Finite Group Databasebeta

← #49133261

Subgroups — #49133261

Order 36224.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827136C211yesmaximal, characteristic, complemented
2#31826831C211yesmaximal, characteristic, complemented
3#31826789C211yesmaximal, characteristic, complemented
4#31826778C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826716C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic, complemented
8#31826660C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826608C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826464C211yesmaximal, characteristic, complemented
14#31826459C211yesmaximal, characteristic, complemented
15#553×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C2×#17985376C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583607C2211yescharacteristic
24#22583606—21no—
25#22583584C2211yescharacteristic
26#22583584C2211yescharacteristic
27#22583583—21no—
28#22583583—21no—
29C4×Dic566C2211yescharacteristic
30#22583572—21no—
31#22583543C2211yescharacteristic
32#22583543C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35#22583533C2211yescharacteristic
36#22583533C2211yescharacteristic
37#22583533C2211yescharacteristic
38#22583531C2211yescharacteristic
39#22583530C2211yescharacteristic
40#22583530C2211yescharacteristic
41#22583530C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47#22583521C2211yescharacteristic
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—22no—
61#17985392—41no—
62#17985392—41no—
63C2×Dic566C2311yescharacteristic
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74#17985380—22no—
75#17985377—41no—
76#17985377—41no—
77#17985376—41no—
78C2×C283⋊C8—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊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—
112C22×D283—21no—
113Dic566—21no—
114Dic566#4112yes—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—42no—
120D1132—81no—
121C22⋊D283—42no—
122C22⋊D283—42no—
123C22⋊D283—81no—
124C22⋊D283—81no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C4×D283—42no—
128C4×D283—42no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134C23×C283C2×D411yescharacteristic
135C23×C283C2×D411yescharacteristic
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—41no—
139D4×C283—42no—
140D4×C283—81no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—81no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2×D411yescharacteristic
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2411yescharacteristic
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—21no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283C22×D411yescharacteristic
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C4×C283—21no—
172C4×C283—21no—
173C4×C283—21no—
174C4×C283—21no—
175C4×C283—41no—
176C4×C283—41no—
177C4×C283—41no—
178C4×C283C2×#4111yescharacteristic
179C4×C283H(5,𝔽2)11yescharacteristic
180Dic283—22no—
181Dic283—41no—
182C2×C283—41no—
183C2×C283—41no—
184C2×C283—81no—
185C2×C283#54611yescharacteristic
186C2×C283#57511yescharacteristic
187C2×C283#57611yescharacteristic
188D283—81no—
189D283—81no—
190C283#330911yescharacteristic, complemented, Sylow
191#3309—2831nomaximal, Sylow
192#553D28311yescharacteristic, complemented
193#550—2831no—
194#490—2831no—
195#482—2831no—
196#480—2831no—
197#479—2831no—
198#469—2831no—
199#466—2831no—
200#459—2831no—
201#449—2831no—
202#449—2831no—
203#440—2831no—
204#435—2831no—
205#417—2831no—
206#416—2831no—
207C2×#41—2831no—
208C2×#41—2831no—
209C2×SD16—2831no—
210C2×D8—2831no—
211C2×D8—2831no—
212C2×M16—2831no—
213C22×C8—2831no—
214#127—2831no—
215#127—5661no—
216#126—21no—
217#125C2×D28311yescharacteristic
218#123—21no—
219#121—21no—
220#121—2831no—
221#121—2831no—
222#121—5661no—
223#121—5661no—
224#121C2×D28311yescharacteristic
225#121C2×D28311yescharacteristic
226C4×Q8—2831no—
227C4×D4—21no—
228C4×D4—5661no—
229C4×D4C2×D28311yescharacteristic
230C4×D4C2×D28311yescharacteristic
231#117C2×D28311yescharacteristic
232C2×C4⋊C4C2×D28311yescharacteristic
233#107—2831no—
234#107—2831no—
235#106—2831no—
236C4⋊C8—2831no—
237#103—2831no—
238#103—2831no—
239#103—2831no—
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247C22⋊C8—2831no—
248C22⋊C8—2831no—
249#97—2831no—
250#41—5662no—
251#41—5662no—
252#41—11321no—
253#41—11321no—
254C2×Q8—2831no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2831no—
258C2×D4—2831no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4C22⋊D28311yescharacteristic
266C2×D4C22×D28311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4C22×D28311yescharacteristic
272C22×C4C22×D28311yescharacteristic
273SD16—5662no—
274D8—11321no—
275D8—11321no—
276M16—11321no—
277C2×C8—2831no—
278C2×C8—2831no—
279C2×C8—2831no—
280C2×C8—2831no—
281C2×C8—11321no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—2831no—
286C4⋊C4—5661no—
287C4⋊C4C22⋊D28311yescharacteristic
288C4⋊C4C22×D28311yescharacteristic
289C4⋊C4C22×D28311yescharacteristic
290C4⋊C4C22×D28311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4C22⋊D28311yescharacteristic
298C22⋊C4C22⋊D28311yescharacteristic
299C42—21no—
300C42—5661no—
301C42C22×D28311yescharacteristic
302C23—21no—
303C23—5661no—
304C23—5661no—
305C23C2×C22⋊D28311yescharacteristic
306C23C2×C22⋊D28311yescharacteristic
307Q8—2832no—
308Q8—5661no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—5661no—
315D4—5661no—
316D4—5661no—
317D4—5661no—
318D4—11322no—
319D4—11322no—
320D4—11322no—
321D4—22641no—
322D4—22641no—
323D4—22641no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—11322no—
336C2×C4—11322no—
337C2×C4C2×C22⋊D28311yescharacteristic
338C2×C4C2×C22⋊D28311yescharacteristic
339C2×C4C2×C22⋊D28311yescharacteristic
340C2×C4C2×C22⋊D28311yescharacteristic
341C2×C4C23×D28311yescharacteristic
342C8—5661no—
343C8—5661no—
344C8—5661no—
345C8—5661no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—11321no—
356C22—11321no—
357C22—11321no—
358C22—11321no—
359C22—11321no—
360C22—11321no—
361C22C22×C22⋊D28311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—5662no—
370C4—11321no—
371C4#41×D28311yescharacteristic
372C4#2258365611yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—22641no—
377C2—22641no—
378C2#3182710311yescharacteristic
379C2#3182726311yescharacteristic
380C2#3182726811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#553×C283C2
socleC22×C283C22×D4
hypercenter#553D283
hypocenterC283#3309
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. #31827136C2semidirect
2. #31826831C2semidirect
3. #31826789C2semidirect
4. #31826778C2semidirect
5. #31826769C2semidirect
6. #31826716C2semidirect
7. #31826699C2semidirect
8. #31826660C2semidirect
9. #31826608C2semidirect
10. #31826608C2semidirect
11. #31826565C2semidirect
12. #31826537C2semidirect
13. #31826464C2semidirect
14. #31826459C2semidirect
15. #553×C283C2semidirect
190. C283#3309semidirect
192. #553D283semidirect

Maximal subgroups

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

subgroupindex
#318271362
#318268312
#318267892
#318267782
#318267692
#318267162
#318266992
#318266602
#318266082
#318265652
#318265372
#318264642
#318264592
#553×C2832
#3309283