Finite Group Databasebeta

← #44562958

Subgroups — #44562958

Order 32128.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632400C211yesmaximal, characteristic, complemented
2#30632337C211yesmaximal, characteristic, complemented
3#30632084C211yesmaximal, characteristic, complemented
4#30632010C211yesmaximal, characteristic, complemented
5#30632007C211yesmaximal, characteristic, complemented
6#30632006C211yesmaximal, characteristic, complemented
7#30631975C211yesmaximal, characteristic, complemented
8#30631966C211yesmaximal, characteristic, complemented
9#30631939C211yesmaximal, characteristic, complemented
10#30631938C211yesmaximal, characteristic, complemented
11#30631767C211yesmaximal, characteristic, complemented
12#30631762C211yesmaximal, characteristic, complemented
13#30631730C211yesmaximal, characteristic, complemented
14#30631728C211yesmaximal, characteristic, complemented
15#482×C251C211yesmaximal, characteristic, complemented
16C2×#16860809—21no—
17C2×#16860795C2211yescharacteristic
18C2×#16860794C2211yescharacteristic
19C2×#16860793C2211yescharacteristic
20#22548714C2211yescharacteristic
21#22548714C2211yescharacteristic
22#22548703—21no—
23#22548701—21no—
24#22548697—21no—
25#22548696—21no—
26#22548692—21no—
27#22548690C2211yescharacteristic
28#22548689C2211yescharacteristic
29#22548688—21no—
30#22548686C2211yescharacteristic
31D4×Dic251C2211yescharacteristic
32#22548677C2211yescharacteristic
33C4×C22⋊D251C2211yescharacteristic
34#22548673C2211yescharacteristic
35#22548672—21no—
36C2×C4⋊Dic251C2211yescharacteristic
37C4⋊C4×D251C2211yescharacteristic
38#22548648C2211yescharacteristic
39#22548648C2211yescharacteristic
40#22548647C2211yescharacteristic
41#22548647C2211yescharacteristic
42#22548646C2211yescharacteristic
43#22548646C2211yescharacteristic
44#22548646C2211yescharacteristic
45Dic251⋊C8C2211yescharacteristic
46#22548637C2211yescharacteristic
47#22548637C2211yescharacteristic
48#22548636C2211yescharacteristic
49#22548635C2211yescharacteristic
50(C2×D251)⋊C8C2211yescharacteristic
51C8×Dic251C2211yescharacteristic
52#121×C251C2211yescharacteristic
53#117×C251C2211yescharacteristic
54#107×C251C2211yescharacteristic
55#106×C251C2211yescharacteristic
56#102×C251C2211yescharacteristic
57#102×C251C2211yescharacteristic
58C22⋊C8×C251C2211yescharacteristic
59#16860809—44no—
60C2×Dic502—21no—
61C2×Dic502—21no—
62C2×D1004—21no—
63C2×D1004C2311yescharacteristic
64C2×C22⋊D251—21no—
65C2×C22⋊D251—21no—
66C2×C22⋊D251D411yescharacteristic
67C22×Dic251—21no—
68C22×Dic251—21no—
69C2×C4×D251—21no—
70C2×C4×D251—21no—
71C2×C4×D251C2311yescharacteristic
72#16860795—22no—
73#16860794—22no—
74#16860793—22no—
75C2×C251⋊C8C2311yescharacteristic
76C2×C251⋊C8C2311yescharacteristic
77C4⋊Dic251—21no—
78C4⋊Dic251C2311yescharacteristic
79C4⋊Dic251C2311yescharacteristic
80C4⋊Dic251C2311yescharacteristic
81Dic251⋊C4—21no—
82Dic251⋊C4—21no—
83Dic251⋊C4—21no—
84Dic251⋊C4D411yescharacteristic
85C22⋊Dic251—21no—
86C22⋊Dic251—21no—
87C22⋊Dic251D411yescharacteristic
88(C2×D251)⋊C4—21no—
89(C2×D251)⋊C4—21no—
