Finite Group Databasebeta

← #37582764

Subgroups — #37582764

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#27133268C211yesmaximal, characteristic, complemented
2#27133137C211yesmaximal, characteristic, complemented
3#27132988C212yesmaximal, complemented
4#27132964C212yesmaximal, complemented
5#27132859C212yesmaximal, complemented
6#27132799C212yesmaximal, complemented
7#27132776C212yesmaximal, complemented
8C4×D1528C212yesmaximal, complemented
9#433×C191C211yesmaximal, characteristic, complemented
10C22×D764C2211yescharacteristic
11C2×D1528C2212yes—
12C2×D1528C2212yes—
13#20259319C2211yescharacteristic, complemented
14#20259314C2211yescharacteristic, complemented
15#20259307—22no—
16#20259296C2212yes—
17#20259295—22no—
18C4×D764C2212yes—
19C4×D764C2212yes—
20C4×D764C2212yescomplemented
21#20259284—22no—
22#20259281C2211yescharacteristic
23C22⋊C4×D191—22no—
24#20259256C2212yescomplemented
25#20259254C2212yescomplemented
26#20259244C2212yes—
27#20259244C2212yes—
28#20259244C2212yescomplemented
29#20259244C2212yescomplemented
30#117×C191C2211yescharacteristic
31C4⋊C8×C191C2212yescomplemented
32C22⋊C8×C191C2212yes—
33#97×C191C2211yescharacteristic, complemented
34C4×C8×C191C2211yescharacteristic, complemented
35C23×D191—21no—
36C2×D764—24no—
37C2×D764—21no—
38C2×D764—22no—
39C2×D764C2312yes—
40C2×D764C2312yes—
41C2×C22⋊D191—22no—
42C2×C4×D191—22no—
43C2×C4×D191—22no—
44C2×C4×D191—22no—
45D1528—24no—
46D1528—24no—
47C4⋊Dic191C2312yes—
48C4⋊Dic191C2312yes—
49Dic191⋊C4—22no—
50C22⋊Dic191—21no—
51(C2×D191)⋊C4—22no—
52(C2×D191)⋊C4—22no—
53(C2×D191)⋊C4—22no—
54(C2×D191)⋊C4—22no—
55C4×Dic191—21no—
56C22×C4×C191C2311yescharacteristic
57C2×C8×C191C2312yes—
58C2×C8×C191C2312yes—
59C4⋊C4×C191D412yes—
60C22⋊C4×C191D412yes—
61C42×C191C2311yescharacteristic
62C42×C191C2311yescharacteristic
63C22×D191—22no—
64C22×D191—24no—
65C22×D191—22no—
66C22×D191—82no—
67D764—24no—
68D764—22no—
69D764—22no—
70D764—22no—
71D764—82no—
72D764#4114yes—
73C22⋊D191—82no—
74C2×Dic191—22no—
75C2×Dic191—22no—
76C4×D191—82no—
77C4×D191—82no—
78C4×D191—82no—
79C23×C191C2×D411yescharacteristic
80C2×C4×C191—22no—
81C2×C4×C191C2×D412yes—
82C2×C4×C191C2×D412yes—
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2411yescharacteristic
85C8×C191—22no—
86C8×C191—22no—
87C22×C191—21no—
88C22×C191—22no—
89C22×C191C22×D411yescharacteristic
90C2×D191—24no—
91C2×D191—42no—
92C2×D191—42no—
93C2×D191—42no—
94C2×D191—42no—
95C2×D191—42no—
96C2×D191—84no—
97C4×C191—21no—
98C4×C191—22no—
99C4×C191—22no—
100C4×C191C2×#4112yes—
101Dic191—42no—
102Dic191—42no—
103C2×C191—41no—
104C2×C191#52511yescharacteristic
105C2×C191#57612yes—
106D191—44no—
107D191—82no—
108C191#312211yescharacteristic, complemented, Sylow
109#3122—1911nomaximal, Sylow
110#540—1911no—
111#518—1911no—
112#482—1912no—
113#478—1912no—
114#459—1912no—
115#447—1912no—
