Finite Group Databasebeta

← #49131080

Subgroups — #49131080

Order 36224.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D283C211yesmaximal, characteristic, complemented
2C4×#17985393C211yesmaximal, characteristic
3#31826774C211yesmaximal, characteristic, complemented
4#31826772C211yesmaximal, characteristic, complemented
5#31826770C211yesmaximal, characteristic, complemented
6#31826768C211yesmaximal, characteristic, complemented
7#31826766C211yesmaximal, characteristic, complemented
8#31826764C211yesmaximal, characteristic, complemented
9#31826762C211yesmaximal, characteristic, complemented
10#31826506C211yesmaximal, characteristic, complemented
11#31826504C211yesmaximal, characteristic, complemented
12#31826487C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic
14#31826465C211yesmaximal, characteristic
15#479×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19#22583602C2211yescharacteristic
20#22583601C2211yescharacteristic
21#22583601C2211yescharacteristic
22#22583600—21no—
23#22583600—21no—
24Q8×Dic283C2211yescharacteristic
25C4×D1132—21no—
26C4×D1132C2211yescharacteristic
27#22583572—21no—
28#22583572C2211yescharacteristic
29#22583568—21no—
30#22583568C2211yescharacteristic
31C4⋊C4×D283—21no—
32C4⋊C4×D283—21no—
33C4⋊C4×D283C2211yescharacteristic
34C4⋊C4×D283C2211yescharacteristic
35C42×D283—21no—
36C42×D283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583530C2211yescharacteristic
51#22583530C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#17985393—22no—
60#17985393Q814yes—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×C4×D283—21no—
64C2×C4×D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283D411yescharacteristic
69C2×C4×D283D411yescharacteristic
70C2×C4×D283C2311yescharacteristic
71#17985375—22no—
72#17985375—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283D411yescharacteristic
93C4×Dic283D411yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C42×C283—21no—
105C42×C283C2311yescharacteristic
106C22×D283—21no—
107C22×D283C2×D411yescharacteristic
108D1132—24no—
109D1132—21no—
110D1132C2×Q812yes—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283C2×D411yescharacteristic
115C2×Dic283C2×D411yescharacteristic
116C2×Dic283C2×D411yescharacteristic
117C4×D283—24no—
118C4×D283—41no—
119C4×D283—41no—
120C4×D283—42no—
121C4×D283—42no—
122C4×D283—42no—
123C4×D283—42no—
124C4×D283C2×Q812yes—
125C4×D283#4112yes—
126C283⋊C8—21no—
127C283⋊C8—21no—
128Q8×C283—21no—
129Q8×C283C2×Q812yes—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283C2×D411yescharacteristic
135C2×C4×C283C2×D411yescharacteristic
136C2×C4×C283C2411yescharacteristic
137C8×C283—21no—
138C8×C283—21no—
139C22×C283C22×D411yescharacteristic
140C2×D283—21no—
141C2×D283—21no—
142C2×D283—22no—
143C2×D283—41no—
144C2×D283—41no—
145C2×D283C22⋊Q812yes—
146C4×C283—22no—
147C4×C283—21no—
148C4×C283—21no—
149C4×C283—41no—
150C4×C283—41no—
151C4×C283—41no—
152C4×C283C22×Q811yescharacteristic
153C4×C283C2×#4111yescharacteristic
154Dic283—21no—
155Dic283—21no—
156Dic283—41no—
157Dic283—41no—
158Dic283—41no—
159Dic283C22⋊Q812yes—
160C2×C283C2×C22⋊Q811yescharacteristic
161C2×C283#57511yescharacteristic
162C2×C283#57511yescharacteristic
163D283—22no—
164D283—42no—
165C283#308011yescharacteristic, complemented, Sylow
166#3080—2831nomaximal, Sylow
167C2×#125—2831no—
168C4×#41—2831no—
169#479—2831no—
170#479—2831no—
171#479—2831no—
172#479D28311yescharacteristic, complemented
173#478—2831no—
174#478—2831no—
175#478—2831no—
