Finite Group Databasebeta

← #37546293

Subgroups — #37546293

Order 23168.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041970C211yesmaximal, characteristic
2#26041967C211yesmaximal, characteristic
3#26041678C211yesmaximal, characteristic, complemented
4#26041623C211yesmaximal, characteristic, complemented
5#26041618C211yesmaximal, characteristic, complemented
6#26041616C211yesmaximal, characteristic, complemented
7#26041613C211yesmaximal, characteristic, complemented
8#26041587C211yesmaximal, characteristic, complemented
9#26041536C211yesmaximal, characteristic, complemented
10#26041536C211yesmaximal, characteristic, complemented
11C4×#15668439C211yesmaximal, characteristic, complemented
12#26041356C211yesmaximal, characteristic
13#26041320C211yesmaximal, characteristic, complemented
14#26041318C211yesmaximal, characteristic, complemented
15#479×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668432C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19#19153811—21no—
20#19153810—21no—
21#19153808C2211yescharacteristic
22#19153807—21no—
23#19153806—21no—
24#19153801—21no—
25#19153801—21no—
26#19153796C2211yescharacteristic
27#19153796C2211yescharacteristic
28#19153792C2211yescharacteristic
29#19153792C2211yescharacteristic
30C4×Dic362C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153774—21no—
33#19153774C2211yescharacteristic
34#19153774C2211yescharacteristic
35#19153773—21no—
36C4⋊C4×D181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×D724D411yescharacteristic
61C2×C4×D181—21no—
62C2×C4×D181—21no—
63C2×C4×D181C2311yescharacteristic
64C2×C4×D181C2311yescharacteristic
65#15668439—22no—
66#15668432—22no—
67#15668432—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181D411yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426D411yescharacteristic
90#15668426D411yescharacteristic
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181—21no—
94C2×Q8×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C42×C181—21no—
104C42×C181C2311yescharacteristic
105C22×D181C2×D411yescharacteristic
106C22×D181C2×D411yescharacteristic
107Dic362—21no—
108Dic362—21no—
109D724—41no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181C2×D411yescharacteristic
115C2×Dic181C2×D411yescharacteristic
116C4×D181—21no—
117C4×D181—21no—
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—42no—
121C4×D181—42no—
122#13089678—21no—
123#13089678#4112yes—
124Q8×C181—21no—
125Q8×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181C2×D411yescharacteristic
131C2×C4×C181C2×D411yescharacteristic
132C2×C4×C181C2411yescharacteristic
133C8×C181—21no—
134C8×C181—21no—
135C22×C181C22×D411yescharacteristic
136C2×D181—21no—
137C2×D181—21no—
138C2×D181—21no—
139C2×D181—21no—
140C2×D181—21no—
141C2×D181—21no—
142C4×C181—21no—
143C4×C181—21no—
144C4×C181—41no—
145C4×C181—41no—
146C4×C181—41no—
147C4×C181—41no—
148C4×C181C2×#4111yescharacteristic
149C4×C1812−1+411yescharacteristic
150Dic181—21no—
151Dic181—21no—
152Dic181—41no—
153Dic181—41no—
154Dic181—41no—
155Dic181—41no—
156C2×C181#54711yescharacteristic
157C2×C181#57511yescharacteristic
158C2×C181#57811yescharacteristic
159D181—41no—
160D181—41no—
161C181#335211yescharacteristic, complemented, Sylow
162#3352—1811nomaximal, Sylow
163#552—1811no—
164#552—1811no—
165#499—1811no—
166#485—1811no—
167#485—1811no—
168#484—1811no—
169#484—1811no—
170#479—1811no—
171#479D18111yescharacteristic, complemented
172#470—1811no—
