Finite Group Databasebeta

← #37544821

Subgroups — #37544821

Order 23168.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041902C211yesmaximal, characteristic, complemented
2#26041843C211yesmaximal, characteristic, complemented
3#26041665C211yesmaximal, characteristic, complemented
4#26041664C211yesmaximal, characteristic, complemented
5#26041640C211yesmaximal, characteristic, complemented
6#26041624C211yesmaximal, characteristic, complemented
7#26041503C211yesmaximal, characteristic, complemented
8#26041497C211yesmaximal, characteristic, complemented
9#26041477C211yesmaximal, characteristic, complemented
10#26041473C211yesmaximal, characteristic, complemented
11#26041429C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041415C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668436C2211yescharacteristic, complemented
20C2×D1448C2211yescharacteristic
21C2×D1448C2211yescharacteristic
22C2×#15668434C2211yescharacteristic, complemented
23#19153815C2211yescharacteristic, complemented
24#19153812C2211yescharacteristic
25#19153812C2211yescharacteristic
26#19153811—21no—
27#19153805C2211yescharacteristic
28#19153805C2211yescharacteristic
29#19153805C2211yescharacteristic, complemented
30#19153802—21no—
31#19153798—21no—
32#19153796—21no—
33#19153790—21no—
34#19153790—21no—
35#19153790C2211yescharacteristic
36#19153784—21no—
37#19153784—21no—
38Q8×Dic181C2211yescharacteristic, complemented
39#19153778C2211yescharacteristic, complemented
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153740C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic, complemented
54C2×SD16×C181C2211yescharacteristic, complemented
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181—21no—
60C2×Dic362—21no—
61C2×D724—21no—
62C2×D724—41no—
63C2×D724—41no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C4×D181—21no—
73#15668436—41no—
74#15668436—41no—
75#15668436—41no—
76D1448—41no—
77D1448—41no—
78#15668434—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181D411yescharacteristic
83C4⋊Dic181D411yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86C22⋊Dic181D411yescharacteristic
87C22⋊Dic181D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108SD16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—21no—
117C22×D181—42no—
118C22×D181—81no—
119C22×D181—81no—
120Dic362—81no—
121D724—21no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—42no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C22⋊D181—81no—
133C2×Dic181—21no—
134C2×Dic181C2×D411yescharacteristic
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C4×D181—81no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181C2×D411yescharacteristic
143Q8×C181—21no—
144Q8×C181—21no—
145Q8×C181—21no—
146Q8×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—42no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—42no—
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2411yescharacteristic
158C8×C181—21no—
159C8×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181C22×D411yescharacteristic
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—84no—
177C4×C181—21no—
178C4×C181—41no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181H(5,𝔽2)11yescharacteristic
182C4×C181H(5,𝔽2)11yescharacteristic
183Dic181—21no—
184Dic181—21no—
185Dic181—21no—
186Dic181—21no—
187Dic181—41no—
188C2×C181—41no—
189C2×C181—81no—
190C2×C181#53511yescharacteristic
191C2×C181#57611yescharacteristic
192C2×C181#57711yescharacteristic
193D181—81no—
194D181—81no—
195D181—81no—
196C181#322411yescharacteristic, complemented, Sylow
197#3224—1811nomaximal, Sylow
198#542—1811no—
199#535—1811no—
200#496—1811no—
201#495—1811no—
202#489—1811no—
203#486—1811no—
204#464—1811no—
205#463—1811no—
206#460—1811no—
207#459—1811no—
208#452D18111yescharacteristic, complemented
209#450—1811no—
210#449—1811no—
211#447—1811no—
212#433—1811no—
213C2×#41C2×D18111yescharacteristic
214C22×D4—1811no—
215C2×Q16C2×D18111yescharacteristic, complemented
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×SD16—1811no—
