Finite Group Databasebeta

← #49130304

Subgroups — #49130304

Order 36224.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826972C211yesmaximal, characteristic
2#31826541C211yesmaximal, characteristic, complemented
3#31826540C211yesmaximal, characteristic, complemented
4#31826539C211yesmaximal, characteristic, complemented
5#31826536C211yesmaximal, characteristic, complemented
6#31826534C211yesmaximal, characteristic, complemented
7#31826533C211yesmaximal, characteristic, complemented
8C8×C22⋊D283C211yesmaximal, characteristic, complemented
9(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
10#31826523C211yesmaximal, characteristic, complemented
11#31826523C211yesmaximal, characteristic, complemented
12#31826432C211yesmaximal, characteristic, complemented
13#31826427C211yesmaximal, characteristic, complemented
14C22⋊C8×D283C211yesmaximal, characteristic, complemented
15#408×C283C211yesmaximal, characteristic, complemented
16C22×C4×D283C2211yescharacteristic
17C2×#17985376C2211yescharacteristic, complemented
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic, complemented
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583591C411yescharacteristic
24#22583591C411yescharacteristic
25#22583586C411yescharacteristic
26#22583586C411yescharacteristic
27#22583581C411yescharacteristic
28#22583581C411yescharacteristic
29#22583578C411yescharacteristic
30#22583578C411yescharacteristic
31C4×C22⋊D283C2211yescharacteristic
32C4×C22⋊D283C2211yescharacteristic
33C4×C22⋊D283C2211yescharacteristic
34C4×C22⋊D283C2211yescharacteristic
35#22583569C2211yescharacteristic
36Dic283⋊C8C2211yescharacteristic, complemented
37Dic283⋊C8C2211yescharacteristic, complemented
38Dic283⋊C8C2211yescharacteristic, complemented
39Dic283⋊C8C2211yescharacteristic, complemented
40C22⋊(C283⋊C8)C2211yescharacteristic
41C22⋊(C283⋊C8)C2211yescharacteristic
42C22⋊(C283⋊C8)C2211yescharacteristic, complemented
43C22⋊(C283⋊C8)C2211yescharacteristic, complemented
44(C2×D283)⋊C8C2211yescharacteristic
45(C2×D283)⋊C8C2211yescharacteristic
46(C2×D283)⋊C8C2211yescharacteristic
47(C2×D283)⋊C8C2211yescharacteristic
48#22583520C2211yescharacteristic, complemented
49#22583520C2211yescharacteristic, complemented
50C8×Dic283C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C2×#41×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic, complemented
54C22×C8×C283C2211yescharacteristic, complemented
55C22⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283C2×C411yescharacteristic
60C2×C22⋊D283C2×C411yescharacteristic
61C2×C22⋊D283C2×C411yescharacteristic
62C2×C22⋊D283C2×C411yescharacteristic
63C2×C22⋊D283C2×C411yescharacteristic
64C22×Dic283C2×C411yescharacteristic
65C2×C4×D283—41no—
66C2×C4×D283—41no—
67C2×C4×D283C2×C411yescharacteristic
68C2×C4×D283C2×C411yescharacteristic
69C2×C4×D283C2311yescharacteristic
70C2×C4×D283C2311yescharacteristic
71#17985376—41no—
72#17985375—41no—
73#17985375—41no—
74C2×C283⋊C8—41no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C8×D283—41no—
80C8×D283—41no—
81C4⋊Dic283C2×C411yescharacteristic
82C4⋊Dic283C2×C411yescharacteristic
83Dic283⋊C4C2×C411yescharacteristic
84Dic283⋊C4C2×C411yescharacteristic
85Dic283⋊C4C2×C411yescharacteristic
86Dic283⋊C4C2×C411yescharacteristic
87C22⋊Dic283C2×C411yescharacteristic
88C22⋊Dic283C2×C411yescharacteristic
89C22⋊Dic283C2×C411yescharacteristic
90C22⋊Dic283C2×C411yescharacteristic
91C22⋊Dic283C2×C411yescharacteristic
92C22⋊Dic283C2×C411yescharacteristic
93(C2×D283)⋊C4C2×C411yescharacteristic
94(C2×D283)⋊C4C2×C411yescharacteristic
95(C2×D283)⋊C4C2×C411yescharacteristic
96(C2×D283)⋊C4C2×C411yescharacteristic
97C4×Dic283C2311yescharacteristic
98C4×Dic283C2311yescharacteristic
