Finite Group Databasebeta

← #49130837

Subgroups — #49130837

Order 36224.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583631C211yesmaximal, characteristic, complemented
2C22×C8×D283C211yesmaximal, characteristic, complemented
3#31826978C211yesmaximal, characteristic, complemented
4#31826975C211yesmaximal, characteristic, complemented
5#31826705C211yesmaximal, characteristic, complemented
6#31826704C211yesmaximal, characteristic, complemented
7#31826700C211yesmaximal, characteristic, complemented
8#31826699C211yesmaximal, characteristic, complemented
9#31826695C211yesmaximal, characteristic, complemented
10#31826694C211yesmaximal, characteristic, complemented
11#31826691C211yesmaximal, characteristic, complemented
12#31826500C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14#31826458C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19#22583631—24no—
20C2×#17985382C2211yescharacteristic, complemented
21C2×#17985381C2211yescharacteristic, complemented
22C2×#17985377C2211yescharacteristic, complemented
23C22×C283⋊C8C2211yescharacteristic
24C2×C8×D283—24no—
25C2×C8×D283C2211yescharacteristic
26C2×C8×D283C2211yescharacteristic
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583595—21no—
30#22583592—21no—
31#22583590C2211yescharacteristic
32#22583589C2211yescharacteristic
33#22583586C2211yescharacteristic
34#22583585C2211yescharacteristic
35#22583584C2211yescharacteristic
36#22583581C2211yescharacteristic
37#22583580—21no—
38#22583578—21no—
39D4×Dic283—21no—
40#22583572—21no—
41(C22⋊D283)⋊C4—21no—
42(C22⋊D283)⋊C4—21no—
43#22583568C2211yescharacteristic
44#22583568C2211yescharacteristic
45#22583543C2211yescharacteristic, complemented
46#22583543C2211yescharacteristic, complemented
47#22583542C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583533C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic, complemented
55C22×C8×C283C2211yescharacteristic
56C22⋊Q8×C283C2211yescharacteristic
57#121×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283D411yescharacteristic
62#17985393—22no—
63#17985393—22no—
64#17985391—22no—
65#17985391—22no—
66C2×Dic566C2311yescharacteristic
67C2×D1132—21no—
68C2×D1132—21no—
69C2×D1132C2311yescharacteristic
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C22×Dic283—21no—
74C22×Dic283D411yescharacteristic
75C2×C4×D283—22no—
76C2×C4×D283—22no—
77C2×C4×D283—21no—
78C2×C4×D283D411yescharacteristic
79C2×C4×D283D411yescharacteristic
80C2×C4×D283C2311yescharacteristic
81C2×C4×D283C2311yescharacteristic
82#17985382—22no—
83#17985381—22no—
84#17985377—22no—
85C2×C283⋊C8—22no—
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C8×D283—22no—
89C8×D283—22no—
90C8×D283—22no—
91C8×D283D414yescomplemented
92C4⋊Dic283—21no—
93C4⋊Dic283C2311yescharacteristic
94C4⋊Dic283C2311yescharacteristic
95Dic283⋊C4—21no—
96Dic283⋊C4—21no—
97C22⋊Dic283—21no—
98C22⋊Dic283—21no—
99(C2×D283)⋊C4—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—
105C4×Dic283—21no—
106C4×Dic283—21no—
107C2×Q8×C283C2311yescharacteristic
108C2×D4×C283—21no—
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283C2311yescharacteristic
111SD16×C283—22no—
112C2×C8×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
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—22no—
123C22×D283—21no—
124C22×D283C2×D411yescharacteristic
