Finite Group Databasebeta

← #37582812

Subgroups — #37582812

Order 24448.

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

normal subgroups only

This group has 382 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
2#27133140C211yesmaximal, characteristic, complemented
3#27132988C212yesmaximal, complemented
4#27132971C212yesmaximal, complemented
5#27132864C212yesmaximal, complemented
6#27132804C212yesmaximal, complemented
7#27132765C212yesmaximal, complemented
8C4×#15690276C212yesmaximal, complemented
9#433×C191C211yesmaximal, characteristic, complemented
10C22×Dic382C2211yescharacteristic
11C2×#15690276C2212yes—
12C2×#15690276C2212yes—
13#20259319C2211yescharacteristic
14#20259314C2211yescharacteristic
15#20259307—22no—
16#20259296C2212yes—
17#20259295—22no—
18C4×Dic382C2212yes—
19C4×Dic382C2212yes—
20#20259287—22no—
21C4×D764C2212yes—
22#20259281C2211yescharacteristic
23#20259278—22no—
24#20259256C2212yes—
25#20259254C2212yes—
26#20259247C2212yes—
27#20259247C2212yes—
28#20259244C2212yes—
29#20259244C2212yes—
30#117×C191C2211yescharacteristic
31C4⋊C8×C191C2212yes—
32C22⋊C8×C191C2212yes—
33#97×C191C2211yescharacteristic
34C4×C8×C191C2211yescharacteristic
35C2×Dic382—24no—
36C2×Dic382—21no—
37C2×Dic382C2312yes—
38C2×D764—22no—
39C2×D764C2312yes—
40C2×C22⋊D191—22no—
41C22×Dic191—21no—
42C2×C4×D191—22no—
43#15690276—24no—
44#15690276—24no—
45C4⋊Dic191C2312yes—
46C4⋊Dic191C2312yes—
47Dic191⋊C4—22no—
48Dic191⋊C4—22no—
49Dic191⋊C4—22no—
50C22⋊Dic191—21no—
51(C2×D191)⋊C4—22no—
52(C2×D191)⋊C4—22no—
53C4×Dic191—22no—
54C4×Dic191—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—
64Dic382—24no—
65Dic382—22no—
66Dic382#4114yes—
67D764—22no—
68D764—22no—
69D764—82no—
70C22⋊D191—82no—
71C2×Dic191—24no—
72C2×Dic191—22no—
73C2×Dic191—22no—
74C2×Dic191—22no—
75C4×D191—82no—
76C23×C191C2×D411yescharacteristic
77C2×C4×C191—22no—
78C2×C4×C191C2×D412yes—
79C2×C4×C191C2×D412yes—
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2411yescharacteristic
82C8×C191—22no—
83C8×C191—22no—
84C22×C191—21no—
85C22×C191—22no—
86C22×C191C22×D411yescharacteristic
87C2×D191—42no—
88C2×D191—42no—
89C2×D191—42no—
90C4×C191—21no—
91C4×C191—22no—
92C4×C191—22no—
93C4×C191C2×#4112yes—
94Dic191—24no—
95Dic191—42no—
96Dic191—42no—
97C2×C191—41no—
98C2×C191#52511yescharacteristic
99C2×C191#57712yes—
100D191—82no—
101C191#312611yescharacteristic, complemented, Sylow
102#3126—1911nomaximal, Sylow
103#540—1911no—
104#519—1911no—
105#482—1912no—
106#479—1912no—
107#460—1912no—
108#448—1912no—
109#440—1912no—
110C4×SD16—1912no—
111#433D19111yescharacteristic, complemented
112C22×Q8—1911no—
113C2×SD16—1912no—
114C2×SD16—1912no—
115#127—1911no—
116#125—1911no—
117#123—3822no—
118#121—3822no—
119#121—1912no—
120C4×Q8—3822no—
121C4×Q8—1912no—
122C4×Q8—1912no—
123C4×D4—1912no—
124#117—3822no—
125#117—1911no—
126#117C2×D19111yescharacteristic
127#107—1912no—
128#106—1912no—
129C4⋊C8C2×D19112yes—
130#103—1912no—
131#103—1912no—
132#102—1912no—
133#102—1912no—
134C22⋊C8C2×D19112yes—
135#97C2×D19111yescharacteristic
136C4×C8C2×D19111yescharacteristic
137C2×Q8—3824no—
138C2×Q8—3821no—
139C2×Q8—1912no—
140C2×D4—3822no—
141C2×D4—3822no—
142C2×D4—1912no—
143C22×C4—3821no—
144C22×C4—3822no—
145C22×C4C22×D19111yescharacteristic
146SD16—3824no—
147SD16—3824no—
148C2×C8C22×D19112yes—
149C2×C8C22×D19112yes—
150C4⋊C4—3822no—
151C4⋊C4—3822no—
152C4⋊C4—3822no—
153C4⋊C4—1912no—
154C4⋊C4—1912no—
155C4⋊C4D76412yes—
156C22⋊C4—3821no—
157C22⋊C4—3822no—
158C22⋊C4—3822no—
159C22⋊C4D76412yes—
160C42—3822no—
161C42—3822no—
162C42—3821no—
163C42C22×D19111yescharacteristic
164C42C22×D19111yescharacteristic
165C23—3822no—
166C23C2×D76411yescharacteristic
167Q8—3824no—
168Q8—3822no—
169Q8—1914no—
170D4—3822no—
171D4—3822no—
172D4—15282no—
173D4—15282no—
174C2×C4—22no—
175C2×C4—3824no—
176C2×C4—3822no—
177C2×C4—3822no—
178C2×C4—3822no—
179C2×C4—15282no—
180C2×C4C2×D76412yes—
181C2×C4C2×D76412yes—
182C2×C4C2×D76411yescharacteristic
183C2×C4C23×D19111yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—7642no—
189C22—7642no—
190C22—7642no—
191C22C22×D76411yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—3824no—
196C4—7642no—
197C4—7642no—
198C4#41×D19112yes—
199C2—41no—
200C2—15282no—
201C2#2713317511yescharacteristic
202C2#2713347512yes—
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#433×C191C2
socleC22×C191C22×D4
prime radical#27133268C2
hypercenter#433D191
hypocenterC191#3126
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
2. #27133140C2semidirect
3. #27132988C2semidirect
4. #27132971C2semidirect
5. #27132864C2semidirect
6. #27132804C2semidirect
7. #27132765C2semidirect
8. C4×#15690276C2semidirect
9. #433×C191C2semidirect
101. C191#3126semidirect
111. #433D191semidirect

Maximal subgroups

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

subgroupindex
#271332682
#271331402
#271329882
#271329712
#271328642
#271328042
#271327652
C4×#156902762
#433×C1912
#3126191