Finite Group Databasebeta

← #49133072

Subgroups — #49133072

Order 36224.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827116C211yesmaximal, characteristic, complemented
2#31827099C211yesmaximal, characteristic, complemented
3#31826810C211yesmaximal, characteristic, complemented
4#31826780C211yesmaximal, characteristic, complemented
5#31826744C211yesmaximal, characteristic, complemented
6#31826702C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic, complemented
8#31826659C211yesmaximal, characteristic, complemented
9#31826601C211yesmaximal, characteristic, complemented
10#31826600C211yesmaximal, characteristic, complemented
11#31826547C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13C2×#22583530C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C22×D1132C2211yescharacteristic
18C2×D4×D283—21no—
19C2×D4×D283C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21C2×D2264C2211yescharacteristic, complemented
22C2×#17985377C2211yescharacteristic, complemented
23C22×C283⋊C8C2211yescharacteristic, complemented
24C2×C8×D283C2211yescharacteristic, complemented
25#22583609C2211yescharacteristic, complemented
26#22583606C2211yescharacteristic
27#22583595—21no—
28#22583593—21no—
29#22583588—21no—
30#22583585C2211yescharacteristic
31#22583585C2211yescharacteristic, complemented
32#22583584C2211yescharacteristic, complemented
33#22583583—21no—
34#22583580—21no—
35#22583578—21no—
36#22583572C2211yescharacteristic
37#22583572C2211yescharacteristic, complemented
38C4×C22⋊D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic, complemented
40#22583543C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583532C2211yescharacteristic
43#22583532C2211yescharacteristic, complemented
44#22583531C2211yescharacteristic, complemented
45#22583530C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic, complemented
49#22583530C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic, complemented
54#107×C283C2211yescharacteristic, complemented
55#107×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61#17985392—44no—
62C2×Dic566—21no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—41no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C2×C22⋊D283D411yescharacteristic
76D4×D283—22no—
77D4×D283—41no—
78D4×D283—44no—
79C2×C4×D283—21no—
80C2×C4×D283—21no—
81C2×C4×D283—21no—
82C2×C4×D283C2311yescharacteristic
83D2264—22no—
84D2264—41no—
85#17985377—41no—
86C2×C283⋊C8—41no—
87C2×C283⋊C8C2311yescharacteristic
88C2×C283⋊C8C2311yescharacteristic
89C8×D283—41no—
90C4⋊Dic283C2311yescharacteristic
91Dic283⋊C4—21no—
92Dic283⋊C4—21no—
93Dic283⋊C4D411yescharacteristic
94C22⋊Dic283D411yescharacteristic
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4D411yescharacteristic
101C4×Dic283C2311yescharacteristic
102C2×D4×C283—21no—
103C2×D4×C283C2311yescharacteristic
104C22×C4×C283—21no—
105C22×C4×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C4⋊C4×C283C2311yescharacteristic
112C22⋊C4×C283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—21no—
116C22×D283—42no—
117C22×D283—42no—
118C22×D283—42no—
119C22×D283—42no—
120C22×D283—81no—
121C22×D283—81no—
122C22×D283C2×D411yescharacteristic
123Dic566—42no—
124D1132—21no—
125D1132—21no—
126D1132—21no—
127D1132—21no—
128D1132—21no—
129D1132—42no—
130D1132—42no—
131D1132—42no—
132D1132#4112yescomplemented
133C22⋊D283—42no—
134C22⋊D283—42no—
135C22⋊D283—42no—
136C22⋊D283—81no—
