Finite Group Databasebeta

← #37535673

Subgroups — #37535673

Order 23168.

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

normal subgroups only

This group has 216 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#26042076C211yesmaximal, characteristic
2#26041722C211yesmaximal, characteristic, complemented
3#26041719C211yesmaximal, characteristic, complemented
4#26041538C211yesmaximal, characteristic, complemented
5#26041088C211yesmaximal, characteristic, complemented
6#26041060C211yesmaximal, characteristic, complemented
7#360×C181C211yesmaximal, characteristic, complemented
8#41×D181—21no—
9#19153848—21no—
10#19153845—21no—
11#19153843—21no—
12#19153840—21no—
13#19153838C2211yescharacteristic
14#19153836—21no—
15C2×Dic724C2211yescharacteristic, complemented
16C2×#15668432C2211yescharacteristic
17#19153796—21no—
18Dic1448—21no—
19#19153762—21no—
20#19153761—21no—
21#19153760—21no—
22#19153756C2211yescharacteristic, complemented
23#19153739—21no—
24#135×C181C2211yescharacteristic
25M32×C181C2211yescharacteristic, complemented
26#106×C181C2211yescharacteristic, complemented
27#15668450—21no—
28#15668449—21no—
29#15668449—41no—
30#15668448—21no—
31#15668448—41no—
32C2×Dic362—21no—
33Q8×D181—21no—
34D4×D181—21no—
35D4×D181—41no—
36C2×C4×D181—41no—
37C2×C4×D181D411yescharacteristic
38Dic724—21no—
39Dic724—21no—
40Dic724D411yescharacteristic
41#15668439—21no—
42#15668438—21no—
43#15668437—21no—
44#15668436—21no—
45D1448D411yescharacteristic
46#15668434—21no—
47#15668432—21no—
48#15668432—21no—
49C2×#13089678D411yescharacteristic
50C4⋊Dic181—41no—
51#15668426—41no—
52#15668424—21no—
53#41×C181—21no—
54Q16×C181D411yescharacteristic
55SD16×C181—21no—
56D8×C181D411yescharacteristic
57C2×C8×C181C2311yescharacteristic
58C4⋊C4×C181—21no—
59C16×C181—21no—
60C22×D181—41no—
61C22×D181D811yescharacteristic
62Dic362—21no—
63Dic362—41no—
64Dic362—41no—
65Dic362—41no—
66D724—21no—
67D724—41no—
68C22⋊D181—41no—
69C22⋊D181—41no—
70C22⋊D181—41no—
71C2×Dic181—41no—
72C2×Dic181—41no—
73C2×Dic181D811yescharacteristic
74C4×D181—21no—
75C4×D181—21no—
76C4×D181—41no—
77C4×D181—41no—
78C4×D181—41no—
79#13089678—21no—
80Q8×C181—21no—
81D4×C181—21no—
82D4×C181—41no—
83C2×C4×C181—41no—
84C2×C4×C181—41no—
85C2×C4×C181C2×D411yescharacteristic
86C8×C181C2×D411yescharacteristic
87C8×C181C2×D411yescharacteristic
88C22×C181—41no—
89C22×C181C2×D811yescharacteristic
90C2×D181—21no—
91C2×D181—41no—
92C2×D181—41no—
93C2×D181—82no—
94C4×C181—41no—
95C4×C181—81no—
96C4×C181#12011yescharacteristic
97C4×C181AGL(1,ℤ/8)11yescharacteristic
98Dic181—21no—
99Dic181—41no—
100Dic181—81no—
101C2×C181—21no—
102C2×C181—81no—
103C2×C181#44711yescharacteristic
104D181—41no—
105D181—81no—
106C181#219111yescharacteristic, complemented, Sylow
107#2191—1811nomaximal, Sylow
108#575—1811no—
109#510—1811no—
110#510—1811no—
111#470—1811no—
112#360—1811no—
113#360D18111yescharacteristic, complemented
114#349—1811no—
115C2×#41—3621no—
116#137—3621no—
117#137—3621no—
118AGL(1,ℤ/8)—3621no—
119AGL(1,ℤ/8)—3621no—
120#135—3621no—
121#135—1811no—
122#135C2×D18111yescharacteristic
123C2×Q16—1811no—
124C2×M16—1811no—
125C22⋊Q8—3621no—
126Q32—3621no—
127Q32—3621no—
128SD32—3621no—
129SD32—3621no—
130M32—1811no—
131M32C2×D18111yescharacteristic, complemented
132#106C2×D18111yescharacteristic, complemented
133#103—3621no—
134#41—21no—
135#41—3621no—
136#41—3621no—
137#41—3621no—
138#41—7241no—
139#41—7241no—
140C2×Q8—3621no—
141C2×Q8—3621no—
142C2×D4—3621no—
143C2×D4—7241no—
144C22×C4—1811no—
145C22×C4—7241no—
146Q16—3621no—
147Q16—3621no—
148Q16—3621no—
149Q16—1811no—
150Q16D72411yescharacteristic
151SD16—21no—
152SD16—3621no—
153SD16—3621no—
154SD16—3621no—
155D8—3621no—
156D8—1811no—
157D8D72411yescharacteristic
158M16—3621no—
159M16—3621no—
160C2×C8—1811no—
161C2×C8C22×D18111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—7241no—
164C22⋊C4—7241no—
165C16—21no—
166C16—3621no—
167C23—1811no—
168C23—7241no—
169Q8—21no—
170Q8—3621no—
171Q8—7241no—
172Q8—7241no—
173Q8—7241no—
174D4—21no—
175D4—41no—
176D4—3621no—
177D4—7241no—
178D4—7241no—
179D4—7241no—
180D4—7241no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—3621no—
184C2×C4—3621no—
185C2×C4—1811no—
186C2×C4—7241no—
187C2×C4—7241no—
188C2×C4—7241no—
189C2×C4—7241no—
190C2×C4—7241no—
191C2×C4D4×D18111yescharacteristic
192C8—3621no—
193C8D4×D18111yescharacteristic
194C8C2×D72411yescharacteristic
195C22—41no—
196C22—3621no—
197C22—14482no—
198C22—7241no—
199C22—7241no—
200C22D8×D18111yescharacteristic
201C4—41no—
202C4—81no—
203C4—3621no—
204C4—14481no—
205C4—7241no—
206C4#1915378611yescharacteristic
207C4#1915384311yescharacteristic
208C2—21no—
209C2—81no—
210C2—14481no—
211C2—7241no—
212C2#2604141411yescharacteristic
subgroupG/H
centerC2#26041414
commutator, cosocleC2×C8×C181C23
FrattiniC2×C8C22×D181
Fitting#360×C181C2
socleC2×C181#447
prime radical#26042076C2
hypercenter#360D181
hypocenterC181#2191
LCSG ▷ C2×C8×C181 ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #26041722C2semidirect
3. #26041719C2semidirect
4. #26041538C2semidirect
5. #26041088C2semidirect
6. #26041060C2semidirect
7. #360×C181C2semidirect
15. C2×Dic724C22semidirect
22. #19153756C22semidirect
25. M32×C181C22semidirect
26. #106×C181C22semidirect
106. C181#2191semidirect
113. #360D181semidirect
131. M32C2×D181semidirect
132. #106C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420762
#260417222
#260417192
#260415382
#260410882
#260410602
#360×C1812
#2191181