Finite Group Databasebeta

← #49133115

Subgroups — #49133115

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827167C211yesmaximal, characteristic, complemented
2#31827109C211yesmaximal, characteristic, complemented
3#31826818C211yesmaximal, characteristic, complemented
4#31826801C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826698C211yesmaximal, characteristic, complemented
8#31826692C211yesmaximal, characteristic, complemented
9#31826678C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11D8×Dic283C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14C2×#22583531C211yesmaximal, characteristic, complemented
15#447×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×#17985380C2211yescharacteristic, complemented
18C22×C283⋊C8C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic, complemented
20#22583603—21no—
21#22583601C2211yescharacteristic, complemented
22#22583597C2211yescharacteristic
23#22583594—21no—
24#22583591—21no—
25#22583589C2211yescharacteristic
26#22583582—21no—
27#22583582—21no—
28#22583581C2211yescharacteristic
29#22583581C2211yescharacteristic, complemented
30#22583579—21no—
31D4×Dic283—21no—
32D4×Dic283C2211yescharacteristic
33D4×Dic283C2211yescharacteristic, complemented
34C4×C22⋊D283C2211yescharacteristic
35#22583568C2211yescharacteristic, complemented
36C2×C4⋊Dic283C2211yescharacteristic
37C2×C22⋊Dic283—21no—
38#22583544C2211yescharacteristic, complemented
39#22583544C2211yescharacteristic, 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
51C8×Dic283C2211yescharacteristic, 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—
61C2×Dic566C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C22×Dic283—21no—
67C22×Dic283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C2×C4×D283C2311yescharacteristic
71#17985380—41no—
72C2×C283⋊C8—41no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C8×D283—41no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283D411yescharacteristic
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C24×C283—21no—
97C2×D4×C283—22no—
98C2×D4×C283—21no—
99C2×D4×C283—21no—
100C2×D4×C283—41no—
101C2×D4×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105D8×C283—22no—
106D8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114C22⋊D283—22no—
115C22⋊D283—42no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—42no—
123C2×Dic283—81no—
124C2×Dic283—81no—
125C2×Dic283—81no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134C23×C283—21no—
135C23×C283—21no—
136C23×C283—42no—
137C23×C283—42no—
138C23×C283—81no—
139C23×C283C2×D411yescharacteristic
140D4×C283—21no—
141D4×C283—21no—
142D4×C283—21no—
143D4×C283—21no—
144D4×C283—21no—
145D4×C283—42no—
146D4×C283—42no—
147D4×C283#4112yes—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—22no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—84no—
167C22×C283#13512yes—
168C22×C283C22×D411yescharacteristic
169C2×D283—21no—
170C2×D283—21no—
171C2×D283—21no—
172C4×C283—21no—
173C4×C283—41no—
174C4×C283C2×#4111yescharacteristic
175C4×C283H(5,𝔽2)11yescharacteristic
176Dic283—21no—
177Dic283—21no—
178Dic283—21no—
179Dic283—41no—
180Dic283—41no—
181Dic283—41no—
182Dic283—41no—
183C2×C283—22no—
184C2×C283—42no—
185C2×C283—81no—
186C2×C283—81no—
187C2×C283#54611yescharacteristic
188C2×C283C2×#13511yescharacteristic
189C2×C283#57611yescharacteristic
190D283—41no—
191C283#329711yescharacteristic, complemented, Sylow
192#3297—2831nomaximal, Sylow
193#553—2831no—
194#546—2831no—
195#488—2831no—
196#484—2831no—
197#482—2831no—
198#478—2831no—
199#466—2831no—
200#465—2831no—
201#463—2831no—
202#449—2831no—
203#447D28311yescharacteristic, complemented
204C4×D8—2831no—
205C8×D4—2831no—
206#416—2831no—
207C2×#102—2831no—
208C2×#41—2831no—
209C22×D4C2×D28311yescharacteristic
210C2×SD16—2831no—
211C2×D8C2×D28311yescharacteristic
212C2×D8C2×D28311yescharacteristic
