Finite Group Databasebeta

← #37544820

Subgroups — #37544820

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#26041901C211yesmaximal, characteristic, complemented
2#26041842C211yesmaximal, characteristic, complemented
3#26041665C211yesmaximal, characteristic, complemented
4#26041660C211yesmaximal, characteristic, complemented
5#26041637C211yesmaximal, characteristic, complemented
6#26041624C211yesmaximal, characteristic, complemented
7#26041501C211yesmaximal, characteristic, complemented
8#26041495C211yesmaximal, characteristic, complemented
9#26041471C211yesmaximal, characteristic, complemented
10#26041438C211yesmaximal, characteristic, complemented
11#26041428C211yesmaximal, characteristic, complemented
12#26041425C211yesmaximal, characteristic, complemented
13#26041414C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#460×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668439C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic, complemented
20C2×#15668436C2211yescharacteristic
21C2×D1448C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic, complemented
24#19153815C2211yescharacteristic, complemented
25#19153812C2211yescharacteristic
26#19153810—21no—
27#19153805C2211yescharacteristic, complemented
28#19153804—21no—
29#19153804C2211yescharacteristic
30#19153803C2211yescharacteristic
31#19153801—21no—
32#19153794—21no—
33#19153792C2211yescharacteristic
34#19153791C2211yescharacteristic
35#19153788—21no—
36#19153788—21no—
37#19153784—21no—
38#19153784—21no—
39C4×D724C2211yescharacteristic, complemented
40#19153773C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×SD16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic, complemented
54#127×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668448—41no—
61#15668448—41no—
62C2×Dic362—21no—
63C2×Dic362C2311yescharacteristic
64C2×D724—21no—
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71D4×D181—41no—
72D4×D181—41no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668439—41no—
77#15668438—41no—
78#15668436—41no—
79D1448—41no—
80#15668434—41no—
81#15668434—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428D411yescharacteristic
88#15668428D411yescharacteristic
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426D411yescharacteristic
99#15668426D411yescharacteristic
100C4×Dic181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106SD16×C181—41no—
107SD16×C181—41no—
108C2×C8×C181C2311yescharacteristic
109C2×C8×C181C2311yescharacteristic
110C4⋊C4×C181—21no—
111C4⋊C4×C181C2311yescharacteristic
112C42×C181—21no—
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—42no—
117C22×D181—81no—
118C22×D181—81no—
119C22×D181C2×D411yescharacteristic
120Dic362—21no—
121Dic362—21no—
122Dic362—81no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—81no—
128C22⋊D181—42no—
129C22⋊D181—42no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—42no—
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C4×D181—21no—
139C4×D181—21no—
140C4×D181—81no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181—21no—
145Q8×C181—21no—
146Q8×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—81no—
152D4×C181—81no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181C2×D411yescharacteristic
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2411yescharacteristic
158C8×C181—21no—
159C8×C181—21no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181C22×D411yescharacteristic
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—21no—
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—21no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181H(5,𝔽2)11yescharacteristic
182C4×C181H(5,𝔽2)11yescharacteristic
183Dic181—21no—
184Dic181—21no—
185Dic181—21no—
186Dic181—41no—
187Dic181—41no—
188C2×C181—81no—
189C2×C181—81no—
190C2×C181#53511yescharacteristic
191C2×C181#57611yescharacteristic
192C2×C181#57711yescharacteristic
193D181—41no—
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#460D18111yescharacteristic, complemented
