Finite Group Databasebeta

← #37583150

Subgroups — #37583150

Order 24448.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#27133276C211yesmaximal, characteristic, complemented
2#27133269C211yesmaximal, characteristic
3#27133036C211yesmaximal, characteristic, complemented
4#27133033C211yesmaximal, characteristic, complemented
5#27133029C211yesmaximal, characteristic, complemented
6#27132910C212yesmaximal, complemented
7#27132893C212yesmaximal, complemented
8#27132762C212yesmaximal, complemented
9#27132750C212yesmaximal, complemented
10#27132617C211yesmaximal, characteristic, complemented
11#499×C191C211yesmaximal, characteristic, complemented
12C2×#15690276C2212yes—
13C2×#15690276C2212yes—
14C2×#15690270C2211yescharacteristic
15C2×C8×D191C2211yescharacteristic
16#20259322C2211yescharacteristic
17#20259319C2211yescharacteristic
18#20259317—22no—
19#20259313—22no—
20#20259307—22no—
21#20259302C2212yes—
22#20259297—22no—
23#20259297C2212yes—
24#20259287C2212yes—
25#20259284C2212yes—
26#20259279C2211yescharacteristic
27#20259245C2212yes—
28#20259245C2212yes—
29#20259242C2212yes—
30#20259242C2212yes—
31#20259233C2211yescharacteristic
32#20259232C2211yescharacteristic
33C8×Dic191C2211yescharacteristic
34#125×C191C2211yescharacteristic
35#125×C191C2211yescharacteristic
36#107×C191C2212yes—
37#106×C191C2212yes—
38C4×C8×C191C2211yescharacteristic
39C2×Dic382C2312yes—
40C2×D764—22no—
41C2×D764—22no—
42C2×D764C2312yes—
43C2×C4×D191—22no—
44C2×C4×D191C2311yescharacteristic
45#15690276—24no—
46#15690276—24no—
47#15690270—22no—
48C2×C191⋊C8C2311yescharacteristic
49C2×C191⋊C8C2311yescharacteristic
50C8×D191—22no—
51C4⋊Dic191—22no—
52C4⋊Dic191—22no—
53Dic191⋊C4—22no—
54Dic191⋊C4D412yes—
55(C2×D191)⋊C4—22no—
56(C2×D191)⋊C4—22no—
57(C2×D191)⋊C4—22no—
58(C2×D191)⋊C4D412yes—
59C4×Dic191—22no—
60C4×Dic191C2311yescharacteristic
61C2×C8×C191C2311yescharacteristic
62C2×C8×C191C2311yescharacteristic
63C4⋊C4×C191—22no—
64C4⋊C4×C191—22no—
65C4⋊C4×C191C2312yes—
66C4⋊C4×C191C2312yes—
67C42×C191C2311yescharacteristic
68C22×D191—22no—
69C22×D191C2×D411yescharacteristic
70Dic382—22no—
71Dic382—22no—
72D764—22no—
73D764—22no—
74D764—82no—
75D764—82no—
76C2×Dic191—22no—
77C2×Dic191C2×D412yes—
78C2×Dic191C2×D411yescharacteristic
79C4×D191—21no—
80C4×D191—21no—
81C4×D191—82no—
82C191⋊C8—21no—
83C191⋊C8—21no—
84C2×C4×C191—22no—
85C2×C4×C191—22no—
86C2×C4×C191C2×D412yes—
87C2×C4×C191C2411yescharacteristic
88C8×C191#4112yes—
89C8×C191#4112yes—
90C22×C191C22×D411yescharacteristic
91C2×D191—21no—
92C2×D191—22no—
93C2×D191—42no—
94C2×D191—42no—
95C2×D191—42no—
96C4×C191—22no—
97C4×C191—42no—
98C4×C191—42no—
99C4×C191C2×#4111yescharacteristic
100C4×C191C2×#4111yescharacteristic
101Dic191—21no—
102Dic191—22no—
103Dic191—42no—
104C2×C191#53211yescharacteristic
105C2×C191#57712yes—
106D191—41no—
