Finite Group Databasebeta

← #27181428

Subgroups — #27181428

Order 12928.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265787C211yesmaximal, characteristic
2#20265654C211yesmaximal, characteristic
3#20265518C211yesmaximal, characteristic
4#20265487C211yesmaximal, characteristic, complemented
5#20265483C211yesmaximal, characteristic, complemented
6#20265386C211yesmaximal, characteristic, complemented
7#20265386C211yesmaximal, characteristic, complemented
8#20265335C211yesmaximal, characteristic
9#20265332C211yesmaximal, characteristic
10#20265283C211yesmaximal, characteristic, complemented
11#20265281C211yesmaximal, characteristic, complemented
12#20265271C211yesmaximal, characteristic, complemented
13#20265269C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic
15#485×C101C211yesmaximal, characteristic
16C22×Dic202C2211yescharacteristic
17C2×Dic404C2211yescharacteristic
18C2×Dic404C2211yescharacteristic
19C2×#13108064C2211yescharacteristic
20C2×#13108064C2211yescharacteristic
21#15692253C2211yescharacteristic
22#15692248—21no—
23#15692248—21no—
24#15692246—21no—
25#15692246C2211yescharacteristic
26#15692245—21no—
27#15692234C2211yescharacteristic
28Q8×Dic101C2211yescharacteristic
29C4×Dic202—21no—
30C4×Dic202—21no—
31#15692220C2211yescharacteristic
32#15692220C2211yescharacteristic
33#15692220C2211yescharacteristic
34#15692220C2211yescharacteristic
35#15692220C2211yescharacteristic
36#15692214C2211yescharacteristic
37#15692211—21no—
38#15692211—21no—
39#15692188C2211yescharacteristic
40#15692186C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692178C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C22⋊Q8×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202—22no—
61C2×Dic202—22no—
62C2×Dic202C2311yescharacteristic
63C2×Dic202C2311yescharacteristic
64C2×Dic202C2311yescharacteristic
65C22×Dic101—21no—
66Dic404—22no—
67Dic404—22no—
68#13108064—22no—
69#13108064—22no—
70C2×#11717579C2311yescharacteristic
71C2×#11717579C2311yescharacteristic
72C4⋊Dic101—21no—
73C4⋊Dic101—21no—
74C4⋊Dic101D411yescharacteristic
75C4⋊Dic101D411yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101D411yescharacteristic
88C22⋊Dic101D411yescharacteristic
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101C2311yescharacteristic
98C22×C4×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101—21no—
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C23×C101C2×D411yescharacteristic
109Q8×C101—21no—
110Q8×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101C2×D411yescharacteristic
118C2×C4×C101C2411yescharacteristic
119C2×Dic101—24no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101C2×D411yescharacteristic
125C2×Dic101C2×D411yescharacteristic
126C2×Dic101C2×D411yescharacteristic
127C2×Dic101C2×D411yescharacteristic
128Dic202—24no—
129Dic202—21no—
130Dic202—21no—
131Dic202—21no—
132Dic202—21no—
133Dic202#4112yes—
134Dic202#4112yes—
135C8×C101—21no—
136C8×C101—21no—
137#11717579—21no—
138#11717579—21no—
139C22×C101—21no—
140C22×C101—21no—
141C22×C101—21no—
142C22×C101C22×D411yescharacteristic
143C4×C101—21no—
144C4×C101—41no—
145C4×C101—41no—
146C4×C101—41no—
147C4×C101—41no—
148C4×C101C2×#4111yescharacteristic
149C4×C101C2×#4111yescharacteristic
150Dic101—22no—
151Dic101—22no—
152Dic101—21no—
153Dic101—21no—
154Dic101—21no—
155Dic101—21no—
156Dic101—41no—
157Dic101—41no—
158C2×C101—41no—
159C2×C101#52511yescharacteristic
160C2×C101#57811yescharacteristic
161C2×C101#57811yescharacteristic
162#3127—1011nomaximal, Sylow
163C101#312711yescharacteristic, complemented, Sylow
164#541—1011no—
165#519—1011no—
