Finite Group Databasebeta

← #37572968

Subgroups — #37572968

Order 24448.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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×#20259250C212yesmaximal, complemented
3#27132627C211yesmaximal, characteristic, complemented
4#27132423C212yesmaximal, complemented
5C2×#117×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2211yescharacteristic
7C2×#15690271C2212yes—
8#20259305—21no—
9#20259301C412yescomplemented
10#20259296C412yescomplemented
11#20259291—21no—
12C4×C22⋊D191—22no—
13#20259281C2211yescharacteristic
14#20259250—24no—
15C22⋊(C191⋊C8)—22no—
16C23×C4×C191C2211yescharacteristic
17#117×C191—24no—
18C2×C4⋊C4×C191—21no—
19C2×C22⋊C4×C191—21no—
20C2×C42×C191C2212yes—
21#15690287—22no—
22#15690287—22no—
23C2×Dic382C2×C411yescharacteristic
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—22no—
26C2×C22⋊D191—21no—
27C2×C4×D191—21no—
28#15690271—22no—
29#15690271—22no—
30C2×C191⋊C8—22no—
31C4⋊Dic191C2×C412yes—
32Dic191⋊C4—22no—
33C22⋊Dic191—22no—
34C22⋊Dic191—21no—
35(C2×D191)⋊C4—22no—
36C4×Dic191—21no—
37C24×C191D411yescharacteristic
38C22×C4×C191—22no—
39C22×C4×C191—22no—
40C22×C4×C191—22no—
41C22×C4×C191C2×C412yes—
42C22×C4×C191D411yescharacteristic
43C22×C4×C191D412yes—
44C22×C4×C191C2311yescharacteristic
45C4⋊C4×C191—24no—
46C22⋊C4×C191—24no—
47C42×C191—22no—
48C42×C191D414yescomplemented
49C22×D191—21no—
50Dic382—22no—
51D764—22no—
52C22⋊D191—44no—
53C22⋊D191—41no—
54C22⋊D191—41no—
55C2×Dic191—22no—
56C2×Dic191—21no—
57C4×D191—42no—
58C191⋊C8—42no—
59C23×C191—21no—
60C23×C191—21no—
61C23×C191—42no—
62C23×C191C22⋊C412yes—
63C23×C191C2×D411yescharacteristic
64C2×C4×C191—21no—
65C2×C4×C191—21no—
66C2×C4×C191—24no—
67C2×C4×C191—24no—
68C2×C4×C191—24no—
69C2×C4×C191—44no—
70C2×C4×C191C22⋊C412yes—
71C2×C4×C191C22×C411yescharacteristic
72C2×C4×C191C2×D412yes—
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191#4112yes—
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×C191—44no—
88C4×C191C4×D412yes—
89C4×C191#12112yes—
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×#117D19111yescharacteristic, complemented
102C2×#104—1912no—
103#407—1911no—
104#339—1912no—
105C2×#41—1911no—
106C23×C4C2×D19111yescharacteristic
107C2×M16—1912no—
108#123—3821no—
109C22⋊Q8—1912no—
110#121—1912no—
111#120—3821no—
112C4×D4—3822no—
113#117—24no—
114#117—1911no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D19112yes—
118#104—3824no—
119C22⋊C8—3822no—
120C24C22⋊D19111yescharacteristic
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—22no—
130C22×C4—3821no—
131C22×C4C4×D19112yes—
132C22×C4C22⋊D19111yescharacteristic
133C22×C4D76412yes—
134C22×C4C22×D19111yescharacteristic
135M16—3822no—
136M16—3822no—
137C2×C8—3822no—
138C4⋊C4—24no—
139C4⋊C4—3822no—
140C4⋊C4—1912no—
141C22⋊C4—24no—
142C22⋊C4—3822no—
143C22⋊C4—3821no—
144C22⋊C4—3822no—
145C42—22no—
146C42—3821no—
147C42C22⋊D19114yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3821no—
152C23(C2×D191)⋊C412yes—
153C23C2×C22⋊D19111yescharacteristic
154Q8—3822no—
155D4—3822no—
156D4—7644no—
157D4—7641no—
158D4—7641no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—3822no—
166C2×C4—3821no—
167C2×C4—7642no—
168C2×C4(C2×D191)⋊C412yes—
169C2×C4C2×C4×D19111yescharacteristic
170C2×C4C2×C22⋊D19112yes—
171C2×C4C2×D76411yescharacteristic
172C2×C4#1569028712yes—
173C8—7642no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—7642no—
181C22—7641no—
182C22C2×(C2×D191)⋊C411yescharacteristic
183C22#2025929111yescharacteristic
184C22#2025930511yescharacteristic
185C4—22no—
186C4—44no—
187C4—7642no—
188C4—7641no—
189C4C4×C22⋊D19112yes—
190C4#2025929612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—15281no—
195C2#2713254211yescharacteristic
196C2#2713268112yes—
subgroupG/H
centerC2×C4C2×D764
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
FittingC2×#117×C191C2
socleC22×C191C2×C22⋊C4
prime radical#27133174C2
cosocleC22×C4×C191C23
hypercenterC2×#117D191
hypocenterC191#1897
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#20259250C2semidirect
3. #27132627C2semidirect
4. #27132423C2semidirect
5. C2×#117×C191C2semidirect
9. #20259301C4semidirect
10. #20259296C4semidirect
48. C42×C191D4semidirect
98. C191#1897semidirect
101. C2×#117D191semidirect
147. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271331742
C2×#202592502
#271326272
#271324232
C2×#117×C1912
#1897191