Finite Group Databasebeta

← #37546543

Subgroups — #37546543

Order 23168.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042003C211yesmaximal, characteristic, complemented
2#26041985C211yesmaximal, characteristic, complemented
3#26041640C211yesmaximal, characteristic, complemented
4#26041635C211yesmaximal, characteristic, complemented
5#26041584C211yesmaximal, characteristic, complemented
6#26041576C211yesmaximal, characteristic, complemented
7#26041562C211yesmaximal, characteristic, complemented
8#26041497C211yesmaximal, characteristic
9#26041497C211yesmaximal, characteristic
10#26041481C211yesmaximal, characteristic, complemented
11#26041407C211yesmaximal, characteristic, complemented
12#26041392C211yesmaximal, characteristic
13#26041382C211yesmaximal, characteristic, complemented
14#26041364C211yesmaximal, characteristic, complemented
15#491×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153811—21no—
21#19153811—21no—
22#19153807C2211yescharacteristic
23#19153805C2211yescharacteristic
24#19153805C2211yescharacteristic
25#19153796—21no—
26#19153796—21no—
27#19153794—21no—
28#19153794—21no—
29Q8×Dic181C2211yescharacteristic
30Q8×Dic181C2211yescharacteristic
31C4×Dic362C2211yescharacteristic
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34#19153778C2211yescharacteristic
35#19153778C2211yescharacteristic
36#19153774—21no—
37C4⋊C4×D181—21no—
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#103×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362D411yescharacteristic
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C4×D181—21no—
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67#15668436—22no—
68#15668436—22no—
69D1448—22no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181D411yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428D411yescharacteristic
81#15668428D411yescharacteristic
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181C2311yescharacteristic
93C4×Dic181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181—21no—
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C42×C181C2311yescharacteristic
105C22×D181—21no—
106C22×D181—21no—
107Dic362—41no—
108Dic362—81no—
109D724—21no—
110D724—21no—
111D724—21no—
112D724#4112yes—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C4×D181—42no—
120C4×D181—42no—
121C4×D181—81no—
122C4×D181—81no—
123#13089678—21no—
124#13089678—21no—
125Q8×C181—21no—
126Q8×C181—21no—
127Q8×C181—21no—
128Q8×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2411yescharacteristic
136C8×C181—21no—
137C8×C181—21no—
138C22×C181C22×D411yescharacteristic
139C2×D181—22no—
140C2×D181—41no—
141C2×D181—41no—
142C2×D181—41no—
143C2×D181—41no—
144C2×D181—41no—
145C4×C181—21no—
146C4×C181—21no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181—41no—
150C4×C181—41no—
151C4×C181C2×#4111yescharacteristic
152C4×C1812−1+411yescharacteristic
153Dic181—21no—
154Dic181—21no—
155Dic181—21no—
156Dic181—21no—
157Dic181—41no—
158Dic181—41no—
159C2×C181#54811yescharacteristic
160C2×C181#57511yescharacteristic
161C2×C181#57711yescharacteristic
162D181—42no—
163D181—81no—
164C181#337611yescharacteristic, complemented, Sylow
165#3376—1811nomaximal, Sylow
166#556—1811no—
167#554—1811no—
168#491D18111yescharacteristic, complemented
169#489—1811no—
170#488—1811no—
171#479—1811no—
172#478—1811no—
173#475—1811no—
174#463—1811no—
175#463—1811no—
176#461—1811no—
177#446—1811no—
178#442—1811no—
179#440—1811no—
180C4×SD16—1811no—
181C2×SD16—1811no—
182C2×SD16—1811no—
183C2×D8—1811no—
184C4⋊Q8—1811no—
185C4⋊Q8C2×D18111yescharacteristic
186#126—3621no—
187#126—3621no—
188#125—1811no—
189#125C2×D18111yescharacteristic
190#124—1811no—
191#124—1811no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194C22⋊Q8—3621no—
195C22⋊Q8—3621no—
196C4×Q8—1811no—
197C4×Q8—1811no—
198C4×Q8—1811no—
199C4×D4—1811no—
200C4×D4—1811no—
201C4×D4—1811no—
202C4×D4—1811no—
203#117—3621no—
204C2×C4⋊C4—3621no—
205#107—1811no—
206#106—1811no—
207#106—1811no—
208C4⋊C8—1811no—
209C4⋊C8—1811no—
210C4⋊C8—1811no—
211#103—1811no—
212#103—1811no—
213#103C2×D18111yescharacteristic
214#103C2×D18111yescharacteristic
215#103C2×D18111yescharacteristic
216#103C2×D18111yescharacteristic
217#102—1811no—
218#102—1811no—
219#102—1811no—
220#102—1811no—
221#97—1811no—
222#97C2×D18111yescharacteristic
223C4×C8—1811no—
224C2×Q8—3621no—
225C2×Q8—1811no—
226C2×Q8C22×D18111yescharacteristic
227C2×Q8C22×D18111yescharacteristic
228C2×D4—1811no—
229C2×D4—1811no—
230C22×C4—3621no—
231C22×C4—3621no—
232C22×C4—3621no—
233C22×C4—3621no—
234SD16—3622no—
235SD16—3622no—
236D8—3622no—
237C2×C8—1811no—
238C2×C8—1811no—
239C2×C8C22×D18111yescharacteristic
240C2×C8C22×D18111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C22⋊C4—3621no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C42—3621no—
266C42—3621no—
267C42—1811no—
268C42—1811no—
269C42C22×D18111yescharacteristic
270C23—3621no—
271C23—3621no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—14481no—
277Q8—7241no—
278D4—3621no—
279D4—3621no—
280D4—3621no—
281D4—1812no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—14481no—
289C2×C4—14481no—
290C2×C4—1811no—
291C2×C4—1811no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—7242no—
295C2×C4—7242no—
296C2×C4D4×D18111yescharacteristic
297C2×C4D4×D18111yescharacteristic
298C2×C4C23×D18111yescharacteristic
299C8—21no—
300C8—21no—
301C8—3621no—
302C8—3621no—
303C22—3622no—
304C22—7241no—
305C22—7241no—
306C22—7241no—
307C22—7241no—
308C22—7241no—
309C22C2×D4×D18111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3621no—
317C4—3621no—
318C4—3621no—
319C4—3621no—
320C4—7241no—
321C4—7241no—
322C4#41×D18111yescharacteristic
323C4#1915386311yescharacteristic
324C2—14481no—
325C2—7242no—
326C2#2604193711yescharacteristic
327C2#2604207811yescharacteristic
328C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#491×C181C2
socleC22×C181C22×D4
prime radicalC2×D1448C22
hypercenter#491D181
hypocenterC181#3376
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #26042003C2semidirect
2. #26041985C2semidirect
3. #26041640C2semidirect
4. #26041635C2semidirect
5. #26041584C2semidirect
6. #26041576C2semidirect
7. #26041562C2semidirect
10. #26041481C2semidirect
11. #26041407C2semidirect
13. #26041382C2semidirect
14. #26041364C2semidirect
15. #491×C181C2semidirect
164. C181#3376semidirect
168. #491D181semidirect

Maximal subgroups

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

subgroupindex
#260420032
#260419852
#260416402
#260416352
#260415842
#260415762
#260415622
#260414972
#260414812
#260414072
#260413922
#260413822
#260413642
#491×C1812
#3376181