Finite Group Databasebeta

← #49130890

Subgroups — #49130890

Order 36224.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583642C211yesmaximal, characteristic, complemented
2C2×M16×D283C211yesmaximal, characteristic, complemented
3#31826978C211yesmaximal, characteristic
4C22⋊Q8×D283C211yesmaximal, characteristic, complemented
5#31826721C211yesmaximal, characteristic, complemented
6#31826713C211yesmaximal, characteristic, complemented
7#31826711C211yesmaximal, characteristic, complemented
8#31826705C211yesmaximal, characteristic, complemented
9#31826703C211yesmaximal, characteristic, complemented
10#31826697C211yesmaximal, characteristic, complemented
11#31826695C211yesmaximal, characteristic, complemented
12#31826504C211yesmaximal, characteristic, complemented
13#31826472C211yesmaximal, characteristic, complemented
14#31826465C211yesmaximal, characteristic, complemented
15#470×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19#22583642—24no—
20C2×#17985382C2211yescharacteristic, complemented
21C2×#17985381C2211yescharacteristic, complemented
22C2×#17985379C2211yescharacteristic, complemented
23C2×#17985376C2211yescharacteristic
24C2×#17985375C2211yescharacteristic
25C2×#17985375C2211yescharacteristic
26M16×D283—24no—
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583595—21no—
30#22583590C2211yescharacteristic
31#22583589C2211yescharacteristic
32#22583588—21no—
33#22583587—21no—
34#22583586C2211yescharacteristic
35#22583586C2211yescharacteristic
36#22583585C2211yescharacteristic
37#22583584C2211yescharacteristic
38#22583580—21no—
39#22583572—21no—
40(C22⋊D283)⋊C4—21no—
41#22583568C2211yescharacteristic
42C4⋊C4×D283—21no—
43C4⋊C4×D283C2211yescharacteristic
44C22⋊C4×D283—21no—
45#22583544C2211yescharacteristic, complemented
46#22583543C2211yescharacteristic, complemented
47#22583541C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583534C2211yescharacteristic, complemented
51#22583533C2211yescharacteristic, complemented
52#22583532C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×Q16×C283C2211yescharacteristic, complemented
55C2×M16×C283C2211yescharacteristic
56C22⋊Q8×C283C2211yescharacteristic
57C22⋊Q8×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#103×C283C2211yescharacteristic, complemented
61C23×D283D411yescharacteristic
62#17985393—22no—
63#17985393—22no—
64C2×Dic566—21no—
65C2×Dic566C2311yescharacteristic
66Q8×D283—22no—
67Q8×D283—22no—
68C2×D1132—21no—
69C2×D1132—21no—
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72C22×Dic283D411yescharacteristic
73C2×C4×D283—22no—
74C2×C4×D283—22no—
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283D411yescharacteristic
79C2×C4×D283D411yescharacteristic
80C2×C4×D283C2311yescharacteristic
81C2×C4×D283C2311yescharacteristic
82#17985382—22no—
83#17985381—22no—
84#17985379—22no—
85#17985376—22no—
86#17985375—22no—
87#17985375D414yescomplemented
88C2×C283⋊C8C2311yescharacteristic
89C2×C283⋊C8C2311yescharacteristic
90C8×D283—22no—
91C8×D283—22no—
92C4⋊Dic283—21no—
93C4⋊Dic283C2311yescharacteristic
94C4⋊Dic283C2311yescharacteristic
95Dic283⋊C4—21no—
96Dic283⋊C4—21no—
97Dic283⋊C4—21no—
98Dic283⋊C4—21no—
99C22⋊Dic283—21no—
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106C4×Dic283—21no—
107C2×Q8×C283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C22×C4×C283C2311yescharacteristic
110Q16×C283—22no—
