Finite Group Databasebeta

← #49131612

Subgroups — #49131612

Order 36224.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827092C211yesmaximal, characteristic, complemented
2#31827033C211yesmaximal, characteristic
3#31826830C211yesmaximal, characteristic, complemented
4#31826828C211yesmaximal, characteristic, complemented
5#31826826C211yesmaximal, characteristic, complemented
6#31826821C211yesmaximal, characteristic, complemented
7#31826819C211yesmaximal, characteristic, complemented
8#31826813C211yesmaximal, characteristic, complemented
9#31826810C211yesmaximal, characteristic, complemented
10#31826468C211yesmaximal, characteristic, complemented
11#31826465C211yesmaximal, characteristic, complemented
12#31826460C211yesmaximal, characteristic, complemented
13#102×D283C211yesmaximal, characteristic, complemented
14#31826422C211yesmaximal, characteristic, complemented
15#489×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583609C2211yescharacteristic, complemented
21#22583608—21no—
22#22583607C2211yescharacteristic
23#22583606C2211yescharacteristic
24#22583602C2211yescharacteristic, complemented
25#22583601C2211yescharacteristic, complemented
26#22583600—21no—
27#22583599C2211yescharacteristic
28#22583588—21no—
29#22583586—21no—
30#22583583—21no—
31#22583583—21no—
32#22583580—21no—
33#22583580—21no—
34#22583568C2211yescharacteristic
35#22583567C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583534C2211yescharacteristic, complemented
38#22583534C2211yescharacteristic, complemented
39#22583532C2211yescharacteristic
40#22583532C2211yescharacteristic
41#22583532C2211yescharacteristic, complemented
42#22583532C2211yescharacteristic, complemented
43#22583531C2211yescharacteristic
44#22583531C2211yescharacteristic
45#22583530C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic, complemented
49#22583520C2211yescharacteristic, complemented
50C4×C283⋊C8C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C4⋊Q8×C283C2211yescharacteristic, complemented
53#124×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic, complemented
55#103×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985393—22no—
61#17985393—22no—
62C2×Dic566—21no—
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71D4×D283—22no—
72D4×D283—22no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76#17985375—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C8×D283—22no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4D411yescharacteristic
89Dic283⋊C4D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283—21no—
98C2×Q8×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—42no—
111C22×D283—81no—
112C22×D283—81no—
113C22×D283C2×D411yescharacteristic
114Dic566—81no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—42no—
120D1132—81no—
121D1132—81no—
122C22⋊D283—42no—
123C22⋊D283—81no—
124C22⋊D283—81no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—42no—
131C4×D283—81no—
132C4×D283#4112yes—
133C4×D283#4112yes—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137Q8×C283—21no—
138Q8×C283—21no—
139Q8×C283—81no—
140D4×C283—21no—
141D4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283C22×D411yescharacteristic
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—84no—
163C2×D283#12412yes—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283C2×#4111yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—41no—
174Dic283—41no—
175Dic283#12412yes—
176C2×C283—81no—
177C2×C283C2×#12411yescharacteristic
178C2×C283#57611yescharacteristic
179C2×C283#57711yescharacteristic
180D283—22no—
181D283—81no—
182D283—81no—
183C283#313611yescharacteristic, complemented, Sylow
184#3136—2831nomaximal, Sylow
185#544—2831no—
186#535—2831no—
187#490—2831no—
188#490—2831no—
189#489—2831no—
190#489D28311yescharacteristic, complemented
191#488—2831no—
192#488—2831no—
193#486—2831no—
194#486—2831no—
195#418—2831no—
196#417—2831no—
197#416—2831no—
198C2×#102—2831no—
199#405—2831no—
200C2×#41—2831no—
201C22×D4—2831no—
202C2×M16—2831no—
203C22×C8—2831no—
