Finite Group Databasebeta

← #37532664

Subgroups — #37532664

Order 23168.

320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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#26041866C211yesmaximal, characteristic, complemented
2#26041430C211yesmaximal, characteristic, complemented
3#26041187C211yesmaximal, characteristic, complemented
4#26041017C211yesmaximal, characteristic, complemented
5#26041013C211yesmaximal, characteristic, complemented
6#26041002C211yesmaximal, characteristic, complemented
7#447×C181C211yesmaximal, characteristic, complemented
8C22×C22⋊D181—21no—
9C2×#15668437—21no—
10#19153811—21no—
11#19153802—21no—
12#19153800—21no—
13#19153795C2211yescharacteristic
14#19153788—21no—
15#19153784—21no—
16D4×Dic181—21no—
17C2×C22⋊Dic181—21no—
18C2×#15668426C2211yescharacteristic
19#19153737—21no—
20C22⋊#13089678C2211yescharacteristic
21#19153723C2211yescharacteristic
22C22×D4×C181C2211yescharacteristic
23C2×D8×C181—21no—
24#121×C181C2211yescharacteristic
25#102×C181—21no—
26C22⋊C8×C181C2211yescharacteristic
27C23×D181D411yescharacteristic
28C2×Dic362D411yescharacteristic, complemented
29C2×C22⋊D181—21no—
30C2×C22⋊D181—21no—
31C2×C22⋊D181—42no—
32C2×C22⋊D181—42no—
33C2×C22⋊D181—42no—
34C22×Dic181—21no—
35C22×Dic181—21no—
36C22×Dic181D411yescharacteristic
37#15668437—42no—
38C2×#13089678—21no—
39C4⋊Dic181—21no—
40C4⋊Dic181D411yescharacteristic, complemented
41#15668428—21no—
42C22⋊Dic181—21no—
43C22⋊Dic181—21no—
44C22⋊Dic181—42no—
45#15668426—21no—
46#15668426—21no—
47#15668426—21no—
48#15668426—21no—
49C4×Dic181—21no—
50C24×C181—21no—
51C2×D4×C181—21no—
52C2×D4×C181—21no—
53C2×D4×C181—21no—
54C2×D4×C181—42no—
55C2×D4×C181D411yescharacteristic, complemented
56C22×C4×C181C2311yescharacteristic
57D8×C181—42no—
58C2×C8×C181—21no—
59C4⋊C4×C181D411yescharacteristic, complemented
60C22⋊C4×C181—21no—
61C22×D181—21no—
62C22×D181—21no—
63C22×D181—21no—
64C22×D181—41no—
65C22×D181—41no—
66Dic362—41no—
67C22⋊D181—48no—
68C22⋊D181—81no—
69C22⋊D181—81no—
70C2×Dic181—22no—
71C2×Dic181—21no—
72C2×Dic181—21no—
73C2×Dic181—21no—
74C2×Dic181—41no—
75C2×Dic181—41no—
76C2×Dic181—41no—
77C2×Dic181—81no—
78#13089678—41no—
79C23×C181—22no—
80C23×C181—21no—
81C23×C181—41no—
82C23×C181—41no—
83C23×C181—41no—
84C23×C181—41no—
85C23×C181—41no—
86C23×C181—41no—
87C23×C181C2×D411yescharacteristic
88D4×C181—22no—
89D4×C181—22no—
90D4×C181—41no—
91D4×C181—41no—
92D4×C181—41no—
93D4×C181—41no—
94D4×C181—41no—
95C2×C4×C181—21no—
96C2×C4×C181—41no—
97C2×C4×C181C2×D411yescharacteristic
98C2×C4×C181C2×D411yescharacteristic
99C8×C181—41no—
100C22×C181—21no—
101C22×C181—21no—
102C22×C181—42no—
103C22×C181—42no—
104C22×C181—41no—
105C22×C181—41no—
106C22×C181—42no—
107C22×C181—41no—
108C22×C181—81no—
109C22×C181—81no—
110C22×C181—81no—
111C22×C181—81no—
112C22×C181#12011yescharacteristic
113C22×C181#13511yescharacteristic
114C22×C181AGL(1,ℤ/8)11yescharacteristic
115C2×D181—42no—
116C2×D181—41no—
117C2×D181—41no—
118C2×D181—41no—
119C2×D181—81no—
120C4×C181—21no—
121C4×C181—21no—
122C4×C181—41no—
123Dic181—42no—
124Dic181—41no—
125Dic181—41no—
126Dic181—41no—
127C2×C181—21no—
