—
99C4⋊Q8—1911no—
100#125—3821no—
101C22⋊Q8—3822no—
102C22⋊Q8—3821no—
103C4×Q8—1911no—
104C4×D4—3821no—
105C4×D4C2×D19111yescharacteristic
106C2×C4⋊C4—3821no—
107#107—3821no—
108C4⋊C8—1911no—
109C4⋊C8C2×D19111yescharacteristic
110#103—3822no—
111#103—3821no—
112#102—3821no—
113C4×C8C2×D19111yescharacteristic
114C2×Q8—3821no—
115C2×Q8—1911no—
116C2×Q8—1912no—
117C2×D4D76411yescharacteristic
118C22×C4—21no—
119C22×C4—3822no—
120Q16—7642no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—3821no—
124C4⋊C4—3822no—
125C4⋊C4—3822no—
126C4⋊C4—3821no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—3821no—
131C4⋊C4—1911no—
132C4⋊C4D76411yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—3822no—
135C42—3821no—
136C42C22×D19111yescharacteristic
137C23—21no—
138Q8—3821no—
139Q8—3821no—
140Q8—7642no—
141Q8—7641no—
142Q8—7641no—
143D4—21no—
144D4Dic76412yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3821no—
149C2×C4—3821no—
150C2×C4—3822no—
151C2×C4—15282no—
152C2×C4—7641no—
153C2×C4D4×D19111yescharacteristic
154C2×C4D4×D19111yescharacteristic
155C2×C4C2×D76411yescharacteristic
156C8—41no—
157C8—41no—
158C8—7641no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#2025929211yescharacteristic
163C4—21no—
164C4—41no—
165C4—15281no—
166C4—7641no—
167C4—7641no—
168C4—7642no—
169C4C2×Dic76411yescharacteristic
170C4#2025934311yescharacteristic
171C4#2025934611yescharacteristic
172C4#2025935511yescharacteristic
173C2—42no—
174C2#2713280911yescharacteristic
175C2#2713282111yescharacteristic
176C2#2713284211yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
FittingD4⋊C8×C191C2
socleC22×C191#120
prime radicalC2×D4×C191D4
hypercenterD4⋊C8D191
hypocenterC191#1644
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #27133014C2semidirect
4. #27132874C2semidirect
5. #27132411C2semidirect
6. #27132395C2semidirect
61. D4×C191Q16semidirect
88. C191#1644semidirect
144. D4Dic764semidirect

Maximal subgroups

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

subgroupindex
#271333702
#271330142
#271329432
#271328742
#271324112
#271323952
D4⋊C8×C1912
#1644191