Finite Group Databasebeta

← #49132836

Subgroups — #49132836

Order 36224.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583643C211yesmaximal, characteristic, complemented
2C22×Dic1132C211yesmaximal, characteristic, complemented
3D4×Dic566C211yesmaximal, characteristic, complemented
4#31827124C211yesmaximal, characteristic
5#31826859C211yesmaximal, characteristic, complemented
6#31826723C211yesmaximal, characteristic, complemented
7#31826694C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826676C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826623C211yesmaximal, characteristic, complemented
12#31826623C211yesmaximal, characteristic, complemented
13#31826606C211yesmaximal, characteristic, complemented
14#31826573C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C22×Dic566C2211yescharacteristic
19C22×Dic566C2211yescharacteristic
20#22583643—24no—
21C2×Dic1132—24no—
22C2×Dic1132C2211yescharacteristic
23C2×Dic1132C2211yescharacteristic
24C2×Dic1132C2211yescharacteristic
25C2×Dic1132C2211yescharacteristic
26C2×Dic1132C2211yescharacteristic
27C2×Dic1132C2211yescharacteristic
28C2×#17985381C2211yescharacteristic
29C2×#17985381C2211yescharacteristic
30C2×#17985381C2211yescharacteristic
31#22583610C2211yescharacteristic
32#22583609—21no—
33#22583598C2211yescharacteristic
34#22583596—21no—
35#22583589C2211yescharacteristic
36#22583589C2211yescharacteristic
37#22583589C2211yescharacteristic
38#22583588—21no—
39#22583587—21no—
40#22583587—21no—
41#22583584C2211yescharacteristic
42#22583582—21no—
43C4×Dic566C2211yescharacteristic
44C4×Dic566C2211yescharacteristic
45D4×Dic283—21no—
46(C22⋊D283)⋊C4—21no—
47#22583542C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583535C2211yescharacteristic
50#22583535C2211yescharacteristic
51#22583535C2211yescharacteristic
52#22583535C2211yescharacteristic
53#22583532C2211yescharacteristic
54C2×M16×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic
60#97×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—41no—
63C2×Dic566—22no—
64C2×Dic566—22no—
65C2×Dic566—22no—
66C2×Dic566—21no—
67C2×Dic566—21no—
68C2×Dic566—21no—
69C2×Dic566—41no—
70C2×Dic566—41no—
71C2×Dic566—41no—
72C2×Dic566C2311yescharacteristic
73C2×Dic566C2311yescharacteristic
74C2×Dic566C2311yescharacteristic
75C2×Dic566C2311yescharacteristic
76C2×Dic566C2311yescharacteristic
77C2×D1132C2311yescharacteristic
78C2×C22⋊D283—21no—
79C2×C22⋊D283—21no—
80C22×Dic283—21no—
81C22×Dic283—21no—
82C22×Dic283—21no—
83C2×C4×D283—21no—
84Dic1132—22no—
85Dic1132—22no—
86Dic1132—22no—
87Dic1132—22no—
88Dic1132—41no—
89Dic1132D414yescomplemented
90#17985381—22no—
91#17985381—22no—
92#17985381—41no—
93C4⋊Dic283—21no—
94C4⋊Dic283—21no—
95C4⋊Dic283C2311yescharacteristic
96C4⋊Dic283C2311yescharacteristic
97Dic283⋊C4—21no—
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—
108C4×Dic283—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—
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—21no—
129Dic566—21no—
130Dic566—21no—
131Dic566—21no—
132Dic566—42no—
133Dic566—42no—
134Dic566—42no—
135Dic566C2×D412yes—
136Dic566C2×D412yes—
137D1132—21no—
138D1132—21no—
139C22⋊D283—42no—
140C22⋊D283—42no—
141C2×Dic283—21no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283—21no—
145C2×Dic283—21no—
146C2×Dic283—21no—
147C2×Dic283—21no—
148C2×Dic283—42no—
149C2×Dic283—42no—
150C2×Dic283—42no—
151C4×D283—42no—
152C23×C283C2×D411yescharacteristic
153C23×C283C2×D411yescharacteristic
154D4×C283—22no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283C2×D411yescharacteristic
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283C2×D411yescharacteristic
162C2×C4×C283C2×D411yescharacteristic
163C2×C4×C283C2411yescharacteristic
164C8×C283—21no—
165C8×C283—21no—
166C8×C283—21no—
167C8×C283C2×D412yes—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283—21no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283#13712yescomplemented
174C22×C283C22×D411yescharacteristic
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—41no—
178C4×C283—21no—
179C4×C283—21no—
180C4×C283—21no—
181C4×C283—21no—
182C4×C283C22×D411yescharacteristic
183C4×C283H(5,𝔽2)11yescharacteristic
184Dic283—22no—
185Dic283—22no—
186Dic283—41no—
187Dic283—41no—
188Dic283—41no—
189Dic283—41no—
190Dic283—41no—
191C2×C283—22no—
192C2×C283—41no—
193C2×C283D4211yescharacteristic
194C2×C283C2×#13711yescharacteristic
195C2×C283#57811yescharacteristic
196D283—81no—
197C283#327011yescharacteristic, complemented, Sylow
198#3270—2831nomaximal, Sylow
