Finite Group Databasebeta

← #37544815

Subgroups — #37544815

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#26041900C211yesmaximal, characteristic, complemented
2#26041666C211yesmaximal, characteristic, complemented
3#26041661C211yesmaximal, characteristic, complemented
4#26041638C211yesmaximal, characteristic, complemented
5#26041625C211yesmaximal, characteristic, complemented
6#26041498C211yesmaximal, characteristic, complemented
7#26041491C211yesmaximal, characteristic, complemented
8#26041476C211yesmaximal, characteristic, complemented
9#26041471C211yesmaximal, characteristic, complemented
10#26041441C211yesmaximal, characteristic, complemented
11#26041430C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041413C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#535×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic, complemented
17C2×#15668437C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668437C2211yescharacteristic, complemented
20C2×#15668436C2211yescharacteristic, complemented
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic, complemented
24#19153816C2211yescharacteristic, complemented
25#19153811—21no—
26#19153804C2211yescharacteristic, complemented
27#19153802—21no—
28#19153798—21no—
29#19153795C2211yescharacteristic
30#19153794—21no—
31#19153790C2211yescharacteristic
32C4×Dic362C2211yescharacteristic, complemented
33C4×D724C2211yescharacteristic, complemented
34C4⋊#13089678C2211yescharacteristic, complemented
35C4⋊#13089678C2211yescharacteristic, complemented
36#19153740C2211yescharacteristic, complemented
37#19153740C2211yescharacteristic, complemented
38#19153737C2211yescharacteristic
39#19153737C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153737C2211yescharacteristic, complemented
43#19153737C2211yescharacteristic, complemented
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic, complemented
47C4×#13089678C2211yescharacteristic, complemented
48C2×#41×C181C2211yescharacteristic
49C22×D4×C181C2211yescharacteristic
50#127×C181C2211yescharacteristic
51#127×C181C2211yescharacteristic
52#124×C181C2211yescharacteristic
53#124×C181C2211yescharacteristic
54#121×C181—21no—
55#121×C181—21no—
56#120×C181—21no—
57#120×C181—21no—
58#117×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C4×D181—21no—
64#15668439—41no—
65#15668437—41no—
66#15668437—41no—
67#15668437—41no—
68#15668436—41no—
69#15668434—41no—
70#15668434—41no—
71#15668434—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81C22⋊Dic181—21no—
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86C4×Dic181—21no—
87C24×C181—21no—
88#41×C181—41no—
89#41×C181—41no—
90C2×Q8×C181C2311yescharacteristic
91C2×D4×C181—21no—
92C2×D4×C181—21no—
93C2×D4×C181—21no—
94C2×D4×C181—21no—
95C2×D4×C181—21no—
96C2×D4×C181—21no—
97C2×D4×C181—41no—
98C2×D4×C181—41no—
99C2×D4×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104C4⋊C4×C181D411yescharacteristic
105C4⋊C4×C181D411yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C22⋊C4×C181D411yescharacteristic
111C22⋊C4×C181D411yescharacteristic
112C42×C181C2311yescharacteristic
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—81no—
118D724—21no—
119D724—21no—
120C22⋊D181—81no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C4×D181—81no—
125#13089678—21no—
126#13089678—21no—
127#13089678—21no—
128#13089678—21no—
129C23×C181—21no—
130C23×C181—21no—
131C23×C181—21no—
132C23×C181—42no—
133C23×C181—81no—
134C23×C181—81no—
135C23×C181C2×D411yescharacteristic
136Q8×C181—21no—
137Q8×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—42no—
145D4×C181—42no—
146D4×C181—81no—
147D4×C181—81no—
148D4×C181—81no—
149D4×C181—81no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—42no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2×D411yescharacteristic
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2×D411yescharacteristic
159C2×C4×C181C2411yescharacteristic
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—84no—
173C22×C181C22×D411yescharacteristic
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C4×C181—21no—
178C4×C181—21no—
179C4×C181—21no—
180C4×C181—21no—
181C4×C181—21no—
182C4×C181—41no—
183C4×C181H(5,𝔽2)11yescharacteristic
184C4×C181H(5,𝔽2)11yescharacteristic
185Dic181—41no—
186Dic181—41no—
187Dic181—41no—
188C2×C181—41no—
189C2×C181—81no—
190C2×C181—81no—
191C2×C181—81no—
192C2×C181#53511yescharacteristic