137C22⋊D283D814yescomplemented
138C2×Dic283—21no—
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C2×Dic283C2×D411yescharacteristic
142C4×D283—21no—
143C4×D283—21no—
144C4×D283—42no—
145C4×D283—42no—
146C4×D283—42no—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C23×C283—21no—
150C23×C283C2×D411yescharacteristic
151D4×C283—21no—
152D4×C283—21no—
153D4×C283—42no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—42no—
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283C2411yescharacteristic
162C8×C283—21no—
163C8×C283—21no—
164C22×C283—21no—
165C22×C283—21no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283—41no—
169C22×C283C2×D812yes—
170C22×C283C22×D411yescharacteristic
171C2×D283—21no—
172C2×D283—21no—
173C2×D283—22no—
174C2×D283—41no—
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—41no—
178C2×D283—41no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C2×D283—84no—
183C2×D283—84no—
184C2×D283C2×D812yes—
185C4×C283—21no—
186C4×C283—41no—
187C4×C283—41no—
188C4×C283—41no—
189C4×C283C2×#4111yescharacteristic
190C4×C283H(5,𝔽2)11yescharacteristic
191Dic283—21no—
192Dic283—21no—
193Dic283—41no—
194Dic283C2×D812yes—
195C2×C283—22no—
196C2×C283—81no—
197C2×C283#54611yescharacteristic
198C2×C283C22×D811yescharacteristic
199C2×C283#57711yescharacteristic
200D283—22no—
201D283—42no—
202D283—81no—
203D283—81no—
204C283#329411yescharacteristic, complemented, Sylow
205#3294—2831nomaximal, Sylow
206#547—2831no—
207D42—2831no—
208#486—2831no—
209#480—2831no—
210#480D28311yescharacteristic, complemented
211#474—2831no—
212#466—2831no—
213#466—2831no—
214#459—2831no—
215#447—2831no—
216#447—2831no—
217C4×D8—2831no—
218C8×D4—2831no—
219C2×#102—2831no—
220C2×#102—2831no—
221C2×#41—5661no—
222C22×D4—2831no—
223C22×D4—2831no—
224C22×D4—5661no—
225C2×D8—2831no—
226C2×D8—2831no—
227C2×D8—2831no—
228C22×C8—2831no—
229C22×C8—2831no—
230C4⋊Q8—2831no—
231#127—2831no—
232#123—5661no—
233#123—5661no—
234C22⋊Q8—5661no—
235#121—2831no—
236#121—2831no—
237#121—2831no—
238#121—5661no—
239#121C2×D28311yescharacteristic
240#120—5661no—
241#120—5661no—
242C4×D4—2831no—
243C4×D4—2831no—
244C4×D4—2831no—
245C2×C4⋊C4—2831no—
246C2×C4⋊C4C2×D28311yescharacteristic, complemented
247#107—2831no—
248#107C2×D28311yescharacteristic, complemented
249#107C2×D28311yescharacteristic, complemented
250C4⋊C8—2831no—
251#102—2831no—
252#102—2831no—
253#102—2831no—
254#102—2831no—
255#102—2831no—
256#102—2831no—
257#102—2831no—
258#102—2831no—
259#102C2×D28311yescharacteristic, complemented
260#102C2×D28311yescharacteristic, complemented
261C22⋊C8—2831no—
262C22⋊C8C2×D28311yescharacteristic, complemented
263C4×C8—2831no—
264C24—5661no—
265C24—5661no—
266#41—11324no—
267C2×Q8—5661no—
268C2×D4—21no—
269C2×D4—2831no—
270C2×D4—2831no—
271C2×D4—2831no—
272C2×D4—2831no—
273C2×D4—5662no—
274C2×D4—5661no—
275C2×D4—5661no—
276C2×D4—5661no—
277C2×D4—5661no—
278C2×D4—5661no—
279C2×D4—5662no—
280C2×D4—5661no—
281C2×D4—5661no—
282C2×D4—11321no—
283C2×D4—11321no—
284C2×D4—11324no—
285C2×D4C22×D28311yescharacteristic
286C22×C4—21no—
287C22×C4—2831no—
288C22×C4—5661no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4C22×D28311yescharacteristic
292D8—5662no—
293D8—11321no—
294D8—11321no—
295C2×C8—2831no—
296C2×C8—2831no—
297C2×C8—11321no—
298C2×C8—11321no—
299C2×C8C22×D28311yescharacteristic
300C2×C8C22×D28311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2831no—
