Finite Group Databasebeta

← #37545803

Subgroups — #37545803

Order 23168.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041984C211yesmaximal, characteristic, complemented
2#26041917C211yesmaximal, characteristic
3#26041640C211yesmaximal, characteristic, complemented
4#26041613C211yesmaximal, characteristic, complemented
5#26041592C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041525C211yesmaximal, characteristic, complemented
8#26041519C211yesmaximal, characteristic, complemented
9#26041504C211yesmaximal, characteristic, complemented
10#26041441C211yesmaximal, characteristic, complemented
11#26041431C211yesmaximal, characteristic, complemented
12#26041376C211yesmaximal, characteristic, complemented
13#26041348C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#417×C181C211yesmaximal, characteristic, complemented
16C2×D4×D181C2211yescharacteristic
17C2×#15668439C2211yescharacteristic, complemented
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153815C2211yescharacteristic, complemented
22#19153806—21no—
23#19153805C2211yescharacteristic
24#19153799—21no—
25#19153796C2211yescharacteristic
26#19153795—21no—
27#19153795C2211yescharacteristic, complemented
28#19153794—21no—
29#19153792C2211yescharacteristic
30#19153790C2211yescharacteristic
31#19153788—21no—
32#19153784—21no—
33#19153781C2211yescharacteristic, complemented
34D4×Dic181C2211yescharacteristic
35C4×C22⋊D181—21no—
36C4×C22⋊D181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38C2×#15668426—21no—
39#19153750C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153749C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153741C2211yescharacteristic, complemented
44#19153740C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic, complemented
52C2×#41×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic, complemented
54C2×C4⋊C4×C181C2211yescharacteristic, complemented
55#103×C181C2211yescharacteristic, complemented
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C23×D181—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181D411yescharacteristic
66D4×D181—22no—
67D4×D181—41no—
68C22×Dic181—21no—
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71#15668439—41no—
72#15668438—41no—
73#15668437—22no—
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C8×D181—41no—
77C4⋊Dic181—21no—
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181D411yescharacteristic
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97#41×C181—22no—
98#41×C181—41no—
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105M16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—42no—
113C22×D181—42no—
114C22×D181—81no—
115C22×D181C2×D411yescharacteristic
116Dic362—21no—
117Dic362—21no—
118Dic362—81no—
119D724—21no—
120D724—21no—
121C22⋊D181—22no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—81no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—81no—
134#13089678—21no—
135#13089678—21no—
136C23×C181—21no—
137C23×C181C2×D411yescharacteristic
138Q8×C181—21no—
139Q8×C181—21no—
140D4×C181—21no—
141D4×C181—42no—
142D4×C181#4112yes—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—42no—
149C2×C4×C181—81no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C8×C181—21no—
153C8×C181—21no—
154C22×C181—21no—
155C22×C181—22no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181C22×D411yescharacteristic
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—84no—
167C2×D181#13712yes—
168C4×C181—21no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181C2×#4111yescharacteristic
173C4×C181H(5,𝔽2)11yescharacteristic
174Dic181—21no—
175Dic181—21no—
176Dic181—21no—
177Dic181—41no—
178Dic181—41no—
179Dic181—41no—
180C2×C181—42no—
181C2×C181—41no—
182C2×C181#54611yescharacteristic
183C2×C181C2×#13711yescharacteristic
184C2×C181#57611yescharacteristic
185D181—22no—
186D181—81no—
187C181#331411yescharacteristic, complemented, Sylow
188#3314—1811nomaximal, Sylow
189#554—1811no—
190#546—1811no—
191#489—1811no—
192#484—1811no—
193#480—1811no—
194#474—1811no—
195#468—1811no—
196#467—1811no—
197#464—1811no—
198#452—1811no—
199#450—1811no—
200#440—1811no—
201#435—1811no—
