Finite Group Databasebeta

← #49132828

Subgroups — #49132828

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×#22583639C211yesmaximal, characteristic, complemented
2C22×Dic1132C211yesmaximal, characteristic, complemented
3#31827128C211yesmaximal, characteristic, complemented
4#31827121C211yesmaximal, characteristic
5#31826856C211yesmaximal, characteristic, complemented
6#31826724C211yesmaximal, characteristic, complemented
7#31826686C211yesmaximal, characteristic, complemented
8#31826674C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826620C211yesmaximal, characteristic, complemented
12#31826603C211yesmaximal, characteristic, complemented
13#31826571C211yesmaximal, characteristic, complemented
14#31826536C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C22×Dic566C2211yescharacteristic
19C2×Q8×D283C2211yescharacteristic
20#22583639—24no—
21C2×Dic1132—24no—
22C2×Dic1132C2211yescharacteristic
23C2×Dic1132C2211yescharacteristic
24C2×Dic1132C2211yescharacteristic
25C2×Dic1132C2211yescharacteristic
26C2×#17985382C2211yescharacteristic
27C2×#17985382C2211yescharacteristic
28C2×#17985380C2211yescharacteristic
29C2×#17985380C2211yescharacteristic
30C2×#17985375C2211yescharacteristic
31#22583609—21no—
32#22583608C2211yescharacteristic
33#22583597C2211yescharacteristic
34#22583596—21no—
35#22583590C2211yescharacteristic
36#22583590C2211yescharacteristic
37#22583588—21no—
38#22583587—21no—
39#22583587—21no—
40#22583582—21no—
41#22583575C2211yescharacteristic
42#22583575C2211yescharacteristic
43D4×Dic283—21no—
44C4×C22⋊D283C2211yescharacteristic
45(C22⋊D283)⋊C4—21no—
46Dic283⋊C8C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583533C2211yescharacteristic
50#22583533C2211yescharacteristic
51C22⋊(C283⋊C8)C2211yescharacteristic
52(C2×D283)⋊C8C2211yescharacteristic
53#22583520C2211yescharacteristic
54C2×SD16×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic
56C22⋊Q8×C283C2211yescharacteristic
57#121×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic
59#103×C283C2211yescharacteristic
60#102×C283C2211yescharacteristic
61#17985391—22no—
62#17985391—41no—
63C2×Dic566—21no—
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
74Q8×D283—22no—
75Q8×D283—41no—
76C2×C22⋊D283—21no—
77C2×C22⋊D283D411yescharacteristic
78C22×Dic283—21no—
79C22×Dic283—21no—
80C22×Dic283—21no—
81C2×C4×D283—21no—
82C2×C4×D283C2311yescharacteristic
83Dic1132—22no—
84Dic1132—22no—
85Dic1132—22no—
86Dic1132D414yescomplemented
87#17985382—22no—
88#17985382—41no—
89#17985380—22no—
90#17985380—41no—
91#17985375—22no—
92C2×C283⋊C8C2311yescharacteristic
93C2×C283⋊C8C2311yescharacteristic
94C4⋊Dic283—21no—
95C4⋊Dic283—21no—
96Dic283⋊C4—21no—
97Dic283⋊C4—21no—
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100Dic283⋊C4D411yescharacteristic
101C22⋊Dic283—21no—
102C22⋊Dic283—21no—
103C22⋊Dic283D411yescharacteristic
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4D411yescharacteristic
107C4×Dic283—21no—
108C4×Dic283—21no—
109C4×Dic283C2311yescharacteristic
110C2×Q8×C283C2311yescharacteristic
111C2×D4×C283—21no—
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283C2311yescharacteristic
114SD16×C283—22no—
115C2×C8×C283—22no—
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C4⋊C4×C283—21no—
119C4⋊C4×C283C2311yescharacteristic
120C4⋊C4×C283C2311yescharacteristic
121C22⋊C4×C283—21no—
122C22⋊C4×C283—21no—
123C22×D283C2×D411yescharacteristic
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—21no—
129Dic566—21no—
130Dic566—42no—
131Dic566—42no—
132Dic566—42no—
133Dic566C2×D412yes—
134Dic566C2×D412yes—
135C22⋊D283—22no—
136C22⋊D283—42no—
137C2×Dic283—21no—
138C2×Dic283—21no—
139C2×Dic283—21no—
140C2×Dic283—21no—
141C2×Dic283—42no—
142C2×Dic283—42no—
143C2×Dic283—42no—
144C2×Dic283C2×D411yescharacteristic
145C2×Dic283C2×D411yescharacteristic
146C2×Dic283C2×D411yescharacteristic
147C4×D283—21no—
148C4×D283—21no—
149C4×D283—42no—
150C283⋊C8—21no—
151C283⋊C8—21no—
152C23×C283—21no—
153C23×C283C2×D411yescharacteristic
154Q8×C283—21no—
155Q8×C283—21no—
156D4×C283—21no—
157D4×C283—21no—
158D4×C283—42no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283C2×D411yescharacteristic
165C2×C4×C283C2411yescharacteristic
166C8×C283—21no—
167C8×C283C2×D412yes—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283—41no—
171C22×C283—41no—
172C22×C283—41no—
173C22×C283#13712yescomplemented
174C22×C283C22×D411yescharacteristic
175C2×D283—21no—
176C2×D283—21no—
177C2×D283—21no—
178C4×C283—21no—
179C4×C283—41no—
180C4×C283—41no—
