Finite Group Databasebeta

← #37546742

Subgroups — #37546742

Order 23168.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042001C211yesmaximal, characteristic, complemented
2#26041950C211yesmaximal, characteristic, complemented
3#26041668C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041650C211yesmaximal, characteristic, complemented
6#26041497C211yesmaximal, characteristic, complemented
7#26041494C211yesmaximal, characteristic, complemented
8#26041483C211yesmaximal, characteristic, complemented
9#26041479C211yesmaximal, characteristic, complemented
10#26041478C211yesmaximal, characteristic, complemented
11#26041473C211yesmaximal, characteristic, complemented
12#26041407C211yesmaximal, characteristic, complemented
13#26041378C211yesmaximal, characteristic, complemented
14#26041361C211yesmaximal, characteristic, complemented
15#440×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668438C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×D1448C2211yescharacteristic
23C2×D1448C2211yescharacteristic
24C2×#15668434C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153813C2211yescharacteristic
27#19153812C2211yescharacteristic
28#19153812C2211yescharacteristic
29#19153811—21no—
30#19153810—21no—
31#19153805C2211yescharacteristic
32#19153804C2211yescharacteristic
33#19153794—21no—
34#19153790—21no—
35#19153789—21no—
36#19153789—21no—
37C4×Dic362C2211yescharacteristic
38#19153781C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153778C2211yescharacteristic
41#19153778C2211yescharacteristic
42#19153773—21no—
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362D411yescharacteristic
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74#15668438—22no—
75#15668438—41no—
76#15668437—41no—
77#15668436—41no—
78#15668436—41no—
79D1448—22no—
80D1448—41no—
81#15668434—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181D411yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181—21no—
98C4×Dic181C2311yescharacteristic
99C4×Dic181C2311yescharacteristic
100C2×Q8×C181C2311yescharacteristic
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103SD16×C181—22no—
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—21no—
115Dic362—22no—
116Dic362—21no—
117Dic362—21no—
118D724—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—21no—
123D724—21no—
124D724—42no—
125D724—81no—
126C22⋊D181—42no—
127C22⋊D181—42no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C2×Dic181—21no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C4×D181—42no—
136C4×D181—42no—
137C4×D181—42no—
138#13089678—21no—
139#13089678—21no—
140C23×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—42no—
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C8×C181—21no—
153C8×C181#4112yescomplemented
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181C22×D411yescharacteristic
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181C2×#4111yescharacteristic
173C4×C181H(5,𝔽2)11yescharacteristic
174Dic181—21no—
175Dic181—21no—
176Dic181—21no—
177Dic181—41no—
178Dic181AGL(1,ℤ/8)12yes—
179C2×C181—81no—
180C2×C181#55011yescharacteristic
181C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
182C2×C181#57711yescharacteristic
183D181—81no—
184D181—81no—
185D181—81no—
186C181#339711yescharacteristic, complemented, Sylow
187#3397—1811nomaximal, Sylow
188#556—1811no—
189#550—1811no—
190#496—1811no—
191#496—1811no—
192#492—1811no—
193#463—1811no—
194#463—1811no—
195#461—1811no—
196#460—1811no—
197#460—1811no—
198#459—1811no—
199#446—1811no—
200#440—1811no—
201#440D18111yescharacteristic, complemented
202C4×D8—1811no—
203C2×#41—3621no—
