Finite Group Databasebeta

← #49133198

Subgroups — #49133198

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#31827133C211yesmaximal, characteristic
3#31826810C211yesmaximal, characteristic, complemented
4#31826792C211yesmaximal, characteristic, complemented
5#31826749C211yesmaximal, characteristic, complemented
6#31826695C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826664C211yesmaximal, characteristic, complemented
9#31826629C211yesmaximal, characteristic, complemented
10#31826628C211yesmaximal, characteristic, complemented
11#31826559C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826459C211yesmaximal, characteristic, complemented
14#31826458C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583609C2211yescharacteristic
24#22583606—21no—
25#22583606C2211yescharacteristic
26#22583604—21no—
27#22583603—21no—
28#22583596—21no—
29#22583590C2211yescharacteristic
30#22583589C2211yescharacteristic
31#22583585C2211yescharacteristic
32#22583583—21no—
33#22583582—21no—
34C4×Dic566—21no—
35#22583575C2211yescharacteristic
36#22583575C2211yescharacteristic
37C4×C22⋊D283C2211yescharacteristic
38(C22⋊D283)⋊C4—21no—
39#22583568C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#121×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—41no—
61#17985391—22no—
62#17985391—41no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283D411yescharacteristic
73C22×Dic283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76Dic1132—22no—
77#17985381—41no—
78#17985380—41no—
79C2×C283⋊C8—41no—
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C8×D283—41no—
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4D411yescharacteristic
90C22⋊Dic283—21no—
91C22⋊Dic283D411yescharacteristic
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117Dic566#4112yes—
118D1132—21no—
119D1132—21no—
120D1132—81no—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C22⋊D283—42no—
125C22⋊D283—81no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—42no—
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C4×D283—21no—
134C4×D283—21no—
135C4×D283—42no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C23×C283—21no—
139C23×C283C2×D411yescharacteristic
140D4×C283—21no—
141D4×C283—21no—
142D4×C283—81no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
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—41no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—22no—
173Dic283—21no—
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#482D28311yescharacteristic, complemented
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#416—2831no—
201C2×#41—2831no—
202C2×#41—2831no—
203C2×Q16—2831no—
204C2×SD16—2831no—
205C2×SD16—2831no—
206C22×C8—2831no—
207C22×C8—2831no—
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—5661no—
218#121—5661no—
219#121C2×D28311yescharacteristic
220C4×Q8—2831no—
221C4×Q8—2831no—
222C4×Q8—5661no—
223C4×D4—2831no—
224C4×D4—5661no—
225#117—2831no—
226#117C2×D28311yescharacteristic
227#107C2×D28311yescharacteristic
228#106—2831no—
229#106C2×D28311yescharacteristic
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102C2×D28311yescharacteristic
240#102C2×D28311yescharacteristic
241C22⋊C8—2831no—
242C22⋊C8C2×D28311yescharacteristic
243C4×C8—2831no—
244#41—5662no—
245#41—5662no—
246#41—11321no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×Q8—5661no—
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—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4C22×D28311yescharacteristic
264Q16—5662no—
265SD16—11321no—
266SD16—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
270C2×C8—11321no—
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2831no—
286C22⋊C4—2831no—
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—2832no—
301Q8—5661no—
302Q8—5661no—
303Q8—5661no—
304Q8—11322no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—5662no—
309D4—5661no—
310D4—5661no—
311D4—11322no—
312D4—11322no—
313D4—11322no—
314D4—22641no—
315D4—22641no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—2831no—
322C2×C4—2831no—
323C2×C4—2831no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—11322no—
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—41no—
352C4—41no—
353C4—41no—
354C4—2832no—
355C4—5661no—
356C4—5661no—
357C4—5662no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365611yescharacteristic
362C2—41no—
363C2—81no—
364C2—11321no—
365C2—22641no—
366C2#3182710711yescharacteristic
367C2#135×D28311yescharacteristic
368C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
prime radical#31827133C2
hypercenter#482D283
hypocenterC283#3304
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31827183C2semidirect
3. #31826810C2semidirect
4. #31826792C2semidirect
5. #31826749C2semidirect
6. #31826695C2semidirect
7. #31826692C2semidirect
8. #31826664C2semidirect
9. #31826629C2semidirect
10. #31826628C2semidirect
11. #31826559C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826459C2semidirect
14. #31826458C2semidirect
15. #482×C283C2semidirect
184. C283#3304semidirect
190. #482D283semidirect

Maximal subgroups

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

subgroupindex
#318271832
#318271332
#318268102
#318267922
#318267492
#318266952
#318266922
#318266642
#318266292
#318266282
#318265592
(C22⋊D283)⋊C82
#318264592
#318264582
#482×C2832
#3304283