204C4⋊Q8—2831no—
205C4⋊Q8—5661no—
206C4⋊Q8C2×D28311yescharacteristic, complemented
207#127—2831no—
208#127—2831no—
209#125—2831no—
210#125—2831no—
211#125—5661no—
212#124—2831no—
213#124C2×D28311yescharacteristic
214C22⋊Q8—5661no—
215C22⋊Q8—5661no—
216#121—5661no—
217#121—5661no—
218#120—5661no—
219#120—5661no—
220#117—2831no—
221#117—2831no—
222C2×C4⋊C4—2831no—
223#103—2831no—
224#103—2831no—
225#103C2×D28311yescharacteristic, complemented
226#103C2×D28311yescharacteristic, complemented
227#102—2831no—
228#102—2831no—
229#102—2831no—
230#102—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102C2×D28311yescharacteristic
238#102C2×D28311yescharacteristic
239#97—2831no—
240#97C2×D28311yescharacteristic, complemented
241C4×C8—2831no—
242C4×C8—2831no—
243C24—5661no—
244#41—5662no—
245#41—5662no—
246C2×Q8—21no—
247C2×Q8—5661no—
248C2×Q8C22×D28311yescharacteristic
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4—5662no—
253C2×D4—5662no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4—5661no—
259C2×D4C22×D28311yescharacteristic
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263M16—5662no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8—5662no—
267C2×C8C22×D28311yescharacteristic
268C2×C8C22×D28311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—2831no—
273C4⋊C4—2831no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—2831no—
290C42—5661no—
291C42C22×D28311yescharacteristic
292C23—21no—
293C23—2831no—
294C23—5661no—
295C23—5661no—
296C23—11322no—
297C23—22641no—
298C23—22641no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—22641no—
303D4—21no—
304D4—21no—
305D4—5661no—
306D4—5661no—
307D4—5661no—
308D4—5661no—
309D4—11322no—
310D4—11322no—
311D4—22641no—
312D4—22641no—
313D4—22641no—
314D4—22641no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2831no—
319C2×C4—2832no—
320C2×C4—2832no—
321C2×C4—2831no—
322C2×C4—2831no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—11322no—
326C2×C4—22641no—
327C2×C4D4×D28311yescharacteristic
328C2×C4D4×D28311yescharacteristic
329C2×C4C23×D28311yescharacteristic
330C8—21no—
331C8—21no—
332C8—5661no—
333C8—5661no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2832no—
338C22—5661no—
339C22—5661no—
340C22—11321no—
341C22—11321no—
342C22—11321no—
343C22—11321no—
344C22—11321no—
345C22—11321no—
346C22—22644no—
347C22C2×D4×D28311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2832no—
354C4—5661no—
355C4—5661no—
356C4—11321no—
357C4—11321no—
358C4#41×D28311yescharacteristic
359C4#41×D28311yescharacteristic
360C2—81no—
361C2—5662no—
362C2—22641no—
363C2—22641no—
364C2#124×D28311yescharacteristic
365C2#3182726911yescharacteristic
366C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#489×C283C2
socleC22×C283C22×D4
prime radical#31827033C2
hypercenter#489D283
hypocenterC283#3136
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31827092C2semidirect
3. #31826830C2semidirect
4. #31826828C2semidirect
5. #31826826C2semidirect
6. #31826821C2semidirect
7. #31826819C2semidirect
8. #31826813C2semidirect
9. #31826810C2semidirect
10. #31826468C2semidirect
11. #31826465C2semidirect
12. #31826460C2semidirect
13. #102×D283C2semidirect
14. #31826422C2semidirect
15. #489×C283C2semidirect
20. #22583609C22semidirect
24. #22583602C22semidirect
25. #22583601C22semidirect
37. #22583534C22semidirect
38. #22583534C22semidirect
41. #22583532C22semidirect
42. #22583532C22semidirect
47. #22583530C22semidirect
48. #22583530C22semidirect
49. #22583520C22semidirect
50. C4×C283⋊C8C22semidirect
51. C8×Dic283C22semidirect
52. C4⋊Q8×C283C22semidirect
54. #103×C283C22semidirect
55. #103×C283C22semidirect
58. #97×C283C22semidirect
183. C283#3136semidirect
190. #489D283semidirect
206. C4⋊Q8C2×D283semidirect
225. #103C2×D283semidirect
226. #103C2×D283semidirect
240. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270922
#318270332
#318268302
#318268282
#318268262
#318268212
#318268192
#318268132
#318268102
#318264682
#318264652
#318264602
#102×D2832
#318264222
#489×C2832
#3136283