90(C2×D251)⋊C4—21no—
91(C2×D251)⋊C4—21no—
92(C2×D251)⋊C4D411yescharacteristic
93C4×Dic251—21no—
94C4×Dic251C2311yescharacteristic
95C2×D4×C251—21no—
96C2×D4×C251C2311yescharacteristic
97C22×C4×C251C2311yescharacteristic
98C2×C8×C251C2311yescharacteristic
99C2×C8×C251C2311yescharacteristic
100C4⋊C4×C251C2311yescharacteristic
101C4⋊C4×C251C2311yescharacteristic
102C4⋊C4×C251C2311yescharacteristic
103C22⋊C4×C251—21no—
104C22⋊C4×C251—21no—
105C42×C251—21no—
106C22×D251—21no—
107C22×D251C2×D411yescharacteristic
108Dic502—42no—
109Dic502—81no—
110D1004—21no—
111D1004—21no—
112D1004—81no—
113C22⋊D251—22no—
114C22⋊D251—42no—
115C22⋊D251—81no—
116C2×Dic251—21no—
117C2×Dic251—21no—
118C2×Dic251—21no—
119C2×Dic251—42no—
120C2×Dic251—42no—
121C2×Dic251C2×D411yescharacteristic
122C2×Dic251C2×D411yescharacteristic
123C2×Dic251C2×D411yescharacteristic
124C4×D251—21no—
125C4×D251—21no—
126C4×D251—42no—
127C4×D251—42no—
128C251⋊C8—21no—
129C251⋊C8#4112yescomplemented
130C23×C251—21no—
131C23×C251C2×D411yescharacteristic
132D4×C251—21no—
133D4×C251—21no—
134D4×C251—42no—
135C2×C4×C251—21no—
136C2×C4×C251—21no—
137C2×C4×C251—21no—
138C2×C4×C251—21no—
139C2×C4×C251—21no—
140C2×C4×C251C2×D411yescharacteristic
141C2×C4×C251C2411yescharacteristic
142C8×C251—21no—
143C8×C251—21no—
144C22×C251—21no—
145C22×C251—21no—
146C22×C251—21no—
147C22×C251—41no—
148C22×C251—41no—
149C22×C251—41no—
150C22×C251C22×D411yescharacteristic
151C2×D251—21no—
152C2×D251—21no—
153C2×D251—21no—
154C2×D251—41no—
155C2×D251—41no—
156C2×D251—41no—
157C4×C251—21no—
158C4×C251—41no—
159C4×C251—41no—
160C4×C251—41no—
161C4×C251C2×#4111yescharacteristic
162C4×C2512−1+411yescharacteristic
163Dic251—21no—
164Dic251—21no—
165Dic251—41no—
166Dic251—41no—
167Dic251—41no—
168Dic251AGL(1,ℤ/8)12yes—
169C2×C251—41no—
170C2×C251—81no—
171C2×C251#54711yescharacteristic
172C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C251#57711yescharacteristic
174D251—41no—
175D251—81no—
176C251#335411yescharacteristic, complemented, Sylow
177#3354—2511nomaximal, Sylow
178#555—2511no—
179#547—2511no—
180#498—2511no—
181#482—2511no—
182#482D25111yescharacteristic, complemented
183#481—2511no—
184#481—2511no—
185#476—2511no—
186#474—2511no—
187#469—2511no—
188#469—2511no—
189C4×D8—2511no—
190#436—2511no—
191#428—2511no—
192#428—2511no—
193C2×#41—5021no—
194C2×D8—2511no—
195C2×M16—2511no—
196C2×M16—2511no—
197C4⋊Q8—2511no—
198C4⋊Q8—2511no—
199#124—5021no—
200#124—5021no—
201#123—5021no—
202#123—5021no—
203C22⋊Q8—5021no—
204#121—5021no—
205#121—2511no—
206#121—2511no—
207#121—2511no—
208#121C2×D25111yescharacteristic
209C4×D4—2511no—
210C4×D4—2511no—
211C4×D4—2511no—
212#117—5021no—
213#117—2511no—
214#117C2×D25111yescharacteristic
215C2×C4⋊C4—2511no—
216C2×C4⋊C4—2511no—
217#107—2511no—
218#107—2511no—
219#107C2×D25111yescharacteristic
220#106—2511no—
221#106—2511no—
222#106—2511no—
223#106—2511no—
224#106—2511no—
225#106C2×D25111yescharacteristic
226C4⋊C8—2511no—
227#102—2511no—
228#102—2511no—
229#102—2511no—
230#102—2511no—
231#102C2×D25111yescharacteristic
