Finite Group Databasebeta

← #49133871

Subgroups — #49133871

Order 36224.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827186C211yesmaximal, characteristic
2#31827173C211yesmaximal, characteristic
3#31826862C211yesmaximal, characteristic, complemented
4#31826805C211yesmaximal, characteristic, complemented
5#31826803C211yesmaximal, characteristic, complemented
6#31826794C211yesmaximal, characteristic, complemented
7#31826793C211yesmaximal, characteristic, complemented
8#31826758C211yesmaximal, characteristic, complemented
9#31826748C211yesmaximal, characteristic, complemented
10#31826720C211yesmaximal, characteristic, complemented
11Q16×Dic283C211yesmaximal, characteristic, complemented
12#31826541C211yesmaximal, characteristic
13#31826507C211yesmaximal, characteristic, complemented
14#31826504C211yesmaximal, characteristic, complemented
15#470×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17#22583609C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583605—21no—
20#22583603—21no—
21#22583600—21no—
22#22583596—21no—
23#22583590—21no—
24#22583587—21no—
25#22583586C2211yescharacteristic
26#22583586C2211yescharacteristic
27Q8×Dic283C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29#22583575—21no—
30C4×C22⋊D283C2211yescharacteristic
31(C22⋊D283)⋊C4—21no—
32#22583569C2211yescharacteristic
33#22583568C2211yescharacteristic
34C2×C4⋊Dic283C2211yescharacteristic
35C4⋊C4×D283C2211yescharacteristic
36#22583544C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583541C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583534C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×C22⋊D283D411yescharacteristic
62C22×Dic283—21no—
63C2×C4×D283—21no—
64C2×C4×D283C2311yescharacteristic
65#17985375—22no—
66C2×C283⋊C8C2311yescharacteristic
67C2×C283⋊C8C2311yescharacteristic
68C4⋊Dic283—21no—
69C4⋊Dic283—21no—
70C4⋊Dic283—21no—
71C4⋊Dic283C2311yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4D411yescharacteristic
81C22⋊Dic283—21no—
82C22⋊Dic283D411yescharacteristic
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4D411yescharacteristic
87C4×Dic283—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C2×Q8×C283C2311yescharacteristic
93C2×Q8×C283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95Q16×C283—22no—
96M16×C283—22no—
97C2×C8×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C4⋊C4×C283—21no—
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22×D283C2×D411yescharacteristic
106Dic566—42no—
107Dic566—81no—
108C22⋊D283—22no—
109C2×Dic283—21no—
110C2×Dic283—21no—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—81no—
114C2×Dic283C2×D411yescharacteristic
115C2×Dic283C2×D411yescharacteristic
116C2×Dic283C2×D411yescharacteristic
117C4×D283—21no—
118C4×D283—21no—
119C4×D283—81no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C23×C283C2×D411yescharacteristic
123Q8×C283—21no—
124Q8×C283—21no—
125Q8×C283—21no—
126Q8×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2411yescharacteristic
135C8×C283—21no—
136C8×C283#4112yes—
137C22×C283—21no—
138C22×C283—21no—
139C22×C283—21no—
140C22×C283C22×D411yescharacteristic
141C2×D283—21no—
142C2×D283—21no—
143C2×D283—21no—
144C4×C283—21no—
145C4×C283—41no—
146C4×C283—41no—
147C4×C283—41no—
148C4×C283—41no—
149C4×C283C2×#4111yescharacteristic
150C4×C2832−1+411yescharacteristic
151Dic283—21no—
152Dic283—21no—
153Dic283—41no—
154Dic283—41no—
155Dic283—41no—
156Dic283—41no—
157Dic283#13712yes—
158C2×C283—41no—
159C2×C283#54711yescharacteristic
160C2×C283C2×#13711yescharacteristic
161C2×C283#57711yescharacteristic
162D283—41no—
163C283#335611yescharacteristic, complemented, Sylow
