Finite Group Databasebeta

← #49132897

Subgroups — #49132897

Order 36224.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583643C211yesmaximal, characteristic, complemented
2C2×#22583638C211yesmaximal, characteristic, complemented
3#31827124C211yesmaximal, characteristic, complemented
4#31827111C211yesmaximal, characteristic, complemented
5#31826849C211yesmaximal, characteristic, complemented
6#31826723C211yesmaximal, characteristic, complemented
7#31826718C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826681C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826618C211yesmaximal, characteristic, complemented
12#31826612C211yesmaximal, characteristic, complemented
13#31826606C211yesmaximal, characteristic, complemented
14C4×#17985381C211yesmaximal, characteristic, complemented
15#436×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C22×Dic566C2211yescharacteristic, complemented
19C22×D1132C2211yescharacteristic
20#22583643—24no—
21#22583638—24no—
22C2×Dic1132C2211yescharacteristic, complemented
23C2×Dic1132C2211yescharacteristic, complemented
24C2×#17985381C2211yescharacteristic
25C2×#17985381C2211yescharacteristic
26C2×#17985381C2211yescharacteristic
27C2×#17985381C2211yescharacteristic
28C2×#17985381C2211yescharacteristic, complemented
29C2×D2264C2211yescharacteristic
30C2×D2264C2211yescharacteristic
31#22583598C2211yescharacteristic
32#22583598C2211yescharacteristic, complemented
33#22583596—21no—
34#22583595—21no—
35#22583589C2211yescharacteristic
36#22583589C2211yescharacteristic
37#22583588—21no—
38#22583584C2211yescharacteristic
39#22583584C2211yescharacteristic, complemented
40#22583583—21no—
41#22583582—21no—
42#22583578—21no—
43C4×Dic566C2211yescharacteristic, complemented
44C4×D1132C2211yescharacteristic
45(C22⋊D283)⋊C4—21no—
46C22⋊C4×D283—21no—
47#22583542C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583535C2211yescharacteristic, complemented
50#22583535C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic
52#22583532C2211yescharacteristic
53#22583532C2211yescharacteristic, complemented
54C2×M16×C283C2211yescharacteristic
55C2×M16×C283C2211yescharacteristic, complemented
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic, complemented
60C4×C8×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985392—22no—
63#17985392—22no—
64#17985392—41no—
65#17985392—41no—
66C2×Dic566—22no—
67C2×Dic566—21no—
68C2×Dic566—41no—
69C2×Dic566C2311yescharacteristic
70C2×Dic566C2311yescharacteristic
71C2×Dic566C2311yescharacteristic
72C2×D1132—22no—
73C2×D1132—21no—
74C2×D1132—41no—
75C2×D1132C2311yescharacteristic
76C2×D1132C2311yescharacteristic
77C2×D1132C2311yescharacteristic
78C2×C22⋊D283—21no—
79C2×C22⋊D283—21no—
80C2×C22⋊D283—21no—
81C2×C22⋊D283—21no—
82C22×Dic283—21no—
83C2×C4×D283—21no—
84C2×C4×D283—21no—
85C2×C4×D283—21no—
86Dic1132—22no—
87Dic1132—22no—
88#17985381—22no—
89#17985381—22no—
90#17985381—41no—
91#17985381—41no—
92#17985381D414yescomplemented
93D2264—22no—
94D2264—22no—
95C4⋊Dic283C2311yescharacteristic
96C4⋊Dic283C2311yescharacteristic
97Dic283⋊C4—21no—
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100C22⋊Dic283—21no—
101C22⋊Dic283—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108(C2×D283)⋊C4—21no—
109C4×Dic283—21no—
110C2×D4×C283D411yescharacteristic
111C22×C4×C283C2311yescharacteristic
112C22×C4×C283C2311yescharacteristic
113M16×C283—22no—
114M16×C283—22no—
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C2×C8×C283C2311yescharacteristic
