Finite Group Databasebeta

← #37545540

Subgroups — #37545540

Order 23168.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041987C211yesmaximal, characteristic, complemented
2#26041913C211yesmaximal, characteristic
3#26041624C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041595C211yesmaximal, characteristic, complemented
6#26041568C211yesmaximal, characteristic, complemented
7#26041511C211yesmaximal, characteristic, complemented
8#26041477C211yesmaximal, characteristic, complemented
9#26041429C211yesmaximal, characteristic, complemented
10#26041428C211yesmaximal, characteristic, complemented
11#26041364C211yesmaximal, characteristic, complemented
12C8×C22⋊D181C211yesmaximal, characteristic, complemented
13C2×#19153738C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#465×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×D4×D181—21no—
18C2×D4×D181C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668436C2211yescharacteristic, complemented
21C2×C8×D181C2211yescharacteristic, complemented
22#19153815C2211yescharacteristic, complemented
23#19153812C2211yescharacteristic
24#19153806—21no—
25#19153796—21no—
26#19153793—21no—
27#19153792C2211yescharacteristic, complemented
28#19153791C2211yescharacteristic
29#19153789—21no—
30#19153786—21no—
31#19153784—21no—
32Q8×Dic181C2211yescharacteristic, complemented
33#19153778C2211yescharacteristic
34C4×C22⋊D181C2211yescharacteristic
35#19153776—21no—
36C2×C4⋊Dic181C2211yescharacteristic, complemented
37C4⋊C4×D181C2211yescharacteristic, complemented
38#19153747C2211yescharacteristic, complemented
39#19153747C2211yescharacteristic, complemented
40#19153745C2211yescharacteristic, complemented
41#19153738C2211yescharacteristic
42#19153738C2211yescharacteristic
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×SD16×C181C2211yescharacteristic, complemented
53C22×C8×C181C2211yescharacteristic, complemented
54C22⋊Q8×C181C2211yescharacteristic, complemented
55#121×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×Dic362—21no—
62C2×D724—22no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—41no—
66C2×D724C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72D4×D181—22no—
73D4×D181—41no—
74D4×D181—44no—
75C22×Dic181—21no—
76C2×C4×D181—21no—
77C2×C4×D181—21no—
78C2×C4×D181C2311yescharacteristic
79#15668436—22no—
80#15668436—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181—21no—
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668428D411yescharacteristic
92C22⋊Dic181D411yescharacteristic
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181C2311yescharacteristic
103SD16×C181—41no—
104C2×C8×C181—41no—
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—42no—
115C22×D181—42no—
116C22×D181—42no—
117C22×D181—42no—
118C22×D181—81no—
119C22×D181—81no—
120C22×D181C2×D411yescharacteristic
121Dic362—81no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—42no—
126D724—42no—
127D724#4112yes—
128C22⋊D181—42no—
129C22⋊D181—42no—
130C22⋊D181—81no—
131C22⋊D181SD1614yescomplemented
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—81no—
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C4×D181—21no—
139C4×D181—21no—
140C4×D181—42no—
141C4×D181—81no—
142#13089678—21no—
143#13089678—21no—
144C23×C181—21no—
145C23×C181C2×D411yescharacteristic
146Q8×C181—21no—
147Q8×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—42no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2411yescharacteristic
158C8×C181—21no—
159C8×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181C2×SD1612yes—
166C22×C181C22×D411yescharacteristic
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—22no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—84no—
176C2×D181—84no—
177C2×D181C2×SD1612yes—
178C4×C181—21no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181—41no—
182C4×C181C2×#4111yescharacteristic
183C4×C181H(5,𝔽2)11yescharacteristic
184Dic181—21no—
185Dic181—21no—
186Dic181—41no—
187Dic181—41no—
188Dic181C2×SD1612yes—
189C2×C181—22no—
190C2×C181—81no—
191C2×C181#54611yescharacteristic
192C2×C181C22×SD1611yescharacteristic
193C2×C181#57611yescharacteristic
194D181—22no—
195D181—42no—
196D181—81no—
197C181#329511yescharacteristic, complemented, Sylow
198#3295—1811nomaximal, Sylow
199#554—1811no—
200D42—1811no—
201#486—1811no—
202#481—1811no—
203#481—1811no—
204#476—1811no—
205#465—1811no—
206#465D18111yescharacteristic, complemented
207#460—1811no—
208#450—1811no—
209#450—1811no—
210C4×SD16—1811no—
211C8×D4—1811no—
212C2×#102—1811no—
213C2×#102—1811no—
214C22×D4—3621no—
215C22×D4—1811no—
216C22×D4—1811no—
217C2×SD16—1811no—
