Finite Group Databasebeta

← #37582758

Subgroups — #37582758

Order 24448.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#27133137C211yesmaximal, characteristic, complemented
2#27132984C212yesmaximal, complemented
3#27132960C212yesmaximal, complemented
4#27132855C212yesmaximal, complemented
5#27132796C212yesmaximal, complemented
6#27132773C212yesmaximal, complemented
7C4×#15690272C212yesmaximal, complemented
8#27132724C211yesmaximal, characteristic, complemented
9#540×C191C211yesmaximal, characteristic, complemented
10C22×D764C2211yescharacteristic
11C2×#15690272C2212yes—
12C2×#15690272C2212yes—
13C4×D764C2212yes—
14C4×D764C2212yes—
15#20259284—22no—
16#20259281C2211yescharacteristic
17C22⋊C4×D191—22no—
18#20259255C2212yescomplemented
19#20259253C2212yescomplemented
20C4⋊(C191⋊C8)C2212yescomplemented
21#20259243C2212yescomplemented
22#20259243C2212yescomplemented
23#20259242C2212yes—
24#20259242C2212yes—
25C22⋊(C191⋊C8)C2212yes—
26#20259233C2211yescharacteristic, complemented
27C4×C191⋊C8C2211yescharacteristic, complemented
28#127×C191C2211yescharacteristic, complemented
29#125×C191C2211yescharacteristic, complemented
30#123×C191—22no—
31#121×C191—22no—
32#121×C191C2212yes—
33C4×D4×C191C2212yescomplemented
34#117×C191C2211yescharacteristic
35C23×D191—21no—
36C2×D764—24no—
37C2×D764—21no—
38C2×D764C2312yes—
39C2×C4×D191—22no—
40C2×C4×D191—22no—
41#15690272—24no—
42#15690272—24no—
43C2×C191⋊C8C2312yes—
44C2×C191⋊C8C2312yes—
45C4⋊Dic191C2312yes—
46C22⋊Dic191—21no—
47(C2×D191)⋊C4—22no—
48(C2×D191)⋊C4—22no—
49C4×Dic191—21no—
50C2×D4×C191—22no—
51C2×D4×C191—22no—
52C2×D4×C191C2312yes—
53C22×C4×C191—22no—
54C22×C4×C191C2311yescharacteristic
55C4⋊C4×C191—22no—
56C4⋊C4×C191D412yes—
57C4⋊C4×C191C2312yes—
58C22⋊C4×C191—22no—
59C22⋊C4×C191—22no—
60C22⋊C4×C191D412yes—
61C42×C191C2311yescharacteristic
62C42×C191C2311yescharacteristic
63C22×D191—22no—
64C22×D191—24no—
65C22×D191—82no—
66D764—24no—
67D764—22no—
68D764#4114yes—
69C2×Dic191—22no—
70C4×D191—82no—
71C4×D191—82no—
72C191⋊C8—22no—
73C191⋊C8—22no—
74C23×C191—22no—
75C23×C191C2×D411yescharacteristic
76D4×C191—22no—
77D4×C191—22no—
78D4×C191—82no—
79D4×C191—82no—
80C2×C4×C191—22no—
81C2×C4×C191—22no—
82C2×C4×C191—82no—
83C2×C4×C191C2×D412yes—
84C2×C4×C191C2×D412yes—
85C2×C4×C191C2×D411yescharacteristic
86C2×C4×C191C2411yescharacteristic
87C22×C191—21no—
88C22×C191—22no—
89C22×C191—42no—
90C22×C191—42no—
91C22×C191—42no—
92C22×C191C22×D411yescharacteristic
93C2×D191—24no—
94C2×D191—42no—
95C2×D191—42no—
96C2×D191—84no—
97C4×C191—21no—
98C4×C191—22no—
99C4×C191—22no—
100C4×C191—42no—
101C4×C191C2×#4112yes—
102Dic191—42no—
103C2×C191—41no—
104C2×C191—82no—
105C2×C191#52511yescharacteristic
106C2×C191#57612yes—
107D191—44no—
108C191#312211yescharacteristic, complemented, Sylow
109#3122—1911nomaximal, Sylow
110#540D19111yescharacteristic, complemented
111#518—1911no—
112#482—1912no—
