Finite Group Databasebeta

← #37534786

Subgroups — #37534786

Order 23168.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#26041790C211yesmaximal, characteristic, complemented
3#26041297C211yesmaximal, characteristic, complemented
4#26041296C211yesmaximal, characteristic, complemented
5#26041243C211yesmaximal, characteristic, complemented
6#26041035C211yesmaximal, characteristic, complemented
7#525×C181C211yesmaximal, characteristic, complemented
8C2×#15668449C2211yescharacteristic
9#19153847—21no—
10#19153846—21no—
11#19153842—21no—
12#19153841—21no—
13#19153836—22no—
14C2×#15668433C2211yescharacteristic
15C2×#15668433C2211yescharacteristic
16#19153799—21no—
17#19153795—21no—
18#19153790—21no—
19#19153785—21no—
20C4×C22⋊D181—22no—
21#19153775C2211yescharacteristic
22#19153744—22no—
23#19153743—22no—
24C22⋊#13089678—22no—
25C2×#41×C181C2211yescharacteristic
26C23×C4×C181C2211yescharacteristic
27#123×C181—21no—
28C22⋊Q8×C181—21no—
29#121×C181—21no—
30#120×C181—21no—
31C4×D4×C181—22no—
32#117×C181C2211yescharacteristic
33#15668449—21no—
34#15668449—21no—
35#15668449—21no—
36#15668449—21no—
37C2×Dic362D411yescharacteristic, complemented
38C2×D724D411yescharacteristic, complemented
39C2×C22⋊D181—22no—
40C2×C22⋊D181—21no—
41C2×C4×D181—21no—
42#15668439—22no—
43#15668437—22no—
44#15668436—22no—
45#15668434—22no—
46#15668433—21no—
47#15668433—21no—
48#15668433—21no—
49#15668433—21no—
50C2×#13089678—21no—
51C2×#13089678D412yescomplemented
52C4⋊Dic181—21no—
53#15668428—22no—
54C22⋊Dic181—22no—
55C22⋊Dic181—21no—
56#15668426—22no—
57C4×Dic181D412yescomplemented
58C24×C181D411yescharacteristic
59#41×C181—21no—
60#41×C181—21no—
61#41×C181—21no—
62#41×C181—21no—
63C2×Q8×C181D411yescharacteristic, complemented
64C2×D4×C181—22no—
65C2×D4×C181—21no—
66C2×D4×C181D411yescharacteristic, complemented
67C22×C4×C181—21no—
68C22×C4×C181—21no—
69C22×C4×C181—21no—
70C22×C4×C181—21no—
71C22×C4×C181—21no—
72C22×C4×C181—21no—
73C22×C4×C181—21no—
74C22×C4×C181D411yescharacteristic
75C22×C4×C181C2311yescharacteristic
76C4⋊C4×C181—22no—
77C4⋊C4×C181—21no—
78C22⋊C4×C181—22no—
79C22⋊C4×C181—22no—
80C22⋊C4×C181—21no—
81C42×C181D412yescomplemented
82C22×D181—21no—
83Dic362—21no—
84Dic362—21no—
85D724—21no—
86D724—21no—
87C22⋊D181—44no—
88C22⋊D181—41no—
89C22⋊D181—41no—
90C2×Dic181—22no—
91C2×Dic181—21no—
92C4×D181—41no—
93C4×D181—41no—
94#13089678—22no—
95#13089678—41no—
96C23×C181—21no—
97C23×C181—21no—
98C23×C181—21no—
99C23×C181—21no—
100C23×C181—42no—
101C23×C181C2×D411yescharacteristic
102Q8×C181—21no—
103Q8×C181—21no—
104D4×C181—21no—
105D4×C181—21no—
106D4×C181—44no—
107D4×C181—41no—
108D4×C181—41no—
109C2×C4×C181—22no—
110C2×C4×C181—21no—
111C2×C4×C181—21no—
112C2×C4×C181—21no—
113C2×C4×C181—21no—
114C2×C4×C181—41no—
115C2×C4×C181—41no—
116C2×C4×C181—41no—
117C2×C4×C181—41no—
118C2×C4×C181—41no—
119C2×C4×C181—41no—
120C2×C4×C181C2×D411yescharacteristic
121C2×C4×C181C2×D411yescharacteristic
122C2×C4×C181C2×D411yescharacteristic
123C2×C4×C181C2×D411yescharacteristic
124C2×C4×C181C2×D411yescharacteristic
125C2×C4×C181#4111yescharacteristic
126C22×C181—22no—
127C22×C181—22no—
128C22×C181—22no—
129C22×C181—41no—
130C22×C181—41no—
131C22×C181—41no—
132C22×C181—41no—
133C22×C181—42no—
134C22×C181—41no—
135C22×C181—41no—
136C22×C181#12011yescharacteristic
137C22×C181#12011yescharacteristic
138C22×C181#12111yescharacteristic
139C2×D181—42no—
140C2×D181—41no—
141C4×C181—42no—
142C4×C181—41no—
143C4×C181—41no—
144C4×C181#12011yescharacteristic
145C4×C181#12111yescharacteristic
146C4×C181#12111yescharacteristic