166#485—1011no—
167#485D10111yescharacteristic
168#479—1011no—
169#479—1011no—
170#462—1011no—
171#462—1011no—
172#451—1011no—
173#451—1011no—
174#441—1011no—
175#441—1011no—
176C4×Q16—1011no—
177C4×Q16—1011no—
178#433—1011no—
179C22×Q8—1011no—
180C2×Q16—1011no—
181C2×Q16—1011no—
182C2×Q16—1011no—
183C2×Q16—1011no—
184C4⋊Q8—1011no—
185#126—2021no—
186#126—2021no—
187#125—1011no—
188#125—2021no—
189#125—2021no—
190C22⋊Q8—1011no—
191C22⋊Q8C2×D10111yescharacteristic
192C4×Q8—1011no—
193C4×Q8—1011no—
194C4×Q8—1011no—
195C4×Q8—1011no—
196C4×Q8—1011no—
197C4×Q8—1011no—
198C4×Q8—2021no—
199C4×Q8—2021no—
200#117—1011no—
201#117—2021no—
202#117—2021no—
203#117C2×D10111yescharacteristic
204#107—1011no—
205#107C2×D10111yescharacteristic
206#106—1011no—
207#106C2×D10111yescharacteristic
208C4⋊C8—1011no—
209C4⋊C8—1011no—
210#103—1011no—
211#103—1011no—
212#103—1011no—
213#103—1011no—
214#103—1011no—
215#103—1011no—
216#103C2×D10111yescharacteristic
217#103C2×D10111yescharacteristic
218C22⋊C8—1011no—
219C22⋊C8C2×D10111yescharacteristic
220#97—1011no—
221C4×C8—1011no—
222C2×Q8—1011no—
223C2×Q8—1011no—
224C2×Q8—1011no—
225C2×Q8—2022no—
226C2×Q8—2022no—
227C2×Q8—2021no—
228C2×Q8C22×D10111yescharacteristic
229C22×C4—2021no—
230C22×C4C22×D10111yescharacteristic
231Q16—2022no—
232Q16—2022no—
233Q16—2022no—
234Q16—2022no—
235C2×C8—1011no—
236C2×C8—1011no—
237C2×C8C22×D10111yescharacteristic
238C2×C8C22×D10111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—1011no—
241C4⋊C4—1011no—
242C4⋊C4—1011no—
243C4⋊C4—2021no—
244C4⋊C4—2021no—
245C4⋊C4—2021no—
246C4⋊C4—2021no—
247C4⋊C4—2021no—
248C4⋊C4—2021no—
249C4⋊C4—2021no—
250C4⋊C4—2021no—
251C4⋊C4—2021no—
252C4⋊C4—2021no—
253C4⋊C4—2021no—
254C4⋊C4C22×D10111yescharacteristic
255C4⋊C4C22×D10111yescharacteristic
256C4⋊C4C22×D10111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—1011no—
260C22⋊C4—1011no—
261C22⋊C4—2021no—
262C42—21no—
263C42—1011no—
264C42—1011no—
265C42—2021no—
266C42—2021no—
267C42—2021no—
268C42—2021no—
269C42—2021no—
270C42—2021no—
271C23D4×D10111yescharacteristic
272Q8—21no—
273Q8—21no—
274Q8—1012no—
275Q8—1012no—
276Q8—2024no—
277Q8—2021no—
278Q8—2021no—
279Q8—2021no—
280Q8—2021no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—1011no—
288C2×C4—1011no—
289C2×C4—1011no—
290C2×C4—1011no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4—2024no—
294C2×C4—2021no—
295C2×C4—2021no—
296C2×C4D4×D10111yescharacteristic
297C2×C4C23×D10111yescharacteristic
298C8—21no—
299C8—21no—
300C8—2021no—
301C8—2021no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22C2×D4×D10111yescharacteristic
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—4041no—
312C4—4041no—
313C4—2021no—
314C4—2021no—
315C4—2021no—
316C4—2021no—
317C4—2022no—
318C4—2022no—
319C4#41×D10111yescharacteristic
320C4#41×D10111yescharacteristic
321C2—41no—
322C2#2026568511yescharacteristic
323C2#2026599111yescharacteristic
324C2#2026599311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#485×C101C2
socleC22×C101C22×D4
prime radicalC23×C101C2×D4
hypercenter#485D101
hypocenterC101#3127
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
4. #20265487C2semidirect
5. #20265483C2semidirect
6. #20265386C2semidirect
7. #20265386C2semidirect
10. #20265283C2semidirect
11. #20265281C2semidirect
12. #20265271C2semidirect
13. #20265269C2semidirect
163. C101#3127semidirect

Maximal subgroups

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

subgroupindex
#202657872
#202656542
#202655182
#202654872
#202654832
#202653862
#202653352
#202653322
#202652832
#202652812
#202652712
#202652692
#202652352
#485×C1012
#3127101