113#478—1912no—
114#459—1912no—
115#447—1912no—
116#442—1912no—
117C4×D8—1912no—
118#433—1911no—
119C22×D4—1911no—
120C2×D8—1912no—
121C2×D8—1912no—
122#127C2×D19111yescharacteristic, complemented
123#125C2×D19111yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D19112yes—
127C4×D4—3822no—
128C4×D4—1912no—
129C4×D4—1912no—
130C4×D4C2×D19112yescomplemented
131#117—1911no—
132#117C2×D19111yescharacteristic
133C2×C22⋊C4—3822no—
134#107—1912no—
135#106—1912no—
136C4⋊C8—1912no—
137#102—1912no—
138#102—1912no—
139#102—1912no—
140#102—1912no—
141C22⋊C8—1912no—
142#97—1911no—
143C4×C8—1911no—
144C24—3821no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—3824no—
148C2×D4—3821no—
149C2×D4—1912no—
150C2×D4C22×D19112yes—
151C22×C4—22no—
152C22×C4—3822no—
153C22×C4—3822no—
154C22×C4C22×D19111yescharacteristic
155D8—3824no—
156D8—3824no—
157C2×C8—1912no—
158C2×C8—1912no—
159C4⋊C4—22no—
160C4⋊C4—1912no—
161C4⋊C4C22⋊D19112yes—
162C4⋊C4C22×D19112yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—3821no—
166C22⋊C4—3822no—
167C22⋊C4—3822no—
168C22⋊C4C22⋊D19112yes—
169C42—3821no—
170C42C22×D19111yescharacteristic
171C42C22×D19111yescharacteristic
172C23—22no—
173C23—3824no—
174C23—3822no—
175C23—15282no—
176C23C2×C22⋊D19111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—3824no—
182D4—3822no—
183D4—1914no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—3822no—
188C2×C4—15282no—
189C2×C4—15282no—
190C2×C4C2×C22⋊D19111yescharacteristic
191C2×C4C2×C22⋊D19112yes—
192C2×C4C2×C22⋊D19112yes—
193C2×C4C23×D19111yescharacteristic
194C8—3822no—
195C8—3822no—
196C22—22no—
197C22—21no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—3824no—
202C22—15284no—
203C22—7642no—
204C22—7642no—
205C22C22×C22⋊D19111yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—42no—
210C4—7642no—
211C4#41×D19112yes—
212C2—41no—
213C2—82no—
214C2—7644no—
215C2#2713317011yescharacteristic
216C2#2713346612yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#540×C191C2
socleC22×C191C22×D4
hypercenter#540D191
hypocenterC191#3122
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #27133137C2semidirect
2. #27132984C2semidirect
3. #27132960C2semidirect
4. #27132855C2semidirect
5. #27132796C2semidirect
6. #27132773C2semidirect
7. C4×#15690272C2semidirect
8. #27132724C2semidirect
9. #540×C191C2semidirect
18. #20259255C22semidirect
19. #20259253C22semidirect
20. C4⋊(C191⋊C8)C22semidirect
21. #20259243C22semidirect
22. #20259243C22semidirect
26. #20259233C22semidirect
27. C4×C191⋊C8C22semidirect
28. #127×C191C22semidirect
29. #125×C191C22semidirect
33. C4×D4×C191C22semidirect
108. C191#3122semidirect
110. #540D191semidirect
122. #127C2×D191semidirect
123. #125C2×D191semidirect
130. C4×D4C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331372
#271329842
#271329602
#271328552
#271327962
#271327732
C4×#156902722
#271327242
#540×C1912
#3122191