Finite Group Databasebeta

← #37574483

Subgroups — #37574483

Order 24448.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#27133476C211yesmaximal, characteristic, complemented
2#27133099C211yesmaximal, characteristic, complemented
3#27132930C211yesmaximal, characteristic, complemented
4#27132479C211yesmaximal, characteristic, complemented
5#27132471C211yesmaximal, characteristic, complemented
6#27132446C211yesmaximal, characteristic, complemented
7C2×SD32×C191C211yesmaximal, characteristic, complemented
8#20259370—21no—
9#20259354—22no—
10#20259353—21no—
11#20259348—21no—
12#20259345—21no—
13#20259344C2211yescharacteristic
14Q16×D191—21no—
15#20259328C2211yescharacteristic
16#20259266—21no—
17#20259263—21no—
18#20259262C2211yescharacteristic
19#20259258C2211yescharacteristic
20#20259239—21no—
21C2×Q16×C191C2211yescharacteristic
22C2×D8×C191C2211yescharacteristic
23SD32×C191—22no—
24C2×C16×C191C2211yescharacteristic
25#15690288—22no—
26#15690288—41no—
27#15690287—21no—
28#15690287—42no—
29#15690287D411yescharacteristic
30Q8×D191—22no—
31Q8×D191—41no—
32Dic764D411yescharacteristic
33#15690277—22no—
34#15690276—21no—
35#15690275—41no—
36#15690274—22no—
37D1528D411yescharacteristic
38#15690272—41no—
39#15690271—21no—
40#15690271D411yescharacteristic
41#15690270—21no—
42C8×D191—21no—
43C191⋊C16—21no—
44C2×Q8×C191—21no—
45C2×D4×C191—21no—
46Q16×C191—21no—
47Q16×C191D412yes—
48D8×C191—21no—
49D8×C191—21no—
50C2×C8×C191C2311yescharacteristic
51C16×C191—21no—
52Dic382—21no—
53Dic382—42no—
54Dic382D811yescharacteristic
55D764—21no—
56D764—42no—
57D764D811yescharacteristic
58C22⋊D191—21no—
59C22⋊D191—41no—
60C4×D191—21no—
61C4×D191—42no—
62C4×D191—42no—
63C4×D191—41no—
64C191⋊C8—21no—
65C191⋊C8—41no—
66C23×C191—41no—
67Q8×C191—22no—
68Q8×C191—41no—
69D4×C191—41no—
70D4×C191—41no—
71C2×C4×C191—41no—
72C2×C4×C191C2×D411yescharacteristic
73C8×C191C2×D411yescharacteristic
74C8×C191C2×D411yescharacteristic
75C22×C191—81no—
76C22×C191—161no—
77C22×C191AGL(1,ℤ/8)11yescharacteristic
78C2×D191—21no—
79C2×D191—41no—
80C4×C191—42no—
81C4×C191#12011yescharacteristic
82C4×C191C2×D811yescharacteristic
83Dic191—21no—
84Dic191—41no—
85C2×C191—21no—
86C2×C191—161no—
87C2×C191#44711yescharacteristic
88D191—41no—
89D191—81no—
90C191#219311yescharacteristic, complemented, Sylow
91#2193—1911nomaximal, Sylow
92#578—1911no—
93#509—1911no—
94C2×SD32D19111yescharacteristic, complemented
95#472—1911no—
96#362—1911no—
97#359—1911no—
98#350—1911no—
992−1+4—3821no—
100#137—3822no—
101#137—3821no—
102AGL(1,ℤ/8)—3821no—
103#135—3821no—
104#135—1911no—
105C2×Q16—3821no—
106C2×Q16C2×D19111yescharacteristic
107C2×D8C2×D19111yescharacteristic
108#131—1911no—
109SD32—22no—
110SD32—3821no—
111D16—3821no—
112M32—1911no—
113C2×C16C2×D19111yescharacteristic
114#108—1911no—
115#100—3821no—
116#41—3822no—
117#41—3821no—
118#41—1911no—
119#41—7642no—
120#41—7641no—
121C2×Q8—21no—
122C2×Q8—3822no—
123C2×Q8—7641no—
124C2×D4—21no—
125Q16—21no—
126Q16—3822no—
127Q16—1911no—
128Q16C22⋊D19112yes—
129SD16—3822no—
130SD16—3821no—
131SD16—7641no—
132D8—21no—
133D8—21no—
134D8—1911no—
135D8—7641no—
136M16—3821no—
137M16—3821no—
138M16—1911no—
139C2×C8—3821no—
140C2×C8C22×D19111yescharacteristic
141C16—21no—
142C16—3821no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—3821no—
147Q8—1911no—
148Q8—7642no—
149D4—41no—
150D4—41no—
151D4—3821no—
152D4—3821no—
153D4—1911no—
154D4—7642no—
155D4—7641no—
156C2×C4—41no—
157C2×C4—3821no—
158C2×C4—7642no—
159C2×C4—7642no—
160C2×C4—7641no—
161C2×C4D4×D19111yescharacteristic
162C8—3821no—
163C8—7641no—
164C8D4×D19111yescharacteristic
165C8C2×C22⋊D19111yescharacteristic
166C22—81no—
167C22—161no—
168C22—3821no—
169C22—7641no—
170C22#2025934611yescharacteristic
171C4—42no—
172C4—3821no—
173C4—7641no—
174C4#2025929011yescharacteristic
175C4D8×D19111yescharacteristic
176C2—21no—
177C2—161no—
178C2—15281no—
179C2—7641no—
180C2#2713279511yescharacteristic
subgroupG/H
centerC2#27132795
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
FittingC2×SD32×C191C2
socleC2×C191#447
hypercenterC2×SD32D191
hypocenterC191#2193
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #27133476C2semidirect
2. #27133099C2semidirect
3. #27132930C2semidirect
4. #27132479C2semidirect
5. #27132471C2semidirect
6. #27132446C2semidirect
7. C2×SD32×C191C2semidirect
90. C191#2193semidirect
94. C2×SD32D191semidirect

Maximal subgroups

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

subgroupindex
#271334762
#271330992
#271329302
#271324792
#271324712
#271324462
C2×SD32×C1912
#2193191