Finite Group Databasebeta

← #49133103

Subgroups — #49133103

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#31827156C211yesmaximal, characteristic, complemented
2#31827108C211yesmaximal, characteristic
3#31826819C211yesmaximal, characteristic, complemented
4#31826794C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826703C211yesmaximal, characteristic, complemented
8#31826691C211yesmaximal, characteristic, complemented
9#31826626C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11C4×#17985379C211yesmaximal, characteristic, complemented
12#31826530C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#464×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic, complemented
21#22583604—21no—
22#22583602C2211yescharacteristic, complemented
23#22583600—21no—
24#22583595—21no—
25#22583592—21no—
26#22583586C2211yescharacteristic
27#22583586C2211yescharacteristic
28#22583586C2211yescharacteristic, complemented
29#22583583—21no—
30#22583581C2211yescharacteristic
31#22583580—21no—
32C4×D1132C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34#22583568C2211yescharacteristic, complemented
35#22583567—21no—
36C4⋊C4×D283C2211yescharacteristic
37C22⋊C4×D283—21no—
38#22583544C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41#22583534C2211yescharacteristic, complemented
42#22583534C2211yescharacteristic, complemented
43#22583534C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C4×C283⋊C8C2211yescharacteristic, complemented
52C2×Q16×C283C2211yescharacteristic, complemented
53C2×SD16×C283C2211yescharacteristic
54#124×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60#17985393—22no—
61#17985393—41no—
62C2×D1132—21no—
63C2×D1132D411yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67D4×D283—22no—
68D4×D283—41no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73C2×C4×D283C2311yescharacteristic
74#17985379—22no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C8×D283—41no—
78C8×D283—41no—
79C4⋊Dic283D411yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89C22⋊Dic283—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101Q16×C283—41no—
102SD16×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116C22×D283C2×D411yescharacteristic
117D1132—22no—
118D1132—21no—
119D1132—42no—
120D1132#4112yes—
121C22⋊D283—42no—
122C22⋊D283—81no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—42no—
134C4×D283—81no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283—21no—
138Q8×C283—21no—
139Q8×C283—21no—
140Q8×C283—21no—
141Q8×C283—21no—
142D4×C283—21no—
143D4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—22no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—84no—
165C2×D283#13512yes—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—41no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283C2×#4111yescharacteristic
172C4×C283H(5,𝔽2)11yescharacteristic
173Dic283—21no—
174Dic283—21no—
175Dic283—41no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—81no—
179C2×C283#54611yescharacteristic
180C2×C283C2×#13511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—22no—
183D283—41no—
184D283—42no—
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#464D28311yescharacteristic, complemented
196#452—2831no—
197#450—2831no—
198C4×SD16—2831no—
199C8×D4—2831no—
200#416—2831no—
201C2×#102—2831no—
202C2×#41—2831no—
203C22×D4—2831no—
204C2×Q16C2×D28311yescharacteristic, complemented
205C2×SD16—2831no—
206C2×SD16C2×D28311yescharacteristic
207C22×C8—2831no—
208C22×C8—2831no—
209#126—5661no—
210#125—2831no—
211#125—5661no—
212#124C2×D28311yescharacteristic
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×Q8C2×D28311yescharacteristic, complemented
222C4×D4—2831no—
223C4×D4—2831no—
224#117—2831no—
225#117—5661no—
226C2×C4⋊C4—2831no—
227C2×C22⋊C4—5661no—
228#107—2831no—
229#106—2831no—
230#106—2831no—
231C4⋊C8C2×D28311yescharacteristic, complemented
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103C2×D28311yescharacteristic, complemented
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102C2×D28311yescharacteristic
242C22⋊C8—2831no—
243C22⋊C8—2831no—
244C4×C8—2831no—
245C24—5661no—
246#41—5662no—
247#41—11321no—
248C2×Q8C22×D28311yescharacteristic
249C2×Q8C22×D28311yescharacteristic
250C2×D4—2831no—
251C2×D4—2831no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5662no—
255C2×D4—5661no—
256C2×D4—11321no—
257C2×D4C22×D28311yescharacteristic
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—5661no—
263Q16—41no—
264SD16—41no—
265SD16—5662no—
266C2×C8—2831no—
267C2×C8—2831no—
268C2×C8—11321no—
269C2×C8—11321no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4C22×D28311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—2831no—
287C22⋊C4—2831no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C42—21no—
295C42—5661no—
296C42C22×D28311yescharacteristic
297C23—21no—
298C23—2831no—
299C23—2831no—
300C23—5661no—
301C23—11322no—
302C23—11322no—
303C23—22641no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—2832no—
311D4—5662no—
312D4—5661no—
313D4—11322no—
314D4—11322no—
315D4—22641no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2831no—
320C2×C4—2831no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—11322no—
329C2×C4—11322no—
330C2×C4—22641no—
331C2×C4D4×D28311yescharacteristic
332C2×C4D4×D28311yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5661no—
337C8—5661no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2832no—
342C22—5661no—
343C22—5661no—
344C22—5661no—
345C22—5661no—
346C22—5661no—
347C22—5662no—
348C22—11321no—
349C22—11321no—
350C22—22644no—
351C22C2×D4×D28311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5661no—
358C4—5661no—
359C4—11321no—
360C4—11321no—
361C4—11321no—
362C4#41×D28311yescharacteristic
363C4#2258365511yescharacteristic
364C2—81no—
365C2—5662no—
366C2—11321no—
367C2—11322no—
368C2#3182711211yescharacteristic
369C2#135×D28311yescharacteristic
370C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#464×C283C2
socleC22×C283C22×D4
prime radical#31827108C2
hypercenter#464D283
hypocenterC283#3296
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #31827156C2semidirect
3. #31826819C2semidirect
4. #31826794C2semidirect
5. #31826787C2semidirect
6. #31826766C2semidirect
7. #31826703C2semidirect
8. #31826691C2semidirect
9. #31826626C2semidirect
10. #31826614C2semidirect
11. C4×#17985379C2semidirect
12. #31826530C2semidirect
13. #31826460C2semidirect
14. #102×D283C2semidirect
15. #464×C283C2semidirect
20. C2×C8×D283C22semidirect
22. #22583602C22semidirect
28. #22583586C22semidirect
34. #22583568C22semidirect
38. #22583544C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. #22583534C22semidirect
42. #22583534C22semidirect
43. #22583534C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C4×C283⋊C8C22semidirect
52. C2×Q16×C283C22semidirect
55. C4×Q8×C283C22semidirect
56. C4⋊C8×C283C22semidirect
57. #103×C283C22semidirect
185. C283#3296semidirect
195. #464D283semidirect
204. C2×Q16C2×D283semidirect
221. C4×Q8C2×D283semidirect
231. C4⋊C8C2×D283semidirect
235. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271562
#318271082
#318268192
#318267942
#318267872
#318267662
#318267032
#318266912
#318266262
#318266142
C4×#179853792
#318265302
#318264602
#102×D2832
#464×C2832
#3296283