204C2×SD16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×SD16C2×D18111yescharacteristic
210C2×D8—1811no—
211C2×D8—1811no—
212C2×D8—1811no—
213C4⋊Q8—1811no—
214#127—1811no—
215#127—1811no—
216#127—1811no—
217#126—3621no—
218#126—3621no—
219#124—1811no—
220#124—1811no—
221C22⋊Q8—3621no—
222#121—3621no—
223#121—3621no—
224#121—3621no—
225C4×Q8—1811no—
226C4×Q8—1811no—
227C4×Q8C2×D18111yescharacteristic
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4—1811no—
231C4×D4C2×D18111yescharacteristic
232#117—3621no—
233#107C2×D18111yescharacteristic
234C4⋊C8—1811no—
235C4⋊C8—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103C2×D18111yescharacteristic
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102C2×D18111yescharacteristic
243#97—1811no—
244#97C2×D18111yescharacteristic
245C4×C8—1811no—
246#41—7244no—
247C2×Q8—1811no—
248C2×Q8—1811no—
249C2×Q8C22×D18111yescharacteristic
250C2×D4—3621no—
251C2×D4—3621no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—1811no—
257C2×D4—1811no—
258C2×D4—1811no—
259C2×D4C22×D18111yescharacteristic
260C22×C4—21no—
261C22×C4—3621no—
262C22×C4—3621no—
263C22×C4—3621no—
264SD16—22no—
265SD16—3622no—
266SD16—7241no—
267SD16—7241no—
268SD16—7241no—
269SD16—7241no—
270D8—3622no—
271D8—7241no—
272D8—7241no—
273C2×C8—1811no—
274C2×C8—1811no—
275C2×C8C22×D18111yescharacteristic
276C2×C8C22×D18111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—3621no—
281C4⋊C4—1811no—
282C4⋊C4—1811no—
283C4⋊C4—1811no—
284C4⋊C4C22×D18111yescharacteristic
285C4⋊C4C22×D18111yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C42—21no—
295C42—3621no—
296C42—1811no—
297C42—1811no—
298C42C22×D18111yescharacteristic
299C23—21no—
300C23—3621no—
301C23—3621no—
302C23—3621no—
303Q8—21no—
304Q8—21no—
305Q8—3622no—
306Q8—3621no—
307Q8—3621no—
308D4—21no—
309D4—21no—
310D4—3621no—
311D4—3621no—
312D4—3621no—
313D4—3621no—
314D4—3621no—
315D4—3621no—
316D4—14481no—
317D4—14481no—
318D4—14481no—
319D4—7242no—
320D4—7242no—
321D4—7242no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—3621no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—1811no—
331C2×C4—7242no—
332C2×C4—7242no—
333C2×C4—7242no—
334C2×C4D4×D18111yescharacteristic
335C2×C4D4×D18111yescharacteristic
336C2×C4C23×D18111yescharacteristic
337C8—21no—
338C8—3621no—
339C8—3621no—
340C8#1566844912yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22—7241no—
352C22—7241no—
353C22C2×D4×D18111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—3621no—
360C4—3621no—
361C4—3621no—
362C4—1812no—
363C4—7241no—
364C4C2×#1566844911yescharacteristic
365C4#1915386211yescharacteristic
366C2—81no—
367C2—14481no—
368C2—14481no—
369C2—14481no—
370C2#2604195011yescharacteristic
371C2AGL(1,ℤ/8)×D18111yescharacteristic
372C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#440×C181C2
socleC22×C181C22×D4
hypercenter#440D181
hypocenterC181#3397
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #26042001C2semidirect
2. #26041950C2semidirect
3. #26041668C2semidirect
4. #26041665C2semidirect
5. #26041650C2semidirect
6. #26041497C2semidirect
7. #26041494C2semidirect
8. #26041483C2semidirect
9. #26041479C2semidirect
10. #26041478C2semidirect
11. #26041473C2semidirect
12. #26041407C2semidirect
13. #26041378C2semidirect
14. #26041361C2semidirect
15. #440×C181C2semidirect
153. C8×C181#41semidirect
186. C181#3397semidirect
201. #440D181semidirect
340. C8#15668449semidirect

Maximal subgroups

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

subgroupindex
#260420012
#260419502
#260416682
#260416652
#260416502
#260414972
#260414942
#260414832
#260414792
#260414782
#260414732
#260414072
#260413782
#260413612
#440×C1812
#3397181