Finite Group Databasebeta

← #49133224

Subgroups — #49133224

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#31827119C211yesmaximal, characteristic, complemented
2#31827111C211yesmaximal, characteristic, complemented
3#31826825C211yesmaximal, characteristic, complemented
4#31826796C211yesmaximal, characteristic, complemented
5#31826784C211yesmaximal, characteristic, complemented
6#31826756C211yesmaximal, characteristic, complemented
7#31826718C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826681C211yesmaximal, characteristic, complemented
10#31826612C211yesmaximal, characteristic, complemented
11#31826601C211yesmaximal, characteristic, complemented
12#31826578C211yesmaximal, characteristic, complemented
13#31826467C211yesmaximal, characteristic, complemented
14C2×#22583532C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985391—21no—
18C22×D1132C2211yescharacteristic
19C2×#17985381C2211yescharacteristic, complemented
20C2×D2264C2211yescharacteristic
21C2×D2264C2211yescharacteristic
22#22583610C2211yescharacteristic, complemented
23#22583598C2211yescharacteristic
24#22583595—21no—
25#22583594—21no—
26#22583594—21no—
27#22583590—21no—
28#22583589C2211yescharacteristic
29#22583584C2211yescharacteristic
30#22583584C2211yescharacteristic
31#22583584C2211yescharacteristic, complemented
32#22583583—21no—
33#22583578—21no—
34C4×D1132C2211yescharacteristic
35C4×D1132C2211yescharacteristic, complemented
36C2×C4⋊Dic283C2211yescharacteristic
37C2×C4⋊Dic283C2211yescharacteristic, complemented
38C22⋊C4×D283—21no—
39#22583542C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583542C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic, complemented
52C2×M16×C283C2211yescharacteristic, complemented
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic, complemented
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic, complemented
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—22no—
61#17985392—41no—
62#17985391—44no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×D1132—22no—
66C2×D1132—21no—
67C2×D1132—41no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C22×Dic283—21no—
76C22×Dic283—21no—
77C2×C4×D283—21no—
78C2×C4×D283—21no—
79C2×C4×D283—21no—
80#17985381—41no—
81D2264—22no—
82D2264—41no—
83C4⋊Dic283—21no—
84C4⋊Dic283—21no—
85C4⋊Dic283—21no—
86C4⋊Dic283C2311yescharacteristic
87C4⋊Dic283C2311yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89C4⋊Dic283C2311yescharacteristic
90Dic283⋊C4—21no—
91C22⋊Dic283—21no—
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—
99C2×D4×C283D411yescharacteristic
100C22×C4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102M16×C283—41no—
103C2×C8×C283—41no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C22⋊C4×C283D411yescharacteristic
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—81no—
118Dic566—21no—
119Dic566—21no—
120Dic566—42no—
121D1132—21no—
122D1132—21no—
123D1132—21no—
124D1132—21no—
125D1132—21no—
126D1132—42no—
127D1132#4112yescomplemented
128C22⋊D283—42no—
129C22⋊D283—42no—
130C22⋊D283—42no—
131C22⋊D283—81no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—42no—
138C2×Dic283—42no—
139C4×D283—42no—
140C4×D283—42no—
141C4×D283—81no—
142C23×C283C2×D411yescharacteristic
143C23×C283C2×D411yescharacteristic
144D4×C283—22no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2×D411yescharacteristic
153C2×C4×C283C2411yescharacteristic
154C8×C283—21no—
155C8×C283—21no—
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—21no—
161C22×C283—21no—
162C22×C283—21no—
163C22×C283AGL(1,ℤ/8)12yes—
164C22×C283C22×D411yescharacteristic
165C2×D283—22no—
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—21no—
177C4×C283—21no—
178C4×C283—21no—
179C4×C283C2×#4111yescharacteristic
180C4×C283H(5,𝔽2)11yescharacteristic
181Dic283—41no—
182Dic283—41no—
183Dic283—41no—
184Dic283—41no—
185Dic283—41no—
186C2×C283—22no—
187C2×C283—41no—
188C2×C283#54611yescharacteristic
189C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C283#57711yescharacteristic
191D283—42no—
192D283—81no—
193D283—81no—