181C4×C283—41no—
182C4×C283C22×D411yescharacteristic
183C4×C283H(5,𝔽2)11yescharacteristic
184Dic283—21no—
185Dic283—22no—
186Dic283—22no—
187Dic283—21no—
188Dic283—21no—
189Dic283—41no—
190Dic283—41no—
191C2×C283—22no—
192C2×C283—81no—
193C2×C283D4211yescharacteristic
194C2×C283C2×#13711yescharacteristic
195C2×C283#57811yescharacteristic
196D283—41no—
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#465D28311yescharacteristic, complemented
206#464—2831no—
207#462—2831no—
208#452—2831no—
209#451—2831no—
210#451—2831no—
211#448—2831no—
212#441—2831no—
213#435—2831no—
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×SD16C2×D28311yescharacteristic
229C2×M16—2831no—
230C22×C8C2×D28311yescharacteristic
231C4⋊Q8—2831no—
232C4⋊Q8—5661no—
233#124—2831no—
234#124—5661no—
235C22⋊Q8—2831no—
236C22⋊Q8—2831no—
237C22⋊Q8—5661no—
238C22⋊Q8—5661no—
239C22⋊Q8—5661no—
240C22⋊Q8C2×D28311yescharacteristic
241#121—5661no—
242#121C2×D28311yescharacteristic
243C4×Q8—2831no—
244C4×Q8—2831no—
245C4×D4—2831no—
246C4×D4—5661no—
247C4×D4—5661no—
248#106C2×D28311yescharacteristic
249C4⋊C8—2831no—
250#103—2831no—
251#103—2831no—
252#103—2831no—
253#103—2831no—
254#103C2×D28311yescharacteristic
255#102C2×D28311yescharacteristic
256C22⋊C8—2831no—
257C22⋊C8—2831no—
258#97—2831no—
259#41—5662no—
260#41—11321no—
261C2×Q8—2831no—
262C2×Q8—2831no—
263C2×Q8—2831no—
264C2×Q8—2831no—
265C2×Q8—5661no—
266C2×Q8—5662no—
267C2×Q8—5662no—
268C2×Q8—5661no—
269C2×Q8—5661no—
270C2×Q8—5662no—
271C2×Q8—11321no—
272C2×Q8—11321no—
273C2×Q8—11321no—
274C2×Q8C22×D28311yescharacteristic
275C2×D4—21no—
276C2×D4—2831no—
277C2×D4—5661no—
278C2×D4C22×D28311yescharacteristic
279C22×C4—2831no—
280C22×C4—5661no—
281C22×C4—5661no—
282C22×C4—5661no—
283C22×C4—5661no—
284C22×C4C22×D28311yescharacteristic
285Q16—2834no—
286Q16—5662no—
287Q16—5662no—
288Q16—5662no—
289Q16—5662no—
290Q16—11321no—
291SD16—22no—
292SD16—5662no—
293SD16—11321no—
294M16—5662no—
295C2×C8—22no—
296C2×C8—2831no—
297C2×C8—2831no—
298C2×C8C22×D28311yescharacteristic
299C2×C8C22×D28311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—2831no—
302C4⋊C4—5661no—
303C4⋊C4—5661no—
304C4⋊C4—5661no—
305C4⋊C4—5661no—
306C4⋊C4—5661no—
307C4⋊C4—5661no—
308C4⋊C4C22×D28311yescharacteristic
309C4⋊C4C22×D28311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—2831no—
313C22⋊C4—2831no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C22⋊C4—5661no—
318C42—2831no—
319C42—5661no—
320C42—5661no—
321C23—21no—
322C23—2831no—
323C23D4×D28311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—2832no—
327Q8—2832no—
328Q8—5661no—
329Q8—5661no—
330Q8—5661no—
331Q8—5661no—
332Q8—5661no—
333Q8—5661no—
334Q8—11322no—
335Q8—11322no—
336Q8—11322no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—5662no—
341D4—11322no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—2831no—
348C2×C4—2831no—
349C2×C4—2831no—
350C2×C4—5661no—
351C2×C4—5661no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—11322no—
357C2×C4—11322no—
358C2×C4—11322no—
359C2×C4—11322no—
360C2×C4D4×D28311yescharacteristic
361C2×C4C23×D28311yescharacteristic
362C8—21no—
363C8—5661no—
364C8—5661no—
365C8D4×D28312yes—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—5661no—
372C22—5661no—
373C22—5661no—
374C22#2258363912yescomplemented
375C22C2×D4×D28311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—5661no—
381C4—5661no—
382C4—5661no—
383C4—5662no—
384C4—5662no—
385C4—11321no—
386C4—11321no—
387C4C2×D4×D28311yescharacteristic
388C4#2258365611yescharacteristic
389C2—22no—
390C2—81no—
391C2—11321no—
392C2#3182709911yescharacteristic
393C2C2×#2258363911yescharacteristic
394C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
prime radical#31827121C2
hypercenter#465D283
hypocenterC283#3270
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#22583639C2semidirect
2. C22×Dic1132C2semidirect
3. #31827128C2semidirect
5. #31826856C2semidirect
6. #31826724C2semidirect
7. #31826686C2semidirect
8. #31826674C2semidirect
9. #31826628C2semidirect
10. #31826622C2semidirect
11. #31826620C2semidirect
12. #31826603C2semidirect
13. #31826571C2semidirect
14. #31826536C2semidirect
15. #465×C283C2semidirect
86. Dic1132D4semidirect
173. C22×C283#137semidirect
197. C283#3270semidirect
205. #465D283semidirect
374. C22#22583639semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
C22×Dic11322
#318271282
#318271212
#318268562
#318267242
#318266862
#318266742
#318266282
#318266222
#318266202
#318266032
#318265712
#318265362
#465×C2832
#3270283