Finite Group Databasebeta

← #37545872

Subgroups — #37545872

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#26041993C211yesmaximal, characteristic, complemented
2#26041920C211yesmaximal, characteristic, complemented
3#26041640C211yesmaximal, characteristic, complemented
4#26041617C211yesmaximal, characteristic, complemented
5#26041606C211yesmaximal, characteristic, complemented
6#26041558C211yesmaximal, characteristic, complemented
7#26041514C211yesmaximal, characteristic, complemented
8#26041496C211yesmaximal, characteristic, complemented
9#26041423C211yesmaximal, characteristic, complemented
10#26041412C211yesmaximal, characteristic, complemented
11#26041388C211yesmaximal, characteristic, complemented
12#26041348C211yesmaximal, characteristic, complemented
13#26041285C211yesmaximal, characteristic, complemented
14#26041274C211yesmaximal, characteristic, complemented
15#468×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic, complemented
21#19153815C2211yescharacteristic, complemented
22#19153805C2211yescharacteristic
23#19153803—21no—
24#19153802—21no—
25#19153801—21no—
26#19153791—21no—
27#19153791C2211yescharacteristic
28#19153788—21no—
29#19153787C2211yescharacteristic, complemented
30#19153786—21no—
31D4×Dic181C2211yescharacteristic, complemented
32#19153778C2211yescharacteristic
33C4×C22⋊D181C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153774C2211yescharacteristic, complemented
36#19153772—21no—
37C22⋊C4×D181—21no—
38#19153749C2211yescharacteristic, complemented
39#19153747C2211yescharacteristic, complemented
40#19153745C2211yescharacteristic, complemented
41#19153740C2211yescharacteristic, complemented
42#19153740C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51#19153726C2211yescharacteristic, complemented
52C2×SD16×C181C2211yescharacteristic, complemented
53C2×M16×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668450—22no—
61#15668450—41no—
62C2×Dic362—21no—
63C2×D724—22no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—41no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668434—22no—
77#15668434—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—41no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181D411yescharacteristic
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181C2311yescharacteristic
101C22×C4×C181C2311yescharacteristic
102SD16×C181—41no—
103M16×C181—41no—
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C22⋊C4×C181—21no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117Dic362—81no—
118D724—21no—
119D724—21no—
120D724—21no—
121D724—42no—
122D724—42no—
123D724—81no—
124D724#4112yes—
125C22⋊D181—41no—
126C22⋊D181—81no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—42no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—42no—
136C4×D181—81no—
137#13089678—21no—
138#13089678—21no—
139C23×C181—21no—
140C23×C181C2×D411yescharacteristic
141Q8×C181—21no—
142Q8×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—81no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—22no—
164C2×D181—21no—
165C2×D181—21no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—84no—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181C2×#4111yescharacteristic
177C4×C181H(5,𝔽2)11yescharacteristic
178Dic181—21no—
179Dic181—21no—
180Dic181—21no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—41no—
184C2×C181—81no—
185C2×C181#54611yescharacteristic
186C2×C181#57511yescharacteristic
187C2×C181#57611yescharacteristic
188D181—41no—
189D181—42no—
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#474—1811no—
199#468D18111yescharacteristic, complemented
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×SD16C2×D18111yescharacteristic, complemented
211C2×D8—1811no—
212C2×D8—1811no—
213C2×M16C2×D18111yescharacteristic
214C22×C8—1811no—
215C4⋊Q8—1811no—
216#124—3621no—
217#124—3621no—
218#124—1811no—
219#123—3621no—
220C22⋊Q8C2×D18111yescharacteristic
221#121—3621no—
222#121—3621no—
223#121—1811no—
224#121—1811no—
225#121C2×D18111yescharacteristic
226#120—3621no—
227C4×D4—1811no—
228C4×D4—1811no—
229C4×D4—1811no—
230#117—3621no—
231#117—1811no—
232#117—1811no—
233C2×C22⋊C4—3621no—
234#107—1811no—
235#107C2×D18111yescharacteristic, complemented
236#106—1811no—
237C4⋊C8—1811no—
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, complemented
248C22⋊C8—1811no—
249C22⋊C8—1811no—
250#97—1811no—
251C24—3621no—
252#41—3622no—
253#41—7241no—
254C2×Q8—3621no—
255C2×Q8C22×D18111yescharacteristic
256C2×D4—21no—
257C2×D4—3622no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—1811no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4—7241no—
266C2×D4C22×D18111yescharacteristic
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4C22×D18111yescharacteristic
272SD16—41no—
273D8—3622no—
274D8—7241no—
275M16—41no—
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⋊C4—1811no—
286C4⋊C4C22×D18111yescharacteristic
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
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—
302C42—1811no—
303C23—21no—
304C23—3621no—
305C23—3621no—
306C23—14481no—
307C23—1811no—
308C23—7242no—
309C23—7242no—
310C23D4×D18111yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—14481no—
314D4—21no—
315D4—21no—
316D4—81no—
317D4—3621no—
318D4—3621no—
319D4—3621no—
320D4—14481no—
321D4—14481no—
322D4—1812no—
323D4—7242no—
324D4—7242no—
325D4—7241no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—14481no—
336C2×C4—1811no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—7242no—
340C2×C4—7242no—
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3621no—
354C22—3622no—
355C22—3621no—
356C22—3621no—
357C22—14484no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22—7241no—
362C22—7241no—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3621no—
369C4—3621no—
370C4—3621no—
371C4—7241no—
372C4—7241no—
373C4#41×D18111yescharacteristic
374C4#1915386111yescharacteristic
375C2—41no—
376C2—81no—
377C2—14481no—
378C2—7241no—
379C2—7242no—
380C2#2604191811yescharacteristic
381C2#2604207811yescharacteristic
382C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#468×C181C2
socleC22×C181C22×D4
hypercenter#468D181
hypocenterC181#3319
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #26041993C2semidirect
2. #26041920C2semidirect
3. #26041640C2semidirect
4. #26041617C2semidirect
5. #26041606C2semidirect
6. #26041558C2semidirect
7. #26041514C2semidirect
8. #26041496C2semidirect
9. #26041423C2semidirect
10. #26041412C2semidirect
11. #26041388C2semidirect
12. #26041348C2semidirect
13. #26041285C2semidirect
14. #26041274C2semidirect
15. #468×C181C2semidirect
20. C2×C8×D181C22semidirect
21. #19153815C22semidirect
29. #19153787C22semidirect
31. D4×Dic181C22semidirect
35. #19153774C22semidirect
38. #19153749C22semidirect
39. #19153747C22semidirect
40. #19153745C22semidirect
41. #19153740C22semidirect
42. #19153740C22semidirect
50. #19153728C22semidirect
51. #19153726C22semidirect
52. C2×SD16×C181C22semidirect
56. #107×C181C22semidirect
57. #103×C181C22semidirect
58. #102×C181C22semidirect
191. C181#3319semidirect
199. #468D181semidirect
210. C2×SD16C2×D181semidirect
235. #107C2×D181semidirect
240. #103C2×D181semidirect
247. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419932
#260419202
#260416402
#260416172
#260416062
#260415582
#260415142
#260414962
#260414232
#260414122
#260413882
#260413482
#260412852
#260412742
#468×C1812
#3319181