Finite Group Databasebeta

← #27181050

Subgroups — #27181050

Order 12928.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265690C211yesmaximal, characteristic
2#117×D101C211yesmaximal, characteristic, complemented
3#20265515C211yesmaximal, characteristic, complemented
4#20265511C211yesmaximal, characteristic, complemented
5#20265506C211yesmaximal, characteristic, complemented
6#20265502C211yesmaximal, characteristic, complemented
7#20265501C211yesmaximal, characteristic, complemented
8#20265497C211yesmaximal, characteristic, complemented
9#20265492C211yesmaximal, characteristic, complemented
10#20265214C211yesmaximal, characteristic, complemented
11#20265212C211yesmaximal, characteristic, complemented
12#20265172C211yesmaximal, characteristic, complemented
13#20265172C211yesmaximal, characteristic, complemented
14C22⋊C8×D101C211yesmaximal, characteristic, complemented
15#485×C101C211yesmaximal, characteristic, complemented
16C2×#13108075C2211yescharacteristic
17C22×C4×D101C2211yescharacteristic
18C2×C8×D101C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692240—21no—
21#15692231C2211yescharacteristic
22#15692230C2211yescharacteristic
23#15692229C2211yescharacteristic
24#15692225—21no—
25#15692217—21no—
26#15692215—21no—
27#15692214C2211yescharacteristic
28#15692213C2211yescharacteristic
29#15692213C2211yescharacteristic
30#15692213C2211yescharacteristic
31#15692212—21no—
32#15692211—21no—
33C4⋊C4×D101C2211yescharacteristic
34C4⋊C4×D101C2211yescharacteristic
35C22⋊C4×D101—21no—
36C42×D101—21no—
37#15692189C2211yescharacteristic, complemented
38#15692188C2211yescharacteristic, complemented
39#15692188C2211yescharacteristic, complemented
40#15692187C2211yescharacteristic, complemented
41#15692186C2211yescharacteristic, complemented
42#15692186C2211yescharacteristic, complemented
43#15692179C2211yescharacteristic, complemented
44#15692179C2211yescharacteristic, complemented
45#15692177C2211yescharacteristic, complemented
46#15692177C2211yescharacteristic, complemented
47#15692175C2211yescharacteristic, complemented
48#15692175C2211yescharacteristic, complemented
49C22⋊#11717579C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692167C2211yescharacteristic
52C22⋊Q8×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56#103×C101C2211yescharacteristic, complemented
57#103×C101C2211yescharacteristic, complemented
58C22⋊C8×C101C2211yescharacteristic
59C23×D101D411yescharacteristic
60#13108075—22no—
61#13108075—22no—
62C2×D404—21no—
63C2×D404—21no—
64C2×D404C2311yescharacteristic
65C2×C22⋊D101—21no—
66C22×Dic101D411yescharacteristic
67C2×C4×D101—22no—
68C2×C4×D101—22no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101D411yescharacteristic
73C2×C4×D101D411yescharacteristic
74C2×C4×D101C2311yescharacteristic
75C2×C4×D101C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C2×#11717579C2311yescharacteristic
78C8×D101—22no—
79C8×D101—22no—
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
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
109C22×D101—22no—
110C22×D101—22no—
111C22×D101—21no—
112C22×D101—41no—
113C22×D101C2×D411yescharacteristic
114C22×D101C2×D411yescharacteristic
115Q8×C101—21no—
116Q8×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2411yescharacteristic
125C22⋊D101—42no—
126C2×Dic101—22no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101C2×D411yescharacteristic
131C2×Dic101C2×D411yescharacteristic
132D404—21no—
133D404—21no—
134D404—42no—
135D404—42no—
136C4×D101—22no—
137C4×D101—21no—
138C4×D101—21no—
139C4×D101—22no—
140C4×D101—42no—
141C4×D101—42no—
142C4×D101—42no—
143C4×D101#4112yes—
144C4×D101#4112yes—
145C8×C101—21no—
146C8×C101—21no—
147#11717579—21no—
148#11717579—21no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101—21no—
152C22×C101C22×D411yescharacteristic
153C2×D101—21no—
154C2×D101—21no—
155C2×D101—21no—
156C2×D101—21no—
157C2×D101—44no—
158C2×D101—41no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101#12312yes—
162C2×D101#13512yes—
163C4×C101—21no—
164C4×C101—41no—
165C4×C101—41no—
166C4×C101—41no—
167C4×C101—41no—
168C4×C101C2×#4111yescharacteristic
169C4×C101C2×#4111yescharacteristic
170Dic101—21no—
171Dic101—41no—
172Dic101—41no—
173Dic101—41no—
174Dic101#12312yes—
175C2×C101—41no—
176C2×C101C2×#12311yescharacteristic
177C2×C101C2×#13511yescharacteristic
178C2×C101#57511yescharacteristic
179D101—22no—
180D101—22no—
181D101—81no—
182#3091—1011nomaximal, Sylow
183C101#309111yescharacteristic, complemented, Sylow
184#525—1011no—
185C2×#117—1011no—