99#41×C283—41no—
100#41×C283—41no—
101C2×Q8×C283C2×C411yescharacteristic
102C2×D4×C283C2×C411yescharacteristic
103C2×D4×C283C2×C411yescharacteristic
104C2×D4×C283C2×C411yescharacteristic
105C22×C4×C283C2311yescharacteristic
106C22×C4×C283C2311yescharacteristic
107C22×C4×C283C2311yescharacteristic
108M16×C283—41no—
109C2×C8×C283—41no—
110C2×C8×C283C2311yescharacteristic
111C2×C8×C283C2311yescharacteristic
112C2×C8×C283C2311yescharacteristic
113C2×C8×C283C2311yescharacteristic
114C22×D283—22no—
115C22×D283—41no—
116C22×D283—41no—
117C22×D283C22×C411yescharacteristic
118C22×D283C22×C411yescharacteristic
119C22⋊D283—22no—
120C22⋊D283—22no—
121C22⋊D283—41no—
122C22⋊D283—41no—
123C2×Dic283—41no—
124C2×Dic283C22×C411yescharacteristic
125C2×Dic283C22×C411yescharacteristic
126C2×Dic283C22×C411yescharacteristic
127C2×Dic283C22×C411yescharacteristic
128C2×Dic283C22×C411yescharacteristic
129C2×Dic283C22×C411yescharacteristic
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—41no—
135C4×D283—41no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C23×C283C22×C411yescharacteristic
141C23×C283C22×C411yescharacteristic
142C23×C283C22×C411yescharacteristic
143Q8×C283—41no—
144D4×C283—41no—
145D4×C283—41no—
146D4×C283—41no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283C22×C411yescharacteristic
154C2×C4×C283C22×C411yescharacteristic
155C2×C4×C283C22×C411yescharacteristic
156C2×C4×C283C2411yescharacteristic
157C8×C283—21no—
158C8×C283—21no—
159C8×C283—21no—
160C8×C283—21no—
161C22×C283—21no—
162C22×C283—21no—
163C22×C283—21no—
164C22×C283—21no—
165C22×C283—21no—
166C22×C283—21no—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283C23×C411yescharacteristic
171C2×D283—21no—
172C2×D283—21no—
173C2×D283—21no—
174C2×D283—21no—
175C2×D283—21no—
176C2×D283—44no—
177C2×D283#13112yes—
178C4×C283—21no—
179C4×C283—21no—
180C4×C283—21no—
181C4×C283H(5,𝔽2)11yescharacteristic
182C4×C283H(5,𝔽2)11yescharacteristic
183Dic283—21no—
184Dic283—21no—
185Dic283—21no—
186Dic283—21no—
187Dic283—21no—
188Dic283—21no—
189C2×C283—41no—
190C2×C283—41no—
191C2×C283—41no—
192C2×C283#51811yescharacteristic
193C2×C283C2×#13111yescharacteristic
194C2×C283#56811yescharacteristic
195D283—22no—
196D283—41no—
197C283#297611yescharacteristic, complemented, Sylow
198#2976—2831nomaximal, Sylow
199#525—2831no—
200#436—2831no—
201#436—2831no—
202#435—2831no—
203#435—2831no—
204#435—2831no—
205#435—2831no—
206C8×D4—2831no—
207C8×D4—2831no—
208#433—2831no—
209#433—2831no—
210#408—2831no—
211#408D28311yescharacteristic, complemented
212#407—2831no—
213C2×C22⋊C8—2831no—
214C2×#41C2×D28311yescharacteristic
215C23×C4—2831no—
216C2×M16—2831no—
217C2×M16—2831no—
218C2×M16—2831no—
219C2×M16C2×D28311yescharacteristic, complemented
220C22×C8—2831no—
221C22×C8—2831no—
222C22×C8—2831no—
223C22×C8C2×D28311yescharacteristic, complemented
224#123—2831no—
225#123—2831no—
226C22⋊Q8—2831no—
227C22⋊Q8—2831no—
228#121—2831no—
229#121—2831no—
230#120—2831no—
231#120—2831no—
232C4×D4—2831no—
233C4×D4—2831no—
234C4×D4—2831no—
235C4×D4—2831no—
236#117—2831no—
237C4⋊C8—2831no—
238C4⋊C8—2831no—
239C4⋊C8—2831no—
240C4⋊C8—2831no—
241C22⋊C8—2831no—
242C22⋊C8—2831no—
243C22⋊C8—2831no—
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246C22⋊C8—2831no—
247C22⋊C8—2831no—
248C22⋊C8—2831no—
249C22⋊C8C2×D28311yescharacteristic
250C22⋊C8C2×D28311yescharacteristic
251C22⋊C8C2×D28311yescharacteristic, complemented
252C22⋊C8C2×D28311yescharacteristic, complemented
253#97—2831no—
254#97—2831no—
255C4×C8—2831no—
256C4×C8—2831no—
257C24—2831no—
258#41—41no—
259#41—41no—
260C2×Q8C4×D28311yescharacteristic
261C2×D4—2831no—
262C2×D4—2831no—
263C2×D4—2831no—
264C2×D4—2831no—
