Finite Group Databasebeta

← #49130117

Subgroups — #49130117

Order 36224.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D283C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic, complemented
3#31826937C211yesmaximal, characteristic
4#31826567C211yesmaximal, characteristic, complemented
5#31826566C211yesmaximal, characteristic, complemented
6#31826564C211yesmaximal, characteristic, complemented
7#31826556C211yesmaximal, characteristic, complemented
8C4×#17985379C211yesmaximal, characteristic, complemented
9C4×#17985380C211yesmaximal, characteristic, complemented
10#31826550C211yesmaximal, characteristic, complemented
11#31826502C211yesmaximal, characteristic, complemented
12#31826472C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic
14#31826422C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21SD16×D283C418yescomplemented
22C2×#17985375C2211yescharacteristic
23C2×C8×D283C2211yescharacteristic
24Q8×Dic283C2211yescharacteristic, complemented
25C4×Dic566—21no—
26C4×Dic566C2211yescharacteristic, complemented
27#22583575—21no—
28#22583575C2211yescharacteristic, complemented
29C4×D1132C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568—21no—
35#22583568C2211yescharacteristic
36#22583568C2211yescharacteristic
37#22583567—21no—
38#22583567C2211yescharacteristic
39C2×(C2×D283)⋊C4—21no—
40C22⋊C4×D283—21no—
41#22583544C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43#22583541C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583534C2211yescharacteristic, complemented
46#22583533C2211yescharacteristic, complemented
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C4×C283⋊C8C2211yescharacteristic, complemented
52C8×Dic283C2211yescharacteristic, complemented
53C2×SD16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic, complemented
55C4×D4×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic
59#97×C283C2211yescharacteristic, complemented
60C23×D283—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283C2×C414yescomplemented
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67D4×D283—22no—
68D4×D283C2×C414yes—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74#17985381C2×C414yescomplemented
75#17985380C2×C414yescomplemented
76#17985379C2×C414yescomplemented
77#17985375—22no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283C2×C414yescomplemented
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4D411yescharacteristic
87Dic283⋊C4D411yescharacteristic
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283—21no—
100C4×Dic283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104SD16×C283C2×C414yescomplemented
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C42×C283—21no—
112C42×C283C2311yescharacteristic
113C22×D283—21no—
114C22×D283—24no—
115C22×D283—81no—
116C22×D283—81no—
117C22×D283C2×D411yescharacteristic
118Dic566—21no—
119Dic566—24no—
120Dic566C22×C412yes—
121D1132—21no—
122D1132C22×C412yes—
123C22⋊D283—24no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—24no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283C22×C412yes—
135C4×D283#4112yes—
136C283⋊C8—21no—
137C283⋊C8C22×C412yes—
138C23×C283—21no—
139Q8×C283—21no—
140Q8×C283C22×C412yes—
141D4×C283—21no—
142D4×C283C22×C412yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283C22×C412yes—
152C22×C283—22no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—22no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—84no—
162C2×D283C4×D412yes—
163C4×C283—22no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283C23×C411yescharacteristic
169C4×C283C2×#4111yescharacteristic
170Dic283—22no—
171Dic283—21no—
172Dic283—21no—
173Dic283—41no—
174Dic283—41no—
175Dic283C4×D412yes—
176C2×C283—42no—
177C2×C283C2×C4×D411yescharacteristic
178C2×C283#57711yescharacteristic
179C2×C283#57711yescharacteristic
180D283—22no—
181D283—42no—
182C283#294911yescharacteristic, complemented, Sylow
183#2949—2831nomaximal, Sylow
184C22×SD16—2831no—
185#519—2831no—
186#518—2831no—
187#440—2831no—
188#440—2831no—
189#440—2831no—
190#440D28311yescharacteristic, complemented
191C4×SD16—2831no—
192C4×SD16—2831no—
193C4×SD16—2831no—
194C4×SD16—2831no—
195#427—2831no—
196#419—2831no—
197#418—2831no—
198#405—2831no—
199C22×Q8—2831no—
200C22×D4—2831no—
201C2×SD16—2831no—
202C2×SD16—2831no—
203C2×SD16—2838no—
204C2×SD16—2831no—
205C2×SD16C2×D28311yescharacteristic
