Finite Group Databasebeta

← #49132776

Subgroups — #49132776

Order 36224.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583643C211yesmaximal, characteristic, complemented
2C22×#17985381C211yesmaximal, characteristic, complemented
3D4×Dic566C211yesmaximal, characteristic, complemented
4#31827111C211yesmaximal, characteristic
5#31826859C211yesmaximal, characteristic, complemented
6#31826711C211yesmaximal, characteristic, complemented
7#31826706C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826671C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826623C211yesmaximal, characteristic, complemented
12#31826618C211yesmaximal, characteristic, complemented
13#31826606C211yesmaximal, characteristic, complemented
14#31826567C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C22×Dic566C2211yescharacteristic, complemented
19C22×D1132C2211yescharacteristic
20#22583643—24no—
21C2×Dic1132C2211yescharacteristic, complemented
22C2×Dic1132C2211yescharacteristic, complemented
23C2×Dic1132C2211yescharacteristic, complemented
24C2×#17985381—24no—
25C2×#17985381C2211yescharacteristic
26C2×#17985381C2211yescharacteristic
27C2×#17985381C2211yescharacteristic
28C2×#17985381C2211yescharacteristic
29C2×#17985381C2211yescharacteristic
30C2×#17985381C2211yescharacteristic
31#22583610C2211yescharacteristic, complemented
32#22583609—21no—
33#22583598C2211yescharacteristic
34#22583595—21no—
35#22583589C2211yescharacteristic
36#22583589C2211yescharacteristic
37#22583589C2211yescharacteristic, complemented
38#22583587—21no—
39#22583587—21no—
40#22583584C2211yescharacteristic
41#22583583—21no—
42#22583578—21no—
43C4×Dic566C2211yescharacteristic, complemented
44C4×D1132C2211yescharacteristic
45D4×Dic283—21no—
46C22⋊C4×D283—21no—
47#22583544C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583535C2211yescharacteristic, complemented
50#22583535C2211yescharacteristic, complemented
51#22583535C2211yescharacteristic, complemented
52#22583532C2211yescharacteristic
53#22583532C2211yescharacteristic
54C2×M16×C283C2211yescharacteristic, complemented
55C22×C8×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic, complemented
60#97×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985392—22no—
63#17985392—41no—
64C2×Dic566—22no—
65C2×Dic566—22no—
66C2×Dic566—21no—
67C2×Dic566—21no—
68C2×Dic566—41no—
69C2×Dic566—41no—
70C2×Dic566C2311yescharacteristic
71C2×Dic566C2311yescharacteristic
72C2×Dic566C2311yescharacteristic
73C2×Dic566C2311yescharacteristic
74C2×D1132—22no—
75C2×D1132—21no—
76C2×D1132—41no—
77C2×D1132C2311yescharacteristic
78C2×D1132C2311yescharacteristic
79C2×C22⋊D283—21no—
80C2×C22⋊D283—21no—
81C22×Dic283—21no—
82C22×Dic283—21no—
83C2×C4×D283—21no—
84C2×C4×D283—21no—
85Dic1132—22no—
86Dic1132—22no—
87Dic1132—41no—
88#17985381—22no—
89#17985381—22no—
90#17985381—22no—
91#17985381—22no—
92#17985381—41no—
93#17985381D414yescomplemented
94C4⋊Dic283—21no—
95C4⋊Dic283—21no—
96C4⋊Dic283C2311yescharacteristic
97C4⋊Dic283C2311yescharacteristic
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100Dic283⋊C4—21no—
101Dic283⋊C4—21no—
102C22⋊Dic283—21no—
103C22⋊Dic283—21no—
104C22⋊Dic283—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—
114C2×C8×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—42no—
126C22×D283—42no—
127C22×D283—81no—
128Dic566—21no—
129Dic566—21no—
130Dic566—21no—
131Dic566—21no—
