Finite Group Databasebeta

← #37544809

Subgroups — #37544809

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#26041848C211yesmaximal, characteristic, complemented
2#26041669C211yesmaximal, characteristic, complemented
3#26041661C211yesmaximal, characteristic, complemented
4#26041641C211yesmaximal, characteristic, complemented
5#26041627C211yesmaximal, characteristic, complemented
6#26041501C211yesmaximal, characteristic, complemented
7#26041494C211yesmaximal, characteristic, complemented
8#26041479C211yesmaximal, characteristic, complemented
9#26041474C211yesmaximal, characteristic, complemented
10#26041439C211yesmaximal, characteristic, complemented
11#26041429C211yesmaximal, characteristic, complemented
12#26041422C211yesmaximal, characteristic, complemented
13#26041412C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#542×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic, complemented
19C2×#15668437C2211yescharacteristic, complemented
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×#15668436C2211yescharacteristic, complemented
23C2×#15668434C2211yescharacteristic
24C2×#15668434C2211yescharacteristic
25C2×#15668434C2211yescharacteristic, complemented
26#19153813C2211yescharacteristic
27#19153813C2211yescharacteristic
28#19153804C2211yescharacteristic
29#19153804C2211yescharacteristic
30#19153791—21no—
31#19153791—21no—
32#19153786—21no—
33#19153786—21no—
34C4⋊#13089678C2211yescharacteristic, complemented
35C4⋊#13089678C2211yescharacteristic, complemented
36#19153739C2211yescharacteristic, complemented
37#19153739C2211yescharacteristic, complemented
38#19153736C2211yescharacteristic
39#19153736C2211yescharacteristic
40#19153736C2211yescharacteristic
41#19153736C2211yescharacteristic
42#19153736C2211yescharacteristic, complemented
43#19153736C2211yescharacteristic, complemented
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic, complemented
47C4×#13089678C2211yescharacteristic, complemented
48C4⋊Q8×C181C2211yescharacteristic, complemented
49#126×C181—21no—
50#124×C181—21no—
51#124×C181C2211yescharacteristic, complemented
52#123×C181—21no—
53C22⋊Q8×C181—21no—
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56C4×Q8×C181C2211yescharacteristic, complemented
57C4×D4×C181C2211yescharacteristic, complemented
58#117×C181C2211yescharacteristic
59C23×D181—21no—
60#15668449—41no—
61#15668449—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—41no—
69C2×D724—41no—
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C4×D181—21no—
75#15668439—41no—
76#15668437—41no—
77#15668436—41no—
78#15668436—41no—
79#15668436—41no—
80#15668434—41no—
81#15668434—41no—
82#15668434—41no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C2×#13089678C2311yescharacteristic
86C2×#13089678C2311yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91C2×Q8×C181—21no—
92C2×Q8×C181C2311yescharacteristic
93C2×D4×C181—21no—
94C2×D4×C181C2311yescharacteristic
95C22×C4×C181—21no—
96C22×C4×C181C2311yescharacteristic
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181D411yescharacteristic
101C4⋊C4×C181D411yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181D411yescharacteristic
110C22⋊C4×C181D411yescharacteristic
111C42×C181—21no—
112C42×C181C2311yescharacteristic
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—21no—
117C22×D181—42no—
118C22×D181—81no—
119C22×D181—81no—
120Dic362—21no—
121Dic362—21no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—42no—
129D724—81no—
130D724—81no—
131D724—81no—
132D724—81no—
133C22⋊D181—42no—
134C2×Dic181—21no—
135C4×D181—42no—
136#13089678—21no—
137#13089678—21no—
138#13089678—21no—
139#13089678—21no—
140C23×C181—21no—
141C23×C181C2×D411yescharacteristic
142Q8×C181—21no—
143Q8×C181—21no—
144Q8×C181—81no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—81no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—81no—
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×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—21no—
179C4×C181—21no—
180C4×C181—21no—
181C4×C181—21no—
182C4×C181—41no—
183C4×C181—41no—
184C4×C181—41no—
185C4×C181H(5,𝔽2)11yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
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#542D18111yescharacteristic, complemented
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#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×SD16—1811no—
219C2×SD16—1811no—
220C2×D8—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C4⋊Q8C2×D18111yescharacteristic, complemented
224#127—1811no—
225#127—1811no—
226#126—21no—
227#124—21no—
228#124—1811no—
229#124—1811no—
230#124C2×D18111yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D18111yescharacteristic
234#121—3621no—
235#121—3621no—
236#121C2×D18111yescharacteristic
237#120—3621no—
238#120—3621no—
239C4×Q8C2×D18111yescharacteristic, complemented
240C4×D4C2×D18111yescharacteristic, complemented
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—3621no—
257#41—7241no—
258#41—7241no—
259C2×Q8—21no—
260C2×Q8—1811no—
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—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—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D18111yescharacteristic
294C4⋊C4C22⋊D18111yescharacteristic
295C4⋊C4C22×D18111yescharacteristic
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4C22⋊D18111yescharacteristic
307C22⋊C4C22⋊D18111yescharacteristic
308C42—21no—
309C42C22×D18111yescharacteristic
310C42C22×D18111yescharacteristic
311C23—21no—
312C23—3621no—
313C23—3621no—
314C23—3621no—
315C23—14481no—
316C23—14481no—
317C23—7242no—
318C23C2×C22⋊D18111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—3621no—
323Q8—3621no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—3621no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—14481no—
334D4—14481no—
335D4—14481no—
336D4—14481no—
337D4—7242no—
338D4—7242no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—3621no—
346C2×C4—7242no—
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—14484no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C22×C22⋊D18111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—7241no—
383C4#1915386211yescharacteristic
384C4#1915386211yescharacteristic
385C2—41no—
386C2—81no—
387C2—14481no—
388C2—14481no—
389C2—14481no—
390C2#2604184311yescharacteristic
391C2#2604208211yescharacteristic
392C2#2604208711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#542×C181C2
socleC22×C181C22×D4
hypercenter#542D181
hypocenterC181#3224
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #26041848C2semidirect
2. #26041669C2semidirect
3. #26041661C2semidirect
4. #26041641C2semidirect
5. #26041627C2semidirect
6. #26041501C2semidirect
7. #26041494C2semidirect
8. #26041479C2semidirect
9. #26041474C2semidirect
10. #26041439C2semidirect
11. #26041429C2semidirect
12. #26041422C2semidirect
13. #26041412C2semidirect
14. #26041340C2semidirect
15. #542×C181C2semidirect
18. C2×#15668439C22semidirect
19. C2×#15668437C22semidirect
22. C2×#15668436C22semidirect
25. C2×#15668434C22semidirect
34. C4⋊#13089678C22semidirect
35. C4⋊#13089678C22semidirect
36. #19153739C22semidirect
37. #19153739C22semidirect
42. #19153736C22semidirect
43. #19153736C22semidirect
46. #19153727C22semidirect
47. C4×#13089678C22semidirect
48. C4⋊Q8×C181C22semidirect
51. #124×C181C22semidirect
56. C4×Q8×C181C22semidirect
57. C4×D4×C181C22semidirect
196. C181#3224semidirect
198. #542D181semidirect
223. C4⋊Q8C2×D181semidirect
230. #124C2×D181semidirect
239. C4×Q8C2×D181semidirect
240. C4×D4C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418482
#260416692
#260416612
#260416412
#260416272
#260415012
#260414942
#260414792
#260414742
#260414392
#260414292
#260414222
#260414122
#260413402
#542×C1812
#3224181