213C22×C8—2831no—
214C22×C8—2831no—
215#126—5661no—
216#125—2831no—
217#124—2831no—
218#123—5661no—
219#123—5661no—
220C22⋊Q8—2831no—
221#121—2831no—
222#121—2831no—
223#121—5661no—
224#121—5661no—
225#121C2×D28311yescharacteristic
226#120—5661no—
227C4×D4—2831no—
228C4×D4—2831no—
229C4×D4—2831no—
230C4×D4—5661no—
231#117—2831no—
232C2×C4⋊C4—2831no—
233C2×C22⋊C4—5661no—
234#107—2831no—
235#107—2831no—
236#106—2831no—
237C4⋊C8—2831no—
238#103—2831no—
239#103—2831no—
240#103—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102C2×D28311yescharacteristic
247#102C2×D28311yescharacteristic
248C22⋊C8—2831no—
249C22⋊C8C2×D28311yescharacteristic
250C4×C8—2831no—
251C24—21no—
252#41—5662no—
253#41—11321no—
254C2×Q8—2831no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—2831no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4C22×D28311yescharacteristic
264C2×D4C22×D28311yescharacteristic
265C2×D4C22×D28311yescharacteristic
266C22×C4—2831no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4C22×D28311yescharacteristic
272SD16—11321no—
273D8—22no—
274D8—41no—
275C2×C8—2831no—
276C2×C8—2831no—
277C2×C8—11321no—
278C2×C8—11321no—
279C2×C8C22×D28311yescharacteristic
280C2×C8C22×D28311yescharacteristic
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—2831no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4—5661no—
288C4⋊C4—5661no—
289C4⋊C4C22×D28311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2831no—
292C22⋊C4—2831no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C42—2831no—
302C42—5661no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—2831no—
310C23D4×D28311yescharacteristic
311Q8—5661no—
312Q8—5661no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—5662no—
321D4—11322no—
322D4—22641no—
323D4—22641no—
324D4#1798539112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2831no—
329C2×C4—2831no—
330C2×C4—2831no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—11322no—
338C2×C4—22641no—
339C2×C4—22641no—
340C2×C4—22641no—
341C2×C4D4×D28311yescharacteristic
342C2×C4C23×D28311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5661no—
346C8—5661no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—5661no—
360C22—5661no—
361C22—5661no—
362C22#2258362912yes—
363C22C2×D4×D28311yescharacteristic
364C4—21no—
365C4—41no—
366C4—5661no—
367C4—5661no—
368C4—5661no—
369C4—11321no—
370C4—11321no—
371C4—11321no—
372C4—11321no—
373C4C2×#1798539111yescharacteristic
374C4#2258365511yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—11321no—
380C2#3182710211yescharacteristic
381C2C2×#2258362911yescharacteristic
382C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#447×C283C2
socleC22×C283C22×D4
hypercenter#447D283
hypocenterC283#3297
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. #31827167C2semidirect
2. #31827109C2semidirect
3. #31826818C2semidirect
4. #31826801C2semidirect
5. #31826787C2semidirect
6. #31826763C2semidirect
7. #31826698C2semidirect
8. #31826692C2semidirect
9. #31826678C2semidirect
10. #31826607C2semidirect
11. D8×Dic283C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826458C2semidirect
14. C2×#22583531C2semidirect
15. #447×C283C2semidirect
17. C2×#17985380C22semidirect
19. C2×C8×D283C22semidirect
21. #22583601C22semidirect
29. #22583581C22semidirect
33. D4×Dic283C22semidirect
35. #22583568C22semidirect
38. #22583544C22semidirect
39. #22583544C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
49. #22583531C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C8×Dic283C22semidirect
191. C283#3297semidirect
203. #447D283semidirect

Maximal subgroups

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

subgroupindex
#318271672
#318271092
#318268182
#318268012
#318267872
#318267632
#318266982
#318266922
#318266782
#318266072
D8×Dic2832
(C22⋊D283)⋊C82
#318264582
C2×#225835312
#447×C2832
#3297283