Finite Group Databasebeta

← #49133196

Subgroups — #49133196

Order 36224.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827183C211yesmaximal, characteristic, complemented
2#31827134C211yesmaximal, characteristic
3#31826810C211yesmaximal, characteristic, complemented
4#31826789C211yesmaximal, characteristic, complemented
5#31826788C211yesmaximal, characteristic, complemented
6#31826748C211yesmaximal, characteristic, complemented
7#31826694C211yesmaximal, characteristic, complemented
8#31826693C211yesmaximal, characteristic, complemented
9#31826664C211yesmaximal, characteristic, complemented
10#31826630C211yesmaximal, characteristic, complemented
11#31826627C211yesmaximal, characteristic, complemented
12#31826557C211yesmaximal, characteristic, complemented
13C8×C22⋊D283C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15#416×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583606—21no—
23#22583606C2211yescharacteristic
24#22583604—21no—
25#22583603—21no—
26#22583596—21no—
27#22583590C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583584—21no—
30#22583584C2211yescharacteristic
31#22583581—21no—
32#22583581C2211yescharacteristic
33Q8×Dic283C2211yescharacteristic
34C4×Dic566—21no—
35#22583575C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4×C22⋊D283C2211yescharacteristic
38#22583568C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283D411yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283C2311yescharacteristic
72#17985382—22no—
73#17985381—41no—
74#17985380—41no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C8×D283—41no—
78C4⋊Dic283—21no—
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97#41×C283—22no—
98#41×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283—41no—
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—42no—
116D1132—21no—
117D1132—21no—
118D1132—42no—
119C22⋊D283—22no—
120C22⋊D283—42no—
121C22⋊D283—81no—
122C22⋊D283—81no—
123C22⋊D283—81no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C283⋊C8—21no—
134C283⋊C8—21no—
135C23×C283—21no—
136C23×C283C2×D411yescharacteristic
137Q8×C283—21no—
138Q8×C283#4112yes—
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—42no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—42no—
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—41no—
163C2×D283—41no—
164C2×D283—41no—
165C4×C283—21no—
166C4×C283—22no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—41no—
174Dic283—41no—
175Dic283—41no—
176Dic283#13512yes—
177C2×C283—41no—
178C2×C283—81no—
179C2×C283#54611yescharacteristic
180C2×C283C2×#13511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—41no—
183D283—81no—
184C283#330411yescharacteristic, complemented, Sylow
185#3304—2831nomaximal, Sylow
186#556—2831no—
187#550—2831no—
188#486—2831no—
189#482—2831no—
190#482—2831no—
191#475—2831no—
192#465—2831no—
193#465—2831no—
194#460—2831no—
195#452—2831no—
196#452—2831no—
197C4×Q16—2831no—
198C8×D4—2831no—
199#416—2831no—
200#416D28311yescharacteristic, complemented
201C2×#41—2831no—
202C2×#41C2×D28311yescharacteristic
203C2×Q16—2831no—
204C2×SD16—2831no—
205C2×SD16—2831no—
206C22×C8—2831no—
207C22×C8C2×D28311yescharacteristic
208C4⋊Q8—2831no—
209#127—2831no—
210#127—5661no—
211#126—5661no—
212#126—5661no—
213#124—5661no—
214C22⋊Q8—2831no—
215C22⋊Q8—2831no—
216#121—2831no—
217#121—2831no—
218#121—5661no—
219#121—5661no—
220C4×Q8—2831no—
221C4×Q8—2831no—
222C4×Q8—5661no—
223C4×D4—2831no—
224C4×D4—5661no—
225#117—2831no—
226#117C2×D28311yescharacteristic
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103C2×D28311yescharacteristic
234#103C2×D28311yescharacteristic
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102C2×D28311yescharacteristic
240#102C2×D28311yescharacteristic
241C22⋊C8—2831no—
242C22⋊C8—2831no—
243C4×C8—2831no—
244#41—22no—
245#41—41no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—5661no—
250C2×Q8C22×D28311yescharacteristic
251C2×D4—21no—
252C2×D4—2831no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4—5661no—
259C2×D4C22×D28311yescharacteristic
260C22×C4—21no—
261C22×C4—2831no—
262C22×C4—5661no—
263C22×C4C22×D28311yescharacteristic
264Q16—5662no—
265SD16—11321no—
266SD16—11321no—
267C2×C8—41no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8—11321no—
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C42—21no—
292C42—2831no—
293C42—5661no—
294C42—5661no—
295C42—5661no—
296C23—21no—
297C23—2831no—
298C23—5661no—
299C23D4×D28311yescharacteristic
300Q8—21no—
301Q8—5661no—
302Q8—5661no—
303Q8—11322no—
304Q8#1798539212yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—5662no—
309D4—5661no—
310D4—5661no—
311D4—11322no—
312D4—11322no—
313D4—22641no—
314D4—22641no—
315D4—22641no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—2831no—
323C2×C4—2831no—
324C2×C4—2831no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—11322no—
331C2×C4D4×D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5661no—
336C8—5661no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—5661no—
344C22—5661no—
345C22—5661no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—2832no—
355C4—5661no—
356C4—5661no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4C2×#1798539211yescharacteristic
361C4#2258365511yescharacteristic
362C2—41no—
363C2—81no—
364C2—11321no—
365C2—22641no—
366C2#3182710511yescharacteristic
367C2#135×D28311yescharacteristic
368C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
prime radical#31827134C2
hypercenter#416D283
hypocenterC283#3304
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #31827183C2semidirect
3. #31826810C2semidirect
4. #31826789C2semidirect
5. #31826788C2semidirect
6. #31826748C2semidirect
7. #31826694C2semidirect
8. #31826693C2semidirect
9. #31826664C2semidirect
10. #31826630C2semidirect
11. #31826627C2semidirect
12. #31826557C2semidirect
13. C8×C22⋊D283C2semidirect
14. #31826460C2semidirect
15. #416×C283C2semidirect
184. C283#3304semidirect
200. #416D283semidirect

Maximal subgroups

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

subgroupindex
#318271832
#318271342
#318268102
#318267892
#318267882
#318267482
#318266942
#318266932
#318266642
#318266302
#318266272
#318265572
C8×C22⋊D2832
#318264602
#416×C2832
#3304283