Finite Group Databasebeta

← #49133226

Subgroups — #49133226

Order 36224.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827115C211yesmaximal, characteristic, complemented
2#31827109C211yesmaximal, characteristic, complemented
3#31826823C211yesmaximal, characteristic, complemented
4#31826796C211yesmaximal, characteristic, complemented
5#31826782C211yesmaximal, characteristic, complemented
6#31826753C211yesmaximal, characteristic, complemented
7#31826715C211yesmaximal, characteristic, complemented
8#31826692C211yesmaximal, characteristic, complemented
9#31826678C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826577C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14C2×#22583531C211yesmaximal, characteristic, complemented
15#447×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C2×#17985391C2211yescharacteristic
18C2×#17985380C2211yescharacteristic, complemented
19C2×#17985375C2211yescharacteristic, complemented
20C22×C283⋊C8C2211yescharacteristic
21#22583609C2211yescharacteristic, complemented
22#22583597C2211yescharacteristic
23#22583592—21no—
24#22583591—21no—
25#22583591—21no—
26#22583589C2211yescharacteristic
27#22583587—21no—
28#22583582—21no—
29#22583581C2211yescharacteristic
30#22583581C2211yescharacteristic, complemented
31#22583579—21no—
32D4×Dic283C2211yescharacteristic
33D4×Dic283C2211yescharacteristic, complemented
34C4×C22⋊D283C2211yescharacteristic
35C2×C4⋊Dic283C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic, complemented
37C2×C22⋊Dic283—21no—
38#22583542C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52C22×D4×C283C2211yescharacteristic
53C2×D8×C283C2211yescharacteristic
54C2×D8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61#17985391—44no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283D411yescharacteristic
68C22×Dic283—21no—
69C22×Dic283—21no—
70C22×Dic283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74#17985380—41no—
75#17985375—41no—
76C2×C283⋊C8—41no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4D411yescharacteristic
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283D411yescharacteristic
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C24×C283—21no—
98C2×D4×C283—22no—
99C2×D4×C283—21no—
100C2×D4×C283—21no—
101C2×D4×C283—41no—
102C2×D4×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104C2×D4×C283C2311yescharacteristic
105C22×C4×C283C2311yescharacteristic
106D8×C283—22no—
107D8×C283—41no—
108C2×C8×C283C2311yescharacteristic
109C2×C8×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—42no—
116C22⋊D283—22no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C22⋊D283—81no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—42no—
125C2×Dic283—42no—
126C2×Dic283—42no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283—21no—
138C23×C283—21no—
139C23×C283—42no—
140C23×C283—42no—
141C23×C283—81no—
142C23×C283C2×D411yescharacteristic
143D4×C283—21no—
144D4×C283—21no—
145D4×C283—21no—
146D4×C283—21no—
147D4×C283—21no—
148D4×C283—42no—
149D4×C283—42no—
150D4×C283#4112yescomplemented
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—21no—
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—22no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283—41no—
169C22×C283—84no—
170C22×C283AGL(1,ℤ/8)12yes—
171C22×C283C22×D411yescharacteristic
172C2×D283—21no—
173C2×D283—21no—
174C2×D283—21no—
175C4×C283—21no—
176C4×C283—41no—
177C4×C283C2×#4111yescharacteristic
178C4×C283H(5,𝔽2)11yescharacteristic
179Dic283—21no—
180Dic283—21no—
181Dic283—21no—
182Dic283—41no—
183Dic283—41no—
184Dic283—41no—
185Dic283—41no—
186C2×C283—22no—
187C2×C283—42no—
188C2×C283—81no—
189C2×C283—81no—
190C2×C283#54611yescharacteristic
191C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C283#57711yescharacteristic
193D283—41no—
194C283#330611yescharacteristic, complemented, Sylow
195#3306—2831nomaximal, Sylow
196#547—2831no—
197#546—2831no—
198#489—2831no—
199#483—2831no—
200#481—2831no—
201#476—2831no—
202#469—2831no—
203#465—2831no—
204#463—2831no—
205#449—2831no—
206#447D28311yescharacteristic, complemented
207#442—2831no—
208#435—2831no—
209#417—2831no—
