Finite Group Databasebeta

← #44560928

Subgroups — #44560928

Order 32128.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632223C211yesmaximal, characteristic, complemented
2#30632218C211yesmaximal, characteristic, complemented
3#30632087C211yesmaximal, characteristic, complemented
4#30632068C211yesmaximal, characteristic, complemented
5#30632043C211yesmaximal, characteristic, complemented
6#30632040C211yesmaximal, characteristic, complemented
7#30631926C211yesmaximal, characteristic, complemented
8#30631921C211yesmaximal, characteristic
9#30631916C211yesmaximal, characteristic, complemented
10#30631779C211yesmaximal, characteristic, complemented
11SD16×Dic251C211yesmaximal, characteristic, complemented
12#30631774C211yesmaximal, characteristic, complemented
13#30631767C211yesmaximal, characteristic, complemented
14C2×C8×Dic251C211yesmaximal, characteristic, complemented
15#465×C251C211yesmaximal, characteristic, complemented
16C2×#16860800C2211yescharacteristic
17C2×#16860799C2211yescharacteristic
18C2×#16860795C2211yescharacteristic
19C22×C251⋊C8C2211yescharacteristic
20#22548710—21no—
21#22548708—21no—
22#22548706C2211yescharacteristic
23#22548706C2211yescharacteristic
24#22548704C2211yescharacteristic
25#22548702C2211yescharacteristic
26#22548699—21no—
27#22548696—21no—
28#22548694C2211yescharacteristic
29#22548689C2211yescharacteristic
30Q8×Dic251C2211yescharacteristic
31#22548680C2211yescharacteristic
32D4×Dic251—21no—
33D4×Dic251C2211yescharacteristic
34#22548677C2211yescharacteristic
35(C22⋊D251)⋊C4—21no—
36#22548673—21no—
37#22548671—21no—
38C2×C4×Dic251C2211yescharacteristic
39#22548648C2211yescharacteristic
40#22548648C2211yescharacteristic
41#22548647C2211yescharacteristic
42#22548640C2211yescharacteristic
43#22548639C2211yescharacteristic
44#22548638C2211yescharacteristic
45#22548637C2211yescharacteristic
46#22548636C2211yescharacteristic
47#22548635C2211yescharacteristic
48C8×Dic251C2211yescharacteristic
49C8×Dic251C2211yescharacteristic
50C8×Dic251C2211yescharacteristic
51C8×Dic251C2211yescharacteristic
52C2×SD16×C251C2211yescharacteristic
53C22×C8×C251C2211yescharacteristic
54C22⋊Q8×C251C2211yescharacteristic
55#121×C251C2211yescharacteristic
56#106×C251C2211yescharacteristic
57#103×C251C2211yescharacteristic
58#102×C251C2211yescharacteristic
59C2×Dic502C2311yescharacteristic
60C2×D1004C2311yescharacteristic
61C2×C22⋊D251—21no—
62C22×Dic251—21no—
63C22×Dic251D411yescharacteristic
64C22×Dic251D411yescharacteristic
65C2×C4×D251—21no—
66#16860800—22no—
67#16860799—22no—
68#16860795—22no—
69C2×C251⋊C8—22no—
70C2×C251⋊C8C2311yescharacteristic
71C2×C251⋊C8C2311yescharacteristic
72C4⋊Dic251—21no—
73C4⋊Dic251—21no—
74C4⋊Dic251—21no—
75C4⋊Dic251C2311yescharacteristic
76C4⋊Dic251C2311yescharacteristic
77Dic251⋊C4—21no—
78Dic251⋊C4—21no—
79Dic251⋊C4—21no—
80Dic251⋊C4—21no—
81C22⋊Dic251—21no—
82C22⋊Dic251—21no—
83C22⋊Dic251—21no—
84C22⋊Dic251—21no—
85(C2×D251)⋊C4—21no—
86(C2×D251)⋊C4—21no—
87(C2×D251)⋊C4—21no—
88(C2×D251)⋊C4—21no—
89C4×Dic251—21no—
