Finite Group Databasebeta

← #37573749

Subgroups — #37573749

Order 24448.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#27133244C211yesmaximal, characteristic
2C2×#20259250C212yesmaximal, complemented
3#27132662C212yesmaximal, complemented
4#27132432C211yesmaximal, characteristic, complemented
5#382×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7C2×#15690271C2212yes—
8#20259302—22no—
9#20259297—22no—
10#20259296—22no—
11#20259250—24no—
12#20259245—22no—
13#20259242—22no—
14C2×C4⋊C4×C191C2211yescharacteristic
15C2×C4⋊C4×C191C2211yescharacteristic
16C2×C42×C191C2211yescharacteristic
17#95×C191—22no—
18#15690287—22no—
19#15690287—22no—
20#15690287—22no—
21#15690287—22no—
22C2×Dic382D412yes—
23C2×D764—22no—
24C2×D764D412yes—
25C2×C22⋊D191—22no—
26C2×C4×D191—22no—
27#15690271—22no—
28#15690271—22no—
29C2×C191⋊C8—22no—
30C4⋊Dic191—22no—
31(C2×D191)⋊C4—24no—
32C22×C4×C191—21no—
33C22×C4×C191—21no—
34C22×C4×C191D412yes—
35C22×C4×C191C2311yescharacteristic
36C4⋊C4×C191—22no—
37C4⋊C4×C191—22no—
38C42×C191—21no—
39C42×C191D412yescomplemented
40C22×D191—22no—
41Dic382—22no—
42Dic382—22no—
43D764—22no—
44D764—22no—
45D764—82no—
46C22⋊D191—42no—
47C22⋊D191—42no—
48C2×Dic191—22no—
49C4×D191—42no—
50C4×D191—42no—
51C191⋊C8—42no—
52C23×C191C2×D411yescharacteristic
53C2×C4×C191—22no—
54C2×C4×C191—22no—
55C2×C4×C191—41no—
56C2×C4×C191—41no—
57C2×C4×C191—42no—
58C2×C4×C191—42no—
59C2×C4×C191—41no—
60C2×C4×C191C2×D412yes—
61C2×C4×C191C2×D411yescharacteristic
62C2×C4×C191#4111yescharacteristic
63C2×C4×C191#4112yes—
64C22×C191—21no—
65C22×C191—21no—
66C22×C191#12011yescharacteristic
67C22×C191#12111yescharacteristic
68C22×C191#12411yescharacteristic
69C2×D191—42no—
70C2×D191—42no—
71C2×D191—42no—
72C4×C191—42no—
73C4×C191—42no—
74C4×C191—81no—
75C4×C191#12112yes—
76C4×C191#12312yes—
77Dic191—42no—
78C2×C191—21no—
79C2×C191—21no—
80C2×C191#39411yescharacteristic
81C2×C191#45411yescharacteristic
82C2×C191#45511yescharacteristic
83D191—82no—
84C191#204011yescharacteristic, complemented, Sylow
85#2040—1911nomaximal, Sylow
86#537—1911no—
87C2×#104—1912no—
88#417—1912no—
89#382D19111yescharacteristic, complemented
90#343—1911no—
91C2×#41—1912no—
92C2×M16—1912no—
93C22⋊Q8—3822no—
94#121—3822no—
95#121—3822no—
96C2×C4⋊C4C2×D19111yescharacteristic
97C2×C4⋊C4C2×D19111yescharacteristic
98C2×C42C2×D19111yescharacteristic
99#104—3824no—
100#103—3822no—
101#102—3822no—
102#95—22no—
103#41—3822no—
104#41—3822no—
105#41—3822no—
106#41—3822no—
107C2×Q8—1912no—
108C2×D4—3822no—
109C2×D4—3822no—
110C2×D4—1912no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—3822no—
114C22×C4C22⋊D19112yes—
115C22×C4C22×D19111yescharacteristic
116M16—3822no—
117M16—3822no—
118C2×C8—3822no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—3822no—
122C22⋊C4—3824no—
123C42—21no—
124C42D76412yescomplemented
125C23—3822no—
126C23C2×C22⋊D19111yescharacteristic
127Q8—3822no—
128Q8—3822no—
129D4—3822no—
130D4—3822no—
131D4—15282no—
132D4—7642no—
133D4—7642no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—3822no—
142C2×C4—7642no—
143C2×C4—7642no—
144C2×C4D4×D19112yes—
145C2×C4C2×D76411yescharacteristic
146C2×C4#1569028711yescharacteristic
147C2×C4#1569028812yes—
148C8—7642no—
149C22—21no—
150C22—21no—
151C22—7642no—
152C22—7642no—
153C22—7642no—
154C22#2025929011yescharacteristic
155C22#2025929611yescharacteristic
156C22#2025931111yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—7642no—
161C4#2025929712yes—
162C4#2025930712yes—
163C2—21no—
164C2—21no—
165C2—15282no—
166C2#2713258011yescharacteristic
167C2#2713283511yescharacteristic
168C2#2713284011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#382×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#382D191
hypocenterC191#2040
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#20259250C2semidirect
3. #27132662C2semidirect
4. #27132432C2semidirect
5. #382×C191C2semidirect
39. C42×C191D4semidirect
84. C191#2040semidirect
89. #382D191semidirect
124. C42D764semidirect

Maximal subgroups

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

subgroupindex
#271332442
C2×#202592502
#271326622
#271324322
#382×C1912
#2040191