Finite Group Databasebeta

← #37549591

Subgroups — #37549591

Order 23168.

356 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D181⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#19153878C212yesmaximal
3#26042223C211yesmaximal, characteristic, complemented
4#26042152C212yesmaximal, complemented
5C4×D4×D181C211yesmaximal, characteristic
6C2×D181⋊C8C2212yes—
7C2×C4⋊#10624382C2212yes—
8#19153883—21no—
9C4⋊#13089685—21no—
10#19153878—24no—
11(C2×#10624382)⋊C4—21no—
12(C2×#10624382)⋊C4—21no—
13C2×D4×D181C2211yescharacteristic
14C22×C4×D181—21no—
15C4×D724C411yescharacteristic, complemented
16D4×Dic181C411yescharacteristic, complemented
17#19153778C411yescharacteristic, complemented
18C4×C22⋊D181—21no—
19#19153776—21no—
20C4⋊C4×D181C2211yescharacteristic
21C22⋊C4×D181—21no—
22C42×D181C2211yescharacteristic
23C4×D4×C181C411yescharacteristic, complemented
24C22×#10624382—22no—
25D181⋊C8—22no—
26D181⋊C8—22no—
27C2×#13089685—22no—
28C4⋊#10624382—22no—
29C4⋊#10624382—22no—
30C23×D181—21no—
31C2×D724C2×C411yescharacteristic
32C2×C22⋊D181—21no—
33D4×D181—21no—
34D4×D181—21no—
35D4×D181D412yes—
36D4×D181Q812yes—
37C22×Dic181—21no—
38C2×C4×D181—21no—
39C2×C4×D181—21no—
40C2×C4×D181—21no—
41C2×C4×D181—44no—
42C2×C4×D181D411yescharacteristic
43C2×C4×D181D411yescharacteristic
44C2×C4×D181C2311yescharacteristic
45C4⋊Dic181C2×C411yescharacteristic
46#15668428—21no—
47C22⋊Dic181—21no—
48#15668426—21no—
49#15668426—21no—
50C4×Dic181C2×C411yescharacteristic
51C4×Dic181D411yescharacteristic
52C4×Dic181D411yescharacteristic
53C2×D4×C181C2×C411yescharacteristic
54C22×C4×C181—21no—
55C4⋊C4×C181C2×C411yescharacteristic
56C22⋊C4×C181—21no—
57C42×C181C2×C411yescharacteristic
58C2×#10624382—42no—
59C2×#10624382—42no—
60C2×#10624382—42no—
61#13089685—42no—
62C22×D181—21no—
63C22×D181—22no—
64C22×D181—22no—
65C22×D181—42no—
66C22×D181—42no—
67C22×D181C2×D411yescharacteristic
68D724—21no—
69D724C4⋊C412yes—
70C22⋊D181—22no—
71C22⋊D181—22no—
72C2×Dic181—21no—
73C2×Dic181—42no—
74C2×Dic181C22⋊C411yescharacteristic
75C2×Dic181C22⋊C411yescharacteristic
76C2×Dic181C2×D411yescharacteristic
77C4×D181—22no—
78C4×D181—22no—
79C4×D181—42no—
80C4×D181—42no—
81C4×D181—42no—
82C4×D181C2×D411yescharacteristic
83C4×D181C2×Q811yescharacteristic
84C4×D181#4111yescharacteristic
85C4×D181#4111yescharacteristic
86C23×C181—21no—
87D4×C181—21no—
88D4×C181C4⋊C412yes—
89C2×C4×C181—21no—
90C2×C4×C181—42no—
91C2×C4×C181C22⋊C411yescharacteristic
92C2×C4×C181C22⋊C411yescharacteristic
93C2×C4×C181C22×C411yescharacteristic
94C22×C181—22no—
95C22×C181—41no—
96C22×C181—41no—
97C22×C181C2×C22⋊C411yescharacteristic
98C2×D181—22no—
99C2×D181—41no—
100C2×D181—41no—
101C2×D181—44no—
102C2×D181—44no—
103C2×D181#12111yescharacteristic
104C2×D181C22⋊Q811yescharacteristic
105C2×D181#13512yes—
106C2×D181AGL(1,ℤ/8)12yes—
107#10624382—82no—
108C4×C181—21no—
109C4×C181—21no—
110C4×C181—41no—
111C4×C181C2×C4⋊C411yescharacteristic
112C4×C181#11711yescharacteristic
113Dic181—21no—
114Dic181—21no—
115Dic181—41no—
116Dic181#12111yescharacteristic
117Dic181C22⋊Q811yescharacteristic
118C2×C181—42no—