90C4×Dic251—21no—
91C4×Dic251D411yescharacteristic
92C4×Dic251D411yescharacteristic
93C4×Dic251C2311yescharacteristic
94C4×Dic251C2311yescharacteristic
95C2×Q8×C251C2311yescharacteristic
96C2×D4×C251—21no—
97C2×D4×C251C2311yescharacteristic
98C22×C4×C251C2311yescharacteristic
99SD16×C251—22no—
100C2×C8×C251—22no—
101C2×C8×C251C2311yescharacteristic
102C2×C8×C251C2311yescharacteristic
103C4⋊C4×C251—21no—
104C4⋊C4×C251C2311yescharacteristic
105C4⋊C4×C251C2311yescharacteristic
106C22⋊C4×C251—21no—
107C22⋊C4×C251—21no—
108C22×D251—21no—
109Dic502—21no—
110Dic502—21no—
111D1004—21no—
112D1004—21no—
113C22⋊D251—42no—
114C2×Dic251—22no—
115C2×Dic251—22no—
116C2×Dic251—21no—
117C2×Dic251—21no—
118C2×Dic251—21no—
119C2×Dic251—42no—
120C2×Dic251C2×D411yescharacteristic
121C2×Dic251C2×D411yescharacteristic
122C2×Dic251C2×D411yescharacteristic
123C2×Dic251C2×D411yescharacteristic
124C4×D251—42no—
125C251⋊C8—21no—
126C251⋊C8#4112yes—
127C23×C251—21no—
128C23×C251C2×D411yescharacteristic
129Q8×C251—21no—
130Q8×C251—21no—
131D4×C251—21no—
132D4×C251—21no—
133D4×C251—42no—
134C2×C4×C251—21no—
135C2×C4×C251—21no—
136C2×C4×C251—21no—
137C2×C4×C251—21no—
138C2×C4×C251—21no—
139C2×C4×C251C2×D411yescharacteristic
140C2×C4×C251C2411yescharacteristic
141C8×C251—21no—
142C8×C251#4112yes—
143C22×C251—21no—
144C22×C251—21no—
145C22×C251—41no—
146C22×C251—41no—
147C22×C251—41no—
148C22×C251#13512yes—
149C22×C251C22×D411yescharacteristic
150C2×D251—41no—
151C2×D251—41no—
152C2×D251—41no—
153C4×C251—21no—
154C4×C251—41no—
155C4×C251—41no—
156C4×C251—41no—
157C4×C251C2×#4111yescharacteristic
158C4×C251C2×#4111yescharacteristic
159Dic251—21no—
160Dic251—21no—
161Dic251—21no—
162Dic251—41no—
163Dic251—41no—
164Dic251—41no—
165Dic251#13512yes—
166C2×C251—22no—
167C2×C251—81no—
168C2×C251#53211yescharacteristic
169C2×C251C2×#13511yescharacteristic
170C2×C251C2×#13511yescharacteristic
171D251—81no—
172C251#316811yescharacteristic, complemented, Sylow
173#3168—2511nomaximal, Sylow
174#529—2511no—
175#529—2511no—
176#499—2511no—
177#495—2511no—
178#488—2511no—
179#488—2511no—
180#467—2511no—
181#466—2511no—
182#465—2511no—
183#465D25111yescharacteristic, complemented
184C4×Q16—2511no—
185C4×SD16—2511no—
186C4×SD16—2511no—
187C4×D8—2511no—
188C2×C4×C8—2511no—
189C2×Q16—2511no—
190C2×SD16—2511no—
191C2×SD16C2×D25111yescharacteristic
192C2×D8—2511no—
193C22×C8—2511no—
194C22×C8C2×D25111yescharacteristic
195#126—5021no—
196#126—5021no—
197#125—2511no—
198#125—2511no—
199#124—2511no—
200#124—2511no—
201#123—5021no—
202#123—5021no—
203C22⋊Q8—2511no—
204C22⋊Q8C2×D25111yescharacteristic
205#121—2511no—
206#121C2×D25111yescharacteristic
207C4×Q8—2511no—
208C4×Q8—2511no—
209C4×D4—5021no—
210C4×D4—5021no—
211C4×D4—2511no—
212C4×D4—2511no—
213#117—5021no—
214#117—5021no—
215C2×C42—2511no—
216#107—2511no—
217#107—2511no—
218#106—2511no—
219#106C2×D25111yescharacteristic
220#103—2511no—
221#103—2511no—
222#103—2511no—
223#103C2×D25111yescharacteristic
224#102—2511no—
225#102—2511no—
226#102—2511no—
