Finite Group Databasebeta

← #37571556

Subgroups — #37571556

Order 24448.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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
2#27132981C212yesmaximal, complemented
3#27132396C212yesmaximal, complemented
4#27132389C211yesmaximal, characteristic, complemented
5#400×C191C211yesmaximal, characteristic, complemented
6C2×#15690287—21no—
7#20259302—22no—
8#20259297—22no—
9#20259296—21no—
10#20259296C2212yes—
11#20259253—22no—
12#20259242—22no—
13C22⋊(C191⋊C8)C2212yes—
14C2×C4⋊C4×C191C2211yescharacteristic
15C2×C4⋊C4×C191C2211yescharacteristic
16#95×C191—21no—
17#95×C191—21no—
18#95×C191C2211yescharacteristic
19#15690287—42no—
20#15690287—42no—
21C2×Dic382—21no—
22C2×D764—21no—
23C2×D764—21no—
24C2×D764D412yes—
25C2×C22⋊D191—22no—
26C2×C4×D191—22no—
27C2×C191⋊C8—22no—
28C4⋊Dic191—21no—
29C4⋊Dic191D412yes—
30(C2×D191)⋊C4—22no—
31(C2×D191)⋊C4—22no—
32C22×C4×C191—21no—
33C22×C4×C191—21no—
34C22×C4×C191D411yescharacteristic
35C22×C4×C191D411yescharacteristic
36C22×C4×C191C2311yescharacteristic
37C4⋊C4×C191—22no—
38C4⋊C4×C191—22no—
39C22×D191—22no—
40Dic382—42no—
41D764—42no—
42D764—42no—
43D764—81no—
44C22⋊D191—42no—
45C22⋊D191—42no—
46C2×Dic191—22no—
47C4×D191—44no—
48C191⋊C8—42no—
49C23×C191C2×D411yescharacteristic
50C2×C4×C191—21no—
51C2×C4×C191—21no—
52C2×C4×C191—21no—
53C2×C4×C191—41no—
54C2×C4×C191—41no—
55C2×C4×C191—41no—
56C2×C4×C191—41no—
57C2×C4×C191—42no—
58C2×C4×C191—41no—
59C2×C4×C191—41no—
60C2×C4×C191SD1612yes—
61C2×C4×C191C2×D412yes—
62C22×C191—21no—
63C22×C191—21no—
64C22×C191#12011yescharacteristic
65C22×C191C2×SD1611yescharacteristic
66C22×C191AGL(1,ℤ/8)11yescharacteristic
67C2×D191—42no—
68C2×D191—42no—
69C2×D191—42no—
70C4×C191—22no—
71C4×C191—22no—
72C4×C191—41no—
73C4×C191—81no—
74C4×C191—81no—
75Dic191—42no—
76C2×C191—21no—
77C2×C191—21no—
78C2×C191#45011yescharacteristic
79C2×C191#45411yescharacteristic
80C2×C191#45811yescharacteristic
81D191—82no—
82C191#161611yescharacteristic, complemented, Sylow
83#1616—1911nomaximal, Sylow
84#537—1911no—
85#481—1912no—
86#400D19111yescharacteristic, complemented
87#327—1912no—
88#324—1911no—
89C2×#41—3821no—
90C22⋊Q8—3822no—
91#121—3822no—
92#121—3821no—
93#121—1912no—
94C2×C4⋊C4C2×D19111yescharacteristic
95C2×C4⋊C4C2×D19111yescharacteristic
96#106—3822no—
97#102—3822no—
98C22⋊C8—1912no—
99#95—21no—
100#95—21no—
101#95C2×D19111yescharacteristic
102#41—7642no—
103#41—7642no—
104C2×Q8—3821no—
105C2×D4—3821no—
106C2×D4—3821no—
107C2×D4—3822no—
108C2×D4—1912no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—3822no—
112C22×C4C22⋊D19111yescharacteristic
113C22×C4C22⋊D19111yescharacteristic
114C22×C4C22×D19111yescharacteristic
115C2×C8—3822no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—3821no—
119C4⋊C4—1912no—
120C22⋊C4—3822no—
121C22⋊C4—3822no—
122C23—3822no—
123C23C2×C22⋊D19111yescharacteristic
124Q8—7642no—
125D4—15281no—
126D4—7642no—
127D4—7642no—
128D4—7642no—
129D4—7642no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3822no—
141C2×C4—7644no—
142C2×C4#1569027412yes—
143C2×C4D4×D19112yes—
144C8—7642no—
145C22—21no—
146C22—21no—
147C22—7642no—
148C22—7642no—
149C22—7642no—
150C22#2025929011yescharacteristic
151C22C2×#1569027411yescharacteristic
152C22#2025934711yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—7642no—
159C2—21no—
160C2—21no—
161C2—15282no—
162C2#2713281311yescharacteristic
163C2#2713283511yescharacteristic
164C2#2713285211yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#400×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#400D191
hypocenterC191#1616
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #27132981C2semidirect
3. #27132396C2semidirect
4. #27132389C2semidirect
5. #400×C191C2semidirect
82. C191#1616semidirect
86. #400D191semidirect

Maximal subgroups

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

subgroupindex
#271332442
#271329812
#271323962
#271323892
#400×C1912
#1616191