Finite Group Databasebeta

← #37544585

Subgroups — #37544585

Order 23168.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041848C211yesmaximal, characteristic, complemented
2#26041845C211yesmaximal, characteristic, complemented
3#26041606C211yesmaximal, characteristic, complemented
4#26041605C211yesmaximal, characteristic, complemented
5#26041603C211yesmaximal, characteristic, complemented
6#26041533C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041516C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041415C211yesmaximal, characteristic, complemented
11#26041414C211yesmaximal, characteristic, complemented
12#26041414C211yesmaximal, characteristic, complemented
13#26041412C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×D724C2211yescharacteristic, complemented
18C2×D4×D181C2211yescharacteristic, complemented
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668432C2211yescharacteristic, complemented
24C2×C8×D181C2211yescharacteristic, complemented
25#19153813—21no—
26#19153812—21no—
27#19153804—21no—
28#19153802—21no—
29#19153791C2211yescharacteristic
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic, complemented
32#19153791C2211yescharacteristic, complemented
33#19153791C2211yescharacteristic, complemented
34#19153790C2211yescharacteristic
35#19153787C2211yescharacteristic, complemented
36#19153786—21no—
37#19153786—21no—
38#19153786—21no—
39#19153784—21no—
40#19153774C2211yescharacteristic, complemented
41#19153749C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153736C2211yescharacteristic, complemented
46#19153736C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61#15668449—41no—
62#15668449—41no—
63C2×Dic362D411yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724—41no—
71C2×D724—41no—
72C2×D724D411yescharacteristic
73C2×D724C2311yescharacteristic
74C2×D724C2311yescharacteristic
75C2×D724C2311yescharacteristic
76C2×C22⋊D181—21no—
77C2×C22⋊D181—21no—
78C2×C22⋊D181—21no—
79C2×C22⋊D181D411yescharacteristic
80C2×C22⋊D181D411yescharacteristic
81D4×D181—41no—
82D4×D181—41no—
83C2×C4×D181C2311yescharacteristic
84C2×C4×D181C2311yescharacteristic
85D1448—41no—
86D1448—41no—
87#15668434—41no—
88#15668434—41no—
89#15668432—41no—
90C2×#13089678C2311yescharacteristic
91C2×#13089678C2311yescharacteristic
92C8×D181—41no—
93C4⋊Dic181C2311yescharacteristic
94C22⋊Dic181—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426—21no—
100#15668426—21no—
101#15668426—21no—
102C4×Dic181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22⋊C4×C181—21no—
113C42×C181—21no—
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—21no—
117C22×D181—42no—
118C22×D181—42no—
119C22×D181—81no—
120C22×D181—81no—
121C22×D181—81no—
122C22×D181—81no—
123C22×D181C2×D411yescharacteristic
124C22×D181C2×D411yescharacteristic
125Dic362—41no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—21no—
130D724—21no—
131D724—21no—
132D724—41no—
133D724—42no—
134D724—81no—
135D724—81no—
136D724—81no—
137D724—81no—
138D724—81no—
139C22⋊D181—41no—
140C22⋊D181—41no—
141C22⋊D181—42no—
142C22⋊D181—81no—
143C22⋊D181—81no—
144C2×Dic181—21no—
145C2×Dic181C2×D411yescharacteristic
146C2×Dic181C2×D411yescharacteristic
147C4×D181—21no—
148C4×D181—21no—
149C4×D181—21no—
150C4×D181—21no—
151#13089678—21no—
152#13089678—21no—
153C23×C181—21no—
154C23×C181C2×D411yescharacteristic
155D4×C181—21no—
156D4×C181—21no—
157D4×C181—81no—
158C2×C4×C181—21no—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181C2×D411yescharacteristic
164C2×C4×C181C2411yescharacteristic
165C8×C181—21no—
166C8×C181—21no—
167C22×C181—21no—
168C22×C181—21no—
169C22×C181—21no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181C22×D411yescharacteristic
174C2×D181—21no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—21no—
178C2×D181—21no—
179C2×D181—21no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—41no—
184C2×D181—41no—
185C2×D181—41no—
186C2×D181—41no—
187C2×D181—41no—
188C2×D181—41no—
189C2×D181—84no—
190C2×D181—84no—
191C4×C181—21no—
192C4×C181—41no—
193C4×C181—41no—
194C4×C181—41no—
195C4×C181H(5,𝔽2)11yescharacteristic
196C4×C181H(5,𝔽2)11yescharacteristic
197Dic181—21no—
198Dic181—21no—
199Dic181—41no—
200C2×C181—41no—
201C2×C181—81no—
202C2×C181#53411yescharacteristic
203C2×C181#57611yescharacteristic
204C2×C181#57611yescharacteristic
205D181—41no—
206D181—41no—
207D181—81no—
208D181—81no—
209D181—81no—
210C181#319911yescharacteristic, complemented, Sylow
211#3199—1811nomaximal, Sylow
212#535—1811no—
213#535—1811no—
214#482—1811no—
215#482—1811no—
216#482—1811no—
217#482D18111yescharacteristic, complemented
218#469—1811no—
219#469—1811no—
220#466—1811no—
221#466—1811no—
222#447—1811no—
223#447—1811no—
224#447—1811no—
225#447—1811no—
226#408—1811no—
227C2×#41—1811no—
