Finite Group Databasebeta

← #37571628

Subgroups — #37571628

Order 24448.

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

normal subgroups only

This group has 216 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#27133383C211yesmaximal, characteristic, complemented
2#27133009C211yesmaximal, characteristic, complemented
3#27132860C211yesmaximal, characteristic, complemented
4#27132410C211yesmaximal, characteristic, complemented
5#27132393C211yesmaximal, characteristic, complemented
6D4⋊(C191⋊C8)C211yesmaximal, characteristic, complemented
7#459×C191C211yesmaximal, characteristic
8C2×#15690275—21no—
9#20259322C2211yescharacteristic
10#20259315—22no—
11#20259309—21no—
12#20259301—21no—
13C4×Dic382C2211yescharacteristic
14#20259287—21no—
15#20259281—21no—
16C4⋊(C191⋊C8)C2211yescharacteristic
17#20259243—22no—
18#20259243—21no—
19C4×C191⋊C8C2211yescharacteristic
20C2×D8×C191—21no—
21#127×C191C2211yescharacteristic
22C4×D4×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24#102×C191—21no—
25C2×Dic382—21no—
26C2×Dic382D411yescharacteristic
27#15690275—42no—
28C2×C191⋊C8—21no—
29C2×C191⋊C8—21no—
30C4⋊Dic191—21no—
31C4⋊Dic191D411yescharacteristic
32C4⋊Dic191D412yes—
33Dic191⋊C4—22no—
34Dic191⋊C4—21no—
35C22⋊Dic191—22no—
36C22⋊Dic191—22no—
37C4×Dic191—22no—
38C4×Dic191—21no—
39C2×D4×C191—21no—
40C2×D4×C191—21no—
41C2×D4×C191—21no—
42C2×D4×C191D411yescharacteristic
43C22×C4×C191—21no—
44D8×C191—42no—
45C2×C8×C191—21no—
46C4⋊C4×C191D411yescharacteristic
47C22⋊C4×C191—21no—
48C42×C191C2311yescharacteristic
49Dic382—21no—
50Dic382—21no—
51Dic382—41no—
52Dic382—41no—
53C2×Dic191—21no—
54C2×Dic191—21no—
55C2×Dic191—22no—
56C191⋊C8—41no—
57C191⋊C8—41no—
58C23×C191—21no—
59C23×C191—41no—
60D4×C191—21no—
61D4×C191—21no—
62D4×C191—42no—
63D4×C191—41no—
64D4×C191—41no—
65D4×C191—41no—
66D4×C191—41no—
67C2×C4×C191—21no—
68C2×C4×C191—41no—
69C2×C4×C191—41no—
70C2×C4×C191C2×D411yescharacteristic
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191C2×D411yescharacteristic
73C8×C191—41no—
74C22×C191—41no—
75C22×C191—41no—
76C22×C191—41no—
77C22×C191—81no—
78C22×C191—81no—
79C22×C191—81no—
80C22×C191#12011yescharacteristic
81C4×C191—21no—
82C4×C191—41no—
83C4×C191#13511yescharacteristic
84C4×C191#13511yescharacteristic
85C4×C191AGL(1,ℤ/8)11yescharacteristic
86C4×C191AGL(1,ℤ/8)11yescharacteristic
87Dic191—41no—
88Dic191—42no—
89Dic191—41no—
90C2×C191—81no—
91C2×C191—161no—
92C2×C191#44911yescharacteristic
93C2×C191#44911yescharacteristic
94C2×C191#45411yescharacteristic
95C191#162811yescharacteristic, complemented, Sylow
96#1628—1911nomaximal, Sylow
97#556—1911no—
98#486—1911no—
99#460—1911no—
100#459D19111yescharacteristic
101#332—1911no—
102Q8⋊C8—1911no—
103D4⋊C8—1911no—
104C2×SD16—3821no—
105C2×D8—21no—
106C4⋊Q8—1911no—
107#127C2×D19111yescharacteristic
108#126—3822no—
109#124—3821no—
110C22⋊Q8—3821no—
111C4×Q8—3821no—
112C4×Q8—1911no—
113C4×D4C2×D19111yescharacteristic
114#117—3821no—
115C4⋊C8—1911no—
116C4⋊C8C2×D19111yescharacteristic
117#102—21no—
118#102—3821no—
119#102—3822no—
120C4×C8—1911no—
121C2×Q8—3821no—
122C2×Q8—1911no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D19111yescharacteristic
127C22×C4—21no—
128SD16—7642no—
129D8—42no—
130C2×C8—21no—
131C2×C8—3821no—
132C2×C8—3821no—
133C4⋊C4—3822no—
134C4⋊C4—3821no—
135C4⋊C4—3821no—
136C4⋊C4—1911no—
137C4⋊C4—1912no—
138C4⋊C4C22⋊D19111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3822no—
141C22⋊C4—3822no—
142C42—3822no—
143C42—3821no—
144C42C22×D19111yescharacteristic
145C23—21no—
146C23—41no—
147Q8—3821no—
148Q8—3821no—
149Q8—7641no—
150Q8—7641no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—3821no—
162C2×C4—3821no—
163C2×C4—3822no—
164C2×C4D4×D19111yescharacteristic
165C2×C4D4×D19111yescharacteristic
166C2×C4C2×C22⋊D19111yescharacteristic
167C8—41no—
168C8—7641no—
169C8—7641no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#2025929011yescharacteristic
177C4—21no—
178C4—41no—
179C4—7641no—
180C4—7642no—
181C4—7641no—
182C4#2025934111yescharacteristic
183C4#2025934211yescharacteristic
184C4#2025934611yescharacteristic
185C4#2025934811yescharacteristic
186C2—81no—
187C2—161no—
188C2#2713280511yescharacteristic
189C2#2713280611yescharacteristic
190C2#2713283411yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting, prime radical#459×C191C2
socleC22×C191#120
hypercenter#459D191
hypocenterC191#1628
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #27133383C2semidirect
2. #27133009C2semidirect
3. #27132860C2semidirect
4. #27132410C2semidirect
5. #27132393C2semidirect
6. D4⋊(C191⋊C8)C2semidirect
95. C191#1628semidirect

Maximal subgroups

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

subgroupindex
#271333832
#271330092
#271328602
#271324102
#271323932
D4⋊(C191⋊C8)2
#459×C1912
#1628191