265C2×D4C4×D28311yescharacteristic
266C2×D4C4×D28311yescharacteristic
267C2×D4C4×D28311yescharacteristic
268C22×C4—2831no—
269C22×C4—2831no—
270C22×C4—2831no—
271C22×C4—2831no—
272C22×C4—2831no—
273C22×C4—11321no—
274C22×C4—11321no—
275C22×C4C22×D28311yescharacteristic
276C22×C4C22×D28311yescharacteristic
277C22×C4C22×D28311yescharacteristic
278M16—41no—
279M16—11321no—
280M16—11321no—
281M16—11321no—
282C2×C8—41no—
283C2×C8—2831no—
284C2×C8—2831no—
285C2×C8—2831no—
286C2×C8—2831no—
287C2×C8—11321no—
288C2×C8—11321no—
289C2×C8—11321no—
290C2×C8C22×D28311yescharacteristic
291C2×C8C22×D28311yescharacteristic
292C2×C8C22×D28311yescharacteristic
293C2×C8C22×D28311yescharacteristic
294C4⋊C4—2831no—
295C4⋊C4—2831no—
296C4⋊C4—2831no—
297C4⋊C4—2831no—
298C4⋊C4—2831no—
299C4⋊C4—2831no—
300C22⋊C4—2831no—
301C22⋊C4—2831no—
302C22⋊C4—2831no—
303C22⋊C4—2831no—
304C22⋊C4—2831no—
305C22⋊C4—2831no—
306C22⋊C4—2831no—
307C22⋊C4—2831no—
308C22⋊C4—2831no—
309C22⋊C4—2831no—
310C42—2831no—
311C42—2831no—
312C23—2831no—
313C23—2831no—
314C23—5662no—
315C23—11321no—
316C23—11321no—
317C23C2×C4×D28311yescharacteristic
318C23C2×C4×D28311yescharacteristic
319C23C2×C4×D28311yescharacteristic
320Q8—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—5662no—
325D4—5662no—
326D4—11321no—
327D4—11321no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2831no—
335C2×C4—2831no—
336C2×C4—2831no—
337C2×C4—2831no—
338C2×C4—2831no—
339C2×C4—2831no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—11321no—
345C2×C4—11321no—
346C2×C4—11321no—
347C2×C4C2×C4×D28311yescharacteristic
348C2×C4C2×C4×D28311yescharacteristic
349C2×C4C2×C4×D28311yescharacteristic
350C2×C4C23×D28311yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—5661no—
356C8—5661no—
357C8—5661no—
358C8—5661no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—2832no—
369C22—5661no—
370C22—5661no—
371C22—5661no—
372C22—5661no—
373C22—5661no—
374C22—11324no—
375C22C22×C4×D28311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—5661no—
380C4—5661no—
381C4—5661no—
382C4—5661no—
383C4—5661no—
384C4—5661no—
385C4#2258365511yescharacteristic
386C4#2258365511yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—5662no—
391C2—11321no—
392C2#3182693811yescharacteristic
393C2#131×D28311yescharacteristic
394C2#3182723011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#408×C283C2
prime radical#31826972C2
cosocleC2×C4×C283C24
hypercenter#408D283
hypocenterC283#2976
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #31826541C2semidirect
3. #31826540C2semidirect
4. #31826539C2semidirect
5. #31826536C2semidirect
6. #31826534C2semidirect
7. #31826533C2semidirect
8. C8×C22⋊D283C2semidirect
9. (C22⋊D283)⋊C8C2semidirect
10. #31826523C2semidirect
11. #31826523C2semidirect
12. #31826432C2semidirect
13. #31826427C2semidirect
14. C22⋊C8×D283C2semidirect
15. #408×C283C2semidirect
17. C2×#17985376C22semidirect
20. C22×C283⋊C8C22semidirect
36. Dic283⋊C8C22semidirect
37. Dic283⋊C8C22semidirect
38. Dic283⋊C8C22semidirect
39. Dic283⋊C8C22semidirect
42. C22⋊(C283⋊C8)C22semidirect
43. C22⋊(C283⋊C8)C22semidirect
48. #22583520C22semidirect
49. #22583520C22semidirect
50. C8×Dic283C22semidirect
51. C8×Dic283C22semidirect
53. C2×M16×C283C22semidirect
54. C22×C8×C283C22semidirect
57. C22⋊C8×C283C22semidirect
58. C22⋊C8×C283C22semidirect
197. C283#2976semidirect
211. #408D283semidirect
219. C2×M16C2×D283semidirect
223. C22×C8C2×D283semidirect
251. C22⋊C8C2×D283semidirect
252. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269722
#318265412
#318265402
#318265392
#318265362
#318265342
#318265332
C8×C22⋊D2832
(C22⋊D283)⋊C82
#318265232
#318264322
#318264272
C22⋊C8×D2832
#408×C2832
#2976283