Finite Group Databasebeta

← #37549054

Subgroups — #37549054

Order 23168.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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#26042300C211yesmaximal, characteristic, complemented
2#26042296C211yesmaximal, characteristic, complemented
3#26042129C212yesmaximal, complemented
4#26042127C212yesmaximal, complemented
5#26041747C211yesmaximal, characteristic
6#19153883—21no—
7C4⋊#13089685C2212yes—
8C22⋊#13089685—21no—
9C22⋊#13089685—21no—
10#19153871—21no—
11C4×#13089685C2212yes—
12C2×#15668449C411yescharacteristic
13#19153781C411yescharacteristic
14#19153781C2211yescharacteristic
15#19153778C411yescharacteristic
16#19153778C2211yescharacteristic
17#19153776—21no—
18#19153776—21no—
19#19153773—21no—
20C2×C4×Dic181C2211yescharacteristic
21C42×D181—21no—
22#117×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25#15668449—22no—
26#15668449—22no—
27C2×Dic362C2×C411yescharacteristic
28C2×D724C2×C411yescharacteristic
29C2×C22⋊D181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×C4×D181—21no—
33C2×C4×D181—21no—
34C2×C4×D181—21no—
35#15668428—21no—
36#15668428—21no—
37#15668426—21no—
38#15668426—21no—
39C4×Dic181—21no—
40C4×Dic181—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181C2311yescharacteristic
45C22×C4×C181C2×C411yescharacteristic
46C4⋊C4×C181C2×C411yescharacteristic
47C4⋊C4×C181C2×C411yescharacteristic
48C22⋊C4×C181—21no—
49C42×C181—21no—
50#13089685—42no—
51#13089685—42no—
52C22×D181—21no—
53Dic362—21no—
54Dic362M1612yes—
55D724—21no—
56D724M1612yes—
57C22⋊D181—24no—
58C2×Dic181—21no—
59C2×Dic181—22no—
60C2×Dic181—41no—
61C2×Dic181C22⋊C411yescharacteristic
62C2×Dic181C22⋊C411yescharacteristic
63C2×Dic181C2×D411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C4×D181—24no—
66C4×D181—42no—
67C4×D181—42no—
68C23×C181C22⋊C411yescharacteristic
69C2×C4×C181—21no—
70C2×C4×C181—21no—
71C2×C4×C181—21no—
72C2×C4×C181—21no—
73C2×C4×C181C22⋊C411yescharacteristic
74C2×C4×C181C22×C411yescharacteristic
75C22×C181—21no—
76C22×C181—21no—
77C22×C181—21no—
78C22×C181C2×C22⋊C411yescharacteristic
79C2×D181—22no—
80C2×D181—41no—
81C2×D181—41no—
82C4×C181—21no—
83C4×C181—41no—
84C4×C181—41no—
85C4×C181C2×M1611yescharacteristic
86C4×C181C2×M1611yescharacteristic
87Dic181—22no—
88Dic181—21no—
89Dic181—21no—
90Dic181—21no—
91Dic181#13512yes—
92C2×C181—41no—
93C2×C181#40711yescharacteristic
94C2×C181#41611yescharacteristic
95C2×C181#42111yescharacteristic
96D181—42no—
97C181#148811yescharacteristic, complemented, Sylow
98#1488—1811nomaximal, Sylow
99C4×#41—1811no—
100#432—1811no—
101#431—1811no—
102Q8⋊C8—1812no—
103D4⋊C8—1812no—
104C2×#41—1811no—
105C4×Q8—1811no—
106C4×Q8—1811no—
107C4×D4—3621no—
108C4×D4—3621no—
109C4×D4—1811no—
110C4×D4—1811no—
111#117—3621no—
112#117#1062438211yescharacteristic
113C2×C42—3621no—
114C2×C42—1811no—
115C4⋊C8—3621no—
116C4⋊C8—1812no—
117C22⋊C8—3621no—
118C22⋊C8—3621no—
119#97—3621no—
120C4×C8—1812no—
121#41—3622no—
122#41—3622no—
123C2×Q8—1811no—
124C2×D4—3621no—
125C2×D4—1811no—
126C22×C4—3621no—
127C22×C4—3621no—
128C22×C4—3621no—
129C22×C4—1811no—
130C22×C4—1811no—
131C22×C4C2×#1062438211yescharacteristic
132C2×C8—3622no—
133C2×C8—3622no—
134C4⋊C4—3621no—
135C4⋊C4—3621no—
136C4⋊C4C2×#1062438211yescharacteristic
137C4⋊C4C2×#1062438211yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—3621no—
140C22⋊C4—3621no—
141C42—21no—
142C42—3621no—
143C42—3621no—
144C42—1811no—
145C42—1811no—
146C42—1811no—
147C42—1811no—
148C23—3621no—
149C23C22⋊#1062438211yescharacteristic
150Q8—3621no—
151Q8—1812no—
152D4—3624no—
153D4—3621no—
154D4—1812no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—3624no—
160C2×C4—3621no—
161C2×C4—3622no—
162C2×C4—1811no—
163C2×C4—1811no—
164C2×C4—1811no—
165C2×C4—1811no—
166C2×C4—7242no—
167C2×C4—7242no—
168C2×C4—7241no—
169C2×C4C22⋊#1062438211yescharacteristic
170C2×C4C22×#1062438211yescharacteristic
171C8—7242no—
172C8—7242no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—3622no—
177C22—7241no—
178C22—7241no—
179C22C2×C22⋊#1062438211yescharacteristic
180C4—21no—
181C4—41no—
182C4—41no—
183C4—3622no—
184C4—3621no—
185C4—3621no—
186C4—3621no—
187C4—1812no—
188C4D181⋊M1611yescharacteristic
189C4D181⋊M1611yescharacteristic
190C2—41no—
191C2—7242no—
192C2#2604225111yescharacteristic
193C2#2604226911yescharacteristic
194C2#2604227611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#117×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#15668449C4
cosocleC4×Dic181C23
hypercenter#117#10624382
hypocenterC181#1488
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #26042300C2semidirect
2. #26042296C2semidirect
3. #26042129C2semidirect
4. #26042127C2semidirect
97. C181#1488semidirect

Maximal subgroups

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

subgroupindex
#260423002
#260422962
#260421292
#260421272
#260417472
#1488181