Finite Group Databasebeta

← #37543908

Subgroups — #37543908

Order 23168.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041902C211yesmaximal, characteristic, complemented
2#26041753C211yesmaximal, characteristic, complemented
3#26041603C211yesmaximal, characteristic, complemented
4#26041568C211yesmaximal, characteristic, complemented
5#26041558C211yesmaximal, characteristic, complemented
6#26041497C211yesmaximal, characteristic, complemented
7#26041497C211yesmaximal, characteristic, complemented
8#26041429C211yesmaximal, characteristic, complemented
9#26041415C211yesmaximal, characteristic
10#26041390C211yesmaximal, characteristic, complemented
11#26041382C211yesmaximal, characteristic, complemented
12#26041364C211yesmaximal, characteristic, complemented
13#26041361C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#485×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21#19153815C2211yescharacteristic, complemented
22#19153811—21no—
23#19153805C2211yescharacteristic, complemented
24#19153802—21no—
25#19153798—21no—
26#19153796—21no—
27#19153790C2211yescharacteristic
28Q8×Dic181C2211yescharacteristic, complemented
29C4×D724—21no—
30C4×D724—21no—
31#19153778C2211yescharacteristic
32#19153778C2211yescharacteristic
33#19153778C2211yescharacteristic
34#19153778C2211yescharacteristic
35#19153778C2211yescharacteristic, complemented
36#19153775C2211yescharacteristic
37C22⋊C4×D181—21no—
38C22⋊C4×D181—21no—
39#19153749C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153736C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C22⋊Q8×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#103×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181—21no—
60C2×Dic362—21no—
61C2×D724—22no—
62C2×D724—22no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73#15668436—22no—
74#15668436—22no—
75D1448—22no—
76D1448—22no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181—21no—
80C4⋊Dic181D411yescharacteristic
81C4⋊Dic181D411yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84C22⋊Dic181D411yescharacteristic
85C22⋊Dic181D411yescharacteristic
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98C22×C4×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181—21no—
108C22×D181—21no—
109C22×D181—21no—
110C22×D181—24no—
111C22×D181—21no—
112C22×D181—81no—
113C22×D181—81no—
114Dic362—81no—
115D724—24no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724#4112yes—
121D724#4112yes—
122C22⋊D181—81no—
123C2×Dic181—21no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—81no—
129C4×D181—81no—
130C4×D181—81no—
131C4×D181—81no—
132C4×D181—81no—
133#13089678—21no—
134#13089678—21no—
135C23×C181C2×D411yescharacteristic
136Q8×C181—21no—
137Q8×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C8×C181—21no—
147C8×C181—21no—
148C22×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181C22×D411yescharacteristic
152C2×D181—22no—
153C2×D181—22no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—84no—
162C4×C181—21no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181C2×#4111yescharacteristic
168C4×C181C2×#4111yescharacteristic
169Dic181—21no—
170Dic181—21no—
171Dic181—21no—
172Dic181—21no—
173Dic181—41no—
174C2×C181—41no—
175C2×C181#52511yescharacteristic
176C2×C181#57611yescharacteristic
177C2×C181#57711yescharacteristic
178D181—42no—
179D181—42no—
180D181—81no—
181C181#311811yescharacteristic, complemented, Sylow
182#3118—1811nomaximal, Sylow
183#542—1811no—
184#518—1811no—
185#485D18111yescharacteristic, complemented
186#482—1811no—
187#476—1811no—
188#474—1811no—
189#463—1811no—
190#463—1811no—
191#450—1811no—
192#447—1811no—
193#442—1811no—
194#440—1811no—
195C4×SD16—1811no—
196C4×D8—1811no—
197#433—1811no—
198C22×D4—1811no—
199C2×SD16—1811no—
200C2×SD16—1811no—
