Finite Group Databasebeta

← #37572966

Subgroups — #37572966

Order 24448.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C2×#20259281C211yesmaximal, characteristic, complemented
3C2×#20259248C212yesmaximal, complemented
4#27132424C212yesmaximal, complemented
5#407×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2211yescharacteristic
7#20259305—21no—
8#20259301C412yescomplemented
9#20259296C412yescomplemented
10#20259291—21no—
11C4×C22⋊D191—22no—
12#20259281—24no—
13#20259281C2211yescharacteristic
14C2×C4⋊Dic191—21no—
15C2×C22⋊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
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—22no—
26C2×C22⋊D191—21no—
27C22×Dic191—22no—
28C2×C4×D191—21no—
29C4⋊Dic191—24no—
30C4⋊Dic191C2×C412yes—
31Dic191⋊C4—22no—
32C22⋊Dic191—24no—
33C22⋊Dic191—22no—
34C22⋊Dic191—21no—
35(C2×D191)⋊C4—22no—
36C4×Dic191—22no—
37C4×Dic191—21no—
38C4×Dic191D414yescomplemented
39C24×C191D411yescharacteristic
40C22×C4×C191—22no—
41C22×C4×C191—22no—
42C22×C4×C191C2×C412yes—
43C22×C4×C191D412yes—
44C22×C4×C191D411yescharacteristic
45C22×C4×C191C2311yescharacteristic
46M16×C191—22no—
47M16×C191—22no—
48C2×C8×C191—22no—
49C22×D191—21no—
50Dic382—22no—
51D764—22no—
52C22⋊D191—44no—
53C22⋊D191—41no—
54C22⋊D191—41no—
55C2×Dic191—22no—
56C2×Dic191—21no—
57C2×Dic191—24no—
58C2×Dic191—44no—
59C4×D191—42no—
60C23×C191—21no—
61C23×C191—21no—
62C23×C191—42no—
63C23×C191C22⋊C412yes—
64C23×C191C2×D411yescharacteristic
65C2×C4×C191—21no—
66C2×C4×C191—21no—
67C2×C4×C191—24no—
68C2×C4×C191—24no—
69C2×C4×C191C22⋊C412yes—
70C2×C4×C191C22×C411yescharacteristic
71C2×C4×C191C2×D412yes—
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191#4112yes—
74C8×C191—42no—
75C22×C191—22no—
76C22×C191—22no—
77C22×C191—22no—
78C22×C191—22no—
79C22×C191—42no—
80C22×C191—42no—
81C22×C191C2×C22⋊C411yescharacteristic
82C22×C191#12011yescharacteristic
83C22×C191#12311yescharacteristic
84C2×D191—41no—
85C2×D191—42no—
86C4×C191—22no—
87C4×C191C4×D412yes—
88C4×C191#12112yes—
89Dic191—44no—
90Dic191—41no—
91Dic191—42no—
92C2×C191—21no—
93C2×C191—21no—
94C2×C191—42no—
95C2×C191#38611yescharacteristic
96C2×C191#42112yes—
97D191—81no—
98C191#189711yescharacteristic, complemented, Sylow
99#1897—1911nomaximal, Sylow
100#525—1911no—
101C2×#117—1911no—
102C2×#104—1912no—
103#407D19111yescharacteristic, complemented
104#339—1912no—
105C2×#41—1911no—
106C23×C4C2×D19111yescharacteristic
107C2×M16C2×D19112yes—
108#123—3821no—
109C22⋊Q8—1912no—
110#121—1912no—
111#120—3821no—
112C4×D4—3822no—
113#117—3824no—
114#117—1911no—
115C2×C4⋊C4—3821no—
116C2×C22⋊C4—3821no—
117C2×C42—1912no—
118#104—3824no—
119C22⋊C8—22no—
120C24D76411yescharacteristic
121#41—3822no—
122#41—3822no—
123C2×Q8—1911no—
124C2×D4—3822no—
125C2×D4—3821no—
126C2×D4—1911no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—3822no—
130C22×C4—3821no—
131C22×C4C4×D19112yes—
132C22×C4C22⋊D19112yes—
133C22×C4D76411yescharacteristic
134C22×C4C22×D19111yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—3824no—
139C4⋊C4—3822no—
140C4⋊C4—1912no—
141C22⋊C4—3824no—
142C22⋊C4—3822no—
143C22⋊C4—3821no—
144C22⋊C4—3822no—
145C42—3822no—
146C42—3821no—
147C42—1914no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3821no—
152C23(C2×D191)⋊C412yes—
153C23C2×D76411yescharacteristic
154Q8—3822no—
155D4—3822no—
156D4—7644no—
157D4—7641no—
158D4—7641no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—3822no—
164C2×C4—3821no—
165C2×C4—3824no—
166C2×C4—7644no—
167C2×C4—7642no—
168C2×C4(C2×D191)⋊C412yes—
169C2×C4C2×C4×D19111yescharacteristic
170C2×C4D4×D19112yes—
171C2×C4C2×C22⋊D19111yescharacteristic
172C2×C4#1569028612yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—7642no—
181C22—7641no—
182C22C2×(C2×D191)⋊C411yescharacteristic
183C22#2025929211yescharacteristic
184C22#2025930611yescharacteristic
185C4—22no—
186C4—7644no—
187C4—7642no—
188C4—7641no—
189C4(C22⋊D191)⋊C412yes—
190C4#2025929412yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—15281no—
195C2#2713254011yescharacteristic
196C2#2713267912yes—
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#1897
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. C2×#20259281C2semidirect
3. C2×#20259248C2semidirect
4. #27132424C2semidirect
5. #407×C191C2semidirect
8. #20259301C4semidirect
9. #20259296C4semidirect
38. C4×Dic191D4semidirect
98. C191#1897semidirect
103. #407D191semidirect

Maximal subgroups

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

subgroupindex
#271331742
C2×#202592812
C2×#202592482
#271324242
#407×C1912
#1897191