Finite Group Databasebeta

← #49131440

Subgroups — #49131440

Order 36224.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827082C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic, complemented
3#31826806C211yesmaximal, characteristic, complemented
4#31826754C211yesmaximal, characteristic, complemented
5#31826744C211yesmaximal, characteristic, complemented
6#31826679C211yesmaximal, characteristic, complemented
7#31826679C211yesmaximal, characteristic, complemented
8#31826618C211yesmaximal, characteristic, complemented
9#31826598C211yesmaximal, characteristic
10#31826574C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583609C2211yescharacteristic, complemented
22#22583603—21no—
23#22583597—21no—
24#22583597C2211yescharacteristic, complemented
25#22583591—21no—
26#22583589C2211yescharacteristic
27#22583587—21no—
28#22583575C2211yescharacteristic, complemented
29C4×D1132—21no—
30C4×D1132—21no—
31D4×Dic283C2211yescharacteristic, complemented
32#22583572C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583569C2211yescharacteristic
37C22⋊C4×D283—21no—
38C22⋊C4×D283—21no—
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—22no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C22×Dic283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72#17985381—22no—
73#17985381—22no—
74#17985377—22no—
75#17985377—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283D411yescharacteristic
79C4⋊Dic283D411yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
89C22⋊Dic283D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—81no—
112C22×D283—81no—
113Dic566—21no—
114Dic566—21no—
115Dic566—81no—
116D1132—24no—
117D1132—21no—
118D1132—21no—
119D1132#4112yes—
120D1132#4112yes—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—81no—
129C4×D283—81no—
130C4×D283—81no—
131C4×D283—81no—
132C283⋊C8—21no—
133C283⋊C8—21no—
134C23×C283—21no—
135C23×C283C2×D411yescharacteristic
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—81no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—22no—
156C2×D283—22no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—84no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—21no—
171Dic283—21no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—41no—
175C2×C283—81no—
176C2×C283#52511yescharacteristic
177C2×C283#57611yescharacteristic
178C2×C283#57711yescharacteristic
179D283—42no—
180D283—42no—
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542—2831no—
184#518—2831no—
185#485—2831no—
186#482D28311yescharacteristic, complemented
187#476—2831no—
188#474—2831no—
189#463—2831no—
190#463—2831no—
191#450—2831no—
192#447—2831no—
193#442—2831no—
194#440—2831no—
195C4×SD16—2831no—
196C4×D8—2831no—
197#433—2831no—
198C22×D4—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8—2831no—
203C4⋊Q8—2831no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—5661no—
210#121C2×D28311yescharacteristic
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218C4×D4—5661no—
219#117—2831no—
220#117C2×D28311yescharacteristic
221C2×C22⋊C4—5661no—
222C2×C22⋊C4—5661no—
223#107—2831no—
224#107C2×D28311yescharacteristic, complemented
225#106—2831no—
226#106C2×D28311yescharacteristic, complemented
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic, complemented
236#102C2×D28311yescharacteristic, complemented
237C22⋊C8—2831no—
238C22⋊C8C2×D28311yescharacteristic
239#97—2831no—
240C4×C8—2831no—
241C24—5661no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—21no—
245C2×D4—2831no—
246C2×D4—2831no—
247C2×D4—5662no—
248C2×D4—5662no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4C22×D28311yescharacteristic
257SD16—5662no—
258SD16—5662no—
259D8—5662no—
260D8—5662no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4C22×D28311yescharacteristic
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2831no—
277C22⋊C4—2831no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—21no—
287C42—2831no—
288C42—2831no—
289C42—5661no—
290C23—21no—
291C23—5664no—
292C23—5661no—
293C23—5661no—
294C23—22641no—
295C23—22641no—
296C23D4×D28311yescharacteristic
297Q8—5661no—
298Q8—5661no—
299Q8—22641no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—2832no—
304D4—2832no—
305D4—5664no—
306D4—5661no—
307D4—5661no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—22641no—
320C2×C4—22641no—
321C2×C4—22641no—
322C2×C4—22641no—
323C2×C4—22641no—
324C2×C4D4×D28311yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5661no—
329C8—5661no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—5662no—
337C22—5662no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22—11321no—
342C22—22644no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5661no—
349C4—5661no—
350C4—5661no—
351C4—5661no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4#41×D28311yescharacteristic
356C2—41no—
357C2—81no—
358C2—11322no—
359C2—11322no—
360C2#3182697311yescharacteristic
361C2#3182726911yescharacteristic
362C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
prime radical#31826598C2
hypercenter#482D283
hypocenterC283#3118
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31827082C2semidirect
2. #31826939C2semidirect
3. #31826806C2semidirect
4. #31826754C2semidirect
5. #31826744C2semidirect
6. #31826679C2semidirect
7. #31826679C2semidirect
8. #31826618C2semidirect
10. #31826574C2semidirect
11. #31826564C2semidirect
12. #31826552C2semidirect
13. #31826545C2semidirect
14. #31826523C2semidirect
15. #482×C283C2semidirect
21. #22583609C22semidirect
24. #22583597C22semidirect
28. #22583575C22semidirect
31. D4×Dic283C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583533C22semidirect
44. #22583533C22semidirect
50. #22583520C22semidirect
51. C8×Dic283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
181. C283#3118semidirect
186. #482D283semidirect
224. #107C2×D283semidirect
226. #106C2×D283semidirect
235. #102C2×D283semidirect
236. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270822
#318269392
#318268062
#318267542
#318267442
#318266792
#318266182
#318265982
#318265742
#318265642
#318265522
#318265452
#318265232
#482×C2832
#3118283