Finite Group Databasebeta

← #44560929

Subgroups — #44560929

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#30632221C211yesmaximal, characteristic, complemented
2#30632086C211yesmaximal, characteristic, complemented
3#30632069C211yesmaximal, characteristic, complemented
4#30632044C211yesmaximal, characteristic, complemented
5#30632041C211yesmaximal, characteristic, complemented
6#30631926C211yesmaximal, characteristic, complemented
7#30631921C211yesmaximal, characteristic
8#30631918C211yesmaximal, characteristic, complemented
9#30631914C211yesmaximal, characteristic, complemented
10C4×#16860800C211yesmaximal, characteristic, complemented
11C4×#16860797C211yesmaximal, characteristic, complemented
12C4×#16860798C211yesmaximal, characteristic, complemented
13C4×#16860795C211yesmaximal, characteristic, complemented
14C2×C4×C251⋊C8C211yesmaximal, characteristic, complemented
15#529×C251C211yesmaximal, characteristic, complemented
16C2×#16860800C2211yescharacteristic
17C2×#16860798C2211yescharacteristic
18C2×#16860797C2211yescharacteristic
19C2×#16860795C2211yescharacteristic
20C22×C251⋊C8C2211yescharacteristic
21C22×C251⋊C8C2211yescharacteristic
22#22548709—21no—
23#22548707C2211yescharacteristic
24#22548703C2211yescharacteristic
25#22548698—21no—
26#22548694C2211yescharacteristic
27#22548689C2211yescharacteristic
28C4×Dic502C2211yescharacteristic
29C4×D1004C2211yescharacteristic
30C4×C22⋊D251—21no—
31#22548672—21no—
32#22548648C2211yescharacteristic
33#22548648C2211yescharacteristic
34#22548646C2211yescharacteristic
35#22548646C2211yescharacteristic
36#22548639C2211yescharacteristic
37#22548639C2211yescharacteristic
38#22548638C2211yescharacteristic
39#22548638C2211yescharacteristic
40#22548636C2211yescharacteristic
41#22548636C2211yescharacteristic
42#22548635C2211yescharacteristic
43#22548635C2211yescharacteristic
44C4×C251⋊C8C2211yescharacteristic
45C4×C251⋊C8C2211yescharacteristic
46C4×C251⋊C8C2211yescharacteristic
47C4×C251⋊C8C2211yescharacteristic
48#126×C251—21no—
49#125×C251C2211yescharacteristic
50#124×C251C2211yescharacteristic
51#123×C251—21no—
52C22⋊Q8×C251C2211yescharacteristic
53#121×C251C2211yescharacteristic
54C4×Q8×C251C2211yescharacteristic
55C4×D4×C251—21no—
56C4×D4×C251C2211yescharacteristic
57#117×C251—21no—
58C2×C42×C251C2211yescharacteristic
59C2×Dic502C2311yescharacteristic
60C2×D1004C2311yescharacteristic
61C2×C22⋊D251—21no—
62C2×C4×D251—21no—
63#16860800—22no—
64#16860798—22no—
65#16860797—22no—
66#16860795—22no—
67C2×C251⋊C8—22no—
68C2×C251⋊C8—22no—
69C2×C251⋊C8C2311yescharacteristic
70C2×C251⋊C8C2311yescharacteristic
71C2×C251⋊C8C2311yescharacteristic
72C2×C251⋊C8C2311yescharacteristic
73C4⋊Dic251C2311yescharacteristic
74C4⋊Dic251C2311yescharacteristic
75Dic251⋊C4—21no—
76Dic251⋊C4—21no—
77Dic251⋊C4—21no—
78Dic251⋊C4—21no—
79C22⋊Dic251—21no—
80(C2×D251)⋊C4—21no—
81(C2×D251)⋊C4—21no—
82(C2×D251)⋊C4—21no—
83(C2×D251)⋊C4—21no—
84C4×Dic251—21no—
85C2×Q8×C251C2311yescharacteristic
86C2×D4×C251—21no—
87C2×D4×C251C2311yescharacteristic
88C22×C4×C251—21no—
89C22×C4×C251D411yescharacteristic
90C22×C4×C251D411yescharacteristic
91C22×C4×C251C2311yescharacteristic
92C4⋊C4×C251—21no—
93C4⋊C4×C251—21no—
94C4⋊C4×C251—21no—
95C4⋊C4×C251—21no—
96C4⋊C4×C251C2311yescharacteristic
97C4⋊C4×C251C2311yescharacteristic
98C22⋊C4×C251—21no—
99C22⋊C4×C251—21no—
100C22⋊C4×C251—21no—
101C22⋊C4×C251—21no—
102C22⋊C4×C251—21no—
103C42×C251—21no—
104C42×C251D411yescharacteristic
105C42×C251D411yescharacteristic
106C42×C251C2311yescharacteristic
107C42×C251C2311yescharacteristic
108C22×D251—21no—
109Dic502—21no—
110Dic502—21no—
111D1004—21no—
112D1004—21no—
113C22⋊D251—42no—
114C2×Dic251—21no—
115C2×Dic251—21no—
116C2×Dic251—21no—
117C4×D251—42no—
118C251⋊C8—21no—
119C251⋊C8—21no—
120C251⋊C8#4112yes—
121C251⋊C8#4112yes—
122C23×C251—21no—
123C23×C251C2×D411yescharacteristic
124Q8×C251—21no—
125Q8×C251—21no—
126D4×C251—21no—
127D4×C251—21no—
128D4×C251—42no—
129C2×C4×C251—22no—
130C2×C4×C251—22no—
131C2×C4×C251—21no—
132C2×C4×C251—21no—
133C2×C4×C251—21no—
134C2×C4×C251—21no—
135C2×C4×C251—21no—
136C2×C4×C251—42no—
137C2×C4×C251C2×D411yescharacteristic
138C2×C4×C251C2×D411yescharacteristic
139C2×C4×C251C2×D411yescharacteristic
