Finite Group Databasebeta

← #37572961

Subgroups — #37572961

Order 24448.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#27133174C211yesmaximal, characteristic
2C22×C4×Dic191C211yesmaximal, characteristic, complemented
3C2×#20259248C212yesmaximal, complemented
4#27132424C212yesmaximal, complemented
5#407×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2211yescharacteristic
7C23×Dic191—21no—
8#20259305—21no—
9#20259301C412yescomplemented
10#20259296C412yescomplemented
11#20259291—21no—
12C4×C22⋊D191—22no—
13#20259281C2211yescharacteristic
14C2×C4×Dic191—24no—
15C2×C4×Dic191—21no—
16C2×C4×Dic191C2212yes—
17#20259248—24no—
18C23×C4×C191C2211yescharacteristic
19C2×M16×C191C2212yes—
20C22⋊C8×C191—22no—
21#15690287—22no—
22#15690287—22no—
23C2×Dic382C2×C411yescharacteristic, complemented
24C2×D764C2×C411yescharacteristic, complemented
25C2×C22⋊D191—22no—
26C2×C22⋊D191—21no—
27C22×Dic191—28no—
28C22×Dic191—24no—
29C22×Dic191—22no—
30C2×C4×D191—21no—
31C4⋊Dic191C2×C412yescomplemented
32Dic191⋊C4—22no—
33C22⋊Dic191—22no—
34C22⋊Dic191—21no—
35(C2×D191)⋊C4—22no—
36C4×Dic191—24no—
37C4×Dic191—22no—
38C4×Dic191—21no—
39C4×Dic191D414yescomplemented
40C24×C191D411yescharacteristic
41C22×C4×C191—22no—
42C22×C4×C191—22no—
43C22×C4×C191C2×C412yes—
44C22×C4×C191D412yes—
45C22×C4×C191D411yescharacteristic
46C22×C4×C191C2311yescharacteristic
47M16×C191—22no—
48M16×C191—22no—
49C2×C8×C191—22no—
50C22×D191—21no—
51Dic382—22no—
52D764—22no—
53C22⋊D191—44no—
54C22⋊D191—41no—
55C22⋊D191—41no—
56C2×Dic191—216no—
57C2×Dic191—28no—
58C2×Dic191—24no—
59C2×Dic191—22no—
60C2×Dic191—21no—
61C4×D191—42no—
62C23×C191—24no—
63C23×C191—21no—
64C23×C191—21no—
65C23×C191C22⋊C412yes—
66C23×C191C2×D411yescharacteristic
67C2×C4×C191—21no—
68C2×C4×C191—21no—
69C2×C4×C191—24no—
70C2×C4×C191—24no—
71C2×C4×C191C22⋊C412yes—
72C2×C4×C191C22×C411yescharacteristic
73C2×C4×C191C2×D412yes—
74C2×C4×C191C2×D411yescharacteristic
75C2×C4×C191#4112yes—
76C8×C191—42no—
77C22×C191—24no—
78C22×C191—24no—
79C22×C191—22no—
80C22×C191—22no—
81C22×C191—22no—
82C22×C191#10414yescomplemented
83C22×C191C2×C22⋊C411yescharacteristic
84C22×C191#12011yescharacteristic
85C22×C191#12311yescharacteristic
86C2×D191—41no—
87C2×D191—42no—
88C4×C191—22no—
89C4×C191C4×D412yes—
90C4×C191#12112yes—
91Dic191—28no—
92Dic191—41no—
93Dic191—42no—
94C2×C191—21no—
95C2×C191—24no—
96C2×C191—21no—
97C2×C191#38611yescharacteristic
98C2×C191C2×#10412yes—
99D191—81no—
100C191#189611yescharacteristic, complemented, Sylow
101#1896—1911nomaximal, Sylow
102#525—1911no—
103C22×C42—1911no—
104C2×#104—1912no—
105#407D19111yescharacteristic, complemented
106#339—1912no—
107C2×#41—1911no—
108C23×C4—3821no—
109C23×C4C2×D19111yescharacteristic
110C2×M16C2×D19112yes—
111#123—3821no—
112C22⋊Q8—1912no—
113#121—1912no—
114#120—3821no—
115C4×D4—3822no—
116#117—1911no—
117C2×C42—3821no—
118C2×C42—3824no—
119C2×C42—1912no—
120#104—3824no—
121C22⋊C8—22no—
122C24D76411yescharacteristic
123#41—3822no—
124#41—3822no—
125C2×Q8—1911no—
126C2×D4—3822no—
127C2×D4—3821no—
128C2×D4—1911no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—3824no—
132C22×C4—3828no—
133C22×C4—3822no—
134C22×C4—3821no—
135C22×C4C4×D19112yes—
136C22×C4C22⋊D19112yes—
137C22×C4D76411yescharacteristic
138C22×C4C22×D19111yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—3822no—
143C4⋊C4—1912no—
144C22⋊C4—3822no—
145C22⋊C4—3821no—
146C22⋊C4—3822no—
147C42—3824no—
148C42—3822no—
149C42—3821no—
150C42—1914no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—3821no—
155C23(C2×D191)⋊C412yes—
156C23C2×D76411yescharacteristic
157Q8—3822no—
158D4—3822no—
159D4—7644no—
160D4—7641no—
161D4—7641no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—38216no—
167C2×C4—3828no—
168C2×C4—3824no—
169C2×C4—3822no—
170C2×C4—3821no—
171C2×C4—7642no—
172C2×C4(C2×D191)⋊C412yes—
173C2×C4C2×C4×D19111yescharacteristic
174C2×C4D4×D19112yes—
175C2×C4C2×C22⋊D19111yescharacteristic
176C2×C4#1569028612yes—
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—7642no—
184C22—7641no—
185C22#2025924814yescomplemented
186C22C2×(C2×D191)⋊C411yescharacteristic
187C22#2025929211yescharacteristic
188C22#2025930611yescharacteristic
189C4—22no—
190C4—3828no—
191C4—7642no—
192C4—7641no—
193C4(C22⋊D191)⋊C412yes—
194C4#2025929412yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—15281no—
199C2#2713254011yescharacteristic
200C2C2×#2025924812yes—
subgroupG/H
centerC2×C4C2×C22⋊D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#407×C191C2
socleC22×C191C2×C22⋊C4
prime radical#27133174C2
cosocleC22×C4×C191C23
hypercenter#407D191
hypocenterC191#1896
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic191C2semidirect
3. C2×#20259248C2semidirect
4. #27132424C2semidirect
5. #407×C191C2semidirect
9. #20259301C4semidirect
10. #20259296C4semidirect
23. C2×Dic382C2×C4semidirect
24. C2×D764C2×C4semidirect
31. C4⋊Dic191C2×C4semidirect
39. C4×Dic191D4semidirect
82. C22×C191#104semidirect
100. C191#1896semidirect
105. #407D191semidirect
185. C22#20259248semidirect

Maximal subgroups

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

subgroupindex
#271331742
C22×C4×Dic1912
C2×#202592482
#271324242
#407×C1912
#1896191