Finite Group Databasebeta

← #49133220

Subgroups — #49133220

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#31827116C211yesmaximal, characteristic, complemented
2#31827106C211yesmaximal, characteristic, complemented
3#31826826C211yesmaximal, characteristic, complemented
4#31826785C211yesmaximal, characteristic, complemented
5#31826754C211yesmaximal, characteristic, complemented
6#31826719C211yesmaximal, characteristic, complemented
7#31826696C211yesmaximal, characteristic, complemented
8#31826683C211yesmaximal, characteristic, complemented
9#31826613C211yesmaximal, characteristic, complemented
10#31826601C211yesmaximal, characteristic, complemented
11#31826576C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic, complemented
14C2×#22583530C211yesmaximal, characteristic, complemented
15#483×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985392—21no—
18C22×D1132C2211yescharacteristic
19C2×#17985379C2211yescharacteristic, complemented
20C2×D2264C2211yescharacteristic
21C2×D2264C2211yescharacteristic
22C2×#17985375C2211yescharacteristic, complemented
23C22×C283⋊C8C2211yescharacteristic
24#22583609C2211yescharacteristic, complemented
25#22583599C2211yescharacteristic
26#22583595—21no—
27#22583595—21no—
28#22583593—21no—
29#22583588—21no—
30#22583585—21no—
31#22583585C2211yescharacteristic
32#22583585C2211yescharacteristic, complemented
33#22583584C2211yescharacteristic
34#22583580—21no—
35#22583572C2211yescharacteristic
36#22583572C2211yescharacteristic, complemented
37C4×C22⋊D283C2211yescharacteristic
38C4⋊C4×D283C2211yescharacteristic, complemented
39C22⋊C4×D283—21no—
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583534C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583530C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52C22⋊Q8×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#106×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283—21no—
60#17985393—22no—
61#17985393—41no—
62#17985392—44no—
63C2×Dic566—21no—
64C2×D1132—22no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132—21no—
69C2×D1132—41no—
70C2×D1132C2311yescharacteristic
71C2×D1132C2311yescharacteristic
72C2×D1132C2311yescharacteristic
73C2×C22⋊D283—21no—
74C2×C22⋊D283D411yescharacteristic
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283—21no—
79C2×C4×D283C2311yescharacteristic
80#17985379—41no—
81D2264—22no—
82D2264—41no—
83#17985375—41no—
84C2×C283⋊C8—41no—
85C2×C283⋊C8C2311yescharacteristic
86C2×C283⋊C8C2311yescharacteristic
87C4⋊Dic283C2311yescharacteristic
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4D411yescharacteristic
91C22⋊Dic283D411yescharacteristic
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4D411yescharacteristic
100C4×Dic283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—81no—
118C22×D283C2×D411yescharacteristic
119Dic566—42no—
120D1132—21no—
121D1132—21no—
122D1132—21no—
123D1132—21no—
124D1132—21no—
125D1132—42no—
126D1132—42no—
127D1132—42no—
128D1132—81no—
129D1132#4112yescomplemented
130C22⋊D283—22no—
131C22⋊D283—42no—
132C2×Dic283—21no—
133C2×Dic283C2×D411yescharacteristic
134C2×Dic283C2×D411yescharacteristic
135C2×Dic283C2×D411yescharacteristic
136C4×D283—21no—
137C4×D283—21no—
138C4×D283—42no—
139C4×D283—42no—
140C4×D283—42no—
141C4×D283—81no—
142C283⋊C8—21no—
143C283⋊C8—21no—
144C23×C283C2×D411yescharacteristic
145Q8×C283—21no—
146Q8×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—42no—
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283AGL(1,ℤ/8)12yes—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—22no—
164C2×D283—21no—
165C2×D283—21no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—84no—
175C4×C283—21no—
176C4×C283—41no—
177C4×C283—41no—
178C4×C283—41no—
179C4×C283—41no—
180C4×C283C2×#4111yescharacteristic
181C4×C283H(5,𝔽2)11yescharacteristic
182Dic283—21no—
183Dic283—21no—
184Dic283—21no—
185Dic283—41no—
186C2×C283—22no—
187C2×C283#54611yescharacteristic
188C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C283#57711yescharacteristic
190D283—41no—
191D283—42no—
192D283—81no—
193D283—81no—
194C283#330611yescharacteristic, complemented, Sylow
195#3306—2831nomaximal, Sylow
196#547—2831no—
197#546—2831no—
198#489—2831no—
199#483D28311yescharacteristic, complemented
200#481—2831no—
201#476—2831no—
202#469—2831no—
203#465—2831no—