132Dic566—21no—
133Dic566—21no—
134Dic566—21no—
135Dic566—42no—
136Dic566—42no—
137Dic566C2×D412yes—
138D1132—21no—
139D1132—21no—
140D1132—21no—
141D1132—42no—
142D1132C2×D412yes—
143C22⋊D283—42no—
144C22⋊D283—81no—
145C2×Dic283—21no—
146C2×Dic283—21no—
147C2×Dic283—21no—
148C2×Dic283—21no—
149C2×Dic283—21no—
150C2×Dic283—21no—
151C2×Dic283—42no—
152C2×Dic283—42no—
153C4×D283—42no—
154C4×D283—81no—
155C23×C283C2×D411yescharacteristic
156C23×C283C2×D411yescharacteristic
157D4×C283—22no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283C2×D411yescharacteristic
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2×D411yescharacteristic
165C2×C4×C283C2×D411yescharacteristic
166C2×C4×C283C2411yescharacteristic
167C8×C283—21no—
168C8×C283—21no—
169C8×C283—21no—
170C8×C283C2×D412yes—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—21no—
176C22×C283#13712yescomplemented
177C22×C283C22×D411yescharacteristic
178C2×D283—22no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C2×D283—41no—
183C2×D283—41no—
184C2×D283—84no—
185C4×C283—21no—
186C4×C283—21no—
187C4×C283—21no—
188C4×C283—21no—
189C4×C283C22×D411yescharacteristic
190C4×C283H(5,𝔽2)11yescharacteristic
191Dic283—22no—
192Dic283—41no—
193Dic283—41no—
194Dic283—41no—
195Dic283—41no—
196Dic283—41no—
197C2×C283—22no—
198C2×C283—41no—
199C2×C283D4211yescharacteristic
200C2×C283C2×#13711yescharacteristic
201C2×C283#57711yescharacteristic
202D283—42no—
203D283—81no—
204C283#326611yescharacteristic, complemented, Sylow
205#3266—2831nomaximal, Sylow
206C2×#137—2831no—
207C22×SD16—2831no—
208D4×Q8—2831no—
209#546—2831no—
210#497—2831no—
211#468—2831no—
212#467—2831no—
213#464—2831no—
214#461—2831no—
215#452—2831no—
216#451—2831no—
217#450—2831no—
218#448—2831no—
219#440—2831no—
220#435D28311yescharacteristic, complemented
221C2×#41—2831no—
222C22×Q8—2831no—
223C22×Q8—2831no—
224C22×D4—2831no—
225#137—5664no—
226C2×Q16—2831no—
227C2×Q16—2831no—
228C2×Q16—2831no—
229C2×SD16—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16—2831no—
233C2×SD16—2831no—
234C2×SD16—2831no—
235C2×SD16—5664no—
236C2×M16C2×D28311yescharacteristic, complemented
237C22×C8C2×D28311yescharacteristic
238C4⋊Q8—2831no—
239C4⋊Q8—5661no—
240#124—2831no—
241#123—5661no—
242C22⋊Q8—2831no—
243C22⋊Q8—2831no—
244C22⋊Q8—2831no—
245C22⋊Q8—5661no—
246C22⋊Q8—5661no—
247#121—2831no—
248#121—5661no—
249#120—5661no—
250C4×Q8—2831no—
251C4×D4—2831no—
252C4×D4—5661no—
253C4×D4C2×D28311yescharacteristic
254C2×C22⋊C4—5661no—
255#107—2831no—
256C4⋊C8C2×D28311yescharacteristic, complemented
257#103—2831no—
258#103—2831no—
259#103—2831no—
260#103—2831no—
261#102—2831no—
262#102—2831no—
263C22⋊C8C2×D28311yescharacteristic
264C22⋊C8C2×D28311yescharacteristic, complemented
265#97C2×D28311yescharacteristic, complemented
266C24—5661no—
267#41—5662no—
268#41—11321no—
269C2×Q8—2831no—
270C2×Q8—2831no—
271C2×Q8—2831no—
272C2×Q8—2831no—
273C2×Q8—5662no—
274C2×Q8—5662no—
275C2×Q8—5661no—
276C2×Q8—5661no—
277C2×Q8—11321no—
278C2×Q8—11321no—
279C2×D4—2831no—
280C2×D4—2831no—
281C2×D4—5662no—
282C2×D4—5661no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4—11321no—
286C2×D4D113211yescharacteristic
287C22×C4—5661no—
288C22×C4—5661no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4C22×D28311yescharacteristic
292C22×C4C22×D28311yescharacteristic
293Q16—5662no—
294Q16—5662no—
295Q16—11321no—
