Finite Group Databasebeta

← #37545874

Subgroups — #37545874

Order 23168.

414 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#26041995C211yesmaximal, characteristic, complemented
2#26041924C211yesmaximal, characteristic, complemented
3#26041641C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041606C211yesmaximal, characteristic, complemented
6#26041526C211yesmaximal, characteristic, complemented
7#26041516C211yesmaximal, characteristic, complemented
8#26041495C211yesmaximal, characteristic, complemented
9#26041425C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#474×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668438C2211yescharacteristic, complemented
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic, complemented
23#19153805—21no—
24#19153805—21no—
25#19153804C2211yescharacteristic
26#19153800—21no—
27#19153796C2211yescharacteristic
28#19153791—21no—
29#19153791C2211yescharacteristic
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic, complemented
32#19153790—21no—
33#19153786—21no—
34C4×D724C2211yescharacteristic
35C4×D724C2211yescharacteristic, complemented
36#19153774—21no—
37#19153774C2211yescharacteristic
38#19153774C2211yescharacteristic, complemented
39C2×#15668426—21no—
40#19153747C2211yescharacteristic, complemented
41#19153741C2211yescharacteristic, complemented
42#19153739C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51#19153727C2211yescharacteristic, complemented
52C4⋊Q8×C181C2211yescharacteristic, complemented
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic, complemented
55#107×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C23×D181—21no—
60#15668448—22no—
61#15668448—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724D411yescharacteristic
67C2×D724C2311yescharacteristic
68C2×D724C2311yescharacteristic
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71D4×D181—22no—
72D4×D181—41no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76C2×C4×D181C2311yescharacteristic
77#15668438—41no—
78D1448—41no—
79#15668434—22no—
80#15668432—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181D411yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×Q8×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117C22×D181C2×D411yescharacteristic
118Dic362—21no—
119Dic362—21no—
120D724—21no—
121D724—21no—
122D724—21no—
123D724—21no—
124D724—41no—
125D724—81no—
126D724—81no—
127D724—81no—
128C22⋊D181—42no—
129C22⋊D181—42no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—42no—
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—21no—
138C4×D181—21no—
139C4×D181—42no—
140#13089678—21no—
141#13089678—21no—
142C23×C181—21no—
143Q8×C181—81no—
144D4×C181—21no—
145D4×C181#4112yes—
146C2×C4×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—22no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—84no—
172C4×C181—21no—
173C4×C181—21no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181C2×#4111yescharacteristic
178C4×C181H(5,𝔽2)11yescharacteristic
179Dic181—21no—
180Dic181—21no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—42no—
184C2×C181#54611yescharacteristic
185C2×C181#57511yescharacteristic
186C2×C181#57611yescharacteristic
187D181—41no—
188D181—41no—
189D181—81no—
190D181—81no—
191C181#331911yescharacteristic, complemented, Sylow
192#3319—1811nomaximal, Sylow
193#555—1811no—
194#546—1811no—
195#489—1811no—
196#485—1811no—
197#482—1811no—
198#474D18111yescharacteristic, complemented
199#468—1811no—
200#466—1811no—
201#463—1811no—
202#449—1811no—
203#447—1811no—
204#442—1811no—
205#435—1811no—
206#418—1811no—
207#416—1811no—
208C2×#41—1811no—
209C22×D4—1811no—
210C2×SD16—1811no—
211C2×D8—1811no—
212C2×D8—1811no—
213C2×M16—1811no—
214C22×C8—1811no—
215C4⋊Q8C2×D18111yescharacteristic, complemented
216#124—3621no—
217#124—3621no—
218#124—1811no—
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—1811no—
228C4×D4—1811no—
229C4×D4C2×D18111yescharacteristic
230#117—3621no—
231#117—1811no—
232#117—1811no—
233C2×C22⋊C4—3621no—
234#107C2×D18111yescharacteristic, complemented
235#107C2×D18111yescharacteristic, complemented
236#106—1811no—
237C4⋊C8C2×D18111yescharacteristic, complemented
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102C2×D18111yescharacteristic
247#102C2×D18111yescharacteristic
248C22⋊C8—1811no—
249C22⋊C8—1811no—
250#97—1811no—
251C24—3621no—
252#41—3622no—
253#41—7241no—
254C2×Q8—21no—
255C2×Q8—1811no—
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3622no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—1811no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4—7241no—
266C2×D4C22×D18111yescharacteristic
267C22×C4—21no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4—1811no—
272SD16—7241no—
273D8—3622no—
274D8—7241no—
275M16—7241no—
276C2×C8—1811no—
277C2×C8—1811no—
278C2×C8—7241no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3621no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4C22×D18111yescharacteristic
286C4⋊C4C22×D18111yescharacteristic
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—1811no—
299C22⋊C4—1811no—
300C42—3621no—
301C42—3621no—
302C42C22×D18111yescharacteristic
303C23—21no—
304C23—3621no—
305C23—3621no—
306C23—14481no—
307C23—1811no—
308C23—1811no—
309C23—7242no—
310C23—7242no—
311Q8—81no—
312Q8—3621no—
313Q8—3621no—
314D4—21no—
315D4—3621no—
316D4—3621no—
317D4—3621no—
318D4—3621no—
319D4—14481no—
320D4—14481no—
321D4—14481no—
322D4—7241no—
323D4—7242no—
324D4—7242no—
325D4#1566845012yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—1811no—
337C2×C4—1811no—
338C2×C4—7242no—
339C2×C4—7242no—
340C2×C4D4×D18111yescharacteristic
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—3621no—
351C22—3621no—
352C22—3621no—
353C22—3621no—
354C22—3621no—
355C22—3621no—
356C22—14484no—
357C22—7241no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22—7241no—
362C22—7241no—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3621no—
370C4—3621no—
371C4—7241no—
372C4—7241no—
373C4C2×#1566845011yescharacteristic
374C4#1915386211yescharacteristic
375C2—42no—
376C2—14481no—
377C2—14481no—
378C2—7241no—
379C2—7241no—
380C2#2604192011yescharacteristic
381C2#2604207811yescharacteristic
382C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#474×C181C2
socleC22×C181C22×D4
hypercenter#474D181
hypocenterC181#3319
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #26041995C2semidirect
2. #26041924C2semidirect
3. #26041641C2semidirect
4. #26041622C2semidirect
5. #26041606C2semidirect
6. #26041526C2semidirect
7. #26041516C2semidirect
8. #26041495C2semidirect
9. #26041425C2semidirect
10. #26041414C2semidirect
11. #26041389C2semidirect
12. #26041349C2semidirect
13. #26041282C2semidirect
14. #26041272C2semidirect
15. #474×C181C2semidirect
18. C2×#15668438C22semidirect
22. C2×C8×D181C22semidirect
31. #19153791C22semidirect
35. C4×D724C22semidirect
38. #19153774C22semidirect
40. #19153747C22semidirect
41. #19153741C22semidirect
42. #19153739C22semidirect
43. #19153739C22semidirect
48. #19153736C22semidirect
50. #19153728C22semidirect
51. #19153727C22semidirect
52. C4⋊Q8×C181C22semidirect
54. #107×C181C22semidirect
55. #107×C181C22semidirect
56. C4⋊C8×C181C22semidirect
191. C181#3319semidirect
198. #474D181semidirect
215. C4⋊Q8C2×D181semidirect
234. #107C2×D181semidirect
235. #107C2×D181semidirect
237. C4⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419952
#260419242
#260416412
#260416222
#260416062
#260415262
#260415162
#260414952
#260414252
#260414142
#260413892
#260413492
#260412822
#260412722
#474×C1812
#3319181