Finite Group Databasebeta

← #49133152

Subgroups — #49133152

Order 36224.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827157C211yesmaximal, characteristic, complemented
2#31827126C211yesmaximal, characteristic
3#31826821C211yesmaximal, characteristic, complemented
4#31826805C211yesmaximal, characteristic, complemented
5#31826779C211yesmaximal, characteristic, complemented
6#31826774C211yesmaximal, characteristic, complemented
7#31826703C211yesmaximal, characteristic, complemented
8#31826696C211yesmaximal, characteristic, complemented
9#31826689C211yesmaximal, characteristic, complemented
10#31826626C211yesmaximal, characteristic, complemented
11Q16×Dic283C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14C2×#22583534C211yesmaximal, characteristic, complemented
15#451×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C22×C283⋊C8C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583605—21no—
21#22583601—21no—
22#22583601C2211yescharacteristic
23#22583599—21no—
24#22583599C2211yescharacteristic
25#22583594—21no—
26#22583586—21no—
27#22583586C2211yescharacteristic
28#22583586C2211yescharacteristic
29#22583584—21no—
30#22583584C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32Q8×Dic283C2211yescharacteristic
33C4×C22⋊D283—21no—
34C4×C22⋊D283C2211yescharacteristic
35#22583568C2211yescharacteristic
36#22583566—21no—
37C2×C4⋊Dic283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C2×Q16×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283D411yescharacteristic
65C22×Dic283—21no—
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68#17985379—41no—
69C2×C283⋊C8—41no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C8×D283—41no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283—21no—
97C2×Q8×C283—22no—
98C2×Q8×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104Q16×C283—22no—
105Q16×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113D1132—21no—
114D1132—21no—
115D1132—42no—
116C22⋊D283—22no—
117C22⋊D283—42no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—42no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—42no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283C2×D411yescharacteristic
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283—21no—
136Q8×C283—42no—
137Q8×C283#4112yes—
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—42no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283#13512yes—
152C22×C283C22×D411yescharacteristic
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—22no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283H(5,𝔽2)11yescharacteristic
166Dic283—21no—
167Dic283—21no—
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—22no—
173C2×C283#54611yescharacteristic
174C2×C283C2×#13511yescharacteristic
175C2×C283#57811yescharacteristic
176D283—41no—
177D283—81no—
178C283#330011yescharacteristic, complemented, Sylow
179#3300—2831nomaximal, Sylow
180#552—2831no—
181#548—2831no—
182#488—2831no—
183#485—2831no—
184#480—2831no—
185#479—2831no—
186#467—2831no—
187#465—2831no—
188#464—2831no—
189#452—2831no—
190#451D28311yescharacteristic, complemented
191C4×Q16—2831no—
192C8×D4—2831no—
193#416—2831no—
194C2×#103—2831no—
195C2×#41—2831no—
196C22×Q8C2×D28311yescharacteristic
197C2×Q16C2×D28311yescharacteristic
198C2×Q16C2×D28311yescharacteristic
199C2×SD16—2831no—
200C22×C8—2831no—
201C22×C8—2831no—
202#126—5661no—
203#125—2831no—
204#125—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—5661no—
211C22⋊Q8C2×D28311yescharacteristic
212#121—2831no—
213#121—5661no—
214C4×Q8—2831no—
215C4×Q8—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218#117—2831no—
219#117—5661no—
220C2×C4⋊C4—2831no—
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8—2831no—
236C22⋊C8C2×D28311yescharacteristic
237C4×C8—2831no—
238#41—5662no—
239#41—11321no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D28311yescharacteristic
244C2×Q8C22×D28311yescharacteristic
245C2×Q8C22×D28311yescharacteristic
246C2×D4—2831no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4—5661no—
250C22×C4—21no—
251C22×C4—2831no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4C22×D28311yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—11321no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—11321no—
261C2×C8—11321no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2831no—
279C22⋊C4—2831no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C23—2831no—
291C23—5661no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#1798539112yes—
300D4—5662no—
301D4—5661no—
302D4—5661no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—11322no—
321C2×C4—11322no—
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—21no—
329C22—21no—
330C22—5661no—
331C22—5661no—
332C22—5661no—
333C22—11321no—
334C22—11321no—
335C22—11321no—
336C22#2258363312yes—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5661no—
344C4—5661no—
345C4—5661no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4C2×#1798539111yescharacteristic
350C4#2258365511yescharacteristic
351C2—22no—
352C2—11321no—
353C2—22641no—
354C2#3182710211yescharacteristic
355C2C2×#2258363311yescharacteristic
356C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#451×C283C2
socleC22×C283C22×D4
prime radical#31827126C2
hypercenter#451D283
hypocenterC283#3300
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #31827157C2semidirect
3. #31826821C2semidirect
4. #31826805C2semidirect
5. #31826779C2semidirect
6. #31826774C2semidirect
7. #31826703C2semidirect
8. #31826696C2semidirect
9. #31826689C2semidirect
10. #31826626C2semidirect
11. Q16×Dic283C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826460C2semidirect
14. C2×#22583534C2semidirect
15. #451×C283C2semidirect
178. C283#3300semidirect
190. #451D283semidirect

Maximal subgroups

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

subgroupindex
#318271572
#318271262
#318268212
#318268052
#318267792
#318267742
#318267032
#318266962
#318266892
#318266262
Q16×Dic2832
(C22⋊D283)⋊C82
#318264602
C2×#225835342
#451×C2832
#3300283