232#102C2×D25111yescharacteristic
233C22⋊C8—2511no—
234C22⋊C8C2×D25111yescharacteristic
235C4×C8—2511no—
236#41—10044no—
237C2×Q8—5021no—
238C2×Q8—5021no—
239C2×D4—21no—
240C2×D4—5021no—
241C2×D4—5021no—
242C2×D4—5021no—
243C2×D4—2511no—
244C2×D4—2511no—
245C2×D4C22×D25111yescharacteristic
246C22×C4—5021no—
247C22×C4—5021no—
248C22×C4—5021no—
249C22×C4—5021no—
250C22×C4—2511no—
251C22×C4C22×D25111yescharacteristic
252D8—5022no—
253M16—5022no—
254M16—5022no—
255C2×C8—2511no—
256C2×C8—2511no—
257C2×C8C22×D25111yescharacteristic
258C2×C8C22×D25111yescharacteristic
259C4⋊C4—5021no—
260C4⋊C4—5021no—
261C4⋊C4—5021no—
262C4⋊C4—5021no—
263C4⋊C4—2511no—
264C4⋊C4—2511no—
265C4⋊C4—2511no—
266C4⋊C4—2511no—
267C4⋊C4C22×D25111yescharacteristic
268C4⋊C4C22×D25111yescharacteristic
269C4⋊C4C22×D25111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—5021no—
273C22⋊C4—5021no—
274C22⋊C4—5021no—
275C22⋊C4—5021no—
276C22⋊C4—5021no—
277C22⋊C4—5021no—
278C22⋊C4—2511no—
279C22⋊C4—2511no—
280C42—21no—
281C42—5021no—
282C42—2511no—
283C23—21no—
284C23—5021no—
285C23—2511no—
286C23D4×D25111yescharacteristic
287Q8—20081no—
288Q8—10042no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—20081no—
293D4—20081no—
294D4—10042no—
295D4—5022no—
296D4—5021no—
297D4—5021no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—10042no—
304C2×C4—10042no—
305C2×C4—10042no—
306C2×C4—10042no—
307C2×C4—5021no—
308C2×C4—5021no—
309C2×C4—5021no—
310C2×C4—5021no—
311C2×C4—5021no—
312C2×C4—2511no—
313C2×C4—2511no—
314C2×C4—2511no—
315C2×C4D4×D25111yescharacteristic
316C2×C4C23×D25111yescharacteristic
317C8—21no—
318C8—21no—
319C8—5021no—
320C8—2512no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—10041no—
328C22—10041no—
329C22—10041no—
330C22—5021no—
331C22—5021no—
332C22—5021no—
333C22C2×D4×D25111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—10041no—
339C4—10041no—
340C4—10041no—
341C4—5021no—
342C4—5021no—
343C4—2512no—
344C4#41×D25111yescharacteristic
345C4#2254876211yescharacteristic
346C2—41no—
347C2—81no—
348C2—20081no—
349C2—10041no—
350C2#3063233511yescharacteristic
351C2AGL(1,ℤ/8)×D25111yescharacteristic
352C2#3063249411yescharacteristic
subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#482×C251C2
socleC22×C251C22×D4
hypercenter#482D251
hypocenterC251#3354
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #30632400C2semidirect
2. #30632337C2semidirect
3. #30632084C2semidirect
4. #30632010C2semidirect
5. #30632007C2semidirect
6. #30632006C2semidirect
7. #30631975C2semidirect
8. #30631966C2semidirect
9. #30631939C2semidirect
10. #30631938C2semidirect
11. #30631767C2semidirect
12. #30631762C2semidirect
13. #30631730C2semidirect
14. #30631728C2semidirect
15. #482×C251C2semidirect
129. C251⋊C8#41semidirect
176. C251#3354semidirect
182. #482D251semidirect

Maximal subgroups

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

subgroupindex
#306324002
#306323372
#306320842
#306320102
#306320072
#306320062
#306319752
#306319662
#306319392
#306319382
#306317672
#306317622
#306317302
#306317282
#482×C2512
#3354251