Finite Group Databasebeta

← #37544584

Subgroups — #37544584

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#26041846C211yesmaximal, characteristic, complemented
2#26041845C211yesmaximal, characteristic, complemented
3#26041604C211yesmaximal, characteristic, complemented
4#26041602C211yesmaximal, characteristic, complemented
5#26041601C211yesmaximal, characteristic, complemented
6#26041600C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041529C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041512C211yesmaximal, characteristic, complemented
11#26041413C211yesmaximal, characteristic, complemented
12#26041411C211yesmaximal, characteristic, complemented
13#26041411C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#447×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic, complemented
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic, complemented
21C2×C8×D181C2211yescharacteristic, complemented
22#19153812—21no—
23#19153812—21no—
24#19153803—21no—
25#19153802—21no—
26#19153791C2211yescharacteristic, complemented
27#19153790C2211yescharacteristic
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic, complemented
31#19153787C2211yescharacteristic, complemented
32#19153787C2211yescharacteristic, complemented
33#19153786—21no—
34#19153785—21no—
35#19153785—21no—
36#19153784—21no—
37#19153775C2211yescharacteristic, complemented
38#19153774C2211yescharacteristic, complemented
39#19153750C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic, complemented
48#19153737C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic, complemented
53C2×D8×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—41no—
61#15668449—41no—
62C2×Dic362D411yescharacteristic
63C2×D724—21no—
64C2×D724D411yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181D411yescharacteristic
74C2×C22⋊D181D411yescharacteristic
75D4×D181—41no—
76D4×D181—41no—
77C2×C4×D181C2311yescharacteristic
78C2×C4×D181C2311yescharacteristic
79#15668434—41no—
80#15668434—41no—
81#15668432—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C8×D181—41no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99C24×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181—41no—
103C2×D4×C181—41no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C2×D4×C181C2311yescharacteristic
107C22×C4×C181C2311yescharacteristic
108D8×C181—41no—
109D8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—42no—
116C22×D181—81no—
117C22×D181—81no—
118C22×D181C2×D411yescharacteristic
119C22×D181C2×D411yescharacteristic
120Dic362—41no—
121D724—21no—
122D724—21no—
123D724—41no—
124D724—81no—
125C22⋊D181—41no—
126C22⋊D181—41no—
127C22⋊D181—42no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C22⋊D181—81no—
133C22⋊D181—81no—
134C2×Dic181—21no—
135C2×Dic181—21no—
136C2×Dic181—21no—
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C4×D181—21no—
140C4×D181—21no—
141C4×D181—21no—
142C4×D181—21no—
143#13089678—21no—
144#13089678—21no—
145C23×C181—21no—
146C23×C181—21no—
147C23×C181—21no—
148C23×C181—42no—
149C23×C181—81no—
150C23×C181—81no—
151C23×C181C2×D411yescharacteristic
152D4×C181—21no—
153D4×C181—21no—
154D4×C181—21no—
155D4×C181—21no—
156D4×C181—21no—
157D4×C181—21no—
158D4×C181—42no—
159D4×C181—81no—
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×C181—41no—
174C22×C181—41no—
175C22×C181—41no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181—41no—
179C22×C181—84no—
180C22×C181C22×D411yescharacteristic
181C2×D181—21no—
182C2×D181—21no—
183C2×D181—21no—
184C2×D181—21no—
185C2×D181—21no—
186C2×D181—21no—
187C2×D181—41no—
188C2×D181—41no—
189C2×D181—41no—
190C2×D181—84no—
191C4×C181—21no—
192C4×C181—41no—
193C4×C181H(5,𝔽2)11yescharacteristic
194C4×C181H(5,𝔽2)11yescharacteristic
195Dic181—21no—
196Dic181—21no—
197Dic181—41no—
198Dic181—41no—
199Dic181—41no—
200C2×C181—41no—
201C2×C181—81no—
202C2×C181—81no—
203C2×C181—81no—
204C2×C181#53411yescharacteristic
205C2×C181#57611yescharacteristic
206C2×C181#57611yescharacteristic