107D191—82no—
108C191#317411yescharacteristic, complemented, Sylow
109#3174—1911nomaximal, Sylow
110#541—1911no—
111#540—1911no—
112#499D19111yescharacteristic, complemented
113#492—1911no—
114#491—1911no—
115#490—1911no—
116#468—1912no—
117#465—1912no—
118#440—1912no—
119C4×SD16—1912no—
120#405—1911no—
121C2×SD16—1912no—
122C2×SD16—1912no—
123C2×M16—1911no—
124C22×C8—1911no—
125C4⋊Q8—1911no—
126#127—1911no—
127#126—3822no—
128#125—3822no—
129#125C2×D19111yescharacteristic
130#125C2×D19111yescharacteristic
131#123—3822no—
132C22⋊Q8—1912no—
133#121—3822no—
134#121—1912no—
135C4×Q8—1912no—
136C4×D4—1912no—
137#117—1911no—
138#107C2×D19112yes—
139#106C2×D19112yes—
140#103—1912no—
141#103—1912no—
142#102—1912no—
143#102—1912no—
144#97—1911no—
145#97—1911no—
146C4×C8—1911no—
147C4×C8C2×D19111yescharacteristic
148C2×Q8—1912no—
149C2×D4—3822no—
150C2×D4—3822no—
151C2×D4—1912no—
152C22×C4—3822no—
153C22×C4—1911no—
154SD16—3824no—
155SD16—3824no—
156M16—3822no—
157C2×C8—3822no—
158C2×C8—1911no—
159C2×C8—1911no—
160C2×C8C22×D19111yescharacteristic
161C2×C8C22×D19111yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—3822no—
165C4⋊C4—3822no—
166C4⋊C4—3822no—
167C4⋊C4—1912no—
168C4⋊C4C22×D19112yes—
169C4⋊C4C22×D19112yes—
170C22⋊C4—3822no—
171C22⋊C4—3822no—
172C22⋊C4—3822no—
173C22⋊C4—1912no—
174C42—3822no—
175C42—1911no—
176C42C22×D19111yescharacteristic
177C23—3822no—
178C23—1911no—
179Q8—3822no—
180Q8—3822no—
181D4—3822no—
182D4—3822no—
183D4—15282no—
184D4—15282no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—3821no—
188C2×C4—3821no—
189C2×C4—3822no—
190C2×C4—1912no—
191C2×C4—1911no—
192C2×C4—15282no—
193C2×C4D4×D19112yes—
194C2×C4C23×D19111yescharacteristic
195C8—3821no—
196C8—3821no—
197C8#1569028812yes—
198C8#1569028812yes—
199C22—3821no—
200C22—3822no—
201C22—7642no—
202C22—7642no—
203C22—7642no—
204C22C2×D4×D19111yescharacteristic
205C4—22no—
206C4—42no—
207C4—42no—
208C4—3821no—
209C4—3822no—
210C4—7642no—
211C4C2×#1569028811yescharacteristic
212C4C2×#1569028811yescharacteristic
213C2—15282no—
214C2—7641no—
215C2#2713321411yescharacteristic
216C2#2713347012yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#499×C191C2
socleC22×C191C22×D4
prime radical#27133269C2
hypercenter#499D191
hypocenterC191#3174
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #27133276C2semidirect
3. #27133036C2semidirect
4. #27133033C2semidirect
5. #27133029C2semidirect
6. #27132910C2semidirect
7. #27132893C2semidirect
8. #27132762C2semidirect
9. #27132750C2semidirect
10. #27132617C2semidirect
11. #499×C191C2semidirect
108. C191#3174semidirect
112. #499D191semidirect

Maximal subgroups

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

subgroupindex
#271332762
#271332692
#271330362
#271330332
#271330292
#271329102
#271328932
#271327622
#271327502
#271326172
#499×C1912
#3174191