204#463—2831no—
205#449—2831no—
206#447—2831no—
207#442—2831no—
208#435—2831no—
209#417—2831no—
210C2×#102—2831no—
211C2×#41—2831no—
212C2×#41—5661no—
213C22×D4—2831no—
214C2×SD16—2831no—
215C2×D8—2831no—
216C2×D8—2831no—
217C2×M16—2831no—
218C22×C8—2831no—
219C4⋊Q8—2831no—
220#124—2831no—
221#123—5661no—
222#123—5661no—
223#123—5661no—
224C22⋊Q8—5661no—
225C22⋊Q8C2×D28311yescharacteristic
226#121—2831no—
227#121—2831no—
228#121—2831no—
229#121—5661no—
230#120—5661no—
231C4×D4—2831no—
232C4×D4—2831no—
233C4×D4—2831no—
234C2×C4⋊C4—2831no—
235C2×C4⋊C4C2×D28311yescharacteristic
236C2×C22⋊C4—5661no—
237#106—2831no—
238#106C2×D28311yescharacteristic, complemented
239#106C2×D28311yescharacteristic, complemented
240C4⋊C8—2831no—
241#103—2831no—
242#103C2×D28311yescharacteristic, complemented
243#103C2×D28311yescharacteristic, complemented
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102—2831no—
250#102—2831no—
251C22⋊C8—2831no—
252C22⋊C8C2×D28311yescharacteristic
253#97—2831no—
254C24—5661no—
255#41—5662no—
256#41—11324no—
257#41—11321no—
258C2×Q8—5661no—
259C2×Q8C22×D28311yescharacteristic
260C2×D4—2831no—
261C2×D4—2831no—
262C2×D4—2831no—
263C2×D4—2831no—
264C2×D4—5662no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—5661no—
270C2×D4—11321no—
271C22×C4—21no—
272C22×C4—2831no—
273C22×C4—5661no—
274C22×C4—5661no—
275C22×C4—5661no—
276C22×C4—5661no—
277C22×C4C22×D28311yescharacteristic
278SD16—11321no—
279D8—5662no—
280D8—11321no—
281M16—11321no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8—11321no—
285C2×C8C22×D28311yescharacteristic
286C2×C8C22×D28311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—2831no—
290C4⋊C4—2831no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4C22×D28311yescharacteristic
294C4⋊C4C22×D28311yescharacteristic
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—2831no—
308C23—5661no—
309C23—5661no—
310C23—5661no—
311C23—11322no—
312C23—11322no—
313C23—22641no—
314C23D4×D28311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—11322no—
318D4—2832no—
319D4—5662no—
320D4—5661no—
321D4—5661no—
322D4—5661no—
323D4—5661no—
324D4—5661no—
325D4—11322no—
326D4—11322no—
327D4—11322no—
328D4—11322no—
329D4—22641no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—2831no—
338C2×C4—2831no—
339C2×C4—2831no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
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—5661no—
356C22—5661no—
357C22—5661no—
358C22—5662no—
359C22—11321no—
360C22—11321no—
361C22—11321no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—22644no—
368C22#2258363712yes—
369C22C2×D4×D28311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—5661no—
376C4—5661no—
377C4—5661no—
378C4—11321no—
379C4#41×D28311yescharacteristic
380C4#2258365611yescharacteristic
381C2—22no—
382C2—11321no—
383C2—11322no—
384C2—22641no—
385C2—22641no—
386C2#3182710711yescharacteristic
387C2C2×#2258363711yescharacteristic
388C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#483×C283C2
socleC22×C283C22×D4
hypercenter#483D283
hypocenterC283#3306
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #31827116C2semidirect
2. #31827106C2semidirect
3. #31826826C2semidirect
4. #31826785C2semidirect
5. #31826754C2semidirect
6. #31826719C2semidirect
7. #31826696C2semidirect
8. #31826683C2semidirect
9. #31826613C2semidirect
10. #31826601C2semidirect
11. #31826576C2semidirect
12. #31826533C2semidirect
13. #31826465C2semidirect
14. C2×#22583530C2semidirect
15. #483×C283C2semidirect
19. C2×#17985379C22semidirect
22. C2×#17985375C22semidirect
24. #22583609C22semidirect
32. #22583585C22semidirect
36. #22583572C22semidirect
38. C4⋊C4×D283C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583534C22semidirect
49. #22583530C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583520C22semidirect
54. #106×C283C22semidirect
55. #106×C283C22semidirect
56. #103×C283C22semidirect
57. #103×C283C22semidirect
129. D1132#41semidirect
194. C283#3306semidirect
199. #483D283semidirect
238. #106C2×D283semidirect
239. #106C2×D283semidirect
242. #103C2×D283semidirect
243. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271162
#318271062
#318268262
#318267852
#318267542
#318267192
#318266962
#318266832
#318266132
#318266012
#318265762
#318265332
#318264652
C2×#225835302
#483×C2832
#3306283