207#459—1811no—
208#452—1811no—
209#450—1811no—
210#449—1811no—
211#447—1811no—
212#433—1811no—
213C2×#41—1811no—
214C22×D4—1811no—
215C2×Q16—1811no—
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×SD16C2×D18111yescharacteristic
219C2×SD16C2×D18111yescharacteristic, complemented
220C2×D8—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C4⋊Q8—1811no—
224#127—1811no—
225#127C2×D18111yescharacteristic
226#126—3621no—
227#124—3621no—
228#124—1811no—
229#124—1811no—
230#124—1811no—
231#123—3621no—
232C22⋊Q8—3621no—
233C22⋊Q8—1811no—
234#121—3621no—
235#121—3621no—
236#121—1811no—
237#120—3621no—
238#120—3621no—
239C4×Q8C2×D18111yescharacteristic, complemented
240C4×D4—1811no—
241#117—1811no—
242C4⋊C8—1811no—
243C4⋊C8C2×D18111yescharacteristic, complemented
244#103—1811no—
245#103—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102C2×D18111yescharacteristic
251#102C2×D18111yescharacteristic, complemented
252C22⋊C8—1811no—
253C22⋊C8—1811no—
254#97—1811no—
255C4×C8—1811no—
256C24—3621no—
257#41—7241no—
258#41—7241no—
259C2×Q8—3621no—
260C2×Q8—1811no—
261C2×Q8C22×D18111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—1811no—
270C2×D4—1811no—
271C2×D4—7241no—
272C2×D4—7241no—
273C2×D4C22×D18111yescharacteristic
274C2×D4C22×D18111yescharacteristic
275C22×C4—3621no—
276C22×C4—3621no—
277C22×C4—1811no—
278Q16—7241no—
279SD16—41no—
280SD16—41no—
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—3621no—
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—21no—
309C42—1811no—
310C42C22×D18111yescharacteristic
311C23—21no—
312C23—21no—
313C23—3621no—
314C23—3621no—
315C23—14481no—
316C23—14481no—
317C23—1811no—
318C23—7242no—
319Q8—21no—
320Q8—21no—
321Q8—3621no—
322Q8—3621no—
323Q8—14481no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—3621no—
334D4—14481no—
335D4—14481no—
336D4—14481no—
337D4—7242no—
338D4—7242no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—14481no—
346C2×C4—1811no—
347C2×C4—1811no—
348C2×C4—1811no—
349C2×C4—7242no—
350C2×C4D4×D18111yescharacteristic
351C2×C4D4×D18111yescharacteristic
352C2×C4C23×D18111yescharacteristic
353C8—21no—
354C8—21no—
355C8—3621no—
356C8—3621no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3621no—
364C22—3621no—
365C22—3621no—
366C22—14484no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C2×D4×D18111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—3621no—
379C4—3621no—
380C4—3621no—
381C4—7241no—
382C4—7241no—
383C4#1915386111yescharacteristic
384C4#1915386211yescharacteristic
385C2—81no—
386C2—81no—
387C2—14481no—
388C2—14481no—
389C2—7241no—
390C2#2604184511yescharacteristic
391C2#2604208311yescharacteristic
392C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#460×C181C2
socleC22×C181C22×D4
hypercenter#460D181
hypocenterC181#3224
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #26041901C2semidirect
2. #26041842C2semidirect
3. #26041665C2semidirect
4. #26041660C2semidirect
5. #26041637C2semidirect
6. #26041624C2semidirect
7. #26041501C2semidirect
8. #26041495C2semidirect
9. #26041471C2semidirect
10. #26041438C2semidirect
11. #26041428C2semidirect
12. #26041425C2semidirect
13. #26041414C2semidirect
14. #26041339C2semidirect
15. #460×C181C2semidirect
18. C2×#15668439C22semidirect
19. C2×#15668438C22semidirect
23. C2×#15668434C22semidirect
24. #19153815C22semidirect
27. #19153805C22semidirect
39. C4×D724C22semidirect
41. C4⋊#13089678C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
46. #19153737C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
53. C2×SD16×C181C22semidirect
55. C4×Q8×C181C22semidirect
56. C4⋊C8×C181C22semidirect
58. #102×C181C22semidirect
196. C181#3224semidirect
206. #460D181semidirect
219. C2×SD16C2×D181semidirect
239. C4×Q8C2×D181semidirect
243. C4⋊C8C2×D181semidirect
251. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419012
#260418422
#260416652
#260416602
#260416372
#260416242
#260415012
#260414952
#260414712
#260414382
#260414282
#260414252
#260414142
#260413392
#460×C1812
#3224181