140C2×C4×C251C2×D411yescharacteristic
141C2×C4×C251C2×D411yescharacteristic
142C2×C4×C251C2411yescharacteristic
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—21no—
155C4×C251—21no—
156C4×C251—21no—
157C4×C251—41no—
158C4×C251—41no—
159C4×C251—41no—
160C4×C251#13512yes—
161C4×C251C2×#4111yescharacteristic
162C4×C251C2×#4111yescharacteristic
163Dic251—41no—
164Dic251—41no—
165Dic251—41no—
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#529D25111yescharacteristic, complemented
176#499—2511no—
177#495—2511no—
178#488—2511no—
179#488—2511no—
180#467—2511no—
181#466—2511no—
182#465—2511no—
183#465—2511no—
184C4×Q16—2511no—
185C4×SD16—2511no—
186C4×SD16—2511no—
187C4×D8—2511no—
188C2×C4×C8—2511no—
189C2×Q16—2511no—
190C2×SD16—2511no—
191C2×SD16—2511no—
192C2×D8—2511no—
193C22×C8—2511no—
194C22×C8—2511no—
195#126—21no—
196#126—5021no—
197#125—2511no—
198#125C2×D25111yescharacteristic
199#124—2511no—
200#124C2×D25111yescharacteristic
201#123—21no—
202#123—5021no—
203C22⋊Q8—2511no—
204C22⋊Q8C2×D25111yescharacteristic
205#121—2511no—
206#121C2×D25111yescharacteristic
207C4×Q8—2511no—
208C4×Q8C2×D25111yescharacteristic
209C4×D4—21no—
210C4×D4—5021no—
211C4×D4—2511no—
212C4×D4C2×D25111yescharacteristic
213#117—21no—
214#117—5021no—
215C2×C42C2×D25111yescharacteristic
216#107—2511no—
217#107—2511no—
218#106—2511no—
219#106—2511no—
220#103—2511no—
221#103—2511no—
222#103—2511no—
223#103—2511no—
224#102—2511no—
225#102—2511no—
226#102—2511no—
227#102—2511no—
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—21no—
239C22×C4—5021no—
240C22×C4C22⋊D25111yescharacteristic
241C22×C4C22⋊D25111yescharacteristic
242C22×C4C22×D25111yescharacteristic
243Q16—5022no—
244SD16—5022no—
245SD16—5022no—
246D8—5022no—
247C2×C8—5022no—
248C2×C8—5022no—
249C2×C8—2511no—
250C2×C8—2511no—
251C2×C8—2511no—
252C2×C8—2511no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
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—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—5021no—
271C22⋊C4—5021no—
272C22⋊C4—5021no—
273C22⋊C4—5021no—
274C22⋊C4—5021no—
275C42—21no—
276C42—5021no—
277C42C22⋊D25111yescharacteristic
278C42C22⋊D25111yescharacteristic
279C42C22×D25111yescharacteristic
280C42C22×D25111yescharacteristic
281C23—21no—
282C23—5021no—
283C23C2×C22⋊D25111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5021no—
287Q8—5021no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—10042no—
292D4—5021no—
293D4—5021no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—10042no—
303C2×C4—5021no—
304C2×C4—5021no—
305C2×C4—5021no—
306C2×C4C2×C22⋊D25111yescharacteristic
307C2×C4C2×C22⋊D25111yescharacteristic
308C2×C4C2×C22⋊D25111yescharacteristic
309C2×C4C2×C22⋊D25111yescharacteristic
310C2×C4C2×C22⋊D25111yescharacteristic
311C2×C4C23×D25111yescharacteristic
312C8—5021no—
313C8—5021no—
314C8—2512no—
315C8—2512no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—10041no—
322C22—10041no—
323C22—10041no—
324C22#2254873512yes—
325C22C22×C22⋊D25111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—10041no—
334C4—10041no—
335C4—10041no—
336C4#2254873512yes—
337C4#41×D25111yescharacteristic
338C4#41×D25111yescharacteristic
339C2—22no—
340C2—81no—
341C2—20081no—
342C2#3063223311yescharacteristic
343C2C2×#2254873511yescharacteristic
344C2C2×#2254873511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#529×C251C2
socleC22×C251C22×D4
prime radical#30631921C2
hypercenter#529D251
hypocenterC251#3168
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #30632221C2semidirect
2. #30632086C2semidirect
3. #30632069C2semidirect
4. #30632044C2semidirect
5. #30632041C2semidirect
6. #30631926C2semidirect
8. #30631918C2semidirect
9. #30631914C2semidirect
10. C4×#16860800C2semidirect
11. C4×#16860797C2semidirect
12. C4×#16860798C2semidirect
13. C4×#16860795C2semidirect
14. C2×C4×C251⋊C8C2semidirect
15. #529×C251C2semidirect
172. C251#3168semidirect
175. #529D251semidirect

Maximal subgroups

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

subgroupindex
#306322212
#306320862
#306320692
#306320442
#306320412
#306319262
#306319212
#306319182
#306319142
C4×#168608002
C4×#168607972
C4×#168607982
C4×#168607952
C2×C4×C251⋊C82
#529×C2512
#3168251