Finite Group Databasebeta

← #37534787

Subgroups — #37534787

Order 23168.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#26042077C211yesmaximal, characteristic, complemented
2#26041791C211yesmaximal, characteristic, complemented
3#26041786C211yesmaximal, characteristic, complemented
4#26041295C211yesmaximal, characteristic, complemented
5#26041242C211yesmaximal, characteristic, complemented
6#26041035C211yesmaximal, characteristic, complemented
7#421×C181C211yesmaximal, characteristic, complemented
8C2×#15668449C2211yescharacteristic
9C22×C4×D181C2211yescharacteristic
10#19153847—21no—
11#19153846—21no—
12#19153842—21no—
13#19153841—21no—
14#19153836—22no—
15C2×#15668433C2211yescharacteristic
16#19153800—21no—
17#19153797—21no—
18#19153796—21no—
19#19153792—21no—
20#19153791—21no—
21#19153787—21no—
22#19153786—21no—
23#19153784—21no—
24C4×D724—22no—
25C4×C22⋊D181—22no—
26#19153775C2211yescharacteristic
27#19153742—22no—
28#19153728—22no—
29C2×#41×C181C2211yescharacteristic
30C2×M16×C181C2211yescharacteristic
31#117×C181C2211yescharacteristic
32#104×C181—22no—
33C23×D181D411yescharacteristic
34#15668449—21no—
35#15668449—21no—
36#15668449—21no—
37#15668449—21no—
38C2×Dic362D411yescharacteristic, complemented
39C2×D724—22no—
40C2×D724D411yescharacteristic, complemented
41C2×C22⋊D181—22no—
42C2×C22⋊D181—21no—
43C22×Dic181D411yescharacteristic
44C2×C4×D181—21no—
45C2×C4×D181—21no—
46C2×C4×D181—21no—
47C2×C4×D181—21no—
48C2×C4×D181—21no—
49C2×C4×D181—21no—
50C2×C4×D181—21no—
51#15668439—22no—
52#15668437—22no—
53#15668436—22no—
54#15668434—22no—
55#15668433—21no—
56#15668433—21no—
57C2×#13089678D412yescomplemented
58C4⋊Dic181—22no—
59C4⋊Dic181—21no—
60#15668428—22no—
61C22⋊Dic181—22no—
62C22⋊Dic181—21no—
63#15668426—22no—
64#15668426—22no—
65#15668426—22no—
66C4×Dic181D412yescomplemented
67#41×C181—21no—
68#41×C181—21no—
69#41×C181—21no—
70#41×C181—21no—
71C2×Q8×C181D411yescharacteristic, complemented
72C2×D4×C181—21no—
73C2×D4×C181D411yescharacteristic, complemented
74C22×C4×C181—21no—
75C22×C4×C181C2311yescharacteristic
76M16×C181—21no—
77M16×C181—21no—
78C2×C8×C181—21no—
79C4⋊C4×C181—21no—
80C22⋊C4×C181—21no—
81C42×C181D412yescomplemented
82C22×D181—21no—
83C22×D181—21no—
84C22×D181—21no—
85C22×D181—21no—
86C22×D181—42no—
87Dic362—21no—
88Dic362—21no—
89D724—21no—
90D724—21no—
91D724—44no—
92C22⋊D181—44no—
93C22⋊D181—41no—
94C22⋊D181—41no—
95C2×Dic181—22no—
96C2×Dic181—21no—
97C2×Dic181—21no—
98C2×Dic181—21no—
99C2×Dic181—21no—
100C4×D181—41no—
101C4×D181—41no—
102C4×D181—41no—
103C4×D181—41no—
104C4×D181—41no—
105C4×D181—41no—
106#13089678—22no—
107C23×C181—21no—
108C23×C181C2×D411yescharacteristic
109Q8×C181—21no—
110Q8×C181—21no—
111D4×C181—21no—
112D4×C181—21no—
113D4×C181—41no—
114D4×C181—41no—
115C2×C4×C181—22no—
116C2×C4×C181—21no—
117C2×C4×C181—41no—
118C2×C4×C181—41no—
119C2×C4×C181C2×D411yescharacteristic
120C2×C4×C181C2×D411yescharacteristic
121C2×C4×C181C2×D411yescharacteristic
122C2×C4×C181C2×D411yescharacteristic
123C2×C4×C181C2×D411yescharacteristic
124C2×C4×C181#4111yescharacteristic
125C8×C181—41no—
126C22×C181—41no—
127C22×C181—42no—
128C22×C181—41no—
129C22×C181#12011yescharacteristic
130C22×C181#12011yescharacteristic
131C22×C181#12111yescharacteristic
132C2×D181—22no—
133C2×D181—22no—
134C2×D181—22no—
135C2×D181—41no—
136C2×D181—41no—
137C2×D181—41no—
138C2×D181—41no—
139C2×D181—42no—
140C2×D181—41no—
141C4×C181—42no—
142C4×C181—41no—
143C4×C181#12011yescharacteristic
144C4×C181#12111yescharacteristic
145C4×C181#12111yescharacteristic
146C4×C181#12711yescharacteristic
147Dic181—42no—
148Dic181—41no—
149Dic181—41no—
150C2×C181—21no—
151C2×C181—21no—
152C2×C181—21no—
153C2×C181—81no—
154C2×C181#39211yescharacteristic
155D181—42no—
156D181—81no—
