Finite Group Databasebeta

← #49133069

Subgroups — #49133069

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#31827115C211yesmaximal, characteristic, complemented
2#31827099C211yesmaximal, characteristic, complemented
3#31826810C211yesmaximal, characteristic, complemented
4#31826780C211yesmaximal, characteristic, complemented
5#31826776C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826700C211yesmaximal, characteristic, complemented
8#31826658C211yesmaximal, characteristic, complemented
9#31826598C211yesmaximal, characteristic, complemented
10#31826597C211yesmaximal, characteristic, complemented
11#31826545C211yesmaximal, characteristic, complemented
12C8×C22⋊D283C211yesmaximal, characteristic, complemented
13C2×#22583532C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#466×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C22×D1132C2211yescharacteristic
18C2×D4×D283—21no—
19C2×D4×D283C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C2×#17985377C2211yescharacteristic, complemented
22C2×C8×D283C2211yescharacteristic, complemented
23#22583609C2211yescharacteristic, complemented
24#22583606C2211yescharacteristic
25#22583592—21no—
26#22583591—21no—
27#22583587—21no—
28#22583585C2211yescharacteristic
29#22583583—21no—
30#22583581C2211yescharacteristic, complemented
31#22583580—21no—
32#22583578—21no—
33D4×Dic283C2211yescharacteristic, complemented
34#22583572C2211yescharacteristic
35C4×C22⋊D283C2211yescharacteristic
36C2×C4⋊Dic283C2211yescharacteristic, complemented
37C4⋊C4×D283C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40Dic283⋊C8C2211yescharacteristic, complemented
41#22583532C2211yescharacteristic
42#22583532C2211yescharacteristic
43#22583532C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic, complemented
46#22583531C2211yescharacteristic, complemented
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C2×D8×C283C2211yescharacteristic, complemented
53C22×C8×C283C2211yescharacteristic, complemented
54#121×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic, complemented
56#107×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61#17985391—44no—
62C2×Dic566—21no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—41no—
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283D411yescharacteristic
74D4×D283—22no—
75D4×D283—41no—
76D4×D283—44no—
77C22×Dic283—21no—
78C22×Dic283—21no—
79C2×C4×D283—21no—
80C2×C4×D283—21no—
81C2×C4×D283C2311yescharacteristic
82#17985377—22no—
83#17985377—41no—
84C2×C283⋊C8C2311yescharacteristic
85C2×C283⋊C8C2311yescharacteristic
86C8×D283—41no—
87C4⋊Dic283—21no—
88C4⋊Dic283C2311yescharacteristic
89C4⋊Dic283C2311yescharacteristic
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92Dic283⋊C4D411yescharacteristic
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95C22⋊Dic283D411yescharacteristic
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283—21no—
102C2×D4×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105D8×C283—41no—
106C2×C8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
112C22⋊C4×C283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—42no—
118C22×D283—42no—
119C22×D283—81no—
120C22×D283—81no—
121C22×D283C2×D411yescharacteristic
122Dic566—42no—
123D1132—21no—
124D1132—21no—
125D1132—21no—
126D1132—42no—
127D1132—42no—
128D1132#4112yescomplemented
129C22⋊D283—42no—
130C22⋊D283—42no—
131C22⋊D283—42no—
132C22⋊D283—81no—
133C22⋊D283D814yescomplemented
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—42no—
137C2×Dic283—42no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—42no—
144C4×D283—42no—
145C283⋊C8—21no—
146C283⋊C8—21no—
147C23×C283—21no—
148C23×C283—21no—
149C23×C283C2×D411yescharacteristic
150D4×C283—21no—
151D4×C283—21no—
152D4×C283—21no—
153D4×C283—21no—
154D4×C283—42no—
155D4×C283—42no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
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×C283—41no—
170C22×C283—41no—
171C22×C283—41no—
172C22×C283C2×D812yes—
173C22×C283C22×D411yescharacteristic
174C2×D283—21no—
175C2×D283—21no—
176C2×D283—22no—
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×C283C2×#4111yescharacteristic
189C4×C283H(5,𝔽2)11yescharacteristic
190Dic283—21no—
191Dic283—21no—
192Dic283—41no—
193Dic283—41no—
194Dic283C2×D812yes—
195C2×C283—22no—
196C2×C283—81no—
197C2×C283—81no—
198C2×C283#54611yescharacteristic
199C2×C283C22×D811yescharacteristic