296SD16—2834no—
297SD16—5662no—
298SD16—5662no—
299SD16—5662no—
300SD16—5662no—
301SD16—11321no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D28311yescharacteristic
305C2×C8C22×D28311yescharacteristic
306C2×C8C22×D28311yescharacteristic
307C2×C8C22×D28311yescharacteristic
308C4⋊C4—2831no—
309C4⋊C4—2831no—
310C4⋊C4—5661no—
311C4⋊C4—5661no—
312C4⋊C4—5661no—
313C4⋊C4—5661no—
314C4⋊C4—5661no—
315C4⋊C4—5661no—
316C4⋊C4D113211yescharacteristic
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4D113211yescharacteristic
325C22⋊C4D113211yescharacteristic
326C42—5661no—
327C42C22×D28311yescharacteristic
328C23—5661no—
329C23—5661no—
330C23—11322no—
331C23—11322no—
332C23—22641no—
333C23C2×D113211yescharacteristic
334C23C2×D113211yescharacteristic
335Q8—2832no—
336Q8—5661no—
337Q8—5661no—
338Q8—5661no—
339Q8—5661no—
340Q8—5661no—
341Q8—5661no—
342Q8—5661no—
343Q8—11322no—
344Q8—11322no—
345D4—22no—
346D4—2832no—
347D4—5661no—
348D4—5661no—
349D4—5661no—
350D4—11322no—
351D4—11322no—
352D4—22641no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—5661no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—11322no—
364C2×C4—11322no—
365C2×C4—11322no—
366C2×C4—22641no—
367C2×C4C2×D113211yescharacteristic
368C2×C4C2×D113211yescharacteristic
369C2×C4C2×D113211yescharacteristic
370C2×C4C2×D113211yescharacteristic
371C2×C4C23×D28311yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D28312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—5662no—
382C22—11321no—
383C22—11321no—
384C22—11321no—
385C22—11321no—
386C22—11321no—
387C22—22644no—
388C22#2258364312yescomplemented
389C22C22×D113211yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—5662no—
395C4—11321no—
396C4—11321no—
397C4—11321no—
398C4—11321no—
399C4—11321no—
400C4C2×D4×D28311yescharacteristic
401C4#2258365611yescharacteristic
402C2—22no—
403C2—41no—
404C2—11322no—
405C2—22641no—
406C2D4×D113211yescharacteristic
407C2C2×#2258364311yescharacteristic
408C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827111C2
hypercenter#435D283
hypocenterC283#3266
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. C2×#22583643C2semidirect
2. C22×#17985381C2semidirect
3. D4×Dic566C2semidirect
5. #31826859C2semidirect
6. #31826711C2semidirect
7. #31826706C2semidirect
8. #31826688C2semidirect
9. #31826671C2semidirect
10. #31826629C2semidirect
11. #31826623C2semidirect
12. #31826618C2semidirect
13. #31826606C2semidirect
14. #31826567C2semidirect
15. #435×C283C2semidirect
18. C22×Dic566C22semidirect
21. C2×Dic1132C22semidirect
22. C2×Dic1132C22semidirect
23. C2×Dic1132C22semidirect
31. #22583610C22semidirect
37. #22583589C22semidirect
43. C4×Dic566C22semidirect
47. #22583544C22semidirect
48. #22583535C22semidirect
49. #22583535C22semidirect
50. #22583535C22semidirect
51. #22583535C22semidirect
54. C2×M16×C283C22semidirect
57. C4⋊C8×C283C22semidirect
59. C22⋊C8×C283C22semidirect
60. #97×C283C22semidirect
93. #17985381D4semidirect
176. C22×C283#137semidirect
204. C283#3266semidirect
220. #435D283semidirect
236. C2×M16C2×D283semidirect
256. C4⋊C8C2×D283semidirect
264. C22⋊C8C2×D283semidirect
265. #97C2×D283semidirect
388. C22#22583643semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C22×#179853812
D4×Dic5662
#318271112
#318268592
#318267112
#318267062
#318266882
#318266712
#318266292
#318266232
#318266182
#318266062
#318265672
#435×C2832
#3266283