157C181#201011yescharacteristic, complemented, Sylow
158#2010—1811nomaximal, Sylow
159#575—1811no—
160#525—1811no—
161#525—1811no—
162#421—1811no—
163#421D18111yescharacteristic, complemented
164#407—1811no—
165H(3,ℤ/4)—1811no—
166C2×#41—1811no—
167C2×#41C2×D18111yescharacteristic
168C23×C4—1811no—
169#137—3621no—
170#137—3621no—
171AGL(1,ℤ/8)—3621no—
172AGL(1,ℤ/8)—3621no—
173#135—3622no—
174C2×M16—1811no—
175C2×M16C2×D18111yescharacteristic
176#123—3621no—
177#123—3621no—
178C22⋊Q8—3621no—
179C22⋊Q8—3621no—
180#121—3621no—
181#121—3621no—
182#120—3621no—
183#120—3621no—
184C4×D4—3622no—
185C4×D4—3622no—
186#117—1811no—
187#117C2×D18111yescharacteristic
188#104—22no—
189#104—3622no—
190C22⋊C8—3622no—
191C24—1811no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—3621no—
197#41—3621no—
198#41—3621no—
199#41—3621no—
200C2×Q8—1811no—
201C2×Q8D72411yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—3622no—
204C2×D4—3622no—
205C2×D4—3621no—
206C2×D4—1811no—
207C2×D4D72411yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—3621no—
210C22×C4—3621no—
211C22×C4—3621no—
212C22×C4—3621no—
213C22×C4—3621no—
214C22×C4—3621no—
215C22×C4—3621no—
216C22×C4—1811no—
217C22×C4C22×D18111yescharacteristic
218Q16—3622no—
219SD16—3622no—
220SD16—3622no—
221D8—3622no—
222M16—21no—
223M16—21no—
224M16—3621no—
225M16—3621no—
226C2×C8—21no—
227C2×C8—1812no—
228C4⋊C4—21no—
229C4⋊C4—3622no—
230C4⋊C4—3622no—
231C4⋊C4—3621no—
232C22⋊C4—21no—
233C22⋊C4—3622no—
234C22⋊C4—3622no—
235C22⋊C4—3622no—
236C22⋊C4—3622no—
237C22⋊C4—3621no—
238C42—1812no—
239C42C22⋊D18112yescomplemented
240C23—21no—
241C23—3621no—
242C23—3621no—
243C23—3621no—
244C23—3621no—
245C23—7242no—
246C23D4×D18111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—3621no—
250Q8—3621no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—3621no—
256D4—3621no—
257D4—7244no—
258D4—7244no—
259D4—7241no—
260D4—7241no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3621no—
266C2×C4—3621no—
267C2×C4—3622no—
268C2×C4—3621no—
269C2×C4—3621no—
270C2×C4—7241no—
271C2×C4—7241no—
272C2×C4—7241no—
273C2×C4—7241no—
274C2×C4—7241no—
275C2×C4—7241no—
276C2×C4D4×D18111yescharacteristic
277C2×C4D4×D18111yescharacteristic
278C2×C4D4×D18111yescharacteristic
279C2×C4C2×C22⋊D18111yescharacteristic
280C2×C4C2×D72411yescharacteristic
281C2×C4#1566844911yescharacteristic
282C8—41no—
283C8—3622no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—3622no—
288C22—3622no—
289C22—3622no—
290C22—7242no—
291C22—7241no—
292C22—7241no—
293C22—7241no—
294C22—7241no—
295C22—7241no—
296C22#1915378411yescharacteristic
297C22#1915378611yescharacteristic
298C22#1915378911yescharacteristic
299C4—42no—
300C4—41no—
301C4—7242no—
302C4—7241no—
303C4—7241no—
304C4#1915378611yescharacteristic
305C4#1915378911yescharacteristic
306C4#1915379011yescharacteristic
307C4#1915381211yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—14481no—
313C2—7242no—
314C2#2604118811yescharacteristic
subgroupG/H
centerC4#19153812
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#421×C181C2
socleC2×C181#392
hypercenter#421D181
hypocenterC181#2010
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #26042077C2semidirect
2. #26041791C2semidirect
3. #26041786C2semidirect
4. #26041295C2semidirect
5. #26041242C2semidirect
6. #26041035C2semidirect
7. #421×C181C2semidirect
38. C2×Dic362D4semidirect
40. C2×D724D4semidirect
57. C2×#13089678D4semidirect
66. C4×Dic181D4semidirect
71. C2×Q8×C181D4semidirect
73. C2×D4×C181D4semidirect
81. C42×C181D4semidirect
157. C181#2010semidirect
163. #421D181semidirect
201. C2×Q8D724semidirect
207. C2×D4D724semidirect
239. C42C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260420772
#260417912
#260417862
#260412952
#260412422
#260410352
#421×C1812
#2010181