111M16×C283—22no—
112C2×C8×C283C2311yescharacteristic
113C2×C8×C283C2311yescharacteristic
114C4⋊C4×C283—21no—
115C4⋊C4×C283—21no—
116C4⋊C4×C283C2311yescharacteristic
117C4⋊C4×C283C2311yescharacteristic
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C22×D283—22no—
121C22×D283—22no—
122C22×D283—21no—
123C22×D283—41no—
124C22×D283C2×D411yescharacteristic
125C22×D283C2×D411yescharacteristic
126Dic566—21no—
127Dic566—21no—
128Dic566—42no—
129D1132—21no—
130D1132—21no—
131D1132—42no—
132D1132—42no—
133C22⋊D283—42no—
134C2×Dic283—22no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—21no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C4×D283—22no—
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—22no—
144C4×D283—42no—
145C4×D283—42no—
146C4×D283—42no—
147C4×D283C2×D412yes—
148C4×D283#4112yes—
149C283⋊C8—21no—
150C283⋊C8C2×D412yes—
151C23×C283C2×D411yescharacteristic
152Q8×C283—21no—
153Q8×C283—21no—
154Q8×C283—21no—
155Q8×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283C2×D411yescharacteristic
163C2×C4×C283C2411yescharacteristic
164C8×C283—21no—
165C8×C283C2×D412yes—
166C22×C283—21no—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283C22×D411yescharacteristic
170C2×D283—21no—
171C2×D283—21no—
172C2×D283—21no—
173C2×D283—21no—
174C2×D283—44no—
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—41no—
178C2×D283#12112yes—
179C2×D283#13712yescomplemented
180C4×C283—21no—
181C4×C283—41no—
182C4×C283—41no—
183C4×C283—41no—
184C4×C283—41no—
185C4×C283C22×D411yescharacteristic
186C4×C283C2×#4111yescharacteristic
187Dic283—21no—
188Dic283—41no—
189Dic283—41no—
190Dic283—41no—
191Dic283#12112yes—
192C2×C283—41no—
193C2×C283C2×#12111yescharacteristic
194C2×C283C2×#13711yescharacteristic
195C2×C283#57511yescharacteristic
196D283—22no—
197D283—22no—
198D283—81no—
199C283#305611yescharacteristic, complemented, Sylow
200#3056—2831nomaximal, Sylow
201C2×#137—2831no—
202C22×M16—2831no—
203#525—2831no—
204C2×C22⋊Q8—2831no—
205#470—2831no—
206#470D28311yescharacteristic, complemented
207#468—2831no—
208#468—2831no—
209#467—2831no—
210#467—2831no—
211#465—2831no—
212#465—2831no—
213#428—2831no—
214#419—2831no—
215#417—2831no—
216C2×#41—2831no—
217C22×Q8—2831no—
218C23×C4—2831no—
219#137—5664no—
220C2×Q16—2831no—
221C2×Q16C2×D28311yescharacteristic, complemented
222C2×SD16—2831no—
223C2×SD16—2831no—
224C2×M16—2831no—
225C2×M16—2831no—
226C2×M16—2831no—
227C2×M16—5664no—
228C2×M16C2×D28311yescharacteristic
229C22×C8—2831no—
230C22×C8—2831no—
231#123—5661no—
232C22⋊Q8—2831no—
233C22⋊Q8—2831no—
234C22⋊Q8—2831no—
235C22⋊Q8—2831no—
236C22⋊Q8—5661no—
237C22⋊Q8—5661no—
238C22⋊Q8C2×D28311yescharacteristic
239C22⋊Q8C2×D28311yescharacteristic
240#121—2831no—
241#121—2831no—
242#120—5661no—
243C4×D4—5661no—
244C4×D4—5661no—
245#117—2831no—
246C2×C4⋊C4—2831no—
247C2×C4⋊C4—5661no—
248C2×C22⋊C4—5661no—
249#107—2831no—
250#107—2831no—
251#106—2831no—
252#106C2×D28311yescharacteristic, complemented
253#103—2831no—
254#103—2831no—
255#103—2831no—
256#103—2831no—
257#103C2×D28311yescharacteristic, complemented
258#103C2×D28311yescharacteristic, complemented
259#102—2831no—
260#102—2831no—
261C24—2831no—
262#41—5662no—
263#41—5662no—
264C2×Q8—2831no—
265C2×Q8—5661no—
266C2×Q8—5662no—
267C2×Q8—5662no—
268C2×Q8C22×D28311yescharacteristic
269C2×Q8C22×D28311yescharacteristic
