Finite Group Databasebeta

← #27183745

Subgroups — #27183745

Order 12928.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265895C211yesmaximal, characteristic
2#20265885C211yesmaximal, characteristic
3#20265574C211yesmaximal, characteristic, complemented
4#20265516C211yesmaximal, characteristic, complemented
5#20265509C211yesmaximal, characteristic, complemented
6#20265508C211yesmaximal, characteristic, complemented
7#20265471C211yesmaximal, characteristic, complemented
8#20265460C211yesmaximal, characteristic, complemented
9#20265434C211yesmaximal, characteristic, complemented
10#20265433C211yesmaximal, characteristic, complemented
11#20265269C211yesmaximal, characteristic, complemented
12#20265252C211yesmaximal, characteristic
13#20265220C211yesmaximal, characteristic, complemented
14#20265218C211yesmaximal, characteristic, complemented
15#485×C101C211yesmaximal, characteristic, complemented
16C2×#13108064C2211yescharacteristic
17C2×#13108058C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19#15692254C2211yescharacteristic
20#15692254C2211yescharacteristic
21#15692249—21no—
22#15692248—21no—
23#15692245—21no—
24#15692241—21no—
25#15692235—21no—
26#15692235C2211yescharacteristic
27#15692234C2211yescharacteristic
28#15692232—21no—
29#15692231C2211yescharacteristic
30Q8×Dic101C2211yescharacteristic
31C4×Dic202—21no—
32#15692220C2211yescharacteristic
33C4×C22⋊D101C2211yescharacteristic
34#15692215—21no—
35#15692213C2211yescharacteristic
36C2×C4⋊Dic101C2211yescharacteristic
37C4⋊C4×D101C2211yescharacteristic
38#15692188C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692187C2211yescharacteristic
41#15692187C2211yescharacteristic
42#15692186C2211yescharacteristic
43#15692186C2211yescharacteristic
44#15692186C2211yescharacteristic
45#15692184C2211yescharacteristic
46#15692180C2211yescharacteristic
47#15692180C2211yescharacteristic
48#15692179C2211yescharacteristic
49#15692178C2211yescharacteristic
50#15692167C2211yescharacteristic
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—21no—
61C2×Dic202C2311yescharacteristic
62C2×C22⋊D101D411yescharacteristic
63C22×Dic101—21no—
64C2×C4×D101—21no—
65C2×C4×D101C2311yescharacteristic
66#13108064—22no—
67#13108058—22no—
68#13108057—22no—
69C2×#11717579C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C4⋊Dic101—21no—
72C4⋊Dic101—21no—
73C4⋊Dic101—21no—
74C4⋊Dic101C2311yescharacteristic
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053D411yescharacteristic
84C22⋊Dic101—21no—
85C22⋊Dic101D411yescharacteristic
86#13108051—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051D411yescharacteristic
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101C2311yescharacteristic
94C2×Q8×C101C2311yescharacteristic
95C22×C4×C101C2311yescharacteristic
96C2×C8×C101C2311yescharacteristic
97C2×C8×C101C2311yescharacteristic
98C4⋊C4×C101—21no—
99C4⋊C4×C101C2311yescharacteristic
100C4⋊C4×C101C2311yescharacteristic
101C4⋊C4×C101C2311yescharacteristic
102C22⋊C4×C101—21no—
103C22⋊C4×C101—21no—
104C42×C101—21no—
105C23×C101C2×D411yescharacteristic
106C22×D101C2×D411yescharacteristic
107Q8×C101—21no—
108Q8×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101C2×D411yescharacteristic
116C2×C4×C101C2411yescharacteristic
117C22⋊D101—22no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—81no—
123C2×Dic101C2×D411yescharacteristic
124C2×Dic101C2×D411yescharacteristic
125C2×Dic101C2×D411yescharacteristic
126C4×D101—21no—
127C4×D101—21no—
128C4×D101—81no—
129Dic202—21no—
130Dic202—21no—
131Dic202—42no—
132Dic202—81no—
133C8×C101—21no—
134C8×C101—21no—
135#11717579—21no—
136#11717579#4112yes—
137C22×C101—21no—
138C22×C101—21no—
139C22×C101—21no—
140C22×C101C22×D411yescharacteristic
141C2×D101—21no—
142C2×D101—21no—
143C2×D101—21no—
144C4×C101—21no—
145C4×C101—41no—
146C4×C101—41no—
147C4×C101—41no—
148C4×C101—41no—
149C4×C101C2×#4111yescharacteristic
