Finite Group Databasebeta

← #49133216

Subgroups — #49133216

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#31827111C211yesmaximal, characteristic, complemented
2#31826827C211yesmaximal, characteristic, complemented
3#31826795C211yesmaximal, characteristic, complemented
4#31826783C211yesmaximal, characteristic, complemented
5#31826752C211yesmaximal, characteristic, complemented
6#31826716C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826680C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826598C211yesmaximal, characteristic, complemented
11#31826575C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826464C211yesmaximal, characteristic, complemented
14C2×#22583530C211yesmaximal, characteristic, complemented
15#547×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C2×#17985380C2211yescharacteristic, complemented
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C2×#17985376C2211yescharacteristic, complemented
22C22×C283⋊C8C2211yescharacteristic
23#22583598C2211yescharacteristic
24#22583595—21no—
25#22583589C2211yescharacteristic
26#22583584C2211yescharacteristic
27#22583583—21no—
28#22583578—21no—
29C4×D1132C2211yescharacteristic
30C22⋊C4×D283—21no—
31#22583541C2211yescharacteristic, complemented
32#22583541C2211yescharacteristic, complemented
33#22583541C2211yescharacteristic, complemented
34C4⋊(C283⋊C8)C2211yescharacteristic, complemented
35#22583533C2211yescharacteristic, complemented
36#22583533C2211yescharacteristic, complemented
37#22583533C2211yescharacteristic, complemented
38#22583531C2211yescharacteristic, complemented
39#22583530C2211yescharacteristic
40#22583530C2211yescharacteristic
41#22583530C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic, complemented
47#22583521C2211yescharacteristic, complemented
48C2×#41×C283—21no—
49C4⋊Q8×C283C2211yescharacteristic, complemented
50#123×C283—21no—
51#123×C283—21no—
52C22⋊Q8×C283—21no—
53#121×C283C2211yescharacteristic
54#121×C283C2211yescharacteristic, complemented
55C4×D4×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic, complemented
57C2×C4⋊C4×C283C2211yescharacteristic
58C2×C4⋊C4×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—22no—
61#17985392—41no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—41no—
66C2×D1132C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72#17985380—41no—
73#17985377—22no—
74#17985377—41no—
75#17985376—41no—
76C2×C283⋊C8—41no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88#41×C283—44no—
89C2×Q8×C283—21no—
90C2×D4×C283—21no—
91C2×D4×C283—21no—
92C2×D4×C283D411yescharacteristic
93C2×D4×C283C2311yescharacteristic
94C22×C4×C283—21no—
95C22×C4×C283—21no—
96C22×C4×C283—21no—
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C4⋊C4×C283—21no—
100C4⋊C4×C283—21no—
101C4⋊C4×C283—21no—
102C4⋊C4×C283D411yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C22⋊C4×C283D411yescharacteristic
110C22⋊C4×C283D411yescharacteristic
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—42no—
115C22×D283—42no—
116C22×D283—81no—
117Dic566—21no—
118Dic566—21no—
119D1132—21no—
120D1132—21no—
121D1132—21no—
122D1132—42no—
123D1132#4112yescomplemented
124C22⋊D283—42no—
125C22⋊D283—81no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C4×D283—42no—
129C4×D283—81no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C283⋊C8—21no—
134C23×C283—21no—
135C23×C283C2×D411yescharacteristic
136C23×C283C2×D411yescharacteristic
137Q8×C283—42no—
138D4×C283—22no—
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—42no—
142D4×C283—42no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283—42no—
152C2×C4×C283—42no—
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2×D411yescharacteristic
156C2×C4×C283C2×D411yescharacteristic
157C2×C4×C283C2411yescharacteristic
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—21no—
161C22×C283—21no—
162C22×C283—21no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283AGL(1,ℤ/8)12yes—
167C22×C283C22×D411yescharacteristic
168C2×D283—22no—
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×C283—41no—
180C4×C283—41no—
181C4×C283—41no—
182C4×C283C2×#4111yescharacteristic
183C4×C283H(5,𝔽2)11yescharacteristic
184Dic283—41no—
185Dic283—41no—
186C2×C283—22no—
187C2×C283—41no—
188C2×C283—81no—
189C2×C283#54611yescharacteristic
190C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C283#57711yescharacteristic
192D283—42no—
193D283—81no—
194C283#330611yescharacteristic, complemented, Sylow