119C4⋊C4×C283D411yescharacteristic
120C22⋊C4×C283D411yescharacteristic
121C22⋊C4×C283D411yescharacteristic
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283—81no—
129Dic566—21no—
130Dic566—21no—
131Dic566—21no—
132Dic566—21no—
133Dic566—21no—
134Dic566—42no—
135Dic566C2×D412yes—
136D1132—21no—
137D1132—21no—
138D1132—21no—
139D1132—21no—
140D1132—21no—
141D1132—42no—
142D1132C2×D412yes—
143C22⋊D283—42no—
144C22⋊D283—42no—
145C22⋊D283—42no—
146C22⋊D283—81no—
147C2×Dic283—21no—
148C2×Dic283—21no—
149C2×Dic283—21no—
150C2×Dic283—21no—
151C2×Dic283—21no—
152C2×Dic283—42no—
153C4×D283—42no—
154C4×D283—42no—
155C4×D283—81no—
156C23×C283C2×D411yescharacteristic
157C23×C283C2×D411yescharacteristic
158D4×C283—41no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2×D411yescharacteristic
165C2×C4×C283C2×D411yescharacteristic
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2411yescharacteristic
168C8×C283—21no—
169C8×C283—21no—
170C8×C283—21no—
171C8×C283C2×D412yes—
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—21no—
176C22×C283—21no—
177C22×C283—21no—
178C22×C283C22×D411yescharacteristic
179C2×D283—22no—
180C2×D283—41no—
181C2×D283—41no—
182C2×D283—41no—
183C2×D283—41no—
184C2×D283—41no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283—41no—
188C2×D283—84no—
189C4×C283—21no—
190C4×C283—21no—
191C4×C283—21no—
192C4×C283—21no—
193C4×C283C22×D411yescharacteristic
194C4×C283H(5,𝔽2)11yescharacteristic
195Dic283—22no—
196Dic283—41no—
197Dic283—41no—
198Dic283—41no—
199Dic283—41no—
200C2×C283—41no—
201C2×C283—41no—
202C2×C283D4211yescharacteristic
203C2×C283#57511yescharacteristic
204C2×C283#57711yescharacteristic
205D283—42no—
206D283—81no—
207D283—81no—
208C283#327511yescharacteristic, complemented, Sylow
209#3275—2831nomaximal, Sylow
210C2×#137—2831no—
211C2×AGL(1,ℤ/8)—2831no—
212#548—2831no—
213#546—2831no—
214#495—2831no—
215#470—2831no—
216#469—2831no—
217#464—2831no—
218#463—2831no—
219#452—2831no—
220#450—2831no—
221#449—2831no—
222#448—2831no—
223C4×SD16—2831no—
224#436D28311yescharacteristic, complemented
225C2×#41—2831no—
226C2×#41—2831no—
227C22×Q8—2831no—
228C22×D4—2831no—
229#137—5664no—
230AGL(1,ℤ/8)—5664no—
231C2×Q16—2831no—
232C2×Q16—2831no—
233C2×SD16—2831no—
234C2×SD16—2831no—
235C2×SD16—2831no—
236C2×SD16—2831no—
237C2×SD16—2831no—
238C2×D8—2831no—
239C2×D8—2831no—
240C2×M16C2×D28311yescharacteristic
241C2×M16C2×D28311yescharacteristic, complemented
242#124—2831no—
243#124—2831no—
244#124—5661no—
245#123—5661no—
246C22⋊Q8—2831no—
247C22⋊Q8—2831no—
248C22⋊Q8—5661no—
249#121—2831no—
250#121—2831no—
251#121—5661no—
252#121—5661no—
253#120—5661no—
254C4×Q8—2831no—
255C4×D4—2831no—
256C4×D4—5661no—
257C4×D4C2×D28311yescharacteristic
258C2×C22⋊C4—5661no—
259#106—2831no—
260C4⋊C8C2×D28311yescharacteristic, complemented
261#103—2831no—
262#103—2831no—
263#103—2831no—
264#102—2831no—
265#102—2831no—
266#102—2831no—
267C22⋊C8C2×D28311yescharacteristic
268C22⋊C8C2×D28311yescharacteristic, complemented
269C4×C8C2×D28311yescharacteristic, complemented
270C24—5661no—
271#41—5662no—
272#41—5662no—
273#41—11321no—
274#41—11321no—
275C2×Q8—2831no—
276C2×Q8—2831no—
277C2×Q8—2831no—
278C2×Q8—5662no—
279C2×Q8—5661no—
280C2×Q8—11321no—
281C2×D4—2831no—
282C2×D4—2831no—
283C2×D4—2831no—
284C2×D4—5662no—
285C2×D4—5661no—
286C2×D4—5661no—
287C2×D4—5661no—
288C2×D4—5661no—
289C2×D4—5661no—
290C2×D4—11321no—
291C2×D4D113211yescharacteristic
292C22×C4—5661no—
293C22×C4—5661no—
294C22×C4—5661no—
295C22×C4—5661no—