303C4⋊C4—2831no—
304C4⋊C4—5661no—
305C4⋊C4—5661no—
306C4⋊C4C22×D28311yescharacteristic
307C4⋊C4C22×D28311yescharacteristic
308C4⋊C4C22×D28311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—2831no—
311C22⋊C4—2831no—
312C22⋊C4—5661no—
313C22⋊C4—5661no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C42—2831no—
318C23—21no—
319C23—2831no—
320C23—5661no—
321C23—5661no—
322C23—5661no—
323C23—11322no—
324C23—11322no—
325C23—11322no—
326C23—11322no—
327C23—22641no—
328C23—22641no—
329C23D4×D28311yescharacteristic
330Q8—11322no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—2834no—
335D4—2832no—
336D4—5661no—
337D4—5661no—
338D4—5661no—
339D4—5661no—
340D4—5661no—
341D4—11322no—
342D4—11322no—
343D4—11322no—
344D4—11322no—
345D4—11322no—
346D4—11322no—
347D4—22641no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—2831no—
355C2×C4—2831no—
356C2×C4—2831no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—11322no—
361C2×C4—11322no—
362C2×C4—11322no—
363C2×C4D4×D28311yescharacteristic
364C2×C4C23×D28311yescharacteristic
365C8—21no—
366C8—21no—
367C8—5661no—
368C8—5661no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—2832no—
375C22—5661no—
376C22—5661no—
377C22—5662no—
378C22—11321no—
379C22—11321no—
380C22—11321no—
381C22—11321no—
382C22—11321no—
383C22—11321no—
384C22—11321no—
385C22—11321no—
386C22—22644no—
387C22—22644no—
388C22D8×D28312yes—
389C22C2×D4×D28311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—2832no—
395C4—5661no—
396C4—5661no—
397C4—11321no—
398C4#41×D28311yescharacteristic
399C4#2258365611yescharacteristic
400C2—22no—
401C2—81no—
402C2—5662no—
403C2—11322no—
404C2—22641no—
405C2—22641no—
406C2#3182710711yescharacteristic
407C2C2×D8×D28311yescharacteristic
408C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
hypercenter#480D283
hypocenterC283#3294
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #31827116C2semidirect
2. #31827099C2semidirect
3. #31826810C2semidirect
4. #31826780C2semidirect
5. #31826744C2semidirect
6. #31826702C2semidirect
7. #31826699C2semidirect
8. #31826659C2semidirect
9. #31826601C2semidirect
10. #31826600C2semidirect
11. #31826547C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. C2×#22583530C2semidirect
14. #102×D283C2semidirect
15. #480×C283C2semidirect
21. C2×D2264C22semidirect
22. C2×#17985377C22semidirect
23. C22×C283⋊C8C22semidirect
24. C2×C8×D283C22semidirect
25. #22583609C22semidirect
31. #22583585C22semidirect
32. #22583584C22semidirect
37. #22583572C22semidirect
39. C4⋊C4×D283C22semidirect
40. #22583543C22semidirect
41. Dic283⋊C8C22semidirect
43. #22583532C22semidirect
44. #22583531C22semidirect
47. #22583530C22semidirect
48. #22583530C22semidirect
49. #22583530C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C8×Dic283C22semidirect
53. C2×C4⋊C4×C283C22semidirect
54. #107×C283C22semidirect
55. #107×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
58. C22⋊C8×C283C22semidirect
132. D1132#41semidirect
137. C22⋊D283D8semidirect
204. C283#3294semidirect
210. #480D283semidirect
246. C2×C4⋊C4C2×D283semidirect
248. #107C2×D283semidirect
249. #107C2×D283semidirect
259. #102C2×D283semidirect
260. #102C2×D283semidirect
262. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271162
#318270992
#318268102
#318267802
#318267442
#318267022
#318266992
#318266592
#318266012
#318266002
#318265472
(C22⋊D283)⋊C82
C2×#225835302
#102×D2832
#480×C2832
#3294283