Finite Group Databasebeta

← #37574497

Subgroups — #37574497

Order 24448.

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

normal subgroups only

This group has 206 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
2#27133104C211yesmaximal, characteristic, complemented
3#27132935C211yesmaximal, characteristic, complemented
4#27132479C211yesmaximal, characteristic, complemented
5#27132471C211yesmaximal, characteristic, complemented
6#27132446C211yesmaximal, characteristic, complemented
7C2×Q32×C191C211yesmaximal, characteristic, complemented
8#20259370—21no—
9#20259354—22no—
10#20259353—21no—
11#20259353—21no—
12#20259345—21no—
13#20259344C2211yescharacteristic
14Q16×D191—21no—
15#20259328C2211yescharacteristic
16#20259268—21no—
17#20259265—21no—
18#20259262C2211yescharacteristic
19#20259258C2211yescharacteristic
20#20259241—21no—
21C2×Q16×C191C2211yescharacteristic
22C2×Q16×C191C2211yescharacteristic
23Q32×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#15690277—41no—
35#15690276—21no—
36#15690274—22no—
37#15690274—41no—
38D1528D411yescharacteristic
39#15690271—21no—
40#15690271D411yescharacteristic
41#15690270—21no—
42C8×D191—21no—
43C191⋊C16—21no—
44C2×Q8×C191—21no—
45C2×Q8×C191—21no—
46Q16×C191—21no—
47Q16×C191—21no—
48Q16×C191—21no—
49Q16×C191D412yes—
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—
66Q8×C191—22no—
67Q8×C191—41no—
68Q8×C191—41no—
69Q8×C191—41no—
70C2×C4×C191—41no—
71C2×C4×C191—41no—
72C2×C4×C191C2×D411yescharacteristic
73C8×C191C2×D411yescharacteristic
74C8×C191C2×D411yescharacteristic
75C22×C191AGL(1,ℤ/8)11yescharacteristic
76C2×D191—21no—
77C2×D191—41no—
78C4×C191—42no—
79C4×C191—81no—
80C4×C191#12011yescharacteristic
81C4×C191C2×D811yescharacteristic
82Dic191—21no—
83Dic191—41no—
84C2×C191—21no—
85C2×C191#44711yescharacteristic
86D191—41no—
87D191—81no—
88C191#219511yescharacteristic, complemented, Sylow
89#2195—1911nomaximal, Sylow
90#578—1911no—
91#510—1911no—
92C2×Q32D19111yescharacteristic, complemented
93#473—1911no—
94#362—1911no—
95#359—1911no—
96#350—1911no—
972−1+4—3821no—
98#137—3822no—
99#137—3821no—
100#137—3821no—
101#135—3821no—
102#135—1911no—
103C2×Q16—3821no—
104C2×Q16C2×D19111yescharacteristic
105C2×Q16C2×D19111yescharacteristic
106#131—1911no—
107Q32—22no—
108Q32—3821no—
109SD32—3821no—
110M32—1911no—
111C2×C16C2×D19111yescharacteristic
112#108—1911no—
113#101—3821no—
114#41—3822no—
115#41—3821no—
116#41—1911no—
117#41—7642no—
118#41—7641no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—3822no—
122C2×Q8—7641no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—3822no—
127Q16—1911no—
128Q16—7641no—
129Q16C22⋊D19112yes—
130SD16—3822no—
131SD16—3821no—
132SD16—7641no—
133D8—1911no—
134M16—3821no—
135M16—3821no—
136M16—1911no—
137C2×C8—3821no—
138C2×C8C22×D19111yescharacteristic
139C16—21no—
140C16—3821no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—3821no—
146Q8—1911no—
147Q8—7642no—
148D4—3821no—
149D4—3821no—
150D4—1911no—
151D4—7642no—
152D4—7641no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3821no—
156C2×C4—7642no—
157C2×C4—7642no—
158C2×C4—7641no—
159C2×C4D4×D19111yescharacteristic
160C8—3821no—
161C8—7641no—
162C8D4×D19111yescharacteristic
163C8C2×C22⋊D19111yescharacteristic
164C22—3821no—
165C22—7641no—
166C22#2025934611yescharacteristic
167C4—42no—
168C4—81no—
169C4—3821no—
170C4—7641no—
171C4#2025929011yescharacteristic
172C4D8×D19111yescharacteristic
173C2—21no—
174C2—15281no—
175C2—7641no—
176C2#2713279511yescharacteristic
subgroupG/H
centerC2#27132795
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
FittingC2×Q32×C191C2
socleC2×C191#447
prime radical#27133476C2
hypercenterC2×Q32D191
hypocenterC191#2195
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #27133104C2semidirect
3. #27132935C2semidirect
4. #27132479C2semidirect
5. #27132471C2semidirect
6. #27132446C2semidirect
7. C2×Q32×C191C2semidirect
88. C191#2195semidirect
92. C2×Q32D191semidirect

Maximal subgroups

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

subgroupindex
#271334762
#271331042
#271329352
#271324792
#271324712
#271324462
C2×Q32×C1912
#2195191