195#3306—2831nomaximal, Sylow
196#547D28311yescharacteristic, complemented
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#435—2831no—
209#417—2831no—
210C2×#102—2831no—
211C2×#41—21no—
212C2×#41—2831no—
213C22×D4—2831no—
214C2×SD16—2831no—
215C2×D8—2831no—
216C2×D8—2831no—
217C2×M16—2831no—
218C22×C8—2831no—
219C4⋊Q8C2×D28311yescharacteristic, complemented
220#124—2831no—
221#123—21no—
222#123—21no—
223#123—5661no—
224C22⋊Q8—21no—
225C22⋊Q8—2831no—
226#121—2831no—
227#121—5661no—
228#121C2×D28311yescharacteristic
229#121C2×D28311yescharacteristic, complemented
230#120—5661no—
231C4×D4—2831no—
232C4×D4C2×D28311yescharacteristic
233C4×D4C2×D28311yescharacteristic, complemented
234C2×C4⋊C4C2×D28311yescharacteristic
235C2×C4⋊C4C2×D28311yescharacteristic, complemented
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#102—2831no—
250#102—2831no—
251C22⋊C8—2831no—
252C22⋊C8—2831no—
253#97—2831no—
254C24—5661no—
255#41—44no—
256#41—5662no—
257#41—11321no—
258C2×Q8—21no—
259C2×Q8—2831no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—2831no—
263C2×D4—2831no—
264C2×D4—5662no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—11321no—
269C2×D4C22⋊D28311yescharacteristic
270C2×D4C22×D28311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—5661no—
275C22×C4—5661no—
276C22×C4C22×D28311yescharacteristic
277C22×C4C22×D28311yescharacteristic
278SD16—11321no—
279D8—5662no—
280D8—11321no—
281M16—11321no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8—2831no—
285C2×C8—2831no—
286C2×C8—11321no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—2831no—
291C4⋊C4—5661no—
292C4⋊C4C22⋊D28311yescharacteristic
293C4⋊C4C22×D28311yescharacteristic
294C4⋊C4C22×D28311yescharacteristic
295C4⋊C4C22×D28311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4C22⋊D28311yescharacteristic
305C22⋊C4C22⋊D28311yescharacteristic
306C42C22×D28311yescharacteristic
307C23—21no—
308C23—5661no—
309C23—5661no—
310C23—11322no—
311C23—11322no—
312C23—22641no—
313C23C2×C22⋊D28311yescharacteristic
314C23C2×C22⋊D28311yescharacteristic
315Q8—42no—
316Q8—5661no—
317Q8—5661no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—2832no—
324D4—5661no—
325D4—5661no—
326D4—5661no—
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—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—11322no—
343C2×C4—22641no—
344C2×C4C2×C22⋊D28311yescharacteristic
345C2×C4C2×C22⋊D28311yescharacteristic
346C2×C4C2×C22⋊D28311yescharacteristic
347C2×C4C2×C22⋊D28311yescharacteristic
348C2×C4C23×D28311yescharacteristic
349C8—5661no—
350C8—5661no—
351C8—5661no—
352C8—5661no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—5662no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—22644no—
368C22#2258363612yes—
369C22C22×C22⋊D28311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—11321no—
378C4—11321no—
379C4#41×D28311yescharacteristic
380C4#2258365611yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—11322no—
385C2—22641no—
386C2#3182710311yescharacteristic
387C2C2×#2258363611yescharacteristic
388C2#3182727311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#547×C283C2
socleC22×C283C22×D4
hypercenter#547D283
hypocenterC283#3306
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #31827111C2semidirect
2. #31826827C2semidirect
3. #31826795C2semidirect
4. #31826783C2semidirect
5. #31826752C2semidirect
6. #31826716C2semidirect
7. #31826692C2semidirect
8. #31826680C2semidirect
9. #31826608C2semidirect
10. #31826598C2semidirect
11. #31826575C2semidirect
12. #31826537C2semidirect
13. #31826464C2semidirect
14. C2×#22583530C2semidirect
15. #547×C283C2semidirect
18. C2×#17985380C22semidirect
21. C2×#17985376C22semidirect
31. #22583541C22semidirect
32. #22583541C22semidirect
33. #22583541C22semidirect
34. C4⋊(C283⋊C8)C22semidirect
35. #22583533C22semidirect
36. #22583533C22semidirect
37. #22583533C22semidirect
38. #22583531C22semidirect
46. C22⋊(C283⋊C8)C22semidirect
47. #22583521C22semidirect
49. C4⋊Q8×C283C22semidirect
54. #121×C283C22semidirect
56. C4×D4×C283C22semidirect
58. C2×C4⋊C4×C283C22semidirect
123. D1132#41semidirect
194. C283#3306semidirect
196. #547D283semidirect
219. C4⋊Q8C2×D283semidirect
229. #121C2×D283semidirect
233. C4×D4C2×D283semidirect
235. C2×C4⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271112
#318268272
#318267952
#318267832
#318267522
#318267162
#318266922
#318266802
#318266082
#318265982
#318265752
#318265372
#318264642
C2×#225835302
#547×C2832
#3306283