207D181—41no—
208D181—41no—
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#482—1811no—
218#469—1811no—
219#469—1811no—
220#466—1811no—
221#466—1811no—
222#447—1811no—
223#447—1811no—
224#447—1811no—
225#447D18111yescharacteristic, complemented
226#408—1811no—
227C2×#41—1811no—
228C22×D4—1811no—
229C22×D4C2×D18111yescharacteristic, complemented
230C2×D8—1811no—
231C2×D8—1811no—
232C2×D8C2×D18111yescharacteristic
233C2×D8C2×D18111yescharacteristic
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#117—1811no—
254#107—1811no—
255#107—1811no—
256#106—1811no—
257#106—1811no—
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—21no—
271C24—3621no—
272#41—7241no—
273#41—7241no—
274C2×Q8—1811no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—3621no—
280C2×D4—3621no—
281C2×D4—3621no—
282C2×D4—3621no—
283C2×D4—3621no—
284C2×D4—3621no—
285C2×D4—3621no—
286C2×D4—3621no—
287C2×D4—1811no—
288C2×D4—1811no—
289C2×D4—1811no—
290C2×D4—1811no—
291C2×D4—7241no—
292C2×D4—7241no—
293C2×D4C22×D18111yescharacteristic
294C2×D4C22×D18111yescharacteristic
295C2×D4C22×D18111yescharacteristic
296C22×C4—1811no—
297C22×C4—1811no—
298C22×C4C22×D18111yescharacteristic
299D8—41no—
300D8—41no—
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⋊C4—1811no—
311C4⋊C4—1811no—
312C4⋊C4C22×D18111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3621no—
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—3621no—
324C42—3621no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—3621no—
332C23—14481no—
333C23—14481no—
334C23—1811no—
335C23—1811no—
336C23—7242no—
337C23D4×D18111yescharacteristic
338Q8—7241no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—3621no—
348D4—3621no—
349D4—14481no—
350D4—14481no—
351D4—14481no—
352D4—14481no—
353D4—14481no—
354D4—14481no—
355D4—14481no—
356D4—7241no—
357D4—7241no—
358D4—7241no—
359D4—7242no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3621no—
364C2×C4—3621no—
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—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—3621no—
392C22—3621no—
393C22—3621no—
394C22—3621no—
395C22—3621no—
396C22—3621no—
397C22—14484no—
398C22—7241no—
399C22—7241no—
400C22—7241no—
401C22C2×D4×D18111yescharacteristic
402C4—21no—
403C4—41no—
404C4—3621no—
405C4—3621no—
406C4—7241no—
407C4—7241no—
408C4—7241no—
409C4#1915386111yescharacteristic
410C4#1915386111yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—14481no—
416C2—7241no—
417C2—7241no—
418C2#2604183911yescharacteristic
419C2#2604208011yescharacteristic
420C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#447×C181C2
socleC22×C181C22×D4
hypercenter#447D181
hypocenterC181#3199
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #26041846C2semidirect
2. #26041845C2semidirect
3. #26041604C2semidirect
4. #26041602C2semidirect
5. #26041601C2semidirect
6. #26041600C2semidirect
7. #26041531C2semidirect
8. #26041529C2semidirect
9. #26041514C2semidirect
10. #26041512C2semidirect
11. #26041413C2semidirect
12. #26041411C2semidirect
13. #26041411C2semidirect
14. #26041244C2semidirect
15. #447×C181C2semidirect
17. C2×D4×D181C22semidirect
20. C2×#15668432C22semidirect
21. C2×C8×D181C22semidirect
26. #19153791C22semidirect
30. #19153787C22semidirect
31. #19153787C22semidirect
32. #19153787C22semidirect
37. #19153775C22semidirect
38. #19153774C22semidirect
39. #19153750C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153747C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
45. #19153737C22semidirect
46. #19153737C22semidirect
47. #19153737C22semidirect
48. #19153737C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. #19153728C22semidirect
52. C22×D4×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
210. C181#3199semidirect
225. #447D181semidirect
229. C22×D4C2×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
#260418462
#260418452
#260416042
#260416022
#260416012
#260416002
#260415312
#260415292
#260415142
#260415122
#260414132
#260414112
#260412442
#447×C1812
#3199181