164#3356—2831nomaximal, Sylow
165#556—2831no—
166#554—2831no—
167#498—2831no—
168#485—2831no—
169#485—2831no—
170#483—2831no—
171#483—2831no—
172#477—2831no—
173#475—2831no—
174#470—2831no—
175#470D28311yescharacteristic, complemented
176C4×Q16—2831no—
177#436—2831no—
178#428—2831no—
179#428—2831no—
180C2×Q16C2×D28311yescharacteristic
181C2×M16—2831no—
182C2×M16C2×D28311yescharacteristic
183C4⋊Q8—2831no—
184C4⋊Q8—2831no—
185#126—5661no—
186#126—5661no—
187#125—5661no—
188#124—5661no—
189C22⋊Q8—2831no—
190C22⋊Q8—2831no—
191C22⋊Q8—5661no—
192C22⋊Q8—5661no—
193C22⋊Q8C2×D28311yescharacteristic
194C22⋊Q8C2×D28311yescharacteristic
195C4×Q8—2831no—
196C4×Q8—2831no—
197C4×Q8—5661no—
198C4×D4—2831no—
199C4×D4—5661no—
200#117—2831no—
201#117—2831no—
202C2×C4⋊C4—2831no—
203C2×C4⋊C4—2831no—
204#107—2831no—
205#107—2831no—
206#107—2831no—
207#106—2831no—
208#106—2831no—
209#106—2831no—
210#106—2831no—
211#106—2831no—
212#106C2×D28311yescharacteristic
213C4⋊C8—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103C2×D28311yescharacteristic
219#103C2×D28311yescharacteristic
220C22⋊C8—2831no—
221C22⋊C8—2831no—
222C4×C8—2831no—
223C2×Q8—5661no—
224C2×Q8—5661no—
225C2×Q8C22×D28311yescharacteristic
226C2×Q8C22×D28311yescharacteristic
227C2×D4—2831no—
228C22×C4—2831no—
229C22×C4—5661no—
230C22×C4—5661no—
231C22×C4C22×D28311yescharacteristic
232Q16—22no—
233M16—22no—
234M16—5662no—
235C2×C8—2831no—
236C2×C8—2831no—
237C2×C8C22×D28311yescharacteristic
238C2×C8C22×D28311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—2831no—
242C4⋊C4—2831no—
243C4⋊C4—2831no—
244C4⋊C4—2831no—
245C4⋊C4—2831no—
246C4⋊C4—5661no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4C22×D28311yescharacteristic
255C4⋊C4C22×D28311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—2831no—
259C22⋊C4—2831no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C42—2831no—
265C42—5661no—
266C42—5661no—
267C42—5661no—
268C42—5661no—
269C23—2831no—
270C23D4×D28311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—11322no—
276Q8—22641no—
277D4—5662no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—2831no—
285C2×C4—2831no—
286C2×C4—2831no—
287C2×C4—5661no—
288C2×C4—5661no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—22641no—
294C2×C4—22641no—
295C2×C4D4×D28311yescharacteristic
296C2×C4C23×D28311yescharacteristic
297C8—21no—
298C8—5661no—
299C8—5661no—
300C8#1798539112yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—5661no—
305C22—5661no—
306C22—5661no—
307C22C2×D4×D28311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—2832no—
314C4—5661no—
315C4—5661no—
316C4—11321no—
317C4—11321no—
318C4—11321no—
319C4—11321no—
320C4C2×#1798539111yescharacteristic
321C4#2258365711yescharacteristic
322C2—41no—
323C2—11321no—
324C2#3182711511yescharacteristic
325C2#137×D28311yescharacteristic
326C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#470×C283C2
socleC22×C283C22×D4
prime radicalC2×C22⋊D283D4
hypercenter#470D283
hypocenterC283#3356
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #31826862C2semidirect
4. #31826805C2semidirect
5. #31826803C2semidirect
6. #31826794C2semidirect
7. #31826793C2semidirect
8. #31826758C2semidirect
9. #31826748C2semidirect
10. #31826720C2semidirect
11. Q16×Dic283C2semidirect
13. #31826507C2semidirect
14. #31826504C2semidirect
15. #470×C283C2semidirect
163. C283#3356semidirect
175. #470D283semidirect

Maximal subgroups

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

subgroupindex
#318271862
#318271732
#318268622
#318268052
#318268032
#318267942
#318267932
#318267582
#318267482
#318267202
Q16×Dic2832
#318265412
#318265072
#318265042
#470×C2832
#3356283