Finite Group Databasebeta

← #37573750

Subgroups — #37573750

Order 24448.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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×#20259248C212yesmaximal, complemented
3#27132665C212yesmaximal, complemented
4#27132528C211yesmaximal, characteristic, complemented
5#343×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7#20259302—22no—
8#20259297—22no—
9#20259296—22no—
10C2×C4⋊Dic191C2211yescharacteristic
11C2×C4×Dic191C2211yescharacteristic
12#20259248—24no—
13#20259247—22no—
14#20259244—22no—
15C191⋊#95—22no—
16C2×M16×C191C2212yes—
17C2×C4⋊C4×C191C2211yescharacteristic
18#15690287—22no—
19#15690287—22no—
20#15690287—22no—
21#15690287—22no—
22C2×Dic382D412yes—
23C2×D764—22no—
24C2×D764D412yes—
25C2×C22⋊D191—22no—
26C22×Dic191—21no—
27C22×Dic191—21no—
28C2×C4×D191—22no—
29C4⋊Dic191—22no—
30C4⋊Dic191—22no—
31(C2×D191)⋊C4—24no—
32C4×Dic191—21no—
33C4×Dic191D412yescomplemented
34C22×C4×C191D412yes—
35C22×C4×C191C2311yescharacteristic
36M16×C191—22no—
37M16×C191—22no—
38C2×C8×C191—22no—
39C4⋊C4×C191—22no—
40C22×D191—22no—
41Dic382—22no—
42Dic382—22no—
43D764—22no—
44D764—22no—
45D764—82no—
46C22⋊D191—42no—
47C22⋊D191—42no—
48C2×Dic191—22no—
49C2×Dic191—22no—
50C2×Dic191—41no—
51C2×Dic191—41no—
52C2×Dic191—42no—
53C2×Dic191—41no—
54C4×D191—42no—
55C4×D191—42no—
56C23×C191C2×D411yescharacteristic
57C2×C4×C191—22no—
58C2×C4×C191—42no—
59C2×C4×C191C2×D411yescharacteristic
60C2×C4×C191C2×D412yes—
61C2×C4×C191#4112yes—
62C2×C4×C191#4111yescharacteristic
63C8×C191—42no—
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#12112yes—
74C4×C191#12312yes—
75Dic191—42no—
76Dic191—42no—
77Dic191—81no—
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#382—1911no—
90#343D19111yescharacteristic, complemented
91C2×#41—1912no—
92C2×M16C2×D19112yes—
93C22⋊Q8—3822no—
94#121—3822no—
95#121—3822no—
96C2×C4⋊C4—1911no—
97C2×C4⋊C4C2×D19111yescharacteristic
98C2×C42—1911no—
99#104—3824no—
100#103—3822no—
101#102—3822no—
102#95—3822no—
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—3821no—
112C22×C4—3822no—
113C22×C4—3821no—
114C22×C4D76412yes—
115C22×C4C22×D19111yescharacteristic
116M16—22no—
117M16—22no—
118C2×C8—22no—
119C4⋊C4—22no—
120C4⋊C4—3822no—
121C4⋊C4—3822no—
122C22⋊C4—3824no—
123C42—3821no—
124C42—1912no—
125C23—3822no—
126C23C2×D76411yescharacteristic
127Q8—3822no—
128Q8—3822no—
129D4—3822no—
130D4—3822no—
131D4—15282no—
132D4—7642no—
133D4—7642no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3822no—
137C2×C4—3822no—
138C2×C4—7642no—
139C2×C4—7641no—
140C2×C4—7641no—
141C2×C4—7641no—
142C2×C4—7642no—
143C2×C4—7642no—
144C2×C4D4×D19111yescharacteristic
145C2×C4D4×D19112yes—
146C2×C4#1569028712yes—
147C2×C4#1569028811yescharacteristic
148C8—42no—
149C22—21no—
150C22—21no—
151C22—7642no—
152C22—7642no—
153C22—7642no—
154C22#2025929211yescharacteristic
155C22#2025929711yescharacteristic
156C22#2025931011yescharacteristic
157C4—42no—
158C4—15281no—
159C4—7642no—
160C4—7642no—
161C4#2025929512yes—
162C4#2025930712yes—
163C2—21no—
164C2—21no—
165C2—15282no—
166C2#2713258111yescharacteristic
167C2#2713283811yescharacteristic
168C2#2713284311yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#343×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#343D191
hypocenterC191#2040
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#20259248C2semidirect
3. #27132665C2semidirect
4. #27132528C2semidirect
5. #343×C191C2semidirect
33. C4×Dic191D4semidirect
84. C191#2040semidirect
90. #343D191semidirect

Maximal subgroups

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

subgroupindex
#271332442
C2×#202592482
#271326652
#271325282
#343×C1912
#2040191