Finite Group Databasebeta

← #49132729

Subgroups — #49132729

Order 36224.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827087C211yesmaximal, characteristic, complemented
2#31827084C211yesmaximal, characteristic, complemented
3#31826756C211yesmaximal, characteristic, complemented
4#31826753C211yesmaximal, characteristic, complemented
5#31826750C211yesmaximal, characteristic, complemented
6#31826748C211yesmaximal, characteristic, complemented
7#31826720C211yesmaximal, characteristic, complemented
8#31826717C211yesmaximal, characteristic
9#31826697C211yesmaximal, characteristic, complemented
10#31826691C211yesmaximal, characteristic, complemented
11#31826689C211yesmaximal, characteristic, complemented
12#31826682C211yesmaximal, characteristic, complemented
13#31826677C211yesmaximal, characteristic, complemented
14#31826490C211yesmaximal, characteristic, complemented
15#464×C283C211yesmaximal, characteristic, complemented
16C2×#17985379C2211yescharacteristic
17C2×#17985377C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583610C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583604—21no—
23#22583603—21no—
24#22583599C2211yescharacteristic
25#22583598—21no—
26#22583596—21no—
27#22583595—21no—
28#22583594—21no—
29#22583588—21no—
30#22583587—21no—
31#22583586C2211yescharacteristic
32#22583586C2211yescharacteristic
33#22583585C2211yescharacteristic
34#22583581C2211yescharacteristic
35Q8×Dic283C2211yescharacteristic
36C4×D1132C2211yescharacteristic
37D4×Dic283C2211yescharacteristic
38#22583567C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583534C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583531C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54#124×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985379—41no—
68#17985377—41no—
69#17985375—41no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C8×D283—41no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98Q16×C283—41no—
99SD16×C283—41no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—81no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114D1132—81no—
115C22⋊D283—81no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—81no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—81no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283—21no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283C22×D411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283H(5,𝔽2)11yescharacteristic
159C4×C2832−1+411yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—81no—
167C2×C283#53711yescharacteristic
168C2×C283#57711yescharacteristic
169C2×C283#57711yescharacteristic
170D283—41no—
171D283—81no—
172C283#326311yescharacteristic, complemented, Sylow
173#3263—2831nomaximal, Sylow
174#542—2831no—
175#542—2831no—
176#476—2831no—
177#476—2831no—
178#475—2831no—
179#475—2831no—
180#470—2831no—
181#469—2831no—
182#465—2831no—
183#465—2831no—
184#464—2831no—
185#464D28311yescharacteristic, complemented
186#463—2831no—
187#463—2831no—
188#424—2831no—
189C2×Q16C2×D28311yescharacteristic
190C2×SD16—2831no—
191C2×SD16C2×D28311yescharacteristic
192C2×D8—2831no—
193C2×M16—2831no—
194C22×C8—2831no—
195C4⋊Q8—2831no—
196C4⋊Q8—2831no—
197#126—5661no—
198#126—5661no—
199#124—2831no—
200#124—5661no—
201#124—5661no—
202#124C2×D28311yescharacteristic
203#123—5661no—
204#123—5661no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209#121—2831no—
210#121—2831no—
211C4×Q8—2831no—
212C4×Q8C2×D28311yescharacteristic
213C4×D4—2831no—
214C4×D4—2831no—
215#117—2831no—
216#106—2831no—
217#106—2831no—
218#106—2831no—
219#106—2831no—
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223C4⋊C8C2×D28311yescharacteristic
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103C2×D28311yescharacteristic
228#102—2831no—
229#102—2831no—
230#102—2831no—
231#102C2×D28311yescharacteristic
232C2×Q8—5661no—
233C2×Q8—5661no—
234C2×Q8C22×D28311yescharacteristic
235C2×Q8C22×D28311yescharacteristic
236C2×D4—2831no—
237C2×D4—5661no—
238C2×D4—5661no—
239C2×D4C22×D28311yescharacteristic
240C22×C4—2831no—
241C22×C4—5661no—
242C22×C4—5661no—
243Q16—41no—
244SD16—41no—
245SD16—11321no—
246D8—11321no—
247M16—11321no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8—11321no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4C22×D28311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2831no—
268C22⋊C4—2831no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C42—21no—
278C42—2831no—
279C42—5661no—
280C42C22×D28311yescharacteristic
281C23—21no—
282C23—2831no—
283C23—5661no—
284Q8—21no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—22641no—
289Q8—22641no—
290D4—21no—
291D4—21no—
292D4—5661no—
293D4—5661no—
294D4—22641no—
295D4—22641no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—22641no—
308C2×C4—22641no—
309C2×C4D4×D28311yescharacteristic
310C2×C4D4×D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—21no—
313C8—21no—
314C8—5661no—
315C8—5661no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—5661no—
320C22—5661no—
321C22—5661no—
322C22—11321no—
323C22—11321no—
324C22—11321no—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4#2258365511yescharacteristic
338C4#2258365711yescharacteristic
339C2—81no—
340C2—11321no—
341C2—22641no—
342C2#3182704411yescharacteristic
343C2#3182727211yescharacteristic
344C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#464×C283C2
socleC22×C283C22×D4
prime radical#31826717C2
hypercenter#464D283
hypocenterC283#3263
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #31827087C2semidirect
2. #31827084C2semidirect
3. #31826756C2semidirect
4. #31826753C2semidirect
5. #31826750C2semidirect
6. #31826748C2semidirect
7. #31826720C2semidirect
9. #31826697C2semidirect
10. #31826691C2semidirect
11. #31826689C2semidirect
12. #31826682C2semidirect
13. #31826677C2semidirect
14. #31826490C2semidirect
15. #464×C283C2semidirect
172. C283#3263semidirect
185. #464D283semidirect

Maximal subgroups

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

subgroupindex
#318270872
#318270842
#318267562
#318267532
#318267502
#318267482
#318267202
#318267172
#318266972
#318266912
#318266892
#318266822
#318266772
#318264902
#464×C2832
#3263283