206C2×M16—2831no—
207C22×C8—2831no—
208C4×Q8—2831no—
209C4×Q8—2831no—
210C4×Q8—2831no—
211C4×Q8—5661no—
212C4×Q8—5661no—
213C4×Q8C2×D28311yescharacteristic, complemented
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218C4×D4—5661no—
219C4×D4C2×D28311yescharacteristic
220#117—2831no—
221#117—2831no—
222#117—2831no—
223#117—5661no—
224#117—5661no—
225C2×C22⋊C4—5661no—
226C2×C22⋊C4—5661no—
227#107—2831no—
228#107C2×D28311yescharacteristic, complemented
229#106—2831no—
230#106—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103C2×D28311yescharacteristic, complemented
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102C2×D28311yescharacteristic
239#97—2831no—
240#97C2×D28311yescharacteristic, complemented
241C4×C8—2831no—
242C4×C8—2831no—
243C24—5661no—
244C2×Q8—2834no—
245C2×Q8—2831no—
246C2×Q8—5661no—
247C2×Q8—5662no—
248C2×Q8C22×D28311yescharacteristic
249C2×D4—2834no—
250C2×D4—2831no—
251C2×D4—5662no—
252C2×D4—5661no—
253C2×D4C22×D28311yescharacteristic
254C22×C4—21no—
255C22×C4—2831no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260SD16—2834no—
261SD16—2834no—
262SD16—2834no—
263SD16C4×D28314yescomplemented
264M16—5662no—
265C2×C8—2831no—
266C2×C8—2834no—
267C2×C8—2831no—
268C2×C8C22×D28311yescharacteristic
269C2×C8C22×D28311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—2831no—
272C4⋊C4—2831no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4C22×D28311yescharacteristic
279C4⋊C4C22×D28311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2831no—
282C22⋊C4—2831no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C42—21no—
289C42—2831no—
290C42—5661no—
291C42—5661no—
292C42—5661no—
293C42—5661no—
294C42—5661no—
295C42C22×D28311yescharacteristic
296C23—21no—
297C23—2831no—
298C23—5664no—
299C23—5661no—
300C23—22641no—
301C23—22641no—
302Q8—21no—
303Q8—2832no—
304Q8—5664no—
305Q8—5661no—
306Q8C2×C4×D28312yes—
307D4—21no—
308D4—2832no—
309D4—5664no—
310D4—5661no—
311D4C2×C4×D28312yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—2831no—
317C2×C4—2832no—
318C2×C4—2832no—
319C2×C4—2831no—
320C2×C4—2831no—
321C2×C4—5664no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—22641no—
326C2×C4—22641no—
327C2×C4—22641no—
328C2×C4D4×D28311yescharacteristic
329C2×C4D4×D28311yescharacteristic
330C2×C4C23×D28311yescharacteristic
331C8—21no—
332C8—2832no—
333C8—5661no—
334C8C2×C4×D28312yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—2832no—
339C22—5661no—
340C22—5661no—
341C22—5662no—
342C22—11321no—
343C22—11321no—
344C22—22644no—
345C22C2×D4×D28311yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—2832no—
352C4—5661no—
353C4—5661no—
354C4—5662no—
355C4—11321no—
356C4—11321no—
357C4C22×C4×D28311yescharacteristic
358C4#41×D28311yescharacteristic
359C2—42no—
360C2—5662no—
361C2—11322no—
362C2C4×D4×D28311yescharacteristic
363C2#3182727411yescharacteristic
364C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
cosocleC2×C4×C283C24
hypercenter#440D283
hypocenterC283#2949
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #31826941C2semidirect
4. #31826567C2semidirect
5. #31826566C2semidirect
6. #31826564C2semidirect
7. #31826556C2semidirect
8. C4×#17985379C2semidirect
9. C4×#17985380C2semidirect
10. #31826550C2semidirect
11. #31826502C2semidirect
12. #31826472C2semidirect
14. #31826422C2semidirect
15. #440×C283C2semidirect
21. SD16×D283C4semidirect
24. Q8×Dic283C22semidirect
26. C4×Dic566C22semidirect
28. #22583575C22semidirect
41. #22583544C22semidirect
42. #22583541C22semidirect
43. #22583541C22semidirect
44. #22583535C22semidirect
45. #22583534C22semidirect
46. #22583533C22semidirect
50. #22583520C22semidirect
51. C4×C283⋊C8C22semidirect
52. C8×Dic283C22semidirect
54. C4×Q8×C283C22semidirect
56. #107×C283C22semidirect
57. #103×C283C22semidirect
59. #97×C283C22semidirect
64. Q8×D283C2×C4semidirect
74. #17985381C2×C4semidirect
75. #17985380C2×C4semidirect
76. #17985379C2×C4semidirect
80. C8×D283C2×C4semidirect
104. SD16×C283C2×C4semidirect
182. C283#2949semidirect
190. #440D283semidirect
213. C4×Q8C2×D283semidirect
228. #107C2×D283semidirect
234. #103C2×D283semidirect
240. #97C2×D283semidirect
263. SD16C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2832
#318269412
#318269372
#318265672
#318265662
#318265642
#318265562
C4×#179853792
C4×#179853802
#318265502
#318265022
#318264722
#318264682
#318264222
#440×C2832
#2949283