Finite Group Databasebeta

← #37535698

Subgroups — #37535698

Order 23168.

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#26042092C211yesmaximal, characteristic
2#26041720C211yesmaximal, characteristic, complemented
3#26041551C211yesmaximal, characteristic, complemented
4#26041095C211yesmaximal, characteristic, complemented
5#26041087C211yesmaximal, characteristic, complemented
6#26041062C211yesmaximal, characteristic, complemented
7C2×Q32×C181C211yesmaximal, characteristic, complemented
8#19153864—21no—
9#19153848—22no—
10#19153847—21no—
11#19153847—21no—
12#19153839—21no—
13#19153838C2211yescharacteristic
14Q16×D181—21no—
15#19153822C2211yescharacteristic
16#19153762—21no—
17#19153759—21no—
18#19153756C2211yescharacteristic
19#19153752C2211yescharacteristic
20#19153735—21no—
21C2×Q16×C181C2211yescharacteristic
22C2×Q16×C181C2211yescharacteristic
23Q32×C181—22no—
24C2×C16×C181C2211yescharacteristic
25#15668450—22no—
26#15668450—41no—
27#15668449—21no—
28#15668449—42no—
29#15668449D411yescharacteristic
30Q8×D181—22no—
31Q8×D181—41no—
32Dic724D411yescharacteristic
33#15668439—22no—
34#15668439—41no—
35#15668438—21no—
36#15668436—22no—
37#15668436—41no—
38D1448D411yescharacteristic
39#15668433—21no—
40#15668433D411yescharacteristic
41#15668432—21no—
42C8×D181—21no—
43#15668424—21no—
44C2×Q8×C181—21no—
45C2×Q8×C181—21no—
46Q16×C181—21no—
47Q16×C181—21no—
48Q16×C181—21no—
49Q16×C181D412yes—
50C2×C8×C181C2311yescharacteristic
51C16×C181—21no—
52Dic362—21no—
53Dic362—42no—
54Dic362D811yescharacteristic
55D724—21no—
56D724—42no—
57D724D811yescharacteristic
58C22⋊D181—21no—
59C22⋊D181—41no—
60C4×D181—21no—
61C4×D181—42no—
62C4×D181—42no—
63C4×D181—41no—
64#13089678—21no—
65#13089678—41no—
66Q8×C181—22no—
67Q8×C181—41no—
68Q8×C181—41no—
69Q8×C181—41no—
70C2×C4×C181—41no—
71C2×C4×C181—41no—
72C2×C4×C181C2×D411yescharacteristic
73C8×C181C2×D411yescharacteristic
74C8×C181C2×D411yescharacteristic
75C22×C181AGL(1,ℤ/8)11yescharacteristic
76C2×D181—21no—
77C2×D181—41no—
78C4×C181—42no—
79C4×C181—81no—
80C4×C181#12011yescharacteristic
81C4×C181C2×D811yescharacteristic
82Dic181—21no—
83Dic181—41no—
84C2×C181—21no—
85C2×C181#44711yescharacteristic
86D181—41no—
87D181—81no—
88C181#219511yescharacteristic, complemented, Sylow
89#2195—1811nomaximal, Sylow
90#578—1811no—
91#510—1811no—
92C2×Q32D18111yescharacteristic, complemented
93#473—1811no—
94#362—1811no—
95#359—1811no—
96#350—1811no—
972−1+4—3621no—
98#137—3622no—
99#137—3621no—
100#137—3621no—
101#135—3621no—
102#135—1811no—
103C2×Q16—3621no—
104C2×Q16C2×D18111yescharacteristic
105C2×Q16C2×D18111yescharacteristic
106#131—1811no—
107Q32—22no—
108Q32—3621no—
109SD32—3621no—
110M32—1811no—
111C2×C16C2×D18111yescharacteristic
112#108—1811no—
113#101—3621no—
114#41—3622no—
115#41—3621no—
116#41—1811no—
117#41—7242no—
118#41—7241no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—3622no—
122C2×Q8—7241no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—3622no—
127Q16—1811no—
128Q16—7241no—
129Q16C22⋊D18112yes—
130SD16—3622no—
131SD16—3621no—
132SD16—7241no—
133D8—1811no—
134M16—3621no—
135M16—3621no—
136M16—1811no—
137C2×C8—3621no—
138C2×C8C22×D18111yescharacteristic
139C16—21no—
140C16—3621no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—3621no—
146Q8—1811no—
147Q8—7242no—
148D4—3621no—
149D4—3621no—
150D4—1811no—
151D4—7242no—
152D4—7241no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3621no—
156C2×C4—7242no—
157C2×C4—7242no—
158C2×C4—7241no—
159C2×C4D4×D18111yescharacteristic
160C8—3621no—
161C8—7241no—
162C8D4×D18111yescharacteristic
163C8C2×C22⋊D18111yescharacteristic
164C22—3621no—
165C22—7241no—
166C22#1915384011yescharacteristic
167C4—42no—
168C4—81no—
169C4—3621no—
170C4—7241no—
171C4#1915378411yescharacteristic
172C4D8×D18111yescharacteristic
173C2—21no—
174C2—14481no—
175C2—7241no—
176C2#2604141111yescharacteristic
subgroupG/H
centerC2#26041411
commutator, cosocleC2×C8×C181C23
FrattiniC2×C8C22×D181
FittingC2×Q32×C181C2
socleC2×C181#447
prime radical#26042092C2
hypercenterC2×Q32D181
hypocenterC181#2195
LCSG ▷ C2×C8×C181 ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #26041720C2semidirect
3. #26041551C2semidirect
4. #26041095C2semidirect
5. #26041087C2semidirect
6. #26041062C2semidirect
7. C2×Q32×C181C2semidirect
88. C181#2195semidirect
92. C2×Q32D181semidirect

Maximal subgroups

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

subgroupindex
#260420922
#260417202
#260415512
#260410952
#260410872
#260410622
C2×Q32×C1812
#2195181