218C2×SD16—1811no—
219C2×SD16C2×D18111yescharacteristic, complemented
220C22×C8—1811no—
221C22×C8C2×D18111yescharacteristic, complemented
222C4⋊Q8—1811no—
223#127—1811no—
224#125—3621no—
225C22⋊Q8—3621no—
226C22⋊Q8—3621no—
227C22⋊Q8—1811no—
228C22⋊Q8C2×D18111yescharacteristic, complemented
229#121—3621no—
230#121—1811no—
231#121C2×D18111yescharacteristic
232#120—3621no—
233#120—3621no—
234C4×Q8—1811no—
235C4×D4—3621no—
236C4×D4—1811no—
237C4×D4—1811no—
238C2×C4⋊C4—1811no—
239C2×C4⋊C4—1811no—
240#106—1811no—
241#106—1811no—
242#106C2×D18111yescharacteristic, complemented
243C4⋊C8—1811no—
244#103C2×D18111yescharacteristic, complemented
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102C2×D18111yescharacteristic, complemented
254C22⋊C8—1811no—
255C22⋊C8—1811no—
256C4×C8—1811no—
257C24—3621no—
258C24—3621no—
259C2×Q8—3621no—
260C2×Q8C22×D18111yescharacteristic
261C2×D4—21no—
262C2×D4—3622no—
263C2×D4—3621no—
264C2×D4—3622no—
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×D4—7244no—
275C2×D4C22×D18111yescharacteristic
276C22×C4—3621no—
277C22×C4—3621no—
278C22×C4—3621no—
279C22×C4—1811no—
280C22×C4C22×D18111yescharacteristic
281SD16—41no—
282SD16—3622no—
283SD16—7241no—
284C2×C8—41no—
285C2×C8—1811no—
286C2×C8—1811no—
287C2×C8—7241no—
288C2×C8C22×D18111yescharacteristic
289C2×C8C22×D18111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3621no—
292C4⋊C4—3621no—
293C4⋊C4—3621no—
294C4⋊C4—3621no—
295C4⋊C4—3621no—
296C4⋊C4—1811no—
297C4⋊C4—1811no—
298C4⋊C4—1811no—
299C4⋊C4C22×D18111yescharacteristic
300C4⋊C4C22×D18111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—1811no—
307C22⋊C4—1811no—
308C42—3621no—
309C42—1811no—
310C23—21no—
311C23—3621no—
312C23—3621no—
313C23—14481no—
314C23—14481no—
315C23—1811no—
316C23—7242no—
317C23—7242no—
318C23—7242no—
319C23—7242no—
320C23D4×D18111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—14481no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3621no—
328D4—3621no—
329D4—3621no—
330D4—14481no—
331D4—1814no—
332D4—1812no—
333D4—7242no—
334D4—7242no—
335D4—7242no—
336D4—7242no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—3621no—
346C2×C4—14481no—
347C2×C4—14481no—
348C2×C4—1811no—
349C2×C4—1811no—
350C2×C4—1811no—
351C2×C4—7242no—
352C2×C4D4×D18111yescharacteristic
353C2×C4C23×D18111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3621no—
357C8—3621no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3621no—
364C22—3621no—
365C22—3622no—
366C22—14484no—
367C22—14484no—
368C22—1812no—
369C22—7241no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22—7241no—
374C22SD16×D18112yes—
375C22C2×D4×D18111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3621no—
381C4—3621no—
382C4—1812no—
383C4—7241no—
384C4—7241no—
385C4#41×D18111yescharacteristic
386C4#1915386111yescharacteristic
387C2—22no—
388C2—81no—
389C2—3622no—
390C2—14481no—
391C2—7242no—
392C2#2604191811yescharacteristic
393C2C2×SD16×D18111yescharacteristic
394C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#465×C181C2
socleC22×C181C22×D4
prime radical#26041913C2
hypercenter#465D181
hypocenterC181#3295
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #26041987C2semidirect
3. #26041624C2semidirect
4. #26041599C2semidirect
5. #26041595C2semidirect
6. #26041568C2semidirect
7. #26041511C2semidirect
8. #26041477C2semidirect
9. #26041429C2semidirect
10. #26041428C2semidirect
11. #26041364C2semidirect
12. C8×C22⋊D181C2semidirect
13. C2×#19153738C2semidirect
14. #102×D181C2semidirect
15. #465×C181C2semidirect
20. C2×#15668436C22semidirect
21. C2×C8×D181C22semidirect
22. #19153815C22semidirect
27. #19153792C22semidirect
32. Q8×Dic181C22semidirect
36. C2×C4⋊Dic181C22semidirect
37. C4⋊C4×D181C22semidirect
38. #19153747C22semidirect
39. #19153747C22semidirect
40. #19153745C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
45. #19153737C22semidirect
46. #19153737C22semidirect
48. #19153736C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
52. C2×SD16×C181C22semidirect
53. C22×C8×C181C22semidirect
54. C22⋊Q8×C181C22semidirect
56. #106×C181C22semidirect
57. #103×C181C22semidirect
58. #102×C181C22semidirect
131. C22⋊D181SD16semidirect
197. C181#3295semidirect
206. #465D181semidirect
219. C2×SD16C2×D181semidirect
221. C22×C8C2×D181semidirect
228. C22⋊Q8C2×D181semidirect
242. #106C2×D181semidirect
244. #103C2×D181semidirect
253. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419872
#260419132
#260416242
#260415992
#260415952
#260415682
#260415112
#260414772
#260414292
#260414282
#260413642
C8×C22⋊D1812
C2×#191537382
#102×D1812
#465×C1812
#3295181