Finite Group Databasebeta

← #49131172

Subgroups — #49131172

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#31826972C211yesmaximal, characteristic
2#117×D283C211yesmaximal, characteristic, complemented
3#31826805C211yesmaximal, characteristic, complemented
4#31826804C211yesmaximal, characteristic, complemented
5#31826799C211yesmaximal, characteristic, complemented
6#31826794C211yesmaximal, characteristic, complemented
7#31826788C211yesmaximal, characteristic, complemented
8#31826787C211yesmaximal, characteristic, complemented
9#31826782C211yesmaximal, characteristic, complemented
10#31826777C211yesmaximal, characteristic, complemented
11#31826503C211yesmaximal, characteristic, complemented
12#31826501C211yesmaximal, characteristic, complemented
13#31826461C211yesmaximal, characteristic, complemented
14C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
15#416×C283C211yesmaximal, characteristic, complemented
16C22×C4×D283C2211yescharacteristic
17C22×C283⋊C8C2211yescharacteristic
18#22583591—21no—
19#22583586C2211yescharacteristic
20#22583586C2211yescharacteristic
21#22583581C2211yescharacteristic
22#22583581C2211yescharacteristic
23#22583578—21no—
24C4×C22⋊D283—21no—
25C4×C22⋊D283—21no—
26#22583569C2211yescharacteristic
27#22583569C2211yescharacteristic
28#22583568C2211yescharacteristic
29#22583568C2211yescharacteristic
30#22583567—21no—
31#22583566—21no—
32C4⋊C4×D283C2211yescharacteristic
33C4⋊C4×D283C2211yescharacteristic
34C22⋊C4×D283—21no—
35C42×D283—21no—
36#22583544C2211yescharacteristic, complemented
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583542C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43#22583541C2211yescharacteristic, complemented
44#22583534C2211yescharacteristic, complemented
45#22583534C2211yescharacteristic, complemented
46#22583531C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic, complemented
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic, complemented
59C23×D283D411yescharacteristic
60C2×C22⋊D283—21no—
61C2×C22⋊D283—21no—
62C22×Dic283D411yescharacteristic
63C2×C4×D283—21no—
64C2×C4×D283—21no—
65C2×C4×D283—22no—
66C2×C4×D283—22no—
67C2×C4×D283D411yescharacteristic
68C2×C4×D283D411yescharacteristic
69C2×C4×D283C2311yescharacteristic
70C2×C4×D283C2311yescharacteristic
71C2×C283⋊C8—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94#41×C283—22no—
95#41×C283—22no—
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283C2311yescharacteristic
101C2×C8×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—22no—
109C22×D283—22no—
110C22×D283—41no—
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113C22⋊D283—42no—
114C22⋊D283—42no—
115C2×Dic283—22no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—22no—
123C4×D283—22no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—21no—
128C4×D283—42no—
129C4×D283—42no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—42no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—42no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283#4112yes—
145C2×C4×C283#4112yes—
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283#12312yes—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—44no—
162C2×D283#13512yes—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283#12312yes—
167C4×C283C2×#4111yescharacteristic
168C4×C283C2×#4111yescharacteristic
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174Dic283—41no—
175C2×C283—22no—
176C2×C283—81no—
177C2×C283C2×#12311yescharacteristic
178C2×C283C2×#13511yescharacteristic
179C2×C283#57511yescharacteristic
180D283—22no—
181D283—41no—
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#482—2831no—
192#481—2831no—
193#480—2831no—
194#427—2831no—
195#427—2831no—
196#416—2831no—
197#416D28311yescharacteristic, complemented
198C2×C22⋊C8—2831no—
199C2×#41C2×D28311yescharacteristic
200C23×C4—2831no—
201C22×C8—2831no—
202C22×C8C2×D28311yescharacteristic
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206#121—2831no—
207#121—2831no—
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#107—2831no—
226#106—2831no—
227#106—2831no—
228#106—2831no—
229#106—2831no—
230#103—2831no—
231#103—2831no—
232#103C2×D28311yescharacteristic, complemented
233#103C2×D28311yescharacteristic, complemented
234#102—2831no—
235#102—2831no—
236#102C2×D28311yescharacteristic, complemented
237#102C2×D28311yescharacteristic, complemented
238C22⋊C8—2831no—
239C22⋊C8—2831no—
240C22⋊C8—2831no—
241C22⋊C8—2831no—
242C24—2831no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D28311yescharacteristic
246C2×D4—21no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C22×C4—21no—
251C22×C4—2831no—
252C22×C4—2831no—
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—2831no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5662no—
259C22×C4—5662no—
260C22×C4C22×D28311yescharacteristic
261C2×C8—22no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8—5662no—
265C2×C8C22×D28311yescharacteristic
266C2×C8C22×D28311yescharacteristic
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
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—5661no—
288C42—5661no—
289C42—5661no—
290C42—5661no—
291C23—21no—
292C23—2831no—
293C23—2831no—
294C23—5662no—
295C23—5662no—
296C23—11321no—
297C23D4×D28311yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—5662no—
312C2×C4—5662no—
313C2×C4—5662no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—11322no—
323C2×C4—11322no—
324C2×C4D4×D28311yescharacteristic
325C2×C4#1798539112yes—
326C2×C4#1798539212yes—
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2832no—
338C22—5661no—
339C22—5661no—
340C22—5661no—
341C22—5661no—
342C22—5661no—
343C22—11324no—
344C22#2258359212yes—
345C22C2×D4×D28311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—5661no—
350C4—5661no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4—11321no—
355C4#2258359212yes—
356C4C2×#1798539111yescharacteristic
357C4C2×#1798539211yescharacteristic
358C2—22no—
359C2—81no—
360C2—5662no—
361C2—11321no—
362C2C2×#2258359211yescharacteristic
363C2#135×D28311yescharacteristic
364C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
prime radical#31826972C2
hypercenter#416D283
hypocenterC283#3091
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D283C2semidirect
3. #31826805C2semidirect
4. #31826804C2semidirect
5. #31826799C2semidirect
6. #31826794C2semidirect
7. #31826788C2semidirect
8. #31826787C2semidirect
9. #31826782C2semidirect
10. #31826777C2semidirect
11. #31826503C2semidirect
12. #31826501C2semidirect
13. #31826461C2semidirect
14. C2×(C2×D283)⋊C8C2semidirect
15. #416×C283C2semidirect
36. #22583544C22semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. #22583542C22semidirect
41. #22583542C22semidirect
42. #22583541C22semidirect
43. #22583541C22semidirect
44. #22583534C22semidirect
45. #22583534C22semidirect
46. #22583531C22semidirect
47. #22583531C22semidirect
55. #103×C283C22semidirect
56. #103×C283C22semidirect
57. #102×C283C22semidirect
58. #102×C283C22semidirect
182. C283#3091semidirect
197. #416D283semidirect
232. #103C2×D283semidirect
233. #103C2×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
#318269722
#117×D2832
#318268052
#318268042
#318267992
#318267942
#318267882
#318267872
#318267822
#318267772
#318265032
#318265012
#318264612
C2×(C2×D283)⋊C82
#416×C2832
#3091283