228C22×D4—1811no—
229C22×D4—1811no—
230C2×D8—1811no—
231C2×D8—1811no—
232C2×D8—1811no—
233C2×D8—1811no—
234C2×M16—1811no—
235C22×C8—1811no—
236#127—3621no—
237#127—3621no—
238#124—3621no—
239#124—3621no—
240#121—1811no—
241#121—1811no—
242#121—1811no—
243#121—1811no—
244#121—1811no—
245#121—1811no—
246#121—1811no—
247#121C2×D18111yescharacteristic
248#120—3621no—
249#120—3621no—
250#120—3621no—
251#120—3621no—
252#117—1811no—
253#117C2×D18111yescharacteristic, complemented
254#107—1811no—
255#107C2×D18111yescharacteristic, complemented
256#106—1811no—
257#106C2×D18111yescharacteristic, complemented
258#102—1811no—
259#102—1811no—
260#102—1811no—
261#102—1811no—
262#102—1811no—
263#102—1811no—
264#102C2×D18111yescharacteristic, complemented
265#102C2×D18111yescharacteristic, complemented
266C22⋊C8—1811no—
267C22⋊C8—1811no—
268C22⋊C8—1811no—
269C22⋊C8C2×D18111yescharacteristic, complemented
270C24—3621no—
271C24—3621no—
272#41—7241no—
273#41—7241no—
274C2×Q8—1811no—
275C2×D4—21no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—3621no—
279C2×D4—3621no—
280C2×D4—3621no—
281C2×D4—3621no—
282C2×D4—3621no—
283C2×D4—3621no—
284C2×D4—3621no—
285C2×D4—1811no—
286C2×D4—1811no—
287C2×D4—1811no—
288C2×D4—1811no—
289C2×D4—1811no—
290C2×D4—1811no—
291C2×D4—7241no—
292C2×D4—7241no—
293C2×D4—7241no—
294C2×D4—7241no—
295C2×D4C22×D18111yescharacteristic
296C22×C4—1811no—
297C22×C4—1811no—
298C22×C4C22×D18111yescharacteristic
299D8—7241no—
300D8—7241no—
301D8—7241no—
302D8—7241no—
303M16—7241no—
304C2×C8—1811no—
305C2×C8—1811no—
306C2×C8—7241no—
307C2×C8C22×D18111yescharacteristic
308C2×C8C22×D18111yescharacteristic
309C4⋊C4—1811no—
310C4⋊C4C22×D18111yescharacteristic
311C4⋊C4C22×D18111yescharacteristic
312C4⋊C4C22×D18111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—3621no—
323C42—21no—
324C42—3621no—
325C23—21no—
326C23—3621no—
327C23—3621no—
328C23—3621no—
329C23—14481no—
330C23—14481no—
331C23—14481no—
332C23—14481no—
333C23—1811no—
334C23—1811no—
335C23—7242no—
336C23—7242no—
337C23D4×D18111yescharacteristic
338Q8—7241no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—3621no—
343D4—3621no—
344D4—3621no—
345D4—3621no—
346D4—3621no—
347D4—3621no—
348D4—14481no—
349D4—14481no—
350D4—14481no—
351D4—14481no—
352D4—14481no—
353D4—14481no—
354D4—14481no—
355D4—7241no—
356D4—7242no—
357D4—7241no—
358D4—7241no—
359D4—7242no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—3621no—
366C2×C4—3621no—
367C2×C4—3621no—
368C2×C4—3621no—
369C2×C4—3621no—
370C2×C4—1811no—
371C2×C4—1811no—
372C2×C4D4×D18111yescharacteristic
373C2×C4C23×D18111yescharacteristic
374C8—21no—
375C8—21no—
376C8—3621no—
377C8—3621no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3621no—
385C22—3621no—
386C22—3621no—
387C22—3621no—
388C22—3621no—
389C22—3621no—
390C22—14484no—
391C22—14484no—
392C22—7241no—
393C22—7241no—
394C22—7241no—
395C22—7241no—
396C22—7241no—
397C22—7241no—
398C22—7241no—
399C22—7241no—
400C22—7241no—
401C22C2×D4×D18111yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3621no—
407C4—3621no—
408C4—7241no—
409C4#1915386211yescharacteristic
410C4#1915386211yescharacteristic
411C2—41no—
412C2—81no—
413C2—14481no—
414C2—14481no—
415C2—14481no—
416C2—7241no—
417C2—7241no—
418C2#2604184011yescharacteristic
419C2#2604208111yescharacteristic
420C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
hypercenter#482D181
hypocenterC181#3199
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26041848C2semidirect
2. #26041845C2semidirect
3. #26041606C2semidirect
4. #26041605C2semidirect
5. #26041603C2semidirect
6. #26041533C2semidirect
7. #26041531C2semidirect
8. #26041516C2semidirect
9. #26041514C2semidirect
10. #26041415C2semidirect
11. #26041414C2semidirect
12. #26041414C2semidirect
13. #26041412C2semidirect
14. #26041244C2semidirect
15. #482×C181C2semidirect
17. C22×D724C22semidirect
18. C2×D4×D181C22semidirect
23. C2×#15668432C22semidirect
24. C2×C8×D181C22semidirect
31. #19153791C22semidirect
32. #19153791C22semidirect
33. #19153791C22semidirect
35. #19153787C22semidirect
40. #19153774C22semidirect
41. #19153749C22semidirect
42. #19153747C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
45. #19153736C22semidirect
46. #19153736C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. #19153728C22semidirect
53. #117×C181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
210. C181#3199semidirect
217. #482D181semidirect
253. #117C2×D181semidirect
255. #107C2×D181semidirect
257. #106C2×D181semidirect
264. #102C2×D181semidirect
265. #102C2×D181semidirect
269. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418482
#260418452
#260416062
#260416052
#260416032
#260415332
#260415312
#260415162
#260415142
#260414152
#260414142
#260414122
#260412442
#482×C1812
#3199181