Finite Group Databasebeta

← #49133271

Subgroups — #49133271

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#31827162C211yesmaximal, characteristic, complemented
2#31827134C211yesmaximal, characteristic, complemented
3#31826828C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic, complemented
5#31826777C211yesmaximal, characteristic, complemented
6#31826770C211yesmaximal, characteristic, complemented
7#31826715C211yesmaximal, characteristic, complemented
8#31826699C211yesmaximal, characteristic, complemented
9#31826658C211yesmaximal, characteristic, complemented
10#31826609C211yesmaximal, characteristic, complemented
11#31826566C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic, complemented
14#31826461C211yesmaximal, characteristic, complemented
15#449×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985377C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583606—21no—
21#22583606C2211yescharacteristic
22#22583603—21no—
23#22583601C2211yescharacteristic
24#22583591—21no—
25#22583584—21no—
26#22583584C2211yescharacteristic
27#22583581—21no—
28#22583581—21no—
29#22583581C2211yescharacteristic
30#22583581C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32D4×Dic283C2211yescharacteristic
33C4×C22⋊D283—21no—
34C4×C22⋊D283C2211yescharacteristic
35(C22⋊D283)⋊C4—21no—
36#22583569C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54C2×D8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283D411yescharacteristic
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73#17985377—41no—
74#17985375—41no—
75C2×C283⋊C8—41no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283—21no—
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283D411yescharacteristic
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96#41×C283—22no—
97#41×C283—41no—
98C2×Q8×C283C2311yescharacteristic
99C2×D4×C283—21no—
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105SD16×C283—22no—
106D8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113D1132—21no—
114D1132—21no—
115D1132—42no—
116C22⋊D283—41no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C22⋊D283—81no—
120C22⋊D283—81no—
121C22⋊D283—81no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—81no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—42no—
132C4×D283—81no—
133C283⋊C8—21no—
134C283⋊C8—21no—
135C23×C283—21no—
136C23×C283—21no—
137C23×C283C2×D411yescharacteristic
138Q8×C283—21no—
139Q8×C283#4112yes—
140D4×C283—21no—
141D4×C283—21no—
142D4×C283—21no—
143D4×C283—21no—
144D4×C283—42no—
145D4×C283—81no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283C22×D411yescharacteristic
165C2×D283—21no—
166C2×D283—21no—
167C2×D283—21no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C4×C283—21no—
172C4×C283—22no—
173C4×C283—41no—
174C4×C283C2×#4111yescharacteristic
175C4×C283H(5,𝔽2)11yescharacteristic
176Dic283—21no—
177Dic283—21no—
178Dic283—21no—
179Dic283—41no—
180Dic283—41no—
181Dic283—41no—
182C2×C283—41no—
183C2×C283—81no—
184C2×C283—81no—
185C2×C283#54611yescharacteristic
186C2×C283#57511yescharacteristic
187C2×C283#57611yescharacteristic
188D283—41no—
189D283—81no—
190C283#330911yescharacteristic, complemented, Sylow
191#3309—2831nomaximal, Sylow
192#553—2831no—
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#449D28311yescharacteristic, complemented
203#440—2831no—
204#435—2831no—
205#417—2831no—
206#416—2831no—
207C2×#41—2831no—
208C2×#41C2×D28311yescharacteristic
209C2×SD16C2×D28311yescharacteristic
210C2×D8—2831no—
211C2×D8C2×D28311yescharacteristic
212C2×M16—2831no—
213C22×C8—2831no—
214#127—2831no—
215#127—5661no—
216#126—5661no—
217#125—2831no—
218#123—5661no—
219#121—2831no—
220#121—2831no—
221#121—2831no—
222#121—5661no—
223#121—5661no—
224#121—5661no—
225#121C2×D28311yescharacteristic
226C4×Q8—2831no—
227C4×D4—2831no—
228C4×D4—2831no—
229C4×D4—5661no—
230C4×D4—5661no—
231#117—2831no—
232C2×C4⋊C4—2831no—
233#107—2831no—
234#107—2831no—
235#106—2831no—
236C4⋊C8—2831no—
237#103—2831no—
238#103—2831no—
239#103C2×D28311yescharacteristic
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102C2×D28311yescharacteristic
247C22⋊C8—2831no—
248C22⋊C8C2×D28311yescharacteristic
249#97—2831no—
250#41—22no—
251#41—41no—
252#41—5662no—
253#41—11321no—
254C2×Q8C22×D28311yescharacteristic
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—2831no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4—5661no—
272C22×C4C22×D28311yescharacteristic
273SD16—22no—
274D8—41no—
275D8—11321no—
276M16—11321no—
277C2×C8—2831no—
278C2×C8—2831no—
279C2×C8—11321no—
280C2×C8C22×D28311yescharacteristic
281C2×C8C22×D28311yescharacteristic
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—2831no—
285C4⋊C4—2831no—
286C4⋊C4—5661no—
287C4⋊C4—5661no—
288C4⋊C4—5661no—
289C4⋊C4—5661no—
290C4⋊C4C22×D28311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—2831no—
293C22⋊C4—2831no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C42—2831no—
300C42—5661no—
301C42—5661no—
302C23—21no—
303C23—21no—
304C23—2831no—
305C23—5661no—
306C23D4×D28311yescharacteristic
307Q8—21no—
308Q8#1798539112yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—5661no—
316D4—5661no—
317D4—11322no—
318D4—11321no—
319D4—11322no—
320D4—11322no—
321D4—22641no—
322D4—22641no—
323D4—22641no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—2831no—
330C2×C4—2831no—
331C2×C4—2831no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—11322no—
338C2×C4—22641no—
339C2×C4—22641no—
340C2×C4D4×D28311yescharacteristic
341C2×C4C23×D28311yescharacteristic
342C8—21no—
343C8—21no—
344C8—5661no—
345C8—5661no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—5661no—
356C22—5661no—
357C22—5661no—
358C22—11321no—
359C22—11321no—
360C22—11321no—
361C22C2×D4×D28311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—5661no—
366C4—5661no—
367C4—5661no—
368C4—11321no—
369C4—11321no—
370C4—11321no—
371C4C2×#1798539111yescharacteristic
372C4#2258365511yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—11321no—
377C2—22641no—
378C2#3182710211yescharacteristic
379C2#3182726211yescharacteristic
380C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#449×C283C2
socleC22×C283C22×D4
hypercenter#449D283
hypocenterC283#3309
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #31827162C2semidirect
2. #31827134C2semidirect
3. #31826828C2semidirect
4. #31826790C2semidirect
5. #31826777C2semidirect
6. #31826770C2semidirect
7. #31826715C2semidirect
8. #31826699C2semidirect
9. #31826658C2semidirect
10. #31826609C2semidirect
11. #31826566C2semidirect
12. #31826533C2semidirect
13. #31826465C2semidirect
14. #31826461C2semidirect
15. #449×C283C2semidirect
190. C283#3309semidirect
202. #449D283semidirect

Maximal subgroups

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

subgroupindex
#318271622
#318271342
#318268282
#318267902
#318267772
#318267702
#318267152
#318266992
#318266582
#318266092
#318265662
#318265332
#318264652
#318264612
#449×C2832
#3309283