219C2×SD16C2×D18111yescharacteristic, complemented
220C2×D8—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C4⋊Q8—1811no—
224#127—1811no—
225#127—1811no—
226#126—3621no—
227#124—3621no—
228#124—1811no—
229#124—1811no—
230#124—1811no—
231#123—3621no—
232C22⋊Q8—3621no—
233C22⋊Q8C2×D18111yescharacteristic
234#121—3621no—
235#121—3621no—
236#121—1811no—
237#120—3621no—
238#120—3621no—
239C4×Q8—1811no—
240C4×D4—1811no—
241#117—1811no—
242C4⋊C8—1811no—
243C4⋊C8—1811no—
244#103—1811no—
245#103C2×D18111yescharacteristic, complemented
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102C2×D18111yescharacteristic, complemented
252C22⋊C8—1811no—
253C22⋊C8C2×D18111yescharacteristic
254#97—1811no—
255C4×C8—1811no—
256C24—3621no—
257#41—41no—
258#41—41no—
259C2×Q8—3621no—
260C2×Q8C22×D18111yescharacteristic
261C2×Q8C22×D18111yescharacteristic
262C2×D4—21no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—1811no—
270C2×D4—1811no—
271C2×D4—1811no—
272C2×D4—7241no—
273C2×D4—7241no—
274C2×D4C22×D18111yescharacteristic
275C22×C4—21no—
276C22×C4—3621no—
277C22×C4C22×D18111yescharacteristic
278Q16—41no—
279SD16—41no—
280SD16—7241no—
281SD16—7241no—
282SD16—7241no—
283D8—7241no—
284D8—7241no—
285D8—7241no—
286C2×C8—1811no—
287C2×C8—1811no—
288C2×C8C22×D18111yescharacteristic
289C2×C8C22×D18111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3621no—
292C4⋊C4—3621no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C4⋊C4—1811no—
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—1811no—
307C22⋊C4—1811no—
308C42—3621no—
309C42—1811no—
310C42—1811no—
311C23—21no—
312C23—3621no—
313C23—3621no—
314C23—3621no—
315C23—14481no—
316C23—14481no—
317C23—7242no—
318C23D4×D18111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—14481no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3621no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—14481no—
334D4—14481no—
335D4—14481no—
336D4—14481no—
337D4—14481no—
338D4—7242no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3621no—
346C2×C4—14481no—
347C2×C4—1811no—
348C2×C4—1811no—
349C2×C4—1811no—
350C2×C4—1811no—
351C2×C4D4×D18111yescharacteristic
352C2×C4C23×D18111yescharacteristic
353C8—21no—
354C8—21no—
355C8—3621no—
356C8—3621no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—14484no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C2×D4×D18111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3621no—
379C4—3621no—
380C4—3621no—
381C4—3621no—
382C4—7241no—
383C4#1915386111yescharacteristic
384C4#1915386111yescharacteristic
385C2—41no—
386C2—81no—
387C2—14481no—
388C2—14481no—
389C2—14481no—
390C2#2604184411yescharacteristic
391C2#2604208111yescharacteristic
392C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
hypercenter#452D181
hypocenterC181#3224
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26041902C2semidirect
2. #26041843C2semidirect
3. #26041665C2semidirect
4. #26041664C2semidirect
5. #26041640C2semidirect
6. #26041624C2semidirect
7. #26041503C2semidirect
8. #26041497C2semidirect
9. #26041477C2semidirect
10. #26041473C2semidirect
11. #26041429C2semidirect
12. #26041424C2semidirect
13. #26041415C2semidirect
14. #26041337C2semidirect
15. #452×C181C2semidirect
19. C2×#15668436C22semidirect
22. C2×#15668434C22semidirect
23. #19153815C22semidirect
29. #19153805C22semidirect
38. Q8×Dic181C22semidirect
39. #19153778C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
43. #19153740C22semidirect
46. #19153737C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
53. C2×Q16×C181C22semidirect
54. C2×SD16×C181C22semidirect
56. #103×C181C22semidirect
57. #102×C181C22semidirect
196. C181#3224semidirect
208. #452D181semidirect
215. C2×Q16C2×D181semidirect
219. C2×SD16C2×D181semidirect
245. #103C2×D181semidirect
251. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419022
#260418432
#260416652
#260416642
#260416402
#260416242
#260415032
#260414972
#260414772
#260414732
#260414292
#260414242
#260414152
#260413372
#452×C1812
#3224181