Finite Group Databasebeta

← #37532206

Subgroups — #37532206

Order 23168.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#26041815C211yesmaximal, characteristic
2#26041329C211yesmaximal, characteristic, complemented
3#26041124C211yesmaximal, characteristic, complemented
4#26041016C211yesmaximal, characteristic, complemented
5#26041014C211yesmaximal, characteristic
6#26041012C211yesmaximal, characteristic
7#328×C181C211yesmaximal, characteristic, complemented
8#19153811—21no—
9#19153807C411yescharacteristic, complemented
10#19153805C411yescharacteristic, complemented
11#19153800—21no—
12#19153790C2211yescharacteristic
13Q8×Dic181C411yescharacteristic, complemented
14#19153778C411yescharacteristic, complemented
15#19153776—21no—
16#19153774—21no—
17C2×C4×Dic181—21no—
18C2×C4×Dic181C2211yescharacteristic
19#19153745—21no—
20C22⋊#13089678C2211yescharacteristic
21C8×Dic181—21no—
22#19153723—21no—
23#19153723C2211yescharacteristic
24C22⋊Q8×C181C2211yescharacteristic
25C22⋊C8×C181C2211yescharacteristic
26#95×C181C2211yescharacteristic
27C2×D724C2×C411yescharacteristic
28C2×C22⋊D181—21no—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×C4×D181—21no—
33C2×#13089678—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38#15668426—21no—
39#15668426—21no—
40#15668426—21no—
41#15668426—21no—
42C4×Dic181—24no—
43C4×Dic181—21no—
44C4×Dic181C2×C411yescharacteristic
45C4×Dic181C2×C411yescharacteristic
46C4×Dic181D411yescharacteristic
47C4×Dic181D411yescharacteristic
48C2×Q8×C181C2×C411yescharacteristic
49C22×C4×C181—21no—
50C22×C4×C181C2311yescharacteristic
51C2×C8×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181C2×C411yescharacteristic
54C22⋊C4×C181—21no—
55C22×D181—21no—
56D724—41no—
57C22⋊D181—41no—
58C22⋊D181—41no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—22no—
62C2×Dic181—22no—
63C2×Dic181—21no—
64C2×Dic181—41no—
65C2×Dic181—41no—
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C22⋊C411yescharacteristic
68C2×Dic181C22⋊C411yescharacteristic
69C2×Dic181C22⋊C411yescharacteristic
70C4×D181—42no—
71#13089678—41no—
72C23×C181C2×D411yescharacteristic
73Q8×C181—41no—
74C2×C4×C181—22no—
75C2×C4×C181—21no—
76C2×C4×C181—21no—
77C2×C4×C181—41no—
78C2×C4×C181—41no—
79C2×C4×C181—41no—
80C2×C4×C181C22×C411yescharacteristic
81C2×C4×C181C2×D411yescharacteristic
82C8×C181—41no—
83C22×C181—21no—
84C22×C181—21no—
85C22×C181C2×C22⋊C411yescharacteristic
86C22×C181#13511yescharacteristic
87C22×C181#13511yescharacteristic
88C2×D181—41no—
89C2×D181—41no—
90C2×D181—41no—
91C4×C181—21no—
92C4×C181—21no—
93C4×C181—42no—
94C4×C181—41no—
95C4×C181—41no—
96Dic181—21no—
97Dic181—21no—
98Dic181—21no—
99Dic181—42no—
100Dic181—41no—
101Dic181#10412yes—
102C2×C181—21no—
103C2×C181—21no—
104C2×C181#41011yescharacteristic
105C2×C181#41611yescharacteristic
106C2×C181C2×#10411yescharacteristic
107D181—81no—
108C181#150011yescharacteristic, complemented, Sylow
109#1500—1811nomaximal, Sylow
110#529—1811no—
111#431—1811no—
112#376—1811no—
113#328—1811no—
114#328D18111yescharacteristic, complemented
115#327—1811no—
116#327—1811no—
117#126—3621no—
118#125—1811no—
119#124—1811no—
120#123—3621no—
121C22⋊Q8C2×D18111yescharacteristic
122#121—1811no—
123C4×Q8—1811no—
124C4×D4—3621no—
125C4×D4—1811no—
126#117—3621no—
127C2×C42—3621no—
128C2×C42—1811no—
129C4⋊C8—3621no—
130C22⋊C8—1811no—
131C22⋊C8C2×D18111yescharacteristic
132C4×C8—3621no—
133#95—3621no—
134#95—1811no—
135#95C2×D18111yescharacteristic
136C2×Q8C4×D18111yescharacteristic
137C2×D4—3621no—
138C2×D4—1811no—
139C22×C4—21no—
140C22×C4—3621no—
141C22×C4—3621no—
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4C22×D18111yescharacteristic
145C2×C8—21no—
146C2×C8—3621no—
147C4⋊C4—21no—
148C4⋊C4—3621no—
149C4⋊C4—3621no—
150C4⋊C4—3621no—
151C4⋊C4—1811no—
152C4⋊C4C4×D18111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C22⋊C4—3621no—
158C42—3624no—
159C42—3621no—
160C42—1811no—
161C42—1811no—
162C42—1811no—
163C42—1811no—
164C23—3621no—
165C23D4×D18111yescharacteristic
166Q8—41no—
167D4—7241no—
168D4—7241no—
169D4—7241no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—3622no—
179C2×C4—3622no—
180C2×C4—3621no—
181C2×C4—1811no—
182C2×C4—1811no—
183C2×C4—1811no—
184C2×C4—1811no—
185C2×C4—7242no—
186C2×C4—7241no—
187C2×C4—7241no—
188C2×C4C2×C4×D18111yescharacteristic
189C2×C4D4×D18111yescharacteristic
190C8—41no—
191C8—7241no—
192C22—21no—
193C22—21no—
194C22—7241no—
195C22—7241no—
196C22—7241no—
197C22C22⋊C4×D18111yescharacteristic
198C22#1915383711yescharacteristic
199C22#1915383911yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3621no—
206C4—3621no—
207C4—3621no—
208C4—1812no—
209C4—7242no—
210C4—7241no—
211C2—21no—
212C2—21no—
213C2—14481no—
214C2#2604125111yescharacteristic
215C2#2604127411yescharacteristic
216C2#104×D18111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D181
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#328×C181C2
socleC22×C181C2×C22⋊C4
prime radical#19153790C22
cosocleC22×C4×C181C23
hypercenter#328D181
hypocenterC181#1500
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #26041329C2semidirect
3. #26041124C2semidirect
4. #26041016C2semidirect
7. #328×C181C2semidirect
9. #19153807C4semidirect
10. #19153805C4semidirect
13. Q8×Dic181C4semidirect
14. #19153778C4semidirect
108. C181#1500semidirect
114. #328D181semidirect

Maximal subgroups

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

subgroupindex
#260418152
#260413292
#260411242
#260410162
#260410142
#260410122
#328×C1812
#1500181