Finite Group Databasebeta

← #37543903

Subgroups — #37543903

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#26041894C211yesmaximal, characteristic, complemented
2#26041751C211yesmaximal, characteristic, complemented
3#26041623C211yesmaximal, characteristic, complemented
4#26041601C211yesmaximal, characteristic, complemented
5#26041568C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041493C211yesmaximal, characteristic, complemented
8#26041492C211yesmaximal, characteristic, complemented
9#26041431C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic
11#26041381C211yesmaximal, characteristic, complemented
12C4×#15668437C211yesmaximal, characteristic, complemented
13C4×#15668434C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic, complemented
15#442×C181C211yesmaximal, characteristic, complemented
16C2×D4×D181C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153815C2211yescharacteristic, complemented
21#19153809—21no—
22#19153803C2211yescharacteristic, complemented
23#19153802—21no—
24#19153799—21no—
25#19153796C2211yescharacteristic
26#19153795—21no—
27#19153787C2211yescharacteristic
28C4×Dic362C2211yescharacteristic, complemented
29C4×D724C2211yescharacteristic
30D4×Dic181C2211yescharacteristic
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33#19153776—21no—
34#19153774C2211yescharacteristic
35#19153773C2211yescharacteristic
36C2×#15668426—21no—
37C22⋊C4×D181—21no—
38#19153750C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153741C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58#97×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65D4×D181—22no—
66D4×D181—22no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71#15668438—22no—
72#15668437—22no—
73#15668434—22no—
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C2×D4×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C22×C4×C181—21no—
100D8×C181—22no—
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—24no—
110C22×D181—81no—
111C22×D181—81no—
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—21no—
115Dic362—81no—
116D724—21no—
117D724#4112yes—
118C22⋊D181—24no—
119C22⋊D181—81no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—81no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C4×D181—21no—
128C4×D181—21no—
129C4×D181—81no—
130C4×D181—81no—
131#13089678—21no—
132#13089678—21no—
133C23×C181—21no—
134C23×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—21no—
138D4×C181#4112yes—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—81no—
142C2×C4×C181—81no—
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C8×C181—21no—
147C8×C181—21no—
148C22×C181—22no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181C22×D411yescharacteristic
155C2×D181—21no—
156C2×D181—22no—
157C2×D181—21no—
158C2×D181—21no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—84no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181C2×#4111yescharacteristic
167C4×C181C2×#4111yescharacteristic
168Dic181—21no—
169Dic181—21no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173Dic181—41no—
174C2×C181—42no—
175C2×C181—81no—
176C2×C181#52511yescharacteristic
177C2×C181#57611yescharacteristic
178C2×C181#57711yescharacteristic
179D181—41no—
180D181—42no—
181C181#311811yescharacteristic, complemented, Sylow
182#3118—1811nomaximal, Sylow
183#542—1811no—
184#518—1811no—
185#485—1811no—
186#482—1811no—
187#476—1811no—
188#474—1811no—
189#463—1811no—
190#463—1811no—
191#450—1811no—
192#447—1811no—
193#442D18111yescharacteristic, complemented
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×D8C2×D18111yescharacteristic
203C4⋊Q8—1811no—
204#126—3621no—
205#124—3621no—
206#124—1811no—
207#123—3621no—
208C22⋊Q8—3621no—
209C22⋊Q8—1811no—
210#121—1811no—
211C4×Q8—1811no—
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4C2×D18111yescharacteristic
218C4×D4C2×D18111yescharacteristic, complemented
219#117—1811no—
220#117—1811no—
221C2×C22⋊C4—3621no—
222C2×C22⋊C4—3621no—
223#107—1811no—
224#107—1811no—
225#106—1811no—
226#106C2×D18111yescharacteristic, complemented
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229#103—1811no—
230#103—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102C2×D18111yescharacteristic
236#102C2×D18111yescharacteristic, complemented
237C22⋊C8—1811no—
238C22⋊C8—1811no—
239#97C2×D18111yescharacteristic, complemented
240C4×C8—1811no—
241C24—3621no—
242C2×Q8—3621no—
243C2×Q8—1811no—
244C2×D4—3622no—
245C2×D4—3622no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4C22×D18111yescharacteristic
250C2×D4C22×D18111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—1811no—
257SD16—3622no—
258SD16—3622no—
259D8—22no—
260D8—3622no—
261C2×C8—1811no—
262C2×C8—1811no—
263C2×C8C22×D18111yescharacteristic
264C2×C8C22×D18111yescharacteristic
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—1811no—
269C4⋊C4—1811no—
270C4⋊C4—1811no—
271C4⋊C4—1811no—
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—3621no—
287C42—3621no—
288C42—1811no—
289C42C22×D18111yescharacteristic
290C23—21no—
291C23—21no—
292C23—3624no—
293C23—3621no—
294C23—14481no—
295C23—14481no—
296C23—1811no—
297Q8—3621no—
298Q8—3621no—
299Q8—14481no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—3624no—
304D4—3621no—
305D4—14481no—
306D4—1812no—
307D4#1566844912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—14481no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4D4×D18111yescharacteristic
324C2×C4D4×D18111yescharacteristic
325C2×C4C23×D18111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3621no—
329C8—3621no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3621no—
337C22—3622no—
338C22—3621no—
339C22—3621no—
340C22—14484no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—3621no—
349C4—3621no—
350C4—3621no—
351C4—7241no—
352C4—7241no—
353C4—7241no—
354C4#41×D18111yescharacteristic
355C4C2×#1566844911yescharacteristic
356C2—42no—
357C2—81no—
358C2—7241no—
359C2—7242no—
360C2#2604178811yescharacteristic
361C2#2604208311yescharacteristic
362C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#442×C181C2
socleC22×C181C22×D4
prime radical#26041411C2
hypercenter#442D181
hypocenterC181#3118
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #26041894C2semidirect
2. #26041751C2semidirect
3. #26041623C2semidirect
4. #26041601C2semidirect
5. #26041568C2semidirect
6. #26041557C2semidirect
7. #26041493C2semidirect
8. #26041492C2semidirect
9. #26041431C2semidirect
11. #26041381C2semidirect
12. C4×#15668437C2semidirect
13. C4×#15668434C2semidirect
14. #26041341C2semidirect
15. #442×C181C2semidirect
20. #19153815C22semidirect
22. #19153803C22semidirect
28. C4×Dic362C22semidirect
38. #19153750C22semidirect
39. #19153749C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
43. #19153741C22semidirect
44. #19153739C22semidirect
47. #19153737C22semidirect
51. C4×#13089678C22semidirect
54. C4×D4×C181C22semidirect
55. #106×C181C22semidirect
57. #102×C181C22semidirect
58. #97×C181C22semidirect
181. C181#3118semidirect
193. #442D181semidirect
218. C4×D4C2×D181semidirect
226. #106C2×D181semidirect
236. #102C2×D181semidirect
239. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418942
#260417512
#260416232
#260416012
#260415682
#260415572
#260414932
#260414922
#260414312
#260414112
#260413812
C4×#156684372
C4×#156684342
#260413412
#442×C1812
#3118181