Finite Group Databasebeta

← #49133092

Subgroups — #49133092

Order 36224.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827150C211yesmaximal, characteristic, complemented
2#31827109C211yesmaximal, characteristic
3#31826818C211yesmaximal, characteristic, complemented
4#31826795C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826706C211yesmaximal, characteristic, complemented
8#31826693C211yesmaximal, characteristic, complemented
9#31826686C211yesmaximal, characteristic, complemented
10#31826628C211yesmaximal, characteristic, complemented
11#31826616C211yesmaximal, characteristic, complemented
12#31826556C211yesmaximal, characteristic, complemented
13C8×C22⋊D283C211yesmaximal, characteristic, complemented
14#31826458C211yesmaximal, characteristic, complemented
15C2×#102×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic, complemented
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic, complemented
21#22583605—21no—
22#22583601C2211yescharacteristic, complemented
23#22583600—21no—
24#22583597C2211yescharacteristic
25#22583593—21no—
26#22583591—21no—
27#22583590C2211yescharacteristic, complemented
28#22583589C2211yescharacteristic
29#22583589C2211yescharacteristic
30#22583582—21no—
31#22583581C2211yescharacteristic
32#22583579—21no—
33#22583575C2211yescharacteristic, complemented
34D4×Dic283C2211yescharacteristic
35C4×C22⋊D283C2211yescharacteristic
36#22583569—21no—
37#22583568C2211yescharacteristic, complemented
38C2×C22⋊Dic283—21no—
39#22583544C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583533C2211yescharacteristic, complemented
46#22583533C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C22×D4×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C2×C4⋊C4×C283C2211yescharacteristic
55#102×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C22×Dic283—21no—
67C22×Dic283—21no—
68C2×C4×D283C2311yescharacteristic
69Dic1132—41no—
70#17985380—22no—
71#17985380—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C8×D283—41no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283D411yescharacteristic
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C24×C283—21no—
98C2×D4×C283—22no—
99C2×D4×C283—21no—
100C2×D4×C283—41no—
101C2×D4×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105C2×C8×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116C22⋊D283—22no—
117C22⋊D283—42no—
118C22⋊D283—81no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—42no—
124C2×Dic283—81no—
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283—21no—
133C23×C283—21no—
134C23×C283—42no—
135C23×C283—42no—
136C23×C283—81no—
137C23×C283C2×D411yescharacteristic
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—42no—
142D4×C283#4112yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—42no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—22no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—84no—
161C22×C283#13512yes—
162C22×C283C22×D411yescharacteristic
163C2×D283—21no—
164C2×D283—21no—
165C2×D283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—21no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—22no—
179C2×C283—42no—
180C2×C283—81no—
181C2×C283#54611yescharacteristic
182C2×C283C2×#13511yescharacteristic
183C2×C283#57711yescharacteristic
184D283—41no—
185C283#329611yescharacteristic, complemented, Sylow
186#3296—2831nomaximal, Sylow
187#552—2831no—
188#546—2831no—
189#488—2831no—
190#483—2831no—
191#482—2831no—
192#478—2831no—
193#467—2831no—
194#465—2831no—
195#464—2831no—
196#452—2831no—
197#450—2831no—
198C4×SD16—2831no—
199C8×D4—2831no—
200#416—2831no—
201C2×#102D28311yescharacteristic, complemented
202C2×#41—2831no—
203C22×D4C2×D28311yescharacteristic
204C2×Q16—2831no—
205C2×SD16—2831no—
206C2×SD16—2831no—
207C22×C8—2831no—
208C22×C8C2×D28311yescharacteristic
209#126—5661no—
210#125—2831no—
211#125—5661no—
212#124—2831no—
213#123—5661no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—2831no—
218#121—2831no—
219#121—5661no—
220#120—5661no—
221C4×Q8—2831no—
222C4×D4—2831no—
223C4×D4—2831no—
224#117—2831no—
225#117—5661no—
226C2×C4⋊C4C2×D28311yescharacteristic
227C2×C22⋊C4—5661no—
228#107—2831no—
229#106—2831no—
230#106—2831no—
231C4⋊C8—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#102—2831no—
237#102—2831no—
238#102C2×D28311yescharacteristic
239#102C2×D28311yescharacteristic
240#102C2×D28311yescharacteristic
241#102C2×D28311yescharacteristic
242C22⋊C8—2831no—
243C22⋊C8—2831no—
244C4×C8—2831no—
245C24—21no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4C22×D28311yescharacteristic
257C2×D4C22×D28311yescharacteristic
258C22×C4—21no—
259C22×C4—2831no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263Q16—11321no—
264SD16—5662no—
265SD16—11321no—
266C2×C8—41no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4C22×D28311yescharacteristic
283C4⋊C4C22×D28311yescharacteristic
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C42—2831no—
295C42—5661no—
296C42—5661no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—2831no—
303C23D4×D28311yescharacteristic
304Q8—5661no—
305Q8—5661no—
306Q8—5661no—
307Q8—5661no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—5662no—
313D4—11322no—
314D4—22641no—
315D4#1798539212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—2831no—
322C2×C4—2831no—
323C2×C4—2831no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—11322no—
331C2×C4—22641no—
332C2×C4D4×D28311yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5661no—
337C8—5661no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—5661no—
348C22—5661no—
349C22—5661no—
350C22#2258362912yes—
351C22C2×D4×D28311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—5661no—
356C4—5661no—
357C4—5661no—
358C4—11321no—
359C4—11321no—
360C4—11321no—
361C4—11321no—
362C4C2×#1798539211yescharacteristic
363C4#2258365511yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—11321no—
368C2#3182710511yescharacteristic
369C2C2×#2258362911yescharacteristic
370C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC22×C283C22×D4
prime radical#31827109C2
hypercenterC2×#102D283
hypocenterC283#3296
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #31827150C2semidirect
3. #31826818C2semidirect
4. #31826795C2semidirect
5. #31826787C2semidirect
6. #31826763C2semidirect
7. #31826706C2semidirect
8. #31826693C2semidirect
9. #31826686C2semidirect
10. #31826628C2semidirect
11. #31826616C2semidirect
12. #31826556C2semidirect
13. C8×C22⋊D283C2semidirect
14. #31826458C2semidirect
15. C2×#102×C283C2semidirect
17. C2×Dic1132C22semidirect
20. C2×C8×D283C22semidirect
22. #22583601C22semidirect
27. #22583590C22semidirect
33. #22583575C22semidirect
37. #22583568C22semidirect
39. #22583544C22semidirect
40. #22583541C22semidirect
41. #22583541C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
45. #22583533C22semidirect
46. #22583533C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C8×Dic283C22semidirect
185. C283#3296semidirect
201. C2×#102D283semidirect

Maximal subgroups

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

subgroupindex
#318271502
#318271092
#318268182
#318267952
#318267872
#318267632
#318267062
#318266932
#318266862
#318266282
#318266162
#318265562
C8×C22⋊D2832
#318264582
C2×#102×C2832
#3296283