227#102C2×D25111yescharacteristic
228C4×C8—2511no—
229C4×C8—2511no—
230C4×C8—2511no—
231C4×C8—2511no—
232C2×Q8—2511no—
233C2×Q8C22×D25111yescharacteristic
234C2×D4—21no—
235C2×D4—5021no—
236C2×D4—2511no—
237C2×D4C22×D25111yescharacteristic
238C22×C4—5021no—
239C22×C4—5021no—
240C22×C4—2511no—
241C22×C4—2511no—
242C22×C4C22×D25111yescharacteristic
243Q16—5022no—
244SD16—22no—
245SD16—5022no—
246D8—5022no—
247C2×C8—22no—
248C2×C8—5022no—
249C2×C8—2511no—
250C2×C8—2511no—
251C2×C8C22×D25111yescharacteristic
252C2×C8C22×D25111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—5021no—
255C4⋊C4—5021no—
256C4⋊C4—5021no—
257C4⋊C4—5021no—
258C4⋊C4—5021no—
259C4⋊C4—5021no—
260C4⋊C4—5021no—
261C4⋊C4—2511no—
262C4⋊C4—2511no—
263C4⋊C4C22×D25111yescharacteristic
264C4⋊C4C22×D25111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5021no—
268C22⋊C4—5021no—
269C22⋊C4—5021no—
270C22⋊C4—5021no—
271C22⋊C4—5021no—
272C22⋊C4—5021no—
273C22⋊C4—5021no—
274C22⋊C4—5021no—
275C42—5021no—
276C42—5021no—
277C42—2511no—
278C42—2511no—
279C42—2511no—
280C42—2511no—
281C23—21no—
282C23—5021no—
283C23D4×D25111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5021no—
287Q8—5021no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—10042no—
292D4—5021no—
293D4—5021no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—10042no—
300C2×C4—10042no—
301C2×C4—5021no—
302C2×C4—5021no—
303C2×C4—5021no—
304C2×C4—5022no—
305C2×C4—5022no—
306C2×C4—2511no—
307C2×C4—2511no—
308C2×C4—2511no—
309C2×C4—2511no—
310C2×C4D4×D25111yescharacteristic
311C2×C4C23×D25111yescharacteristic
312C8—21no—
313C8—5021no—
314C8—2512no—
315C8#1686080912yes—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—10041no—
322C22—10041no—
323C22—10041no—
324C22#2254873612yes—
325C22C2×D4×D25111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—10041no—
331C4—10041no—
332C4—10041no—
333C4—5021no—
334C4—5021no—
335C4—5021no—
336C4—2512no—
337C4#41×D25111yescharacteristic
338C4C2×#1686080911yescharacteristic
339C2—22no—
340C2—81no—
341C2—20081no—
342C2#3063223211yescharacteristic
343C2#135×D25111yescharacteristic
344C2C2×#2254873611yescharacteristic
subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#465×C251C2
socleC22×C251C22×D4
prime radical#30631921C2
hypercenter#465D251
hypocenterC251#3168
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #30632223C2semidirect
2. #30632218C2semidirect
3. #30632087C2semidirect
4. #30632068C2semidirect
5. #30632043C2semidirect
6. #30632040C2semidirect
7. #30631926C2semidirect
9. #30631916C2semidirect
10. #30631779C2semidirect
11. SD16×Dic251C2semidirect
12. #30631774C2semidirect
13. #30631767C2semidirect
14. C2×C8×Dic251C2semidirect
15. #465×C251C2semidirect
172. C251#3168semidirect
183. #465D251semidirect

Maximal subgroups

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

subgroupindex
#306322232
#306322182
#306320872
#306320682
#306320432
#306320402
#306319262
#306319212
#306319162
#306317792
SD16×Dic2512
#306317742
#306317672
C2×C8×Dic2512
#465×C2512
#3168251