Finite Group Databasebeta

← #37571652

Subgroups — #37571652

Order 24448.

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

normal subgroups only

This group has 214 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#27133042C211yesmaximal, characteristic, complemented
3#27132955C211yesmaximal, characteristic, complemented
4#27132411C211yesmaximal, characteristic, complemented
5#27132393C211yesmaximal, characteristic, complemented
6D4⋊(C191⋊C8)C211yesmaximal, characteristic
7#476×C191C211yesmaximal, characteristic
8C2×#15690277—22no—
9#20259322C2211yescharacteristic
10#20259313—21no—
11#20259301—21no—
12#20259299—22no—
13C4×Dic382C2211yescharacteristic
14D4×Dic191—21no—
15C2×C4⋊Dic191—21no—
16#20259255—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18#20259245—21no—
19C4×C191⋊C8C2211yescharacteristic
20C4⋊Q8×C191C2211yescharacteristic
21C4×D4×C191C2211yescharacteristic
22#106×C191—21no—
23C4⋊C8×C191C2211yescharacteristic
24#102×C191—21no—
25C2×Dic382D411yescharacteristic
26C2×Dic382D412yes—
27C22×Dic191—22no—
28#15690277—44no—
29C2×C191⋊C8—21no—
30C2×C191⋊C8—21no—
31C4⋊Dic191—22no—
32C4⋊Dic191—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191D411yescharacteristic
35Dic191⋊C4—22no—
36Dic191⋊C4—21no—
37C22⋊Dic191—22no—
38C4×Dic191—21no—
39C2×Q8×C191—21no—
40C2×D4×C191D411yescharacteristic
41C22×C4×C191—21no—
42C2×C8×C191—21no—
43C4⋊C4×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191D411yescharacteristic
46C22⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48Dic382—21no—
49Dic382—21no—
50Dic382—42no—
51C2×Dic191—21no—
52C2×Dic191—21no—
53C2×Dic191—22no—
54C2×Dic191—82no—
55C191⋊C8—22no—
56C191⋊C8—41no—
57C23×C191—21no—
58Q8×C191—42no—
59D4×C191—21no—
60D4×C191Q1612yescomplemented
61C2×C4×C191—21no—
62C2×C4×C191—41no—
63C2×C4×C191—41no—
64C2×C4×C191—41no—
65C2×C4×C191C2×D411yescharacteristic
66C2×C4×C191C2×D411yescharacteristic
67C2×C4×C191C2×D411yescharacteristic
68C8×C191—41no—
69C22×C191—22no—
70C22×C191—41no—
71C22×C191—41no—
72C22×C191#12011yescharacteristic
73C4×C191—21no—
74C4×C191—41no—
75C4×C191—81no—
76C4×C191C2×Q1611yescharacteristic
77C4×C191#13511yescharacteristic
78C4×C191#13711yescharacteristic
79C4×C191#13711yescharacteristic
80Dic191—41no—
81Dic191—41no—
82Dic191—42no—
83C2×C191—42no—
84C2×C191#45111yescharacteristic
85C2×C191#45211yescharacteristic
86C2×C191#45311yescharacteristic
87C191#163211yescharacteristic, complemented, Sylow
88#1632—1911nomaximal, Sylow
89#554—1911no—
90#494—1911no—
91#477—1911no—
92#476D19111yescharacteristic
93#333—1911no—
94Q8⋊C8—1911no—
95D4⋊C8—1911no—
96C2×Q16—3822no—
97C4⋊Q8—1911no—
98C4⋊Q8C2×D19111yescharacteristic
99#125—3821no—
100C22⋊Q8—3822no—
101C22⋊Q8—3821no—
102C4×Q8—1911no—
103C4×D4—3821no—
104C4×D4C2×D19111yescharacteristic
105C2×C4⋊C4—3821no—
106#107—3821no—
107#106—21no—
108C4⋊C8—1911no—
109C4⋊C8C2×D19111yescharacteristic
110#103—3821no—
111#102—21no—
112C4×C8—1911no—
113C2×Q8—21no—
114C2×Q8—1911no—
115C2×Q8—1912no—
116C2×D4C22⋊D19111yescharacteristic
117C22×C4—21no—
118C22×C4—3822no—
119Q16—7644no—
120C2×C8—21no—
121C2×C8—3821no—
122C2×C8—3821no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—3822no—
126C4⋊C4—3822no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—1911no—
131C4⋊C4C22⋊D19111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—3822no—
134C42—3821no—
135C42C22×D19111yescharacteristic
136C23—21no—
137Q8—42no—
138Q8—3821no—
139Q8—3821no—
140Q8—7642no—
141D4—21no—
142D4#1569027712yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—3821no—
148C2×C4—3821no—
149C2×C4—3822no—
150C2×C4—15282no—
151C2×C4D4×D19111yescharacteristic
152C2×C4D4×D19111yescharacteristic
153C2×C4C2×C22⋊D19111yescharacteristic
154C8—41no—
155C8—3822no—
156C8—7641no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2025929011yescharacteristic
161C4—21no—
162C4—41no—
163C4—81no—
164C4—7641no—
165C4—7641no—
166C4—7642no—
167C4C2×#1569027711yescharacteristic
168C4#2025934311yescharacteristic
169C4#2025935111yescharacteristic
170C4#2025935211yescharacteristic
171C2—42no—
172C2#2713281811yescharacteristic
173C2#2713282211yescharacteristic
174C2#2713282911yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#476×C191C2
socleC22×C191#120
prime radicalC2×D4×C191D4
hypercenter#476D191
hypocenterC191#1632
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #27133042C2semidirect
3. #27132955C2semidirect
4. #27132411C2semidirect
5. #27132393C2semidirect
60. D4×C191Q16semidirect
87. C191#1632semidirect
142. D4#15690277semidirect

Maximal subgroups

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

subgroupindex
#271333702
#271330422
#271329552
#271324112
#271323932
D4⋊(C191⋊C8)2
#476×C1912
#1632191