119C2×C181#38011yescharacteristic
120C2×C181#41611yescharacteristic
121C2×C181#41811yescharacteristic
122D181—42no—
123D181#46312yes—
124D181#47812yes—
125C181#180411yescharacteristic, complemented, Sylow
126#1804—1811nomaximal, Sylow
127C2×C4×D4—1811no—
128C2×C4⋊C8—1811no—
129C2×#102—1812no—
130#382—1811no—
131#340—1812no—
132C22×D4—1811no—
133C23×C4—3621no—
134C22×C8—1812no—
135C4×D4—3621no—
136C4×D4—3621no—
137C4×D4—1811no—
138C4×D4—1811no—
139C4×D4—1811no—
140C4×D4#1062438211yescharacteristic, complemented
141C2×C4⋊C4—1812no—
142C2×C4⋊C4—1811no—
143C2×C22⋊C4—3621no—
144C2×C42—1811no—
145C4⋊C8—3621no—
146C4⋊C8—3621no—
147#102—3624no—
148#95—3621no—
149#95—3621no—
150C24—3621no—
151C2×D4—3621no—
152C2×D4—3621no—
153C2×D4—3621no—
154C2×D4—1812no—
155C2×D4—1812no—
156C2×D4—1811no—
157C2×D4C2×#1062438211yescharacteristic
158C22×C4—21no—
159C22×C4—3621no—
160C22×C4—3621no—
161C22×C4—3621no—
162C22×C4—3621no—
163C22×C4—3622no—
164C22×C4—1811no—
165C22×C4—1811no—
166C22×C4—1811no—
167C22×C4—7244no—
168C2×C8—3622no—
169C2×C8—3622no—
170C2×C8—3622no—
171C4⋊C4—3621no—
172C4⋊C4—3622no—
173C4⋊C4—3622no—
174C4⋊C4—1811no—
175C4⋊C4C2×#1062438211yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—3621no—
178C22⋊C4—3621no—
179C22⋊C4—3621no—
180C42—1811no—
181C42—1811no—
182C42—1811no—
183C42C2×#1062438211yescharacteristic
184C23—21no—
185C23—3622no—
186C23—3622no—
187C23—3621no—
188C23—1811no—
189C23—7242no—
190C23—7242no—
191D4—21no—
192D4—3622no—
193D4—3622no—
194D4—3621no—
195D4—1812no—
196D4C4⋊#1062438212yes—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—3622no—
200C2×C4—3622no—
201C2×C4—3621no—
202C2×C4—1811no—
203C2×C4—1811no—
204C2×C4—1811no—
205C2×C4—1811no—
206C2×C4—1811no—
207C2×C4—1811no—
208C2×C4—1811no—
209C2×C4—7242no—
210C2×C4—7242no—
211C2×C4—7242no—
212C2×C4—7242no—
213C2×C4—7242no—
214C2×C4—7242no—
215C2×C4—7242no—
216C2×C4C22⋊#1062438211yescharacteristic
217C2×C4C22⋊#1062438211yescharacteristic
218C2×C4C22×#1062438211yescharacteristic
219C8—7242no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—3622no—
224C22—1811no—
225C22—1811no—
226C22—1812no—
227C22—1812no—
228C22—7244no—
229C22—7244no—
230C22—7241no—
231C22—7241no—
232C22C2×C22⋊#1062438211yescharacteristic
233C4—21no—
234C4—21no—
235C4—41no—
236C4—3621no—
237C4—3621no—
238C4—14482no—
239C4—1811no—
240C4—1811no—
241C4—7241no—
242C4C2×C4⋊#1062438211yescharacteristic
243C4#1915389511yescharacteristic
244C2—42no—
245C2—1812no—
246C2—1812no—
247C2—7242no—
248C2#2604222111yescharacteristic
249C2#2604226911yescharacteristic
250C2#2604227111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×D4×D181C22
cosocleC2×C4×D181C23
hypercenterC4×D4#10624382
hypocenterC181#1804
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D181⋊(C4⋊C8)C2semidirect
3. #26042223C2semidirect
4. #26042152C2semidirect
15. C4×D724C4semidirect
16. D4×Dic181C4semidirect
17. #19153778C4semidirect
23. C4×D4×C181C4semidirect
125. C181#1804semidirect
140. C4×D4#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C4⋊C8)2
C2×#191538782
#260422232
#260421522
C4×D4×D1812
#1804181