176#478—2831no—
177#428—2831no—
178#428—2831no—
179#423—2831no—
180#417—2831no—
181#417—2831no—
182C2×#41—2831no—
183C2×M16—2831no—
184C2×M16—2831no—
185#125—2831no—
186#125—2831no—
187#125—2831no—
188#125—5661no—
189#125—5661no—
190#125C2×D28311yescharacteristic
191C4×Q8—2831no—
192C4×Q8C2×D28311yescharacteristic
193C4×D4—2831no—
194C4×D4—2831no—
195C4×D4—5661no—
196C4×D4—5661no—
197#117—2831no—
198#117—5661no—
199C2×C4⋊C4—2831no—
200C2×C4⋊C4—2831no—
201C2×C4⋊C4—5661no—
202C2×C4⋊C4—5661no—
203C2×C42—2831no—
204C2×C42—5661no—
205#107—2831no—
206#107—2831no—
207#107—2831no—
208#107C2×D28311yescharacteristic
209#106—2831no—
210#106—2831no—
211#106—2831no—
212#106C2×D28311yescharacteristic
213C4⋊C8—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216C4⋊C8C2×D28311yescharacteristic
217#103—2831no—
218#103—2831no—
219#103C2×D28311yescharacteristic
220#103C2×D28311yescharacteristic
221#102—2831no—
222#102—2831no—
223#102—2831no—
224#102—2831no—
225#41—2834no—
226#41—5662no—
227C2×Q8C22×D28311yescharacteristic
228C2×D4—2831no—
229C2×D4—5661no—
230C22×C4—2831no—
231C22×C4—2831no—
232C22×C4—2831no—
233C22×C4—5661no—
234C22×C4—5661no—
235C22×C4—5661no—
236C22×C4—5661no—
237C22×C4—5661no—
238M16—5662no—
239M16—5662no—
240C2×C8—2831no—
241C2×C8—2831no—
242C2×C8C22×D28311yescharacteristic
243C2×C8C22×D28311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—2831no—
248C4⋊C4—2831no—
249C4⋊C4—2831no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C4⋊C4C22×D28311yescharacteristic
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C42—21no—
266C42—2831no—
267C42—2831no—
268C42—2831no—
269C42—5661no—
270C42—5661no—
271C42C22×D28311yescharacteristic
272C23—2831no—
273C23—5661no—
274Q8—21no—
275Q8Q8×D28312yes—
276D4—2832no—
277D4—5664no—
278D4—5661no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—2831no—
284C2×C4—2832no—
285C2×C4—2832no—
286C2×C4—2831no—
287C2×C4—2831no—
288C2×C4—5664no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4—5661no—
292C2×C4—11321no—
293C2×C4—11321no—
294C2×C4—11322no—
295C2×C4—11322no—
296C2×C4—11322no—
297C2×C4—11322no—
298C2×C4D4×D28311yescharacteristic
299C2×C4D4×D28311yescharacteristic
300C2×C4C23×D28311yescharacteristic
301C8—21no—
302C8—21no—
303C8—5661no—
304C8—5661no—
305C22—2832no—
306C22—5661no—
307C22—5661no—
308C22—5662no—
309C22—11321no—
310C22—11321no—
311C22C2×D4×D28311yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2832no—
319C4—5661no—
320C4—5661no—
321C4—11321no—
322C4—11321no—
323C4—11321no—
324C4C2×Q8×D28311yescharacteristic
325C4#41×D28311yescharacteristic
326C2—5662no—
327C2—11322no—
328C2C22⋊Q8×D28311yescharacteristic
329C2#3182726211yescharacteristic
330C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#479×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985393C22
hypercenter#479D283
hypocenterC283#3080
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #125×D283C2semidirect
3. #31826774C2semidirect
4. #31826772C2semidirect
5. #31826770C2semidirect
6. #31826768C2semidirect
7. #31826766C2semidirect
8. #31826764C2semidirect
9. #31826762C2semidirect
10. #31826506C2semidirect
11. #31826504C2semidirect
12. #31826487C2semidirect
15. #479×C283C2semidirect
165. C283#3080semidirect
172. #479D283semidirect

Maximal subgroups

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

subgroupindex
#125×D2832
C4×#179853932
#318267742
#318267722
#318267702
#318267682
#318267662
#318267642
#318267622
#318265062
#318265042
#318264872
#318264652
#479×C2832
#3080283