186#485—1011no—
187#485D10111yescharacteristic, complemented
188#484—1011no—
189#483—1011no—
190#482—1011no—
191#482—1011no—
192#481—1011no—
193#480—1011no—
194#427—1011no—
195#427—1011no—
196#416—1011no—
197#416—1011no—
198C2×C22⋊C8—1011no—
199C2×#41—1011no—
200C23×C4—1011no—
201C22×C8—1011no—
202C22×C8—1011no—
203#123—2021no—
204C22⋊Q8—1011no—
205C22⋊Q8C2×D10111yescharacteristic
206#121—1011no—
207#121—1011no—
208#120—2021no—
209C4×D4—2021no—
210C4×D4—2021no—
211#117—1011no—
212#117—1011no—
213#117—1011no—
214#117—1011no—
215#117—2021no—
216#117—2021no—
217#117C2×D10111yescharacteristic
218C2×C4⋊C4—1011no—
219C2×C4⋊C4—1011no—
220C2×C22⋊C4—2021no—
221C2×C42—2021no—
222#107—1011no—
223#107—1011no—
224#107—1011no—
225#107C2×D10111yescharacteristic, complemented
226#106—1011no—
227#106—1011no—
228#106—1011no—
229#106C2×D10111yescharacteristic, complemented
230#103—1011no—
231#103—1011no—
232#103C2×D10111yescharacteristic, complemented
233#103C2×D10111yescharacteristic, complemented
234#102—1011no—
235#102—1011no—
236#102—1011no—
237#102—1011no—
238C22⋊C8—1011no—
239C22⋊C8—1011no—
240C22⋊C8—1011no—
241C22⋊C8C2×D10111yescharacteristic
242C24—1011no—
243#41—2022no—
244#41—2022no—
245C2×Q8C22×D10111yescharacteristic
246C2×D4—1011no—
247C2×D4—2021no—
248C2×D4—2021no—
249C2×D4—2021no—
250C22×C4—1011no—
251C22×C4—1011no—
252C22×C4—1011no—
253C22×C4—1011no—
254C22×C4—1011no—
255C22×C4—2021no—
256C22×C4—2022no—
257C22×C4—2022no—
258C22×C4—2021no—
259C22×C4—2021no—
260C22×C4C22×D10111yescharacteristic
261C2×C8—1011no—
262C2×C8—1011no—
263C2×C8—2022no—
264C2×C8—2022no—
265C2×C8C22×D10111yescharacteristic
266C2×C8C22×D10111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—1011no—
269C4⋊C4—1011no—
270C4⋊C4—1011no—
271C4⋊C4—2021no—
272C4⋊C4—2021no—
273C4⋊C4—2021no—
274C4⋊C4C22×D10111yescharacteristic
275C4⋊C4C22×D10111yescharacteristic
276C4⋊C4C22×D10111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C42—21no—
287C42—2021no—
288C42—2021no—
289C42—2021no—
290C42—2021no—
291C23—1011no—
292C23—1011no—
293C23—4041no—
294C23—2022no—
295C23—2022no—
296C23—2021no—
297C23D4×D10111yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—4042no—
301D4—4042no—
302D4—4042no—
303D4—2021no—
304D4—2021no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1011no—
312C2×C4—1012no—
313C2×C4—1012no—
314C2×C4—1011no—
315C2×C4—4042no—
316C2×C4—4042no—
317C2×C4—4042no—
318C2×C4—2022no—
319C2×C4—2022no—
320C2×C4—2022no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4—2021no—
325C2×C4—2021no—
326C2×C4D4×D10111yescharacteristic
327C2×C4C23×D10111yescharacteristic
328C8—21no—
329C8—21no—
330C8—2021no—
331C8—2021no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—1012no—
336C22—1012no—
337C22—4044no—
338C22—4041no—
339C22—4041no—
340C22—4041no—
341C22—2021no—
342C22—2021no—
343C22—2021no—
344C22—2021no—
345C22C2×D4×D10111yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—1012no—
352C4—4041no—
353C4—4041no—
354C4—4041no—
355C4—2021no—
356C4#41×D10111yescharacteristic
357C4#41×D10111yescharacteristic
358C2—41no—
359C2—8081no—
360C2—2022no—
361C2—2022no—
362C2#123×D10111yescharacteristic
363C2#135×D10111yescharacteristic
364C2#2026597611yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#485×C101C2
socleC22×C101C22×D4
prime radical#20265690C2
hypercenter#485D101
hypocenterC101#3091
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
2. #117×D101C2semidirect
3. #20265515C2semidirect
4. #20265511C2semidirect
5. #20265506C2semidirect
6. #20265502C2semidirect
7. #20265501C2semidirect
8. #20265497C2semidirect
9. #20265492C2semidirect
10. #20265214C2semidirect
11. #20265212C2semidirect
12. #20265172C2semidirect
13. #20265172C2semidirect
14. C22⋊C8×D101C2semidirect
15. #485×C101C2semidirect
37. #15692189C22semidirect
38. #15692188C22semidirect
39. #15692188C22semidirect
40. #15692187C22semidirect
41. #15692186C22semidirect
42. #15692186C22semidirect
43. #15692179C22semidirect
44. #15692179C22semidirect
45. #15692177C22semidirect
46. #15692177C22semidirect
47. #15692175C22semidirect
48. #15692175C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
56. #103×C101C22semidirect
57. #103×C101C22semidirect
183. C101#3091semidirect
187. #485D101semidirect
225. #107C2×D101semidirect
229. #106C2×D101semidirect
232. #103C2×D101semidirect
233. #103C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202656902
#117×D1012
#202655152
#202655112
#202655062
#202655022
#202655012
#202654972
#202654922
#202652142
#202652122
#202651722
C22⋊C8×D1012
#485×C1012
#3091101