202#417D18111yescharacteristic, complemented
203C2×#102—1811no—
204C2×#41C2×D18111yescharacteristic
205C22×D4—1811no—
206C2×Q16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×M16C2×D18111yescharacteristic, complemented
210C22×C8—1811no—
211C4⋊Q8—1811no—
212#125—3621no—
213#124—1811no—
214#123—3621no—
215C22⋊Q8—3621no—
216C22⋊Q8—3621no—
217C22⋊Q8—1811no—
218C22⋊Q8—1811no—
219C22⋊Q8—1811no—
220#121—3621no—
221#121—1811no—
222#120—3621no—
223C4×Q8—1811no—
224C4×D4—3621no—
225C4×D4—1811no—
226C4×D4—1811no—
227C2×C4⋊C4—1811no—
228C2×C4⋊C4C2×D18111yescharacteristic, complemented
229C2×C22⋊C4—3621no—
230#107—1811no—
231#107—1811no—
232#107—1811no—
233C4⋊C8—1811no—
234#103—1811no—
235#103—1811no—
236#103C2×D18111yescharacteristic, complemented
237#103C2×D18111yescharacteristic, complemented
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102C2×D18111yescharacteristic
243#102C2×D18111yescharacteristic
244C22⋊C8—1811no—
245C22⋊C8—1811no—
246#97—1811no—
247C24—3621no—
248#41—22no—
249#41—41no—
250C2×Q8—3621no—
251C2×Q8—1811no—
252C2×Q8C22×D18111yescharacteristic
253C2×D4—21no—
254C2×D4—3622no—
255C2×D4—3621no—
256C2×D4—3621no—
257C2×D4—1811no—
258C2×D4—1811no—
259C2×D4—7241no—
260C2×D4C22×D18111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—3621no—
264C22×C4—3621no—
265C22×C4—1811no—
266C22×C4C22×D18111yescharacteristic
267Q16—7241no—
268SD16—3622no—
269SD16—7241no—
270M16—41no—
271C2×C8—1811no—
272C2×C8—1811no—
273C2×C8—7241no—
274C2×C8C22×D18111yescharacteristic
275C2×C8C22×D18111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4C22×D18111yescharacteristic
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—1811no—
296C22⋊C4—1811no—
297C42—3621no—
298C42—1811no—
299C23—21no—
300C23—3621no—
301C23—14481no—
302C23—1811no—
303C23—7242no—
304C23—7242no—
305C23D4×D18111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—3621no—
309Q8—3621no—
310Q8—14481no—
311D4—21no—
312D4—42no—
313D4—3622no—
314D4—3621no—
315D4—3621no—
316D4—14481no—
317D4—7242no—
318D4#1566844912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—14481no—
332C2×C4—14481no—
333C2×C4—1811no—
334C2×C4—1811no—
335C2×C4—1811no—
336C2×C4D4×D18111yescharacteristic
337C2×C4C23×D18111yescharacteristic
338C8—21no—
339C8—21no—
340C8—3621no—
341C8—3621no—
342C22—21no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—3621no—
349C22—3621no—
350C22—14484no—
351C22—1812no—
352C22—7241no—
353C22—7241no—
354C22—7241no—
355C22C2×D4×D18111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3621no—
361C4—3621no—
362C4—3621no—
363C4—7241no—
364C4—7241no—
365C4—7241no—
366C4C2×#1566844911yescharacteristic
367C4#1915386111yescharacteristic
368C2—41no—
369C2—42no—
370C2—3622no—
371C2—14481no—
372C2#2604191911yescharacteristic
373C2#137×D18111yescharacteristic
374C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#417×C181C2
socleC22×C181C22×D4
prime radical#26041917C2
hypercenter#417D181
hypocenterC181#3314
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #26041984C2semidirect
3. #26041640C2semidirect
4. #26041613C2semidirect
5. #26041592C2semidirect
6. #26041557C2semidirect
7. #26041525C2semidirect
8. #26041519C2semidirect
9. #26041504C2semidirect
10. #26041441C2semidirect
11. #26041431C2semidirect
12. #26041376C2semidirect
13. #26041348C2semidirect
14. #102×D181C2semidirect
15. #417×C181C2semidirect
17. C2×#15668439C22semidirect
21. #19153815C22semidirect
27. #19153795C22semidirect
33. #19153781C22semidirect
39. #19153750C22semidirect
40. #19153749C22semidirect
41. #19153749C22semidirect
42. #19153745C22semidirect
43. #19153741C22semidirect
44. #19153740C22semidirect
49. C22⋊#13089678C22semidirect
51. #19153726C22semidirect
53. C2×M16×C181C22semidirect
54. C2×C4⋊C4×C181C22semidirect
55. #103×C181C22semidirect
56. #103×C181C22semidirect
187. C181#3314semidirect
202. #417D181semidirect
209. C2×M16C2×D181semidirect
228. C2×C4⋊C4C2×D181semidirect
236. #103C2×D181semidirect
237. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419842
#260419172
#260416402
#260416132
#260415922
#260415572
#260415252
#260415192
#260415042
#260414412
#260414312
#260413762
#260413482
#102×D1812
#417×C1812
#3314181