193C2×C181#57611yescharacteristic
194C2×C181#57711yescharacteristic
195D181—81no—
196C181#322411yescharacteristic, complemented, Sylow
197#3224—1811nomaximal, Sylow
198#542—1811no—
199#535D18111yescharacteristic, complemented
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#452—1811no—
209#450—1811no—
210#449—1811no—
211#447—1811no—
212#433—1811no—
213C2×#41C2×D18111yescharacteristic
214C22×D4C2×D18111yescharacteristic
215C2×Q16—1811no—
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×SD16—1811no—
219C2×SD16—1811no—
220C2×D8—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C4⋊Q8—1811no—
224#127C2×D18111yescharacteristic
225#127C2×D18111yescharacteristic
226#126—3621no—
227#124—3621no—
228#124—1811no—
229#124C2×D18111yescharacteristic
230#124C2×D18111yescharacteristic
231#123—3621no—
232C22⋊Q8—3621no—
233C22⋊Q8—1811no—
234#121—21no—
235#121—21no—
236#121—1811no—
237#120—21no—
238#120—21no—
239C4×Q8—1811no—
240C4×D4—1811no—
241#117C2×D18111yescharacteristic
242C4⋊C8—1811no—
243C4⋊C8—1811no—
244#103—1811no—
245#103—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252C22⋊C8—1811no—
253C22⋊C8—1811no—
254#97—1811no—
255C4×C8—1811no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—3621no—
260C2×Q8—1811no—
261C2×Q8C22×D18111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—3621no—
271C2×D4—1811no—
272C2×D4C22×D18111yescharacteristic
273C2×D4C22×D18111yescharacteristic
274C2×D4C22×D18111yescharacteristic
275C22×C4—21no—
276C22×C4—3621no—
277C22×C4C22×D18111yescharacteristic
278Q16—7241no—
279SD16—7241no—
280SD16—7241no—
281SD16—7241no—
282SD16—7241no—
283D8—7241no—
284D8—7241no—
285D8—7241no—
286C2×C8—1811no—
287C2×C8—1811no—
288C2×C8—1811no—
289C2×C8—1811no—
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—3621no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C4⋊C4C22⋊D18111yescharacteristic
296C4⋊C4C22⋊D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4C22⋊D18111yescharacteristic
307C22⋊C4C22⋊D18111yescharacteristic
308C42—3621no—
309C42C22×D18111yescharacteristic
310C42C22×D18111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—3621no—
318C23C2×C22⋊D18111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3621no—
322Q8—3621no—
323Q8—14481no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—3621no—
337D4—3621no—
338D4—14481no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—3621no—
346C2×C4—14481no—
347C2×C4C2×C22⋊D18111yescharacteristic
348C2×C4C2×C22⋊D18111yescharacteristic
349C2×C4C2×C22⋊D18111yescharacteristic
350C2×C4C2×C22⋊D18111yescharacteristic
351C2×C4C2×C22⋊D18111yescharacteristic
352C2×C4C23×D18111yescharacteristic
353C8—3621no—
354C8—3621no—
355C8—3621no—
356C8—3621no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C22×C22⋊D18111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—7241no—
381C4—7241no—
382C4—7241no—
383C4#1915386111yescharacteristic
384C4#1915386111yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—14481no—
390C2#2604184611yescharacteristic
391C2#2604208211yescharacteristic
392C2#2604209011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#535×C181C2
socleC22×C181C22×D4
hypercenter#535D181
hypocenterC181#3224
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #26041900C2semidirect
2. #26041666C2semidirect
3. #26041661C2semidirect
4. #26041638C2semidirect
5. #26041625C2semidirect
6. #26041498C2semidirect
7. #26041491C2semidirect
8. #26041476C2semidirect
9. #26041471C2semidirect
10. #26041441C2semidirect
11. #26041430C2semidirect
12. #26041424C2semidirect
13. #26041413C2semidirect
14. #26041340C2semidirect
15. #535×C181C2semidirect
16. C2×#15668439C22semidirect
19. C2×#15668437C22semidirect
20. C2×#15668436C22semidirect
23. C2×#15668434C22semidirect
24. #19153816C22semidirect
26. #19153804C22semidirect
32. C4×Dic362C22semidirect
33. C4×D724C22semidirect
34. C4⋊#13089678C22semidirect
35. C4⋊#13089678C22semidirect
36. #19153740C22semidirect
37. #19153740C22semidirect
42. #19153737C22semidirect
43. #19153737C22semidirect
46. #19153727C22semidirect
47. C4×#13089678C22semidirect
196. C181#3224semidirect
199. #535D181semidirect

Maximal subgroups

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

subgroupindex
#260419002
#260416662
#260416612
#260416382
#260416252
#260414982
#260414912
#260414762
#260414712
#260414412
#260414302
#260414242
#260414132
#260413402
#535×C1812
#3224181