125C22×D283C2×D411yescharacteristic
126Dic566—21no—
127Dic566—21no—
128D1132—21no—
129D1132—21no—
130D1132—42no—
131D1132—42no—
132C22⋊D283—42no—
133C22⋊D283—42no—
134C22⋊D283—42no—
135C2×Dic283—22no—
136C2×Dic283—21no—
137C2×Dic283—21no—
138C2×Dic283—21no—
139C2×Dic283—42no—
140C2×Dic283C2×D411yescharacteristic
141C2×Dic283C2×D411yescharacteristic
142C4×D283—22no—
143C4×D283—21no—
144C4×D283—21no—
145C4×D283—22no—
146C4×D283—42no—
147C4×D283C2×D412yes—
148C4×D283#4112yes—
149C283⋊C8—21no—
150C283⋊C8C2×D412yes—
151C23×C283—21no—
152C23×C283C2×D411yescharacteristic
153Q8×C283—21no—
154Q8×C283—21no—
155D4×C283—21no—
156D4×C283—21no—
157D4×C283—42no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2411yescharacteristic
165C8×C283—21no—
166C8×C283C2×D412yes—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283—41no—
170C22×C283—41no—
171C22×C283—41no—
172C22×C283#13512yescomplemented
173C22×C283C22×D411yescharacteristic
174C2×D283—28no—
175C2×D283—21no—
176C2×D283—21no—
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C2×D283#12112yes—
183C2×D283#13512yescomplemented
184C4×C283—21no—
185C4×C283—41no—
186C4×C283—41no—
187C4×C283—41no—
188C4×C283C22×D411yescharacteristic
189C4×C283C2×#4111yescharacteristic
190Dic283—21no—
191Dic283—41no—
192Dic283—41no—
193Dic283—41no—
194Dic283#12112yes—
195C2×C283—22no—
196C2×C283—81no—
197C2×C283C2×#12111yescharacteristic
198C2×C283C2×#13511yescharacteristic
199C2×C283C2×#13511yescharacteristic
200D283—22no—
201D283—22no—
202D283—81no—
203C283#305011yescharacteristic, complemented, Sylow
204#3050—2831nomaximal, Sylow
205C2×#135—2831no—
206C23×C8—2831no—
207#525—2831no—
208#525—2831no—
209#467—2831no—
210#467—2831no—
211#466—2831no—
212#466—2831no—
213#465—2831no—
214#465—2831no—
215#465—2831no—
216#465D28311yescharacteristic, complemented
217#427—2831no—
218#416—2831no—
219#416—2831no—
220C2×#41—2831no—
221C2×#41—2831no—
222C23×C4—2831no—
223#135—5664no—
224C2×Q16—2831no—
225C2×SD16—2831no—
226C2×SD16C2×D28311yescharacteristic, complemented
227C2×D8—2831no—
228C22×C8—2831no—
229C22×C8—2831no—
230C22×C8—2831no—
231C22×C8—2831no—
232C22×C8—2831no—
233C22×C8—5664no—
234C22×C8C2×D28311yescharacteristic
235#123—5661no—
236#123—5661no—
237C22⋊Q8—2831no—
238C22⋊Q8—2831no—
239C22⋊Q8—2831no—
240C22⋊Q8C2×D28311yescharacteristic
241#121—2831no—
242#121—2831no—
243#121—2831no—
244#121C2×D28311yescharacteristic
245#120—5661no—
246#120—5661no—
247C4×D4—5661no—
248C4×D4—5661no—
249C4×D4—5661no—
250C4×D4—5661no—
251#117—2831no—
252#117—2831no—
253#107—2831no—
254#107—2831no—
255#106—2831no—
256#106C2×D28311yescharacteristic, complemented
257#103—2831no—
258#103—2831no—
259#103—2831no—
260#103C2×D28311yescharacteristic, complemented
261#102—2831no—
262#102—2831no—
263#102—2831no—
264#102C2×D28311yescharacteristic, complemented
265C24—2831no—
266#41—5662no—
267#41—5662no—
268#41—5662no—
269#41—5662no—
270C2×Q8—2831no—
271C2×Q8C22×D28311yescharacteristic
272C2×D4—21no—
273C2×D4—2831no—
274C2×D4—5661no—
275C2×D4—5661no—
276C2×D4—5661no—
277C2×D4—5661no—
278C2×D4—5661no—
279C2×D4C22×D28311yescharacteristic
280C22×C4—2831no—
281C22×C4—2831no—
282C22×C4—2831no—
283C22×C4—2831no—
284C22×C4—2831no—
285C22×C4—5662no—
286C22×C4—5662no—
287C22×C4—5661no—
288C22×C4—5661no—
289C22×C4C22×D28311yescharacteristic
290Q16—5662no—
291SD16—22no—
