Finite Group Databasebeta

← #37545578

Subgroups — #37545578

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041979C211yesmaximal, characteristic, complemented
2#26041922C211yesmaximal, characteristic, complemented
3#26041633C211yesmaximal, characteristic, complemented
4#26041613C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041512C211yesmaximal, characteristic, complemented
8#26041505C211yesmaximal, characteristic, complemented
9#26041423C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11C4×#15668434C211yesmaximal, characteristic, complemented
12#26041344C211yesmaximal, characteristic, complemented
13#26041274C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#463×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic, complemented
21#19153809—21no—
22#19153808C2211yescharacteristic, complemented
23#19153799—21no—
24#19153798—21no—
25#19153792C2211yescharacteristic
26#19153789—21no—
27#19153789—21no—
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic, complemented
31#19153786—21no—
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34C4×C22⋊D181—21no—
35#19153774C2211yescharacteristic, complemented
36C4⋊C4×D181C2211yescharacteristic
37C22⋊C4×D181—21no—
38#19153750C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153748C2211yescharacteristic, complemented
41#19153740C2211yescharacteristic, complemented
42#19153740C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51C4×#13089678C2211yescharacteristic, complemented
52C2×SD16×C181C2211yescharacteristic, complemented
53C2×D8×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic
59C23×D181—21no—
60#15668450—22no—
61#15668450—41no—
62C2×D724—21no—
63C2×D724D411yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69D4×D181—22no—
70D4×D181—41no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75C2×C4×D181C2311yescharacteristic
76#15668434—22no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C8×D181—41no—
80C8×D181—41no—
81C4⋊Dic181D411yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101C22×C4×C181—21no—
102SD16×C181—41no—
103D8×C181—41no—
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—42no—
113C22×D181—42no—
114C22×D181—81no—
115C22×D181C2×D411yescharacteristic
116C22×D181C2×D411yescharacteristic
117D724—22no—
118D724—21no—
119D724—42no—
120D724#4112yes—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135C4×D181—81no—
136C4×D181—81no—
137#13089678—21no—
138#13089678—21no—
139C23×C181—21no—
140C23×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—81no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C2×D181—22no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—84no—
171C2×D181#13512yes—
172C4×C181—21no—
173C4×C181—21no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181C2×#4111yescharacteristic
177C4×C181H(5,𝔽2)11yescharacteristic
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—81no—
184C2×C181—81no—
185C2×C181#54611yescharacteristic
186C2×C181C2×#13511yescharacteristic
187C2×C181#57611yescharacteristic
188D181—22no—
189D181—41no—
190D181—42no—
191C181#329711yescharacteristic, complemented, Sylow
192#3297—1811nomaximal, Sylow
193#553—1811no—
194#546—1811no—
195#488—1811no—
196#484—1811no—
197#482—1811no—
198#478—1811no—
199#466—1811no—
200#465—1811no—
201#463D18111yescharacteristic, complemented
202#449—1811no—
203#447—1811no—
204C4×D8—1811no—
205C8×D4—1811no—
206#416—1811no—
207C2×#102—1811no—
208C2×#41—1811no—
209C22×D4—1811no—
210C2×SD16C2×D18111yescharacteristic, complemented
211C2×D8—1811no—
212C2×D8C2×D18111yescharacteristic
213C22×C8—1811no—
214C22×C8—1811no—
215#126—3621no—
216#125—1811no—
217#124C2×D18111yescharacteristic
218#123—3621no—
219#123—3621no—
220C22⋊Q8—1811no—
221#121—3621no—
222#121—3621no—
223#121—1811no—
224#121—1811no—
225#121—1811no—
226#120—3621no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4C2×D18111yescharacteristic, complemented
231#117—1811no—
232C2×C4⋊C4—1811no—
233C2×C22⋊C4—3621no—
234#107—1811no—
235#107—1811no—
236#106—1811no—
237C4⋊C8C2×D18111yescharacteristic, complemented
238#103—1811no—
239#103—1811no—
240#103C2×D18111yescharacteristic, complemented
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102C2×D18111yescharacteristic
248C22⋊C8—1811no—
249C22⋊C8—1811no—
250C4×C8—1811no—
251C24—3621no—
252#41—3622no—
253#41—7241no—
254C2×Q8C22×D18111yescharacteristic
255C2×D4—3621no—
256C2×D4—3622no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—1811no—
262C2×D4—1811no—
263C2×D4—7241no—
264C2×D4C22×D18111yescharacteristic
265C2×D4C22×D18111yescharacteristic
266C22×C4—21no—
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4—1811no—
272SD16—41no—
273D8—41no—
274D8—3622no—
275C2×C8—1811no—
276C2×C8—1811no—
277C2×C8—7241no—
278C2×C8—7241no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4—1811no—
288C4⋊C4—1811no—
289C4⋊C4C22×D18111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—1811no—
300C22⋊C4—1811no—
301C42—3621no—
302C42C22×D18111yescharacteristic
303C23—21no—
304C23—21no—
305C23—3621no—
306C23—14481no—
307C23—1811no—
308C23—1811no—
309C23—7242no—
310C23—7242no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—3622no—
318D4—3621no—
319D4—14481no—
320D4—14481no—
321D4—1812no—
322D4—7242no—
323D4—7242no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—7242no—
340C2×C4D4×D18111yescharacteristic
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3621no—
354C22—3621no—
355C22—3621no—
356C22—3622no—
357C22—3621no—
358C22—3621no—
359C22—14484no—
360C22—1812no—
361C22—7241no—
362C22—7241no—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3621no—
369C4—3621no—
370C4—7241no—
371C4—7241no—
372C4—7241no—
373C4#41×D18111yescharacteristic
374C4#1915386111yescharacteristic
375C2—81no—
376C2—81no—
377C2—3622no—
378C2—7241no—
379C2—7242no—
380C2#2604192611yescharacteristic
381C2#135×D18111yescharacteristic
382C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#463×C181C2
socleC22×C181C22×D4
hypercenter#463D181
hypocenterC181#3297
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #26041979C2semidirect
2. #26041922C2semidirect
3. #26041633C2semidirect
4. #26041613C2semidirect
5. #26041602C2semidirect
6. #26041580C2semidirect
7. #26041512C2semidirect
8. #26041505C2semidirect
9. #26041423C2semidirect
10. #26041411C2semidirect
11. C4×#15668434C2semidirect
12. #26041344C2semidirect
13. #26041274C2semidirect
14. #102×D181C2semidirect
15. #463×C181C2semidirect
20. C2×C8×D181C22semidirect
22. #19153808C22semidirect
30. #19153787C22semidirect
35. #19153774C22semidirect
38. #19153750C22semidirect
39. #19153749C22semidirect
40. #19153748C22semidirect
41. #19153740C22semidirect
42. #19153740C22semidirect
47. #19153737C22semidirect
50. #19153728C22semidirect
51. C4×#13089678C22semidirect
52. C2×SD16×C181C22semidirect
55. C4×D4×C181C22semidirect
56. C4⋊C8×C181C22semidirect
57. #103×C181C22semidirect
191. C181#3297semidirect
201. #463D181semidirect
210. C2×SD16C2×D181semidirect
230. C4×D4C2×D181semidirect
237. C4⋊C8C2×D181semidirect
240. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419792
#260419222
#260416332
#260416132
#260416022
#260415802
#260415122
#260415052
#260414232
#260414112
C4×#156684342
#260413442
#260412742
#102×D1812
#463×C1812
#3297181