150C4×C1012−1+411yescharacteristic
151Dic101—21no—
152Dic101—21no—
153Dic101—41no—
154Dic101—41no—
155Dic101—41no—
156Dic101—41no—
157Dic101#13712yes—
158C2×C101—41no—
159C2×C101#54711yescharacteristic
160C2×C101C2×#13711yescharacteristic
161C2×C101#57711yescharacteristic
162D101—41no—
163#3356—1011nomaximal, Sylow
164C101#335611yescharacteristic, complemented, Sylow
165#556—1011no—
166#554—1011no—
167#498—1011no—
168#485—1011no—
169#485D10111yescharacteristic, complemented
170#483—1011no—
171#483—1011no—
172#477—1011no—
173#475—1011no—
174#470—1011no—
175#470—1011no—
176C4×Q16—1011no—
177#436—1011no—
178#428—1011no—
179#428—1011no—
180C2×Q16—1011no—
181C2×M16—1011no—
182C2×M16—1011no—
183C4⋊Q8—1011no—
184C4⋊Q8—1011no—
185#126—2021no—
186#126—2021no—
187#125—2021no—
188#124—2021no—
189C22⋊Q8—1011no—
190C22⋊Q8—1011no—
191C22⋊Q8—1011no—
192C22⋊Q8—2021no—
193C22⋊Q8—2021no—
194C22⋊Q8C2×D10111yescharacteristic
195C4×Q8—1011no—
196C4×Q8—1011no—
197C4×Q8—2021no—
198C4×D4—1011no—
199C4×D4—2021no—
200#117—1011no—
201#117C2×D10111yescharacteristic
202C2×C4⋊C4—1011no—
203C2×C4⋊C4—1011no—
204#107—1011no—
205#107—1011no—
206#107C2×D10111yescharacteristic
207#106—1011no—
208#106—1011no—
209#106—1011no—
210#106—1011no—
211#106—1011no—
212#106C2×D10111yescharacteristic
213C4⋊C8—1011no—
214#103—1011no—
215#103—1011no—
216#103—1011no—
217#103—1011no—
218#103C2×D10111yescharacteristic
219#103C2×D10111yescharacteristic
220C22⋊C8—1011no—
221C22⋊C8C2×D10111yescharacteristic
222C4×C8—1011no—
223C2×Q8—1011no—
224C2×Q8—2021no—
225C2×Q8—2021no—
226C2×Q8C22×D10111yescharacteristic
227C2×D4—1011no—
228C22×C4—1011no—
229C22×C4—2021no—
230C22×C4—2021no—
231C22×C4C22×D10111yescharacteristic
232Q16—2022no—
233M16—2022no—
234M16—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—1011no—
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⋊C4C22×D10111yescharacteristic
254C4⋊C4C22×D10111yescharacteristic
255C4⋊C4C22×D10111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—1011no—
259C22⋊C4—1011no—
260C22⋊C4—2021no—
261C22⋊C4—2021no—
262C22⋊C4—2021no—
263C22⋊C4—2021no—
264C42—21no—
265C42—1011no—
266C42—2021no—
267C42—2021no—
268C42—2021no—
269C23—1011no—
270C23D4×D10111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—8081no—
274Q8—4042no—
275Q8—2021no—
276Q8—2021no—
277D4—2022no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—8081no—
285C2×C4—8081no—
286C2×C4—1011no—
287C2×C4—1011no—
288C2×C4—1011no—
289C2×C4—2021no—
290C2×C4—2021no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4D4×D10111yescharacteristic
296C2×C4C23×D10111yescharacteristic
297C8—21no—
298C8—21no—
299C8—1012no—
300C8—2021no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—2021no—
305C22—2021no—
306C22—2021no—
307C22C2×D4×D10111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1012no—
314C4—4041no—
315C4—4041no—
316C4—4041no—
317C4—4041no—
318C4—2021no—
319C4—2021no—
320C4#41×D10111yescharacteristic
321C4#1569230211yescharacteristic
322C2—41no—
323C2—4041no—
324C2#2026582511yescharacteristic
325C2#137×D10111yescharacteristic
326C2#2026598411yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#485×C101C2
socleC22×C101C22×D4
prime radicalC2×C22⋊D101D4
hypercenter#485D101
hypocenterC101#3356
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
3. #20265574C2semidirect
4. #20265516C2semidirect
5. #20265509C2semidirect
6. #20265508C2semidirect
7. #20265471C2semidirect
8. #20265460C2semidirect
9. #20265434C2semidirect
10. #20265433C2semidirect
11. #20265269C2semidirect
13. #20265220C2semidirect
14. #20265218C2semidirect
15. #485×C101C2semidirect
164. C101#3356semidirect
169. #485D101semidirect

Maximal subgroups

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

subgroupindex
#202658952
#202658852
#202655742
#202655162
#202655092
#202655082
#202654712
#202654602
#202654342
#202654332
#202652692
#202652522
#202652202
#202652182
#485×C1012
#3356101