199C2×#137—2831no—
200C22×Q16—2831no—
201D4×Q8—2831no—
202#548—2831no—
203#497—2831no—
204#470—2831no—
205#465—2831no—
206#464—2831no—
207#462—2831no—
208#452—2831no—
209#451—2831no—
210#451—2831no—
211#448—2831no—
212#441—2831no—
213#435D28311yescharacteristic, complemented
214C2×#41—2831no—
215C22×Q8—2831no—
216C22×Q8—2831no—
217C22×Q8—2831no—
218#137—5664no—
219C2×Q16—2831no—
220C2×Q16—2831no—
221C2×Q16—2831no—
222C2×Q16—2831no—
223C2×Q16—2831no—
224C2×Q16—2831no—
225C2×Q16—5664no—
226C2×SD16—2831no—
227C2×SD16—2831no—
228C2×SD16—2831no—
229C2×M16C2×D28311yescharacteristic
230C22×C8C2×D28311yescharacteristic
231C4⋊Q8—2831no—
232C4⋊Q8—5661no—
233#124—2831no—
234#124—5661no—
235C22⋊Q8—2831no—
236C22⋊Q8—2831no—
237C22⋊Q8—2831no—
238C22⋊Q8—5661no—
239C22⋊Q8—5661no—
240C22⋊Q8—5661no—
241#121—2831no—
242#121—5661no—
243C4×Q8—2831no—
244C4×Q8—2831no—
245C4×D4—5661no—
246C4×D4—5661no—
247C4×D4C2×D28311yescharacteristic
248#106—2831no—
249C4⋊C8C2×D28311yescharacteristic
250#103—2831no—
251#103—2831no—
252#103—2831no—
253#103—2831no—
254#103—2831no—
255#102—2831no—
256C22⋊C8C2×D28311yescharacteristic
257C22⋊C8C2×D28311yescharacteristic
258#97C2×D28311yescharacteristic
259#41—5662no—
260#41—11321no—
261C2×Q8—2831no—
262C2×Q8—2831no—
263C2×Q8—2831no—
264C2×Q8—2831no—
265C2×Q8—2831no—
266C2×Q8—5662no—
267C2×Q8—5662no—
268C2×Q8—5662no—
269C2×Q8—5661no—
270C2×Q8—5661no—
271C2×Q8—5661no—
272C2×Q8—11321no—
273C2×Q8—11321no—
274C2×Q8—11321no—
275C2×D4—2831no—
276C2×D4—5661no—
277C2×D4—5661no—
278C2×D4D113211yescharacteristic
279C22×C4—5661no—
280C22×C4—5661no—
281C22×C4—5661no—
282C22×C4—5661no—
283C22×C4C22×D28311yescharacteristic
284C22×C4C22×D28311yescharacteristic
285Q16—2834no—
286Q16—5662no—
287Q16—5662no—
288Q16—5662no—
289Q16—5662no—
290Q16—11321no—
291SD16—5662no—
292SD16—5662no—
293SD16—11321no—
294M16—22no—
295C2×C8—22no—
296C2×C8C22×D28311yescharacteristic
297C2×C8C22×D28311yescharacteristic
298C2×C8C22×D28311yescharacteristic
299C2×C8C22×D28311yescharacteristic
300C4⋊C4—2831no—
301C4⋊C4—2831no—
302C4⋊C4—5661no—
303C4⋊C4—5661no—
304C4⋊C4—5661no—
305C4⋊C4—5661no—
306C4⋊C4—5661no—
307C4⋊C4—5661no—
308C4⋊C4—5661no—
309C4⋊C4D113211yescharacteristic
310C22⋊C4—5661no—
311C22⋊C4—5661no—
312C22⋊C4—5661no—
313C22⋊C4—5661no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4D113211yescharacteristic
317C22⋊C4D113211yescharacteristic
318C42—5661no—
319C42—5661no—
320C42C22×D28311yescharacteristic
321C23—5661no—
322C23C2×D113211yescharacteristic
323C23C2×D113211yescharacteristic
324Q8—2832no—
325Q8—2832no—
326Q8—5661no—
327Q8—5661no—
328Q8—5661no—
329Q8—5661no—
330Q8—5661no—
331Q8—5661no—
332Q8—5661no—
333Q8—5661no—
334Q8—11322no—
335Q8—11322no—
336Q8—11322no—
337D4—22no—
338D4—5661no—
339D4—5661no—
340D4—11322no—
341D4—11322no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—5661no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—5661no—
351C2×C4—5661no—
352C2×C4—5661no—
353C2×C4—11322no—
354C2×C4—11322no—
355C2×C4—11322no—
356C2×C4—11322no—
357C2×C4C2×D113211yescharacteristic
358C2×C4C2×D113211yescharacteristic
359C2×C4C2×D113211yescharacteristic
360C2×C4C2×D113211yescharacteristic
361C2×C4C23×D28311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8D4×D28312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—11321no—
372C22—11321no—
373C22—11321no—
374C22#2258364312yescomplemented
375C22C22×D113211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—5662no—
381C4—5662no—
382C4—11321no—
383C4—11321no—
384C4—11321no—
385C4—11321no—
386C4—11321no—
387C4C2×D4×D28311yescharacteristic
388C4#2258365611yescharacteristic
389C2—22no—
390C2—41no—
391C2—22641no—
392C2D4×D113211yescharacteristic
393C2C2×#2258364311yescharacteristic
394C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827124C2
hypercenter#435D283
hypocenterC283#3270
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×Dic1132C2semidirect
3. D4×Dic566C2semidirect
5. #31826859C2semidirect
6. #31826723C2semidirect
7. #31826694C2semidirect
8. #31826688C2semidirect
9. #31826676C2semidirect
10. #31826629C2semidirect
11. #31826623C2semidirect
12. #31826623C2semidirect
13. #31826606C2semidirect
14. #31826573C2semidirect
15. #435×C283C2semidirect
89. Dic1132D4semidirect
173. C22×C283#137semidirect
197. C283#3270semidirect
213. #435D283semidirect
374. 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×Dic11322
D4×Dic5662
#318271242
#318268592
#318267232
#318266942
#318266882
#318266762
#318266292
#318266232
#318266062
#318265732
#435×C2832
#3270283