270C2×D4—2831no—
271C2×D4—5661no—
272C2×D4—5661no—
273C2×D4—5661no—
274C22×C4—2831no—
275C22×C4—2831no—
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—5662no—
280C22×C4—5662no—
281C22×C4—5661no—
282C22×C4—5661no—
283C22×C4—5661no—
284C22×C4C22×D28311yescharacteristic
285Q16—22no—
286Q16—5662no—
287SD16—5662no—
288SD16—5662no—
289M16—22no—
290M16—2834no—
291M16—5662no—
292M16—5662no—
293C2×C8—2831no—
294C2×C8—2831no—
295C2×C8—5662no—
296C2×C8—5662no—
297C2×C8C22×D28311yescharacteristic
298C2×C8C22×D28311yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—2831no—
302C4⋊C4—2831no—
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—5661no—
313C22⋊C4—5661no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C42—5661no—
320C23—2831no—
321C23—2831no—
322C23—5662no—
323C23—5662no—
324C23—5661no—
325C23—11321no—
326C23D4×D28311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—21no—
331Q8—5661no—
332Q8—5661no—
333Q8—11322no—
334D4—5661no—
335D4—5661no—
336D4—11322no—
337D4—11322no—
338D4—11322no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—2831no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2831no—
349C2×C4—5662no—
350C2×C4—5662no—
351C2×C4—5662no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—11322no—
358C2×C4—11322no—
359C2×C4—11322no—
360C2×C4D4×D28311yescharacteristic
361C2×C4C23×D28311yescharacteristic
362C8—21no—
363C8—2832no—
364C8—5661no—
365C8D4×D28312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—2832no—
370C22—2832no—
371C22—5661no—
372C22—5661no—
373C22—5661no—
374C22—5661no—
375C22—11324no—
376C22—11321no—
377C22—11321no—
378C22—11321no—
379C22C2×D4×D28311yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—2832no—
386C4—5661no—
387C4—11321no—
388C4—11321no—
389C4—11321no—
390C4C2×D4×D28311yescharacteristic
391C4#41×D28311yescharacteristic
392C2—41no—
393C2—5662no—
394C2—5662no—
395C2—22641no—
396C2#121×D28311yescharacteristic
397C2#137×D28311yescharacteristic
398C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#470×C283C2
socleC22×C283C22×D4
prime radical#31826978C2
hypercenter#470D283
hypocenterC283#3056
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#22583642C2semidirect
2. C2×M16×D283C2semidirect
4. C22⋊Q8×D283C2semidirect
5. #31826721C2semidirect
6. #31826713C2semidirect
7. #31826711C2semidirect
8. #31826705C2semidirect
9. #31826703C2semidirect
10. #31826697C2semidirect
11. #31826695C2semidirect
12. #31826504C2semidirect
13. #31826472C2semidirect
14. #31826465C2semidirect
15. #470×C283C2semidirect
20. C2×#17985382C22semidirect
21. C2×#17985381C22semidirect
22. C2×#17985379C22semidirect
45. #22583544C22semidirect
46. #22583543C22semidirect
47. #22583541C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583534C22semidirect
51. #22583533C22semidirect
52. #22583532C22semidirect
53. #22583530C22semidirect
54. C2×Q16×C283C22semidirect
58. #106×C283C22semidirect
59. #103×C283C22semidirect
60. #103×C283C22semidirect
87. #17985375D4semidirect
179. C2×D283#137semidirect
199. C283#3056semidirect
206. #470D283semidirect
221. C2×Q16C2×D283semidirect
252. #106C2×D283semidirect
257. #103C2×D283semidirect
258. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836422
C2×M16×D2832
#318269782
C22⋊Q8×D2832
#318267212
#318267132
#318267112
#318267052
#318267032
#318266972
#318266952
#318265042
#318264722
#318264652
#470×C2832
#3056283