Finite Group Databasebeta

← #37549134

Subgroups — #37549134

Order 23168.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#26042302C211yesmaximal, characteristic, complemented
2#26042223C211yesmaximal, characteristic, complemented
3#26042133C212yesmaximal, complemented
4#26042131C212yesmaximal
5#26041816C211yesmaximal, characteristic
6C2×C4⋊#10624382—21no—
7#19153883—21no—
8#19153873C2212yes—
9#19153871—21no—
10(C2×#10624382)⋊C4—21no—
11(C2×#10624382)⋊C4C2212yes—
12#19153811—21no—
13#19153807C411yescharacteristic, complemented
14#19153805C411yescharacteristic, complemented
15#19153801—21no—
16#19153792C2211yescharacteristic
17#19153791C2211yescharacteristic
18C4×D724—21no—
19C4×D724C411yescharacteristic, complemented
20#19153773—21no—
21C42×D181C2211yescharacteristic
22C4×Q8×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4⋊#10624382—42no—
26C2×D724—21no—
27C2×D724C2×C411yescharacteristic
28C2×C4×D181—21no—
29C2×C4×D181D411yescharacteristic
30C2×C4×D181D411yescharacteristic
31C2×C4×D181C2311yescharacteristic
32C4⋊Dic181—21no—
33C4⋊Dic181C2×C411yescharacteristic
34#15668428—21no—
35#15668428—21no—
36#15668426—21no—
37#15668426—21no—
38#15668426—21no—
39#15668426—21no—
40#15668426—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C2×Q8×C181C2×C411yescharacteristic
45C4⋊C4×C181—21no—
46C4⋊C4×C181C2×C411yescharacteristic
47C42×C181—21no—
48C42×C181C2×C411yescharacteristic
49C2×#10624382—42no—
50C2×#10624382—42no—
51C2×#10624382—42no—
52#13089685—42no—
53C22×D181—21no—
54C22×D181C2×D411yescharacteristic
55D724—41no—
56D724—41no—
57D724—41no—
58C2×Dic181—21no—
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C2×D411yescharacteristic
62C4×D181—21no—
63C4×D181—21no—
64C4×D181—41no—
65C4×D181—41no—
66C4×D181—42no—
67Q8×C181—41no—
68C2×C4×C181—21no—
69C2×C4×C181—21no—
70C2×C4×C181C22⋊C411yescharacteristic
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22×C411yescharacteristic
73C22×C181C2×C22⋊C411yescharacteristic
74C2×D181—21no—
75C2×D181—21no—
76C2×D181—41no—
77C2×D181—41no—
78C2×D181—41no—
79C2×D181AGL(1,ℤ/8)11yescharacteristic
80C2×D181#13711yescharacteristic
81#10624382—82no—
82C4×C181—21no—
83C4×C181—21no—
84C4×C181—21no—
85C4×C181—41no—
86C4×C181—41no—
87Dic181—21no—
88Dic181—21no—
89Dic181—21no—
90Dic181—41no—
91C2×C181#41011yescharacteristic
92C2×C181#41711yescharacteristic
93C2×C181#42111yescharacteristic
94D181—21no—
95D181—21no—
96D181—81no—
97C181#151211yescharacteristic, complemented, Sylow
98#1512—1811nomaximal, Sylow
99#529—1811no—
100#432—1811no—
101#382—1811no—
102#328—1812no—
103#327—1812no—
104#126—3621no—
105#125—1811no—
106#124—1811no—
107#123—3621no—
108C22⋊Q8—1811no—
109#121—1811no—
110C4×Q8#1062438211yescharacteristic, complemented
111C4×D4—3621no—
112C4×D4—1811no—
113#117—3621no—
114C2×C4⋊C4—3621no—
115C2×C42—1811no—
116C4⋊C8—3621no—
117C22⋊C8—1812no—
118#97—3621no—
119#95—3621no—
120#95—1812no—
121C2×Q8C2×#1062438211yescharacteristic
122C2×D4—3621no—
123C2×D4—1811no—
124C22×C4—3621no—
125C22×C4—3622no—
126C22×C4—1811no—
127C22×C4—1811no—
128C22×C4—1811no—
129C2×C8—3622no—
130C4⋊C4—21no—
131C4⋊C4—3621no—
132C4⋊C4—3621no—
133C4⋊C4—3621no—
134C4⋊C4—1811no—
135C4⋊C4—7242no—
136C4⋊C4C2×#1062438211yescharacteristic
137C22⋊C4—3621no—
138C22⋊C4—3621no—
139C22⋊C4—3621no—
140C22⋊C4—3621no—
141C22⋊C4—3621no—
142C42—21no—
143C42—1811no—
144C42—1811no—
145C42—1811no—
146C42C2×#1062438211yescharacteristic
147C23—3621no—
148C23—1811no—
149Q8—41no—
150D4—7241no—
151D4—7241no—
152D4—7241no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—3621no—
158C2×C4—1811no—
159C2×C4—1811no—
160C2×C4—1811no—
161C2×C4—7241no—
162C2×C4—7241no—
163C2×C4—7242no—
164C2×C4—7242no—
165C2×C4—7242no—
166C2×C4—7242no—
167C2×C4C22⋊#1062438211yescharacteristic
168C2×C4C22⋊#1062438211yescharacteristic
169C2×C4C22×#1062438211yescharacteristic
170C8—7242no—
171C22—3621no—
172C22—3621no—
173C22—1811no—
174C22—1811no—
175C22—7241no—
176C22—7241no—
177C22—7241no—
178C22C2×C22⋊#1062438211yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—3621no—
185C4—3621no—
186C4—3621no—
187C4—14482no—
188C4—7241no—
189C2—3621no—
190C2—3621no—
191C2—14481no—
192C2#2604225811yescharacteristic
193C2#2604227011yescharacteristic
194C2#2604227811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153791C22
cosocleC2×C4×D181C23
hypercenterC4×Q8#10624382
hypocenterC181#1512
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. #26042223C2semidirect
3. #26042133C2semidirect
13. #19153807C4semidirect
14. #19153805C4semidirect
19. C4×D724C4semidirect
22. C4×Q8×C181C4semidirect
97. C181#1512semidirect
110. C4×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260422232
#260421332
#260421312
#260418162
#1512181