Finite Group Databasebeta

← #27183778

Subgroups — #27183778

Order 12928.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265896C211yesmaximal, characteristic, complemented
2#20265883C211yesmaximal, characteristic, complemented
3#20265530C211yesmaximal, characteristic, complemented
4#20265526C211yesmaximal, characteristic, complemented
5#20265482C211yesmaximal, characteristic, complemented
6#20265481C211yesmaximal, characteristic, complemented
7#20265465C211yesmaximal, characteristic, complemented
8#20265391C211yesmaximal, characteristic
9#20265389C211yesmaximal, characteristic
10#20265381C211yesmaximal, characteristic, complemented
11C8×Dic202C211yesmaximal, characteristic, complemented
12C4×#13108063C211yesmaximal, characteristic, complemented
13#20265262C211yesmaximal, characteristic, complemented
14#20265257C211yesmaximal, characteristic
15#488×C101C211yesmaximal, characteristic, complemented
16C2×#13108063C2211yescharacteristic
17C2×#13108061C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19#15692254C2211yescharacteristic
20#15692253C2211yescharacteristic
21#15692248—21no—
22#15692248—21no—
23#15692246C2211yescharacteristic
24#15692242C2211yescharacteristic
25#15692235—21no—
26#15692233—21no—
27#15692233—21no—
28#15692232—21no—
29Q8×Dic101C2211yescharacteristic
30C4×Dic202C2211yescharacteristic
31C4×Dic202C2211yescharacteristic
32C4×D404C2211yescharacteristic
33D4×Dic101C2211yescharacteristic
34#15692217C2211yescharacteristic
35#15692217C2211yescharacteristic
36#15692211—21no—
37C4⋊C4×D101—21no—
38#15692188C2211yescharacteristic
39#15692187C2211yescharacteristic
40#15692186C2211yescharacteristic
41C4⋊#11717579C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692184C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692179C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692176C2211yescharacteristic
50C8×Dic101C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52#125×C101C2211yescharacteristic
53#124×C101C2211yescharacteristic
54#103×C101C2211yescharacteristic
55#103×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202D411yescharacteristic
61C2×Dic202C2311yescharacteristic
62C2×D404C2311yescharacteristic
63C22×Dic101—21no—
64C2×C4×D101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67#13108063—22no—
68#13108061—22no—
69#13108059—22no—
70C2×#11717579C2311yescharacteristic
71C2×#11717579C2311yescharacteristic
72C4⋊Dic101—21no—
73C4⋊Dic101—21no—
74C4⋊Dic101D411yescharacteristic
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053D411yescharacteristic
83#13108053D411yescharacteristic
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101C2311yescharacteristic
93C4×Dic101C2311yescharacteristic
94C2×Q8×C101C2311yescharacteristic
95C2×D4×C101C2311yescharacteristic
96C2×C8×C101C2311yescharacteristic
97C2×C8×C101C2311yescharacteristic
98C4⋊C4×C101—21no—
99C4⋊C4×C101—21no—
100C4⋊C4×C101C2311yescharacteristic
101C4⋊C4×C101C2311yescharacteristic
102C22⋊C4×C101—21no—
103C22⋊C4×C101—21no—
104C42×C101C2311yescharacteristic
105C23×C101—21no—
106C22×D101—21no—
107Q8×C101—21no—
108Q8×C101—21no—
109D4×C101—21no—
110D4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101C2×D411yescharacteristic
115C2×C4×C101C2×D411yescharacteristic
116C2×C4×C101C2411yescharacteristic
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101—42no—
121C2×Dic101C2×D411yescharacteristic
122C2×Dic101C2×D411yescharacteristic
123C2×Dic101C2×D411yescharacteristic
124C2×Dic101C2×D411yescharacteristic
125D404—21no—
126D404#4112yes—
127C4×D101—42no—
128C4×D101—81no—
129C4×D101—81no—
130Dic202—22no—
131Dic202—21no—
132Dic202—21no—
133Dic202—81no—
134C8×C101—21no—
135C8×C101—21no—
136#11717579—21no—
137#11717579—21no—
138C22×C101—41no—
139C22×C101—41no—
140C22×C101—41no—
141C22×C101C22×D411yescharacteristic
142C2×D101—22no—
143C2×D101—41no—
144C2×D101—41no—
145C4×C101—21no—
146C4×C101—21no—
147C4×C101—41no—
148C4×C101—41no—
149C4×C101—41no—
150C4×C101C2×#4111yescharacteristic
151C4×C1012−1+411yescharacteristic
152Dic101—21no—
153Dic101—21no—
154Dic101—21no—
155Dic101—41no—
156Dic101—41no—
157Dic101—41no—