210C2×#102—2831no—
211C2×#41—2831no—
212C2×#41—5661no—
213C22×D4C2×D28311yescharacteristic
214C2×SD16—2831no—
215C2×D8C2×D28311yescharacteristic
216C2×D8C2×D28311yescharacteristic
217C2×M16—2831no—
218C22×C8—2831no—
219C4⋊Q8—2831no—
220#124—2831no—
221#123—5661no—
222#123—5661no—
223#123—5661no—
224C22⋊Q8—2831no—
225C22⋊Q8—5661no—
226#121—2831no—
227#121—2831no—
228#121—5661no—
229#121C2×D28311yescharacteristic
230#120—5661no—
231C4×D4—2831no—
232C4×D4—2831no—
233C4×D4—2831no—
234C2×C4⋊C4—2831no—
235C2×C4⋊C4—2831no—
236C2×C22⋊C4—5661no—
237#106—2831no—
238#106—2831no—
239#106—2831no—
240C4⋊C8—2831no—
241#103—2831no—
242#103—2831no—
243#103—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102C2×D28311yescharacteristic
250#102C2×D28311yescharacteristic
251C22⋊C8—2831no—
252C22⋊C8C2×D28311yescharacteristic
253#97—2831no—
254C24—21no—
255#41—5662no—
256#41—11321no—
257#41—11324no—
258C2×Q8—2831no—
259C2×Q8—5661no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2831no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4C22×D28311yescharacteristic
269C2×D4C22×D28311yescharacteristic
270C2×D4C22×D28311yescharacteristic
271C22×C4—2831no—
272C22×C4—5661no—
273C22×C4—5661no—
274C22×C4—5661no—
275C22×C4—5661no—
276C22×C4—5661no—
277C22×C4C22×D28311yescharacteristic
278SD16—11321no—
279D8—22no—
280D8—41no—
281M16—11321no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8—11321no—
285C2×C8C22×D28311yescharacteristic
286C2×C8C22×D28311yescharacteristic
287C4⋊C4—2831no—
288C4⋊C4—2831no—
289C4⋊C4—2831no—
290C4⋊C4—2831no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4C22×D28311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—2831no—
298C22⋊C4—2831no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C22⋊C4—5661no—
306C42—2831no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2831no—
314C23D4×D28311yescharacteristic
315Q8—5661no—
316Q8—5661no—
317Q8—11322no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—5662no—
326D4—11322no—
327D4—11322no—
328D4—22641no—
329D4#1798539112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2831no—
334C2×C4—2831no—
335C2×C4—2831no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—11322no—
343C2×C4—11322no—
344C2×C4—11322no—
345C2×C4—11322no—
346C2×C4—22641no—
347C2×C4D4×D28311yescharacteristic
348C2×C4C23×D28311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5661no—
352C8—5661no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—5661no—
366C22—5661no—
367C22—5661no—
368C22#2258363412yes—
369C22C2×D4×D28311yescharacteristic
370C4—21no—
371C4—41no—
372C4—5661no—
373C4—5661no—
374C4—5661no—
375C4—11321no—
376C4—11321no—
377C4—11321no—
378C4—11321no—
379C4C2×#1798539111yescharacteristic
380C4#2258365511yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—11321no—
386C2#3182710211yescharacteristic
387C2C2×#2258363411yescharacteristic
388C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#447×C283C2
socleC22×C283C22×D4
hypercenter#447D283
hypocenterC283#3306
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #31827115C2semidirect
2. #31827109C2semidirect
3. #31826823C2semidirect
4. #31826796C2semidirect
5. #31826782C2semidirect
6. #31826753C2semidirect
7. #31826715C2semidirect
8. #31826692C2semidirect
9. #31826678C2semidirect
10. #31826607C2semidirect
11. #31826577C2semidirect
12. #31826533C2semidirect
13. #31826463C2semidirect
14. C2×#22583531C2semidirect
15. #447×C283C2semidirect
18. C2×#17985380C22semidirect
19. C2×#17985375C22semidirect
21. #22583609C22semidirect
30. #22583581C22semidirect
33. D4×Dic283C22semidirect
36. C4⋊C4×D283C22semidirect
38. #22583542C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
49. #22583531C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583520C22semidirect
150. D4×C283#41semidirect
194. C283#3306semidirect
206. #447D283semidirect
329. D4#17985391semidirect

Maximal subgroups

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

subgroupindex
#318271152
#318271092
#318268232
#318267962
#318267822
#318267532
#318267152
#318266922
#318266782
#318266072
#318265772
#318265332
#318264632
C2×#225835312
#447×C2832
#3306283