Finite Group Databasebeta

← #49131212

Subgroups — #49131212

Order 36224.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827031C211yesmaximal, characteristic
2#31826946C211yesmaximal, characteristic, complemented
3#31826792C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826786C211yesmaximal, characteristic, complemented
7#31826783C211yesmaximal, characteristic, complemented
8#31826782C211yesmaximal, characteristic, complemented
9#31826780C211yesmaximal, characteristic, complemented
10#31826506C211yesmaximal, characteristic, complemented
11#31826502C211yesmaximal, characteristic, complemented
12#31826468C211yesmaximal, characteristic, complemented
13#102×D283C211yesmaximal, characteristic, complemented
14#31826430C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583606—21no—
21#22583596—21no—
22#22583585C2211yescharacteristic
23#22583584C2211yescharacteristic
24#22583581C2211yescharacteristic
25#22583580—21no—
26#22583578—21no—
27#22583575—21no—
28#22583572—21no—
29C4×C22⋊D283—21no—
30C4×C22⋊D283—21no—
31#22583569C2211yescharacteristic, complemented
32#22583568C2211yescharacteristic
33#22583568C2211yescharacteristic
34#22583568C2211yescharacteristic, complemented
35C4⋊C4×D283C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic, complemented
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51(C2×D283)⋊C8C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic, complemented
54#107×C283C2211yescharacteristic, complemented
55#107×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—22no—
61#17985392—22no—
62C2×Dic566D411yescharacteristic
63C2×D1132—21no—
64C2×D1132D411yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283D411yescharacteristic
70C2×C22⋊D283D411yescharacteristic
71D4×D283—22no—
72D4×D283—22no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76C2×C4×D283C2311yescharacteristic
77#17985375—22no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—22no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22×D283—21no—
109C22×D283—42no—
110C22×D283—81no—
111C22×D283—81no—
112C22×D283C2×D411yescharacteristic
113C22×D283C2×D411yescharacteristic
114Dic566—22no—
115D1132—22no—
116D1132—21no—
117D1132—21no—
118D1132—81no—
119C22⋊D283—22no—
120C22⋊D283—22no—
121C22⋊D283—42no—
122C22⋊D283—81no—
123C22⋊D283—81no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—81no—
132C4×D283—81no—
133C4×D283#4112yes—
134C4×D283#4112yes—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283—21no—
138C23×C283C2×D411yescharacteristic
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—81no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—81no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—84no—
168C2×D283#12312yes—
169C4×C283—21no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283—41no—
173C4×C283C2×#4111yescharacteristic
174C4×C283C2×#4111yescharacteristic
175Dic283—21no—
176Dic283—41no—
177Dic283—41no—
178Dic283—41no—
179Dic283#12312yes—
180C2×C283—41no—
181C2×C283—81no—
182C2×C283C2×#12311yescharacteristic
183C2×C283#57611yescharacteristic
184C2×C283#57711yescharacteristic
185D283—22no—
186D283—41no—
187D283—81no—
188C283#309611yescharacteristic, complemented, Sylow
189#3096—2831nomaximal, Sylow
190#535—2831no—
191#520—2831no—
192#482—2831no—
193#482—2831no—
194#482—2831no—
195#482—2831no—
196#481—2831no—
197#481—2831no—
198#480—2831no—
199#480D28311yescharacteristic, complemented
200#428—2831no—
201#427—2831no—
202#418—2831no—
203C2×#102—2831no—
204#408—2831no—
205C2×#41—2831no—
206C22×D4—2831no—
207C2×M16—2831no—
208C22×C8—2831no—
209#127—5661no—
210#124—5661no—
211#121—2831no—
212#121—2831no—
213#121—2831no—
214#121C2×D28311yescharacteristic
215#120—5661no—
216#120—5661no—
217C4×Q8—5661no—
218C4×D4—5661no—
219C4×D4—5661no—
220C4×D4—5661no—
221#117—2831no—
222#117—2831no—
223#117—2831no—
224#117—2831no—