201C2×D8—1811no—
202C2×D8—1811no—
203C4⋊Q8—1811no—
204#126—3621no—
205#124—3621no—
206#124—1811no—
207#123—3621no—
208C22⋊Q8—3621no—
209C22⋊Q8C2×D18111yescharacteristic
210#121—1811no—
211C4×Q8—1811no—
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4—1811no—
218C4×D4—1811no—
219#117—1811no—
220#117C2×D18111yescharacteristic
221C2×C22⋊C4—3621no—
222C2×C22⋊C4—3621no—
223#107—1811no—
224#107C2×D18111yescharacteristic, complemented
225#106—1811no—
226#106C2×D18111yescharacteristic, complemented
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229#103C2×D18111yescharacteristic, complemented
230#103C2×D18111yescharacteristic, complemented
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
237C22⋊C8—1811no—
238C22⋊C8C2×D18111yescharacteristic
239#97—1811no—
240C4×C8—1811no—
241C24—3621no—
242C2×Q8—3621no—
243C2×Q8C22×D18111yescharacteristic
244C2×D4—3622no—
245C2×D4—3622no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4—1811no—
250C2×D4—1811no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4C22×D18111yescharacteristic
257SD16—3622no—
258SD16—3622no—
259D8—3622no—
260D8—3622no—
261C2×C8—1811no—
262C2×C8—1811no—
263C2×C8C22×D18111yescharacteristic
264C2×C8C22×D18111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—1811no—
269C4⋊C4—1811no—
270C4⋊C4—1811no—
271C4⋊C4C22×D18111yescharacteristic
272C4⋊C4C22×D18111yescharacteristic
273C4⋊C4C22×D18111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—3621no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—1811no—
285C22⋊C4—1811no—
286C42—21no—
287C42—3621no—
288C42—1811no—
289C42—1811no—
290C23—3624no—
291C23—3621no—
292C23—3621no—
293C23—3621no—
294C23—14481no—
295C23—14481no—
296C23D4×D18111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—14481no—
300D4—3624no—
301D4—3621no—
302D4—3621no—
303D4—3621no—
304D4—3621no—
305D4—14481no—
306D4—1812no—
307D4—1812no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3621no—
315C2×C4—14481no—
316C2×C4—14481no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—14481no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4—1811no—
324C2×C4D4×D18111yescharacteristic
325C2×C4C23×D18111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3621no—
329C8—3621no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3622no—
334C22—3622no—
335C22—14484no—
336C22—7241no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3621no—
350C4—3621no—
351C4—3621no—
352C4—3621no—
353C4—7241no—
354C4#41×D18111yescharacteristic
355C4#41×D18111yescharacteristic
356C2—41no—
357C2—14481no—
358C2—7242no—
359C2—7242no—
360C2#2604178711yescharacteristic
361C2#2604208111yescharacteristic
362C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#485×C181C2
socleC22×C181C22×D4
prime radical#26041415C2
hypercenter#485D181
hypocenterC181#3118
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #26041902C2semidirect
2. #26041753C2semidirect
3. #26041603C2semidirect
4. #26041568C2semidirect
5. #26041558C2semidirect
6. #26041497C2semidirect
7. #26041497C2semidirect
8. #26041429C2semidirect
10. #26041390C2semidirect
11. #26041382C2semidirect
12. #26041364C2semidirect
13. #26041361C2semidirect
14. #26041337C2semidirect
15. #485×C181C2semidirect
21. #19153815C22semidirect
23. #19153805C22semidirect
28. Q8×Dic181C22semidirect
35. #19153778C22semidirect
39. #19153749C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. #103×C181C22semidirect
57. #103×C181C22semidirect
181. C181#3118semidirect
185. #485D181semidirect
224. #107C2×D181semidirect
226. #106C2×D181semidirect
229. #103C2×D181semidirect
230. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419022
#260417532
#260416032
#260415682
#260415582
#260414972
#260414292
#260414152
#260413902
#260413822
#260413642
#260413612
#260413372
#485×C1812
#3118181