158Dic101#13512yes—
159C2×C101—81no—
160C2×C101#54811yescharacteristic
161C2×C101C2×#13511yescharacteristic
162C2×C101#57711yescharacteristic
163D101—42no—
164#3360—1011nomaximal, Sylow
165C101#336011yescharacteristic, complemented, Sylow
166#556—1011no—
167#554—1011no—
168#488—1011no—
169#488D10111yescharacteristic, complemented
170#487—1011no—
171#479—1011no—
172#479—1011no—
173#476—1011no—
174#463—1011no—
175#463—1011no—
176#461—1011no—
177C8×Q8—1011no—
178C4×SD16—1011no—
179C4×SD16—1011no—
180C4×D8—1011no—
181C2×SD16—1011no—
182C2×SD16—1011no—
183C2×D8—1011no—
184C4⋊Q8—1011no—
185C4⋊Q8—1011no—
186#126—2021no—
187#126—2021no—
188#125—1011no—
189#125C2×D10111yescharacteristic
190#124—1011no—
191#124C2×D10111yescharacteristic
192C22⋊Q8—2021no—
193C22⋊Q8—2021no—
194C22⋊Q8—2021no—
195C22⋊Q8—2021no—
196C4×Q8—1011no—
197C4×Q8—1011no—
198C4×Q8—1011no—
199C4×D4—1011no—
200C4×D4—1011no—
201C4×D4—1011no—
202C4×D4—1011no—
203#117—2021no—
204C2×C4⋊C4—2021no—
205#107—1011no—
206#106—1011no—
207#106—1011no—
208C4⋊C8—1011no—
209C4⋊C8—1011no—
210C4⋊C8—1011no—
211#103—1011no—
212#103—1011no—
213#103—1011no—
214#103—1011no—
215#103C2×D10111yescharacteristic
216#103C2×D10111yescharacteristic
217#102—1011no—
218#102—1011no—
219#102C2×D10111yescharacteristic
220#102C2×D10111yescharacteristic
221C4×C8—1011no—
222C4×C8—1011no—
223C4×C8C2×D10111yescharacteristic
224C2×Q8—1011no—
225C2×Q8—1011no—
226C2×Q8—2021no—
227C2×Q8C22×D10111yescharacteristic
228C2×D4—1011no—
229C2×D4C22×D10111yescharacteristic
230C22×C4—2021no—
231C22×C4—2021no—
232C22×C4—2021no—
233C22×C4—2021no—
234SD16—2022no—
235SD16—2022no—
236D8—2022no—
237C2×C8—1011no—
238C2×C8—1011no—
239C2×C8C22×D10111yescharacteristic
240C2×C8C22×D10111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—1011no—
244C4⋊C4—1011no—
245C4⋊C4—1011no—
246C4⋊C4—1011no—
247C4⋊C4—1011no—
248C4⋊C4—2021no—
249C4⋊C4—2021no—
250C4⋊C4—2021no—
251C4⋊C4—2021no—
252C4⋊C4—2021no—
253C4⋊C4—2021no—
254C4⋊C4—2021no—
255C4⋊C4C22×D10111yescharacteristic
256C4⋊C4C22×D10111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—2021no—
260C22⋊C4—2021no—
261C22⋊C4—2021no—
262C22⋊C4—2021no—
263C22⋊C4—2021no—
264C22⋊C4—2021no—
265C42—1011no—
266C42—1011no—
267C42—2021no—
268C42—2021no—
269C42C22×D10111yescharacteristic
270C23—21no—
271C23—2021no—
272Q8—21no—
273Q8—21no—
274Q8—8081no—
275Q8—2022no—
276Q8—2021no—
277Q8—2021no—
278D4—21no—
279D4—21no—
280D4—1012no—
281D4—2021no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—8081no—
286C2×C4—8081no—
287C2×C4—1011no—
288C2×C4—1011no—
289C2×C4—1011no—
290C2×C4—1011no—
291C2×C4—4042no—
292C2×C4—4042no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4—2021no—
296C2×C4D4×D10111yescharacteristic
297C2×C4D4×D10111yescharacteristic
298C2×C4C23×D10111yescharacteristic
299C8—21no—
300C8—21no—
301C8—2021no—
302C8—2021no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—4041no—
307C22—4041no—
308C22—2022no—
309C22C2×D4×D10111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—1012no—
316C4—4041no—
317C4—4041no—
318C4—4041no—
319C4—2021no—
320C4—2021no—
321C4—2021no—
322C4#41×D10111yescharacteristic
323C4#1569230211yescharacteristic
324C2—81no—
325C2—4042no—
326C2#2026583511yescharacteristic
327C2#135×D10111yescharacteristic
328C2#2026598411yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#488×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108059C22
hypercenter#488D101
hypocenterC101#3360
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20265896C2semidirect
2. #20265883C2semidirect
3. #20265530C2semidirect
4. #20265526C2semidirect
5. #20265482C2semidirect
6. #20265481C2semidirect
7. #20265465C2semidirect
10. #20265381C2semidirect
11. C8×Dic202C2semidirect
12. C4×#13108063C2semidirect
13. #20265262C2semidirect
15. #488×C101C2semidirect
165. C101#3360semidirect
169. #488D101semidirect

Maximal subgroups

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

subgroupindex
#202658962
#202658832
#202655302
#202655262
#202654822
#202654812
#202654652
#202653912
#202653892
#202653812
C8×Dic2022
C4×#131080632
#202652622
#202652572
#488×C1012
#3360101