225C2×C4⋊C4—2831no—
226C2×C4⋊C4—2831no—
227C2×C4⋊C4C2×D28311yescharacteristic, complemented
228#107—2831no—
229#107—2831no—
230#107C2×D28311yescharacteristic, complemented
231#107C2×D28311yescharacteristic, complemented
232#106—2831no—
233#106—2831no—
234#106—2831no—
235#106—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102C2×D28311yescharacteristic
243#102C2×D28311yescharacteristic
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246C22⋊C8—2831no—
247C22⋊C8C2×D28311yescharacteristic, complemented
248C24—5661no—
249#41—5662no—
250#41—5662no—
251C2×Q8—2831no—
252C2×D4—21no—
253C2×D4—2831no—
254C2×D4—2831no—
255C2×D4—2831no—
256C2×D4—2831no—
257C2×D4—5661no—
258C2×D4—5662no—
259C2×D4—5662no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4C22×D28311yescharacteristic
264C22×C4—21no—
265C22×C4—2831no—
266C22×C4—2831no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4C22×D28311yescharacteristic
270M16—5662no—
271C2×C8—2831no—
272C2×C8—2831no—
273C2×C8—5662no—
274C2×C8C22×D28311yescharacteristic
275C2×C8C22×D28311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—2831no—
278C4⋊C4—2831no—
279C4⋊C4—2831no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4C22×D28311yescharacteristic
283C4⋊C4C22×D28311yescharacteristic
284C4⋊C4C22×D28311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—5661no—
294C42—5661no—
295C42—5661no—
296C42—5661no—
297C23—21no—
298C23—2831no—
299C23—2831no—
300C23—5661no—
301C23—11322no—
302C23—22641no—
303C23—22641no—
304C23D4×D28311yescharacteristic
305Q8—5662no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—5662no—
310D4—5662no—
311D4—5662no—
312D4—5661no—
313D4—5661no—
314D4—11322no—
315D4—22641no—
316D4—22641no—
317D4—22641no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—2831no—
325C2×C4—2832no—
326C2×C4—2832no—
327C2×C4—2831no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—22641no—
334C2×C4—22641no—
335C2×C4D4×D28311yescharacteristic
336C2×C4C23×D28311yescharacteristic
337C8—21no—
338C8—21no—
339C8—5661no—
340C8—5661no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—2832no—
348C22—5661no—
349C22—5661no—
350C22—5661no—
351C22—5661no—
352C22—5661no—
353C22—11321no—
354C22—11321no—
355C22—11321no—
356C22—22644no—
357C22C2×D4×D28311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—2832no—
363C4—5661no—
364C4—11321no—
365C4—11321no—
366C4—11321no—
367C4#41×D28311yescharacteristic
368C4#41×D28311yescharacteristic
369C2—41no—
370C2—81no—
371C2—5662no—
372C2—11321no—
373C2—22641no—
374C2#123×D28311yescharacteristic
375C2#3182726611yescharacteristic
376C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
prime radical#31827031C2
hypercenter#480D283
hypocenterC283#3096
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #31826946C2semidirect
3. #31826792C2semidirect
4. #31826790C2semidirect
5. #31826787C2semidirect
6. #31826786C2semidirect
7. #31826783C2semidirect
8. #31826782C2semidirect
9. #31826780C2semidirect
10. #31826506C2semidirect
11. #31826502C2semidirect
12. #31826468C2semidirect
13. #102×D283C2semidirect
14. #31826430C2semidirect
15. #480×C283C2semidirect
31. #22583569C22semidirect
34. #22583568C22semidirect
36. C4⋊C4×D283C22semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. #22583541C22semidirect
42. #22583541C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. (C2×D283)⋊C8C22semidirect
53. C2×C4⋊C4×C283C22semidirect
54. #107×C283C22semidirect
55. #107×C283C22semidirect
58. C22⋊C8×C283C22semidirect
188. C283#3096semidirect
199. #480D283semidirect
227. C2×C4⋊C4C2×D283semidirect
230. #107C2×D283semidirect
231. #107C2×D283semidirect
247. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270312
#318269462
#318267922
#318267902
#318267872
#318267862
#318267832
#318267822
#318267802
#318265062
#318265022
#318264682
#102×D2832
#318264302
#480×C2832
#3096283