Finite Group Databasebeta

← #49133299

Subgroups — #49133299

Order 36224.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827185C211yesmaximal, characteristic, complemented
2#31827111C211yesmaximal, characteristic
3#31826825C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826790C211yesmaximal, characteristic, complemented
6#31826756C211yesmaximal, characteristic, complemented
7#31826723C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826688C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826618C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826471C211yesmaximal, characteristic, complemented
14#31826462C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic, complemented
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21#22583610C2211yescharacteristic, complemented
22#22583603—21no—
23#22583603—21no—
24#22583598C2211yescharacteristic
25#22583597—21no—
26#22583595—21no—
27#22583589C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583589C2211yescharacteristic, complemented
30#22583584C2211yescharacteristic
31#22583583—21no—
32#22583578—21no—
33C4×Dic566C2211yescharacteristic, complemented
34#22583575—21no—
35C4×D1132C2211yescharacteristic
36#22583569C2211yescharacteristic
37#22583569C2211yescharacteristic, complemented
38C22⋊C4×D283—21no—
39#22583544C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583542C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583535C2211yescharacteristic, complemented
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic, complemented
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic, complemented
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic, complemented
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—22no—
61#17985392—41no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132—22no—
66C2×D1132—21no—
67C2×D1132—41no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74Dic1132—41no—
75#17985381—22no—
76#17985381—41no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C2×D4×C283D411yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101M16×C283—41no—
102C2×C8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116Dic566—21no—
117Dic566—21no—
118Dic566—21no—
119Dic566—21no—
120Dic566—42no—
121D1132—21no—
122D1132—21no—
123D1132—21no—
124D1132—42no—
125D1132#4112yes—
126C22⋊D283—42no—
127C22⋊D283—81no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C4×D283—42no—
135C4×D283—81no—
136C23×C283C2×D411yescharacteristic
137C23×C283C2×D411yescharacteristic
138D4×C283—41no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283C22×D411yescharacteristic
159C2×D283—22no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—84no—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—21no—
169C4×C283—21no—
170C4×C283C2×#4111yescharacteristic
171C4×C283H(5,𝔽2)11yescharacteristic
172Dic283—41no—
173Dic283—41no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—41no—
179C2×C283—41no—
180C2×C283#54611yescharacteristic
181C2×C283#57511yescharacteristic
182C2×C283#57711yescharacteristic
183D283—42no—
184D283—81no—
185C283#331111yescharacteristic, complemented, Sylow
186#3311—2831nomaximal, Sylow
187#556—2831no—
188#546—2831no—
189#489—2831no—
190#485—2831no—
191#482—2831no—
192#476—2831no—
193#470—2831no—
194#465—2831no—
195#464—2831no—
196#452—2831no—
197#450—2831no—
198#440—2831no—
199#435D28311yescharacteristic, complemented
200#418—2831no—
201#416—2831no—
202C2×#41—2831no—
203C22×D4—2831no—
204C2×Q16—2831no—
205C2×SD16—2831no—
206C2×SD16—2831no—
207C2×M16C2×D28311yescharacteristic
208C22×C8C2×D28311yescharacteristic, complemented
209C4⋊Q8—2831no—
210#126—5661no—
211#126—5661no—
212#124—2831no—
213#124—5661no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—2831no—
218#121—2831no—
219#121—5661no—
220#120—5661no—
221C4×Q8—2831no—
222C4×Q8—5661no—
223C4×D4—2831no—
224C4×D4C2×D28311yescharacteristic
225#117—2831no—
226#117—2831no—
227C2×C22⋊C4—5661no—
228#107—2831no—
229#106—2831no—
230#106—2831no—
231C4⋊C8C2×D28311yescharacteristic, complemented
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242C22⋊C8C2×D28311yescharacteristic
243C22⋊C8C2×D28311yescharacteristic, complemented
244#97C2×D28311yescharacteristic, complemented
245C24—5661no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×Q8—5661no—
251C2×D4—2831no—
252C2×D4—2831no—
253C2×D4—5662no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—11321no—
258C2×D4D113211yescharacteristic
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4C22×D28311yescharacteristic
262C22×C4C22×D28311yescharacteristic
263Q16—11321no—
264SD16—5662no—
265SD16—11321no—
266M16—41no—
267C2×C8—41no—
268C2×C8C22×D28311yescharacteristic
269C2×C8C22×D28311yescharacteristic
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—2831no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4D113211yescharacteristic
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4D113211yescharacteristic
292C22⋊C4D113211yescharacteristic
293C42—5661no—
294C42—5661no—
295C42—5661no—
296C42C22×D28311yescharacteristic
297C23—5661no—
298C23—5661no—
299C23—11322no—
300C23—11322no—
301C23—22641no—
302C23C2×D113211yescharacteristic
303C23C2×D113211yescharacteristic
304Q8—5661no—
305Q8—5661no—
306Q8—5661no—
307Q8—5661no—
308Q8—11322no—
309D4—41no—
310D4—2832no—
311D4—5661no—
312D4—5661no—
313D4—5661no—
314D4—11322no—
315D4—11322no—
316D4—22641no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—11322no—
328C2×C4—22641no—
329C2×C4C2×D113211yescharacteristic
330C2×C4C2×D113211yescharacteristic
331C2×C4C2×D113211yescharacteristic
332C2×C4C2×D113211yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—5662no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—22644no—
351C22C22×D113211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—11321no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4—11321no—
361C4—11321no—
362C4#41×D28311yescharacteristic
363C4#2258365511yescharacteristic
364C2—41no—
365C2—41no—
366C2—11322no—
367C2—22641no—
368C2#3182711011yescharacteristic
369C2#3182726511yescharacteristic
370C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827111C2
hypercenter#435D283
hypocenterC283#3311
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31827185C2semidirect
3. #31826825C2semidirect
4. #31826807C2semidirect
5. #31826790C2semidirect
6. #31826756C2semidirect
7. #31826723C2semidirect
8. #31826694C2semidirect
9. #31826688C2semidirect
10. #31826629C2semidirect
11. #31826618C2semidirect
12. #31826567C2semidirect
13. #31826471C2semidirect
14. #31826462C2semidirect
15. #435×C283C2semidirect
18. C2×Dic1132C22semidirect
21. #22583610C22semidirect
29. #22583589C22semidirect
33. C4×Dic566C22semidirect
37. #22583569C22semidirect
39. #22583544C22semidirect
40. #22583542C22semidirect
41. #22583542C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
45. #22583535C22semidirect
53. C22×C8×C283C22semidirect
55. C4⋊C8×C283C22semidirect
57. C22⋊C8×C283C22semidirect
58. #97×C283C22semidirect
185. C283#3311semidirect
199. #435D283semidirect
208. C22×C8C2×D283semidirect
231. C4⋊C8C2×D283semidirect
243. C22⋊C8C2×D283semidirect
244. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271852
#318271112
#318268252
#318268072
#318267902
#318267562
#318267232
#318266942
#318266882
#318266292
#318266182
#318265672
#318264712
#318264622
#435×C2832
#3311283