Finite Group Databasebeta

← #49133867

Subgroups — #49133867

Order 36224.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827163C211yesmaximal, characteristic, complemented
2#31827162C211yesmaximal, characteristic, complemented
3#31826866C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826780C211yesmaximal, characteristic, complemented
7#31826768C211yesmaximal, characteristic, complemented
8#31826767C211yesmaximal, characteristic, complemented
9#31826717C211yesmaximal, characteristic, complemented
10#31826716C211yesmaximal, characteristic, complemented
11#31826545C211yesmaximal, characteristic, complemented
12#31826540C211yesmaximal, characteristic, complemented
13#31826506C211yesmaximal, characteristic, complemented
14#31826505C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985377C2211yescharacteristic
17C2×#17985376C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19#22583605—21no—
20#22583603—21no—
21#22583601C2211yescharacteristic
22#22583601C2211yescharacteristic
23#22583595—21no—
24#22583591—21no—
25#22583585C2211yescharacteristic
26#22583584—21no—
27#22583584C2211yescharacteristic
28#22583581—21no—
29#22583581C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33C4×C22⋊D283C2211yescharacteristic
34(C22⋊D283)⋊C4—21no—
35#22583569C2211yescharacteristic
36#22583568C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583541C2211yescharacteristic
44#22583541C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×D1132—21no—
60C2×D1132C2311yescharacteristic
61C2×C22⋊D283—21no—
62C2×C22⋊D283—21no—
63C2×C22⋊D283D411yescharacteristic
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68#17985377—22no—
69#17985376—22no—
70#17985375—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283D411yescharacteristic
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4D411yescharacteristic
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283C2311yescharacteristic
94C2×D4×C283—21no—
95C2×D4×C283C2311yescharacteristic
96C22×C4×C283—21no—
97C22×C4×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C22⋊C4×C283—21no—
105C22×D283—21no—
106C22×D283C2×D411yescharacteristic
107D1132—21no—
108D1132—21no—
109D1132—81no—
110C22⋊D283—41no—
111C22⋊D283—42no—
112C22⋊D283—42no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—81no—
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C4×D283—21no—
121C4×D283—21no—
122C4×D283—81no—
123C4×D283—81no—
124C283⋊C8—21no—
125C283⋊C8#4112yes—
126C23×C283—21no—
127C23×C283C2×D411yescharacteristic
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—81no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—81no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C22×C283—21no—
142C22×C283—21no—
143C22×C283—21no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283C22×D411yescharacteristic
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—21no—
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283C2×#4111yescharacteristic
159C4×C2832−1+411yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—41no—
167C2×C283—81no—
168C2×C283#54711yescharacteristic
169C2×C283#57511yescharacteristic
170C2×C283#57611yescharacteristic
171D283—41no—
172D283—81no—
173C283#335511yescharacteristic, complemented, Sylow
174#3355—2831nomaximal, Sylow
175#553—2831no—
176#553—2831no—
177#499—2831no—
178#482—2831no—
179#482—2831no—
180#480—2831no—
181#480D28311yescharacteristic, complemented
182#478—2831no—
183#478—2831no—
184#469—2831no—
185#469—2831no—
186C4×D8—2831no—
187#436—2831no—
188#428—2831no—
189#428—2831no—
190C2×D8—2831no—
191C2×M16—2831no—
192C2×M16—2831no—
193#126—5661no—
194#126—5661no—
195#125—2831no—
196#125—2831no—
197#123—5661no—
198#123—5661no—
199#121—2831no—
200#121—2831no—
201#121—2831no—
202#121—5661no—
203#121—5661no—
204#121C2×D28311yescharacteristic
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4—5661no—
209C4×D4—5661no—
210#117—2831no—
211#117—2831no—
212C2×C4⋊C4—2831no—
213C2×C4⋊C4C2×D28311yescharacteristic
214#107—2831no—
215#107—2831no—
216#107—2831no—
217#107C2×D28311yescharacteristic
218#107C2×D28311yescharacteristic
219#106—2831no—
220#106—2831no—
221#106—2831no—
222#106—2831no—
223C4⋊C8—2831no—
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102—2831no—
228#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8C2×D28311yescharacteristic
232C4×C8—2831no—
233C2×D4—21no—
234C2×D4—2831no—
235C2×D4—2831no—
236C2×D4—5661no—
237C2×D4—5661no—
238C2×D4—5661no—
239C2×D4C22×D28311yescharacteristic
240C22×C4—21no—
241C22×C4—2831no—
242C22×C4—5661no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4C22×D28311yescharacteristic
246D8—5662no—
247M16—5662no—
248M16—5662no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4C22×D28311yescharacteristic
264C4⋊C4C22×D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—2831no—
268C22⋊C4—2831no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—2831no—
277C42—5661no—
278C42—5661no—
279C23—21no—
280C23—2831no—
281C23—5661no—
282C23D4×D28311yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—5661no—
287D4—5661no—
288D4—11321no—
289D4—11322no—
290D4—11322no—
291D4—22641no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—2831no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—22641no—
307C2×C4—22641no—
308C2×C4—22641no—
309C2×C4D4×D28311yescharacteristic
310C2×C4C23×D28311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2832no—
314C8—5661no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—5661no—
322C22—5661no—
323C22—5661no—
324C22—11321no—
325C22—11321no—
326C22—11321no—
327C22C2×D4×D28311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—5661no—
333C4—5661no—
334C4—5661no—
335C4—11321no—
336C4—11321no—
337C4—11321no—
338C4#41×D28311yescharacteristic
339C4#2258365711yescharacteristic
340C2—41no—
341C2—81no—
342C2—11321no—
343C2—22641no—
344C2#3182711311yescharacteristic
345C2#3182726411yescharacteristic
346C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
hypercenter#480D283
hypocenterC283#3355
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #31827163C2semidirect
2. #31827162C2semidirect
3. #31826866C2semidirect
4. #31826790C2semidirect
5. #31826787C2semidirect
6. #31826780C2semidirect
7. #31826768C2semidirect
8. #31826767C2semidirect
9. #31826717C2semidirect
10. #31826716C2semidirect
11. #31826545C2semidirect
12. #31826540C2semidirect
13. #31826506C2semidirect
14. #31826505C2semidirect
15. #480×C283C2semidirect
173. C283#3355semidirect
181. #480D283semidirect

Maximal subgroups

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

subgroupindex
#318271632
#318271622
#318268662
#318267902
#318267872
#318267802
#318267682
#318267672
#318267172
#318267162
#318265452
#318265402
#318265062
#318265052
#480×C2832
#3355283