116#442—1912no—
117C4×D8—1912no—
118#433D19111yescharacteristic, complemented
119C22×D4—1911no—
120C2×D8—1912no—
121C2×D8—1912no—
122#127—1911no—
123#125—1911no—
124#123—3822no—
125#121—3822no—
126#121—1912no—
127C4×D4—3822no—
128C4×D4—1912no—
129C4×D4—1912no—
130C4×D4—1912no—
131#117—1911no—
132#117C2×D19111yescharacteristic
133C2×C22⋊C4—3822no—
134#107—1912no—
135#106—1912no—
136C4⋊C8C2×D19112yescomplemented
137#102—1912no—
138#102—1912no—
139#102—1912no—
140#102—1912no—
141C22⋊C8C2×D19112yes—
142#97C2×D19111yescharacteristic, complemented
143C4×C8C2×D19111yescharacteristic, complemented
144C24—3821no—
145C2×D4—3824no—
146C2×D4—3822no—
147C2×D4—3821no—
148C2×D4—3822no—
149C2×D4—1912no—
150C2×D4—1912no—
151C22×C4—3822no—
152C22×C4—3822no—
153C22×C4—3822no—
154C22×C4C22×D19111yescharacteristic
155D8—3824no—
156D8—3824no—
157C2×C8C22×D19112yes—
158C2×C8C22×D19112yes—
159C4⋊C4—3822no—
160C4⋊C4—1912no—
161C4⋊C4—1912no—
162C4⋊C4D76412yes—
163C22⋊C4—3821no—
164C22⋊C4—3822no—
165C22⋊C4—3822no—
166C22⋊C4—3822no—
167C22⋊C4—3822no—
168C22⋊C4D76412yes—
169C42—3821no—
170C42C22×D19111yescharacteristic
171C42C22×D19111yescharacteristic
172C23—3824no—
173C23—3822no—
174C23—3822no—
175C23—15282no—
176C23C2×D76411yescharacteristic
177D4—3824no—
178D4—3822no—
179D4—3822no—
180D4—3822no—
181D4—1914no—
182D4—15282no—
183D4—15282no—
184C2×C4—22no—
185C2×C4—3822no—
186C2×C4—3822no—
187C2×C4—15282no—
188C2×C4—15282no—
189C2×C4—15282no—
190C2×C4C2×D76411yescharacteristic
191C2×C4C2×D76412yes—
192C2×C4C2×D76412yes—
193C2×C4C23×D19111yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—3824no—
199C22—15284no—
200C22—7642no—
201C22—7642no—
202C22—7642no—
203C22—7642no—
204C22—7642no—
205C22C22×D76411yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—7642no—
210C4—7642no—
211C4#41×D19112yes—
212C2—41no—
213C2—15282no—
214C2—7644no—
215C2#2713317511yescharacteristic
216C2#2713346812yes—
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#433×C191C2
socleC22×C191C22×D4
hypercenter#433D191
hypocenterC191#3122
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #27133268C2semidirect
2. #27133137C2semidirect
3. #27132988C2semidirect
4. #27132964C2semidirect
5. #27132859C2semidirect
6. #27132799C2semidirect
7. #27132776C2semidirect
8. C4×D1528C2semidirect
9. #433×C191C2semidirect
13. #20259319C22semidirect
14. #20259314C22semidirect
20. C4×D764C22semidirect
24. #20259256C22semidirect
25. #20259254C22semidirect
28. #20259244C22semidirect
29. #20259244C22semidirect
31. C4⋊C8×C191C22semidirect
33. #97×C191C22semidirect
34. C4×C8×C191C22semidirect
108. C191#3122semidirect
118. #433D191semidirect
136. C4⋊C8C2×D191semidirect
142. #97C2×D191semidirect
143. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332682
#271331372
#271329882
#271329642
#271328592
#271327992
#271327762
C4×D15282
#433×C1912
#3122191