128C2×C181—21no—
129C2×C181—81no—
130C2×C181—82no—
131C2×C181#44911yescharacteristic
132C2×C181#45311yescharacteristic
133C2×C181B(4,𝔽2)11yescharacteristic
134D181—81no—
135C181#160011yescharacteristic, complemented, Sylow
136#1600—1811nomaximal, Sylow
137#538—1811no—
138#450—1811no—
139#447D18111yescharacteristic, complemented
140#392—1811no—
141#328—1811no—
142#327—1811no—
143#323—1811no—
144C22×D4—3621no—
145C22×D4C2×D18111yescharacteristic
146C2×SD16—3621no—
147C2×D8—21no—
148#126—3621no—
149#124—3621no—
150#123—3621no—
151C22⋊Q8—1811no—
152#121—3621no—
153#121C2×D18111yescharacteristic
154#120—3621no—
155C4×D4—3621no—
156C2×C22⋊C4—3621no—
157C2×C22⋊C4—1811no—
158#102—21no—
159#102—3621no—
160C22⋊C8—1811no—
161C22⋊C8C2×D18111yescharacteristic
162#95—1811no—
163C24—21no—
164C24—1811no—
165C2×Q8—1811no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—3621no—
171C2×D4—3621no—
172C2×D4—7242no—
173C2×D4—7242no—
174C2×D4—7242no—
175C2×D4C22⋊D18111yescharacteristic, complemented
176C22×C4—3621no—
177C22×C4—3621no—
178C22×C4—1811no—
179C22×C4C22×D18111yescharacteristic
180SD16—7242no—
181D8—42no—
182C2×C8—21no—
183C2×C8—3621no—
184C4⋊C4—3621no—
185C4⋊C4—3621no—
186C4⋊C4—1811no—
187C4⋊C4C22⋊D18111yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—3621no—
190C22⋊C4—3621no—
191C22⋊C4—3621no—
192C22⋊C4—3621no—
193C22⋊C4—3621no—
194C22⋊C4—3621no—
195C22⋊C4—7242no—
196C42—3621no—
197C23—22no—
198C23—21no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—3621no—
206C23—3621no—
207C23—3621no—
208C23—7241no—
209C23—7241no—
210C23D4×D18111yescharacteristic
211Q8—7241no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—14481no—
220D4—14481no—
221D4—7248no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—3622no—
225C2×C4—3621no—
226C2×C4—3621no—
227C2×C4—3621no—
228C2×C4—14481no—
229C2×C4—7241no—
230C2×C4—7241no—
231C2×C4—7241no—
232C2×C4D4×D18111yescharacteristic
233C2×C4C2×C22⋊D18111yescharacteristic
234C8—41no—
235C8—7241no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—14481no—
249C22—7242no—
250C22—7241no—
251C22—7241no—
252C22—7241no—
253C22#1915378411yescharacteristic
254C22#1915383511yescharacteristic
255C22#1915384011yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—7242no—
260C4—7241no—
261C4—7241no—
262C4—7241no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2—81no—
267C2—14481no—
268C2#2604142111yescharacteristic
269C2#2604144511yescharacteristic
270C2#2604146511yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#447×C181C2
socleC22×C181#120
hypercenter#447D181
hypocenterC181#1600
LCSG ▷ C22×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #26041866C2semidirect
2. #26041430C2semidirect
3. #26041187C2semidirect
4. #26041017C2semidirect
5. #26041013C2semidirect
6. #26041002C2semidirect
7. #447×C181C2semidirect
28. C2×Dic362D4semidirect
40. C4⋊Dic181D4semidirect
55. C2×D4×C181D4semidirect
59. C4⋊C4×C181D4semidirect
135. C181#1600semidirect
139. #447D181semidirect
175. C2×D4C22⋊D181semidirect
187. C4⋊C4C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260418662
#260414302
#260411872
#260410172
#260410132
#260410022
#447×C1812
#1600181