173#470—1811no—
174C4×Q16—1811no—
175#436—1811no—
176#428—1811no—
177#428—1811no—
178C2×Q16—1811no—
179C2×M16—1811no—
180C2×M16—1811no—
181#126—3621no—
182#126—3621no—
183#125—3621no—
184#125—3621no—
185#125—1811no—
186#125C2×D18111yescharacteristic
187#123—3621no—
188#123—3621no—
189C22⋊Q8—1811no—
190C22⋊Q8—1811no—
191C22⋊Q8—1811no—
192C22⋊Q8—1811no—
193C4×Q8—1811no—
194C4×Q8C2×D18111yescharacteristic
195C4×D4—1811no—
196#117—3621no—
197#117—3621no—
198#117—1811no—
199#117—1811no—
200C2×C4⋊C4—1811no—
201C2×C4⋊C4—1811no—
202#107—1811no—
203#107—1811no—
204#107—1811no—
205#107—1811no—
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106C2×D18111yescharacteristic
211C4⋊C8C2×D18111yescharacteristic
212#103—1811no—
213#103—1811no—
214#103—1811no—
215#103—1811no—
216#103C2×D18111yescharacteristic
217#103C2×D18111yescharacteristic
218C22⋊C8—1811no—
219C22⋊C8—1811no—
220C4×C8—1811no—
221C2×Q8—1811no—
222C2×Q8C22×D18111yescharacteristic
223C2×D4—1811no—
224C22×C4—3621no—
225C22×C4—3621no—
226C22×C4—1811no—
227C22×C4—1811no—
228Q16—3622no—
229M16—3622no—
230M16—3622no—
231C2×C8—1811no—
232C2×C8—1811no—
233C2×C8C22×D18111yescharacteristic
234C2×C8C22×D18111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—3621no—
239C4⋊C4—3621no—
240C4⋊C4—3621no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—1811no—
248C4⋊C4—1811no—
249C4⋊C4—1811no—
250C4⋊C4—1811no—
251C4⋊C4C22×D18111yescharacteristic
252C4⋊C4C22×D18111yescharacteristic
253C4⋊C4C22×D18111yescharacteristic
254C22⋊C4—3621no—
255C22⋊C4—3621no—
256C22⋊C4—3621no—
257C22⋊C4—3621no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—1811no—
261C22⋊C4—1811no—
262C42—21no—
263C42—3621no—
264C42—3621no—
265C42—3621no—
266C42C22×D18111yescharacteristic
267C23—1811no—
268C23—1811no—
269Q8—21no—
270Q8—21no—
271Q8—3621no—
272Q8—3621no—
273D4—7241no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—3621no—
279C2×C4—3621no—
280C2×C4—3621no—
281C2×C4—3621no—
282C2×C4—3621no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—1811no—
287C2×C4—1811no—
288C2×C4—7242no—
289C2×C4—7242no—
290C2×C4D4×D18111yescharacteristic
291C2×C4D4×D18111yescharacteristic
292C2×C4C23×D18111yescharacteristic
293C8—21no—
294C8—21no—
295C8—3621no—
296C8—1812no—
297C22—3621no—
298C22—3621no—
299C22—3621no—
300C22—3621no—
301C22—3621no—
302C22—3621no—
303C22C2×D4×D18111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—3621no—
311C4—3621no—
312C4—7241no—
313C4—7241no—
314C4—7241no—
315C4—7241no—
316C4#41×D18111yescharacteristic
317C4#1915386411yescharacteristic
318C2—7241no—
319C2—7241no—
320C2#2604193111yescharacteristic
321C2#2604207611yescharacteristic
322C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#479×C181C2
socleC22×C181C22×D4
prime radicalC2×D724D4
hypercenter#479D181
hypocenterC181#3352
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #26041678C2semidirect
4. #26041623C2semidirect
5. #26041618C2semidirect
6. #26041616C2semidirect
7. #26041613C2semidirect
8. #26041587C2semidirect
9. #26041536C2semidirect
10. #26041536C2semidirect
11. C4×#15668439C2semidirect
13. #26041320C2semidirect
14. #26041318C2semidirect
15. #479×C181C2semidirect
161. C181#3352semidirect
171. #479D181semidirect

Maximal subgroups

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

subgroupindex
#260419702
#260419672
#260416782
#260416232
#260416182
#260416162
#260416132
#260415872
#260415362
C4×#156684392
#260413562
#260413202
#260413182
#479×C1812
#3352181