296C22×C4C22×D28311yescharacteristic
297C22×C4C22×D28311yescharacteristic
298Q16—5662no—
299Q16—5662no—
300SD16—2834no—
301SD16—5662no—
302SD16—5662no—
303SD16—11321no—
304SD16—11321no—
305D8—5662no—
306D8—5662no—
307M16—22no—
308M16—22no—
309C2×C8C22×D28311yescharacteristic
310C2×C8C22×D28311yescharacteristic
311C2×C8C22×D28311yescharacteristic
312C2×C8C22×D28311yescharacteristic
313C4⋊C4—2831no—
314C4⋊C4—2831no—
315C4⋊C4—5661no—
316C4⋊C4—5661no—
317C4⋊C4—5661no—
318C4⋊C4D113211yescharacteristic
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C22⋊C4—5661no—
327C22⋊C4—5661no—
328C22⋊C4D113211yescharacteristic
329C22⋊C4D113211yescharacteristic
330C42—5661no—
331C42C22×D28311yescharacteristic
332C23—5661no—
333C23—5661no—
334C23—5661no—
335C23—11322no—
336C23—11322no—
337C23—22641no—
338C23C2×D113211yescharacteristic
339C23C2×D113211yescharacteristic
340Q8—2832no—
341Q8—5661no—
342Q8—5661no—
343Q8—5661no—
344Q8—5661no—
345Q8—5661no—
346Q8—11322no—
347D4—41no—
348D4—2832no—
349D4—5661no—
350D4—5661no—
351D4—5661no—
352D4—5661no—
353D4—5661no—
354D4—11322no—
355D4—11322no—
356D4—11322no—
357D4—11322no—
358D4—22641no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—5661no—
366C2×C4—5661no—
367C2×C4—5661no—
368C2×C4—11322no—
369C2×C4—11322no—
370C2×C4—11322no—
371C2×C4—22641no—
372C2×C4C2×D113211yescharacteristic
373C2×C4C2×D113211yescharacteristic
374C2×C4C2×D113211yescharacteristic
375C2×C4C2×D113211yescharacteristic
376C2×C4C23×D28311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D28312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—5662no—
388C22—11321no—
389C22—11321no—
390C22—11321no—
391C22—11321no—
392C22—11321no—
393C22—11321no—
394C22—11321no—
395C22—11321no—
396C22—22644no—
397C22C22×D113211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—5662no—
403C4—11321no—
404C4—11321no—
405C4—11321no—
406C4—11321no—
407C4C2×D4×D28311yescharacteristic
408C4#2258365611yescharacteristic
409C2—41no—
410C2—41no—
411C2—11322no—
412C2—22641no—
413C2—22641no—
414C2D4×D113211yescharacteristic
415C2#3182726511yescharacteristic
416C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#436×C283C2
socleC22×C283C22×D4
hypercenter#436D283
hypocenterC283#3275
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#22583643C2semidirect
2. C2×#22583638C2semidirect
3. #31827124C2semidirect
4. #31827111C2semidirect
5. #31826849C2semidirect
6. #31826723C2semidirect
7. #31826718C2semidirect
8. #31826688C2semidirect
9. #31826681C2semidirect
10. #31826629C2semidirect
11. #31826618C2semidirect
12. #31826612C2semidirect
13. #31826606C2semidirect
14. C4×#17985381C2semidirect
15. #436×C283C2semidirect
18. C22×Dic566C22semidirect
22. C2×Dic1132C22semidirect
23. C2×Dic1132C22semidirect
28. C2×#17985381C22semidirect
32. #22583598C22semidirect
39. #22583584C22semidirect
43. C4×Dic566C22semidirect
47. #22583542C22semidirect
48. #22583535C22semidirect
49. #22583535C22semidirect
50. #22583535C22semidirect
53. #22583532C22semidirect
55. C2×M16×C283C22semidirect
57. C4⋊C8×C283C22semidirect
59. C22⋊C8×C283C22semidirect
60. C4×C8×C283C22semidirect
92. #17985381D4semidirect
208. C283#3275semidirect
224. #436D283semidirect
241. C2×M16C2×D283semidirect
260. C4⋊C8C2×D283semidirect
268. C22⋊C8C2×D283semidirect
269. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C2×#225836382
#318271242
#318271112
#318268492
#318267232
#318267182
#318266882
#318266812
#318266292
#318266182
#318266122
#318266062
C4×#179853812
#436×C2832
#3275283