292SD16—5662no—
293D8—5662no—
294C2×C8—22no—
295C2×C8—2831no—
296C2×C8—2834no—
297C2×C8—2831no—
298C2×C8—5662no—
299C2×C8—5662no—
300C2×C8—5662no—
301C2×C8—5662no—
302C2×C8C22×D28311yescharacteristic
303C2×C8C22×D28311yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—2831no—
306C4⋊C4—2831no—
307C4⋊C4—5661no—
308C4⋊C4—5661no—
309C4⋊C4—5661no—
310C4⋊C4C22×D28311yescharacteristic
311C4⋊C4C22×D28311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C42—5661no—
323C42—5661no—
324C23—21no—
325C23—2831no—
326C23—2831no—
327C23—5662no—
328C23—5662no—
329C23—5662no—
330C23—5661no—
331C23D4×D28311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—5661no—
335Q8—5661no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—5661no—
340D4—5661no—
341D4—11322no—
342D4—11322no—
343D4—11322no—
344D4—11322no—
345D4—11322no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—2831no—
352C2×C4—2832no—
353C2×C4—2832no—
354C2×C4—2831no—
355C2×C4—5662no—
356C2×C4—5662no—
357C2×C4—5662no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—5661no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—11322no—
364C2×C4—11322no—
365C2×C4D4×D28311yescharacteristic
366C2×C4C23×D28311yescharacteristic
367C8—21no—
368C8—2832no—
369C8—5661no—
370C8D4×D28312yes—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—2832no—
377C22—2832no—
378C22—5668no—
379C22—5661no—
380C22—5661no—
381C22—5661no—
382C22—5661no—
383C22—11321no—
384C22—11321no—
385C22—11321no—
386C22#2258363112yescomplemented
387C22C2×D4×D28311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—2832no—
393C4—5661no—
394C4—11321no—
395C4—11321no—
396C4—11321no—
397C4C2×D4×D28311yescharacteristic
398C4#41×D28311yescharacteristic
399C2—22no—
400C2—81no—
401C2—5662no—
402C2—5662no—
403C2—22641no—
404C2#121×D28311yescharacteristic
405C2#135×D28311yescharacteristic
406C2C2×#2258363111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
hypercenter#465D283
hypocenterC283#3050
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×#22583631C2semidirect
2. C22×C8×D283C2semidirect
3. #31826978C2semidirect
4. #31826975C2semidirect
5. #31826705C2semidirect
6. #31826704C2semidirect
7. #31826700C2semidirect
8. #31826699C2semidirect
9. #31826695C2semidirect
10. #31826694C2semidirect
11. #31826691C2semidirect
12. #31826500C2semidirect
13. #31826460C2semidirect
14. #31826458C2semidirect
15. #465×C283C2semidirect
20. C2×#17985382C22semidirect
21. C2×#17985381C22semidirect
22. C2×#17985377C22semidirect
45. #22583543C22semidirect
46. #22583543C22semidirect
47. #22583542C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583533C22semidirect
51. #22583532C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
54. C2×SD16×C283C22semidirect
58. #106×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
91. C8×D283D4semidirect
172. C22×C283#135semidirect
183. C2×D283#135semidirect
203. C283#3050semidirect
216. #465D283semidirect
226. C2×SD16C2×D283semidirect
256. #106C2×D283semidirect
260. #103C2×D283semidirect
264. #102C2×D283semidirect
386. C22#22583631semidirect

Maximal subgroups

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

subgroupindex
C2×#225836312
C22×C8×D2832
#318269782
#318269752
#318267052
#318267042
#318267002
#318266992
#318266952
#318266942
#318266912
#318265002
#318264602
#318264582
#465×C2832
#3050283