200C2×C283#57711yescharacteristic
201D283—22no—
202D283—42no—
203D283—81no—
204C283#329411yescharacteristic, complemented, Sylow
205#3294—2831nomaximal, Sylow
206#547—2831no—
207D42—2831no—
208#486—2831no—
209#480—2831no—
210#480—2831no—
211#474—2831no—
212#466—2831no—
213#466D28311yescharacteristic, complemented
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×D8C2×D28311yescharacteristic, complemented
228C22×C8—2831no—
229C22×C8C2×D28311yescharacteristic, complemented
230C4⋊Q8—2831no—
231#127—2831no—
232#123—5661no—
233#123—5661no—
234C22⋊Q8—5661no—
235#121—2831no—
236#121—2831no—
237#121—5661no—
238#121C2×D28311yescharacteristic
239#121C2×D28311yescharacteristic, complemented
240#120—5661no—
241#120—5661no—
242C4×D4—2831no—
243C4×D4—2831no—
244C4×D4—2831no—
245C2×C4⋊C4—2831no—
246C2×C4⋊C4—2831no—
247#107—2831no—
248#107—2831no—
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⋊C8—2831no—
263C4×C8—2831no—
264C24—5661no—
265C24—5661no—
266#41—11324no—
267C2×Q8—5661no—
268C2×D4—21no—
269C2×D4—21no—
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—5662no—
279C2×D4—5661no—
280C2×D4—5661no—
281C2×D4—11321no—
282C2×D4—11321no—
283C2×D4—11324no—
284C2×D4C22×D28311yescharacteristic
285C2×D4C22×D28311yescharacteristic
286C22×C4—2831no—
287C22×C4—5661no—
288C22×C4—5661no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4C22×D28311yescharacteristic
292D8—41no—
293D8—5662no—
294D8—11321no—
295C2×C8—41no—
296C2×C8—2831no—
297C2×C8—2831no—
298C2×C8—11321no—
299C2×C8C22×D28311yescharacteristic
300C2×C8C22×D28311yescharacteristic
301C4⋊C4—2831no—
302C4⋊C4—2831no—
303C4⋊C4—2831no—
304C4⋊C4—5661no—
305C4⋊C4—5661no—
306C4⋊C4—5661no—
307C4⋊C4C22×D28311yescharacteristic
308C4⋊C4C22×D28311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—2831no—
312C22⋊C4—2831no—
313C22⋊C4—5661no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C42—2831no—
318C23—21no—
319C23—21no—
320C23—2831no—
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—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—2834no—
338D4—2832no—
339D4—5661no—
340D4—5661no—
341D4—5661no—
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—2831no—
353C2×C4—2831no—
354C2×C4—2831no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—11322no—
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—41no—
375C22—41no—
376C22—41no—
377C22—2832no—
378C22—5661no—
379C22—5661no—
380C22—5662no—
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—2832no—
394C4—5661no—
395C4—5661no—
396C4—11321no—
397C4—11321no—
398C4#41×D28311yescharacteristic
399C4#2258365511yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—5662no—
404C2—11322no—
405C2—22641no—
406C2#3182710411yescharacteristic
407C2C2×D8×D28311yescharacteristic
408C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#466×C283C2
socleC22×C283C22×D4
hypercenter#466D283
hypocenterC283#3294
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31827115C2semidirect
2. #31827099C2semidirect
3. #31826810C2semidirect
4. #31826780C2semidirect
5. #31826776C2semidirect
6. #31826744C2semidirect
7. #31826700C2semidirect
8. #31826658C2semidirect
9. #31826598C2semidirect
10. #31826597C2semidirect
11. #31826545C2semidirect
12. C8×C22⋊D283C2semidirect
13. C2×#22583532C2semidirect
14. #102×D283C2semidirect
15. #466×C283C2semidirect
21. C2×#17985377C22semidirect
22. C2×C8×D283C22semidirect
23. #22583609C22semidirect
30. #22583581C22semidirect
33. D4×Dic283C22semidirect
36. C2×C4⋊Dic283C22semidirect
37. C4⋊C4×D283C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. Dic283⋊C8C22semidirect
43. #22583532C22semidirect
44. #22583532C22semidirect
45. #22583531C22semidirect
46. #22583531C22semidirect
48. #22583530C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C8×Dic283C22semidirect
52. C2×D8×C283C22semidirect
53. C22×C8×C283C22semidirect
55. #121×C283C22semidirect
56. #107×C283C22semidirect
57. #102×C283C22semidirect
58. #102×C283C22semidirect
128. D1132#41semidirect
133. C22⋊D283D8semidirect
204. C283#3294semidirect
213. #466D283semidirect
227. C2×D8C2×D283semidirect
229. C22×C8C2×D283semidirect
239. #121C2×D283semidirect
249. #107C2×D283semidirect
259. #102C2×D283semidirect
260. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271152
#318270992
#318268102
#318267802
#318267762
#318267442
#318267002
#318266582
#318265982
#318265972
#318265452
C8×C22⋊D2832
C2×#225835322
#102×D2832
#466×C2832
#3294283