147C4×C181#12711yescharacteristic
148Dic181—42no—
149Dic181—41no—
150C2×C181—21no—
151C2×C181—21no—
152C2×C181—21no—
153C2×C181—42no—
154C2×C181—81no—
155C2×C181#39211yescharacteristic
156D181—81no—
157C181#201011yescharacteristic, complemented, Sylow
158#2010—1811nomaximal, Sylow
159#575—1811no—
160#525—1811no—
161#525D18111yescharacteristic, complemented
162#421—1811no—
163#421—1811no—
164#407—1811no—
165H(3,ℤ/4)—1811no—
166C2×#41—1811no—
167C2×#41C2×D18111yescharacteristic
168C23×C4C2×D18111yescharacteristic
169#137—3621no—
170#137—3621no—
171AGL(1,ℤ/8)—3621no—
172AGL(1,ℤ/8)—3621no—
173#135—3622no—
174C2×M16—1811no—
175C2×M16—1811no—
176#123—21no—
177#123—3621no—
178C22⋊Q8—21no—
179C22⋊Q8—3621no—
180#121—21no—
181#121—3621no—
182#120—21no—
183#120—3621no—
184C4×D4—22no—
185C4×D4—3622no—
186#117—1811no—
187#117C2×D18111yescharacteristic
188#104—3622no—
189#104—3622no—
190C22⋊C8—3622no—
191C24C22⋊D18111yescharacteristic
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×Q8C22⋊D18111yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—3622no—
205C2×D4—3621no—
206C2×D4—1811no—
207C2×D4C22⋊D18111yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—3621no—
216C22×C4C22⋊D18111yescharacteristic
217C22×C4C22×D18111yescharacteristic
218Q16—3622no—
219SD16—3622no—
220SD16—3622no—
221D8—3622no—
222M16—3621no—
223M16—3621no—
224M16—3621no—
225M16—3621no—
226C2×C8—3621no—
227C2×C8—1812no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—3622no—
231C4⋊C4—3621no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—3622no—
236C22⋊C4—3622no—
237C22⋊C4—3621no—
238C42—1812no—
239C42C22⋊D18112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—3621no—
246C23C2×C22⋊D18111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—3621no—
250Q8—3621no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—3621no—
257D4—3621no—
258D4—7244no—
259D4—7241no—
260D4—7241no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3622no—
273C2×C4—3621no—
274C2×C4—7241no—
275C2×C4—7241no—
276C2×C4D4×D18111yescharacteristic
277C2×C4D4×D18111yescharacteristic
278C2×C4D4×D18111yescharacteristic
279C2×C4C2×C22⋊D18111yescharacteristic
280C2×C4C2×C22⋊D18111yescharacteristic
281C2×C4#1566844811yescharacteristic
282C8—3622no—
283C8—7241no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—7242no—
295C22—7241no—
296C22#1915378411yescharacteristic
297C22#1915378511yescharacteristic
298C22#1915378811yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—7242no—
303C4—7241no—
304C4#1915378411yescharacteristic
305C4#1915378711yescharacteristic
306C4#1915378811yescharacteristic
307C4#1915381211yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—14481no—
314C2#2604118711yescharacteristic
subgroupG/H
centerC4#19153812
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#525×C181C2
socleC2×C181#392
hypercenter#525D181
hypocenterC181#2010
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #26042077C2semidirect
2. #26041790C2semidirect
3. #26041297C2semidirect
4. #26041296C2semidirect
5. #26041243C2semidirect
6. #26041035C2semidirect
7. #525×C181C2semidirect
37. C2×Dic362D4semidirect
38. C2×D724D4semidirect
51. C2×#13089678D4semidirect
57. C4×Dic181D4semidirect
63. C2×Q8×C181D4semidirect
66. C2×D4×C181D4semidirect
81. C42×C181D4semidirect
157. C181#2010semidirect
161. #525D181semidirect
201. C2×Q8C22⋊D181semidirect
207. C2×D4C22⋊D181semidirect
239. C42C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260420772
#260417902
#260412972
#260412962
#260412432
#260410352
#525×C1812
#2010181