Finite Group Databasebeta

← #49133157

Subgroups — #49133157

Order 36224.

398 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#31827124C211yesmaximal, characteristic, complemented
2#31826822C211yesmaximal, characteristic, complemented
3#31826806C211yesmaximal, characteristic, complemented
4#31826783C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826699C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826680C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826603C211yesmaximal, characteristic, complemented
11C4×#17985380C211yesmaximal, characteristic, complemented
12D4×C283⋊C8C211yesmaximal, characteristic, complemented
13#31826459C211yesmaximal, characteristic, complemented
14C2×#22583533C211yesmaximal, characteristic, complemented
15#553×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583598C2211yescharacteristic
24#22583596—21no—
25#22583589C2211yescharacteristic
26#22583588—21no—
27#22583584C2211yescharacteristic
28#22583582—21no—
29C4×Dic566C2211yescharacteristic
30(C22⋊D283)⋊C4—21no—
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35#22583533C2211yescharacteristic
36#22583533C2211yescharacteristic
37#22583533C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48#126×C283—21no—
49#125×C283C2211yescharacteristic
50#123×C283—21no—
51#121×C283—21no—
52#121×C283C2211yescharacteristic
53#121×C283C2211yescharacteristic
54C4×D4×C283—21no—
55C4×D4×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57#117×C283C2211yescharacteristic
58C2×C4⋊C4×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—41no—
61C2×Dic566—22no—
62C2×Dic566—21no—
63C2×Dic566—41no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71#17985380—22no—
72#17985380—41no—
73#17985377—41no—
74C2×C283⋊C8—41no—
75C2×C283⋊C8—41no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87C4×Dic283—21no—
88C2×D4×C283—21no—
89C2×D4×C283—21no—
90C2×D4×C283D411yescharacteristic
91C2×D4×C283C2311yescharacteristic
92C22×C4×C283—21no—
93C22×C4×C283—21no—
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C4⋊C4×C283—21no—
97C4⋊C4×C283—21no—
98C4⋊C4×C283—21no—
99C4⋊C4×C283D411yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C22⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—42no—
116Dic566#4112yes—
117D1132—21no—
118D1132—21no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—42no—
125C4×D283—42no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283—21no—
131C23×C283C2×D411yescharacteristic
132C23×C283C2×D411yescharacteristic
133D4×C283—22no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—42no—
137D4×C283—81no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—81no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2411yescharacteristic
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283#13512yes—
161C22×C283C22×D411yescharacteristic
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—22no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—22no—
178C2×C283—41no—
179C2×C283—81no—
180C2×C283#54611yescharacteristic
181C2×C283C2×#13511yescharacteristic
182C2×C283#57711yescharacteristic
183D283—81no—
184C283#330111yescharacteristic, complemented, Sylow
185#3301—2831nomaximal, Sylow
186#553D28311yescharacteristic, complemented
187#548—2831no—
188#488—2831no—
189#485—2831no—
190#481—2831no—
191#479—2831no—
192#466—2831no—
193#465—2831no—
194#463—2831no—
195#449—2831no—
196#448—2831no—
197C4×SD16—2831no—
198C8×D4—2831no—
199#416—2831no—
200C2×#103—2831no—
201C2×#41—2831no—
202C22×Q8—2831no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C22×C8—2831no—
207C22×C8—2831no—
208#126—21no—
209#125C2×D28311yescharacteristic
210#124—2831no—
211#124—5661no—
212#123—21no—
213C22⋊Q8—2831no—
214C22⋊Q8—5661no—
215#121—21no—
216#121—2831no—
217#121—5661no—
218#121C2×D28311yescharacteristic
219#121C2×D28311yescharacteristic
220C4×Q8—2831no—
221C4×D4—21no—
222C4×D4—5661no—
223C4×D4C2×D28311yescharacteristic
224C4×D4C2×D28311yescharacteristic
225#117C2×D28311yescharacteristic
226C2×C4⋊C4C2×D28311yescharacteristic
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241C22⋊C8—2831no—
242C22⋊C8—2831no—
243C4×C8—2831no—
244#41—5662no—
245#41—11321no—
246C2×Q8—2831no—
247C2×Q8—2831no—
248C2×Q8—5662no—
249C2×Q8—5661no—
250C2×Q8—11321no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4C22⋊D28311yescharacteristic
257C2×D4C22×D28311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263C22×C4C22×D28311yescharacteristic
264SD16—5662no—
265SD16—11321no—
266D8—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8—2831no—
271C2×C8—11321no—
272C2×C8—11321no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22⋊D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4C22⋊D28311yescharacteristic
292C22⋊C4C22⋊D28311yescharacteristic
293C42—21no—
294C42—5661no—
295C42C22×D28311yescharacteristic
296C23—21no—
297C23—5661no—
298C23C2×C22⋊D28311yescharacteristic
299C23C2×C22⋊D28311yescharacteristic
300Q8—2832no—
301Q8—5661no—
302Q8—5661no—
303Q8—5661no—
304Q8—11322no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—5661no—
311D4—5661no—
312D4—11322no—
313D4—11322no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—11322no—
327C2×C4—11322no—
328C2×C4C2×C22⋊D28311yescharacteristic
329C2×C4C2×C22⋊D28311yescharacteristic
330C2×C4C2×C22⋊D28311yescharacteristic
331C2×C4C2×C22⋊D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—5661no—
334C8—5661no—
335C8—5661no—
336C8—5661no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22#2258363012yes—
349C22C22×C22⋊D28311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5662no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365611yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—22641no—
366C2#3182710311yescharacteristic
367C2C2×#2258363011yescharacteristic
368C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#553×C283C2
socleC22×C283C22×D4
hypercenter#553D283
hypocenterC283#3301
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #31827124C2semidirect
2. #31826822C2semidirect
3. #31826806C2semidirect
4. #31826783C2semidirect
5. #31826769C2semidirect
6. #31826699C2semidirect
7. #31826692C2semidirect
8. #31826680C2semidirect
9. #31826608C2semidirect
10. #31826603C2semidirect
11. C4×#17985380C2semidirect
12. D4×C283⋊C8C2semidirect
13. #31826459C2semidirect
14. C2×#22583533C2semidirect
15. #553×C283C2semidirect
184. C283#3301semidirect
186. #553D283semidirect

Maximal subgroups

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

subgroupindex
#318271242
#318268222
#318268062
#318267832
#318267692
#318266992
#318266922
#318266802
#318266082
#318266032
C4×#179853802
D4×C283⋊C82
#318264592
C2×#225835332
#553×C2832
#3301283