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#447—2831no—
207#442—2831no—
208#435D28311yescharacteristic, complemented
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×M16C2×D28311yescharacteristic, complemented
218C22×C8C2×D28311yescharacteristic
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—2831no—
229#121—5661no—
230#120—5661no—
231C4×D4—2831no—
232C4×D4—2831no—
233C4×D4C2×D28311yescharacteristic
234C2×C4⋊C4—2831no—
235C2×C4⋊C4—2831no—
236C2×C22⋊C4—5661no—
237#106—2831no—
238#106—2831no—
239#106—2831no—
240C4⋊C8C2×D28311yescharacteristic, complemented
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#102—2831no—
250#102—2831no—
251C22⋊C8C2×D28311yescharacteristic
252C22⋊C8C2×D28311yescharacteristic, complemented
253#97C2×D28311yescharacteristic, complemented
254C24—5661no—
255#41—5662no—
256#41—11321no—
257#41—11324no—
258C2×Q8—2831no—
259C2×Q8—5661no—
260C2×D4—2831no—
261C2×D4—2831no—
262C2×D4—2831no—
263C2×D4—5662no—
264C2×D4—5661no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—11321no—
270C2×D4D113211yescharacteristic
271C22×C4—5661no—
272C22×C4—5661no—
273C22×C4—5661no—
274C22×C4—5661no—
275C22×C4—5661no—
276C22×C4C22×D28311yescharacteristic
277C22×C4C22×D28311yescharacteristic
278SD16—11321no—
279D8—5662no—
280D8—11321no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D28311yescharacteristic
284C2×C8C22×D28311yescharacteristic
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⋊C4D113211yescharacteristic
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4D113211yescharacteristic
305C22⋊C4D113211yescharacteristic
306C42C22×D28311yescharacteristic
307C23—5661no—
308C23—5661no—
309C23—5661no—
310C23—11322no—
311C23—11322no—
312C23—22641no—
313C23C2×D113211yescharacteristic
314C23C2×D113211yescharacteristic
315Q8—5661no—
316Q8—5661no—
317Q8—11322no—
318D4—22no—
319D4—2832no—
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—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—5661no—
339C2×C4—11322no—
340C2×C4—11322no—
341C2×C4—11322no—
342C2×C4—11322no—
343C2×C4—22641no—
344C2×C4C2×D113211yescharacteristic
345C2×C4C2×D113211yescharacteristic
346C2×C4C2×D113211yescharacteristic
347C2×C4C2×D113211yescharacteristic
348C2×C4C23×D28311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—5662no—
359C22—11321no—
360C22—11321no—
361C22—11321no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—22644no—
368C22#2258363812yes—
369C22C22×D113211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—11321no—
375C4—11321no—
376C4—11321no—
377C4—11321no—
378C4—11321no—
379C4#41×D28311yescharacteristic
380C4#2258365511yescharacteristic
381C2—22no—
382C2—41no—
383C2—11322no—
384C2—22641no—
385C2—22641no—
386C2#3182711011yescharacteristic
387C2C2×#2258363811yescharacteristic
388C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
hypercenter#435D283
hypocenterC283#3306
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31827119C2semidirect
2. #31827111C2semidirect
3. #31826825C2semidirect
4. #31826796C2semidirect
5. #31826784C2semidirect
6. #31826756C2semidirect
7. #31826718C2semidirect
8. #31826694C2semidirect
9. #31826681C2semidirect
10. #31826612C2semidirect
11. #31826601C2semidirect
12. #31826578C2semidirect
13. #31826467C2semidirect
14. C2×#22583532C2semidirect
15. #435×C283C2semidirect
19. C2×#17985381C22semidirect
22. #22583610C22semidirect
31. #22583584C22semidirect
35. C4×D1132C22semidirect
37. C2×C4⋊Dic283C22semidirect
39. #22583542C22semidirect
40. #22583542C22semidirect
41. #22583542C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
51. #22583532C22semidirect
52. C2×M16×C283C22semidirect
55. C4⋊C8×C283C22semidirect
57. C22⋊C8×C283C22semidirect
58. #97×C283C22semidirect
127. D1132#41semidirect
194. C283#3306semidirect
208. #435D283semidirect
217. C2×M16C2×D283semidirect
240. C4⋊C8C2×D283semidirect
252. C22⋊C8C2×D283semidirect
253. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271192
#318271112
#318268252
#318267962
#318267842
#318267562
#318267182
#318266942
#318266812
#318266122
#318266012
#318265782
#318264672
C2×#225835322
#435×C2832
#3306283