Finite Group Databasebeta

← #49131173

Subgroups — #49131173

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826975C211yesmaximal, characteristic
2#117×D283C211yesmaximal, characteristic, complemented
3#31826807C211yesmaximal, characteristic, complemented
4#31826806C211yesmaximal, characteristic, complemented
5#31826802C211yesmaximal, characteristic, complemented
6#31826797C211yesmaximal, characteristic, complemented
7#31826786C211yesmaximal, characteristic, complemented
8#31826782C211yesmaximal, characteristic, complemented
9#31826777C211yesmaximal, characteristic, complemented
10#31826502C211yesmaximal, characteristic, complemented
11#31826500C211yesmaximal, characteristic, complemented
12#31826458C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14C22⋊C8×D283C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583592—21no—
21#22583590C2211yescharacteristic
22#22583589C2211yescharacteristic
23#22583581C2211yescharacteristic
24#22583578—21no—
25D4×Dic283—21no—
26(C22⋊D283)⋊C4—21no—
27#22583569C2211yescharacteristic
28#22583568C2211yescharacteristic
29#22583568C2211yescharacteristic
30#22583568C2211yescharacteristic
31#22583567—21no—
32#22583566—21no—
33C4⋊C4×D283C2211yescharacteristic
34C4⋊C4×D283C2211yescharacteristic
35C22⋊C4×D283—21no—
36C42×D283—21no—
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583533C2211yescharacteristic, complemented
46#22583533C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic, complemented
48#22583531C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
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×D283D411yescharacteristic
60#17985391—22no—
61#17985391—22no—
62C2×Dic566C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C22×Dic283—21no—
66C22×Dic283D411yescharacteristic
67C2×C4×D283—22no—
68C2×C4×D283—22no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283D411yescharacteristic
72C2×C4×D283D411yescharacteristic
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C8×D283—22no—
78C8×D283—22no—
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
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—22no—
109C22×D283—22no—
110C22×D283—41no—
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115C22⋊D283—42no—
116C22⋊D283—42no—
117C2×Dic283—22no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—42no—
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—22no—
126C4×D283—21no—
127C4×D283—21no—
128C4×D283—22no—
129C4×D283—42no—
130C4×D283—42no—
131C4×D283#4112yes—
132C4×D283#4112yes—
133C283⋊C8—21no—
134C283⋊C8—21no—
135C23×C283—21no—
136C23×C283C2×D411yescharacteristic
137D4×C283—21no—
138D4×C283—21no—
139D4×C283—42no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×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—21no—
160C2×D283—44no—
161C2×D283#12312yes—
162C2×D283#13512yes—
163C4×C283—21no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283—41no—
167C4×C283C2×#4111yescharacteristic
168C4×C283C2×#4111yescharacteristic
169Dic283—21no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174Dic283#12312yes—
175C2×C283—41no—
176C2×C283—81no—
177C2×C283C2×#12311yescharacteristic
178C2×C283C2×#13511yescharacteristic
179C2×C283#57511yescharacteristic
180D283—22no—
181D283—22no—
182C283#309111yescharacteristic, complemented, Sylow
183#3091—2831nomaximal, Sylow
184#525—2831no—
185C2×#117—2831no—
186#485—2831no—
187#485—2831no—
188#484—2831no—
189#483—2831no—
190#482—2831no—
191#482D28311yescharacteristic, complemented
192#481—2831no—
193#480—2831no—
194#427—2831no—
195#427—2831no—
196#416—2831no—
197#416—2831no—
198C2×C22⋊C8—2831no—
199C2×#41—2831no—
200C23×C4—2831no—
201C22×C8—2831no—
202C22×C8—2831no—
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206#121—2831no—
207#121C2×D28311yescharacteristic
208#120—5661no—
209C4×D4—5661no—
210C4×D4—5661no—
211#117—2831no—
212#117—2831no—
213#117—2831no—
214#117—2831no—
215#117—5661no—
216#117—5661no—
217#117C2×D28311yescharacteristic
218C2×C4⋊C4—2831no—
219C2×C4⋊C4—2831no—
220C2×C22⋊C4—5661no—
221C2×C42—5661no—
222#107—2831no—
223#107—2831no—
224#107—2831no—
225#107C2×D28311yescharacteristic, complemented
226#106—2831no—
227#106—2831no—
228#106—2831no—
229#106C2×D28311yescharacteristic, complemented
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102—2831no—
236#102C2×D28311yescharacteristic, complemented
237#102C2×D28311yescharacteristic, complemented
238C22⋊C8—2831no—
239C22⋊C8—2831no—
240C22⋊C8—2831no—
241C22⋊C8C2×D28311yescharacteristic
242C24—2831no—
243#41—5662no—
244#41—5662no—
245C2×Q8—2831no—
246C2×D4—21no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—2831no—
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—5662no—
256C22×C4—5662no—
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4C22×D28311yescharacteristic
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8—5662no—
264C2×C8—5662no—
265C2×C8C22×D28311yescharacteristic
266C2×C8C22×D28311yescharacteristic
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4C22×D28311yescharacteristic
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—21no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C42—5661no—
291C23—21no—
292C23—2831no—
293C23—2831no—
294C23—5662no—
295C23—5662no—
296C23—11321no—
297C23D4×D28311yescharacteristic
298Q8—5661no—
299Q8—5661no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2831no—
311C2×C4—2832no—
312C2×C4—2832no—
313C2×C4—2831no—
314C2×C4—5662no—
315C2×C4—5662no—
316C2×C4—5662no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—11322no—
324C2×C4—11322no—
325C2×C4—11322no—
326C2×C4D4×D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2832no—
339C22—2832no—
340C22—5661no—
341C22—5661no—
342C22—5661no—
343C22—5661no—
344C22—11324no—
345C22C2×D4×D28311yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2832no—
351C4—5661no—
352C4—11321no—
353C4—11321no—
354C4—11321no—
355C4—11321no—
356C4#41×D28311yescharacteristic
357C4#41×D28311yescharacteristic
358C2—41no—
359C2—81no—
360C2—5662no—
361C2—5662no—
362C2#123×D28311yescharacteristic
363C2#135×D28311yescharacteristic
364C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
prime radical#31826975C2
hypercenter#482D283
hypocenterC283#3091
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
2. #117×D283C2semidirect
3. #31826807C2semidirect
4. #31826806C2semidirect
5. #31826802C2semidirect
6. #31826797C2semidirect
7. #31826786C2semidirect
8. #31826782C2semidirect
9. #31826777C2semidirect
10. #31826502C2semidirect
11. #31826500C2semidirect
12. #31826458C2semidirect
13. #31826458C2semidirect
14. C22⋊C8×D283C2semidirect
15. #482×C283C2semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. #22583542C22semidirect
41. #22583541C22semidirect
42. #22583541C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
45. #22583533C22semidirect
46. #22583533C22semidirect
47. #22583531C22semidirect
48. #22583531C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
182. C283#3091semidirect
191. #482D283semidirect
225. #107C2×D283semidirect
229. #106C2×D283semidirect
236. #102C2×D283semidirect
237. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269752
#117×D2832
#318268072
#318268062
#318268022
#318267972
#318267862
#318267822
#318267772
#318265022
#318265002
#318264582
C22⋊C8×D2832
#482×C2832
#3091283