Finite Group Databasebeta

← #27181083

Subgroups — #27181083

Order 12928.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265743C211yesmaximal, characteristic
2#20265658C211yesmaximal, characteristic, complemented
3#20265504C211yesmaximal, characteristic, complemented
4#20265502C211yesmaximal, characteristic, complemented
5#20265499C211yesmaximal, characteristic, complemented
6#20265498C211yesmaximal, characteristic, complemented
7#20265495C211yesmaximal, characteristic, complemented
8#20265494C211yesmaximal, characteristic, complemented
9#20265492C211yesmaximal, characteristic, complemented
10#20265218C211yesmaximal, characteristic, complemented
11#20265214C211yesmaximal, characteristic, complemented
12#20265180C211yesmaximal, characteristic, complemented
13#102×D101C211yesmaximal, characteristic, complemented
14#20265142C211yesmaximal, characteristic, complemented
15#480×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692251—21no—
21#15692241—21no—
22#15692230C2211yescharacteristic
23#15692229C2211yescharacteristic
24#15692226C2211yescharacteristic
25#15692225—21no—
26#15692223—21no—
27#15692220—21no—
28#15692217—21no—
29C4×C22⋊D101—21no—
30C4×C22⋊D101—21no—
31#15692214C2211yescharacteristic, complemented
32#15692213C2211yescharacteristic
33#15692213C2211yescharacteristic
34#15692213C2211yescharacteristic, complemented
35C4⋊C4×D101C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic, complemented
37#15692189C2211yescharacteristic, complemented
38#15692188C2211yescharacteristic, complemented
39#15692187C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41#15692186C2211yescharacteristic, complemented
42#15692186C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic
44#15692177C2211yescharacteristic
45#15692176C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692175C2211yescharacteristic
48#15692175C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic, complemented
50#15692167C2211yescharacteristic, complemented
51#15692167C2211yescharacteristic, complemented
52#121×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic, complemented
54#107×C101C2211yescharacteristic, complemented
55#107×C101C2211yescharacteristic, complemented
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—22no—
62C2×Dic202D411yescharacteristic
63C2×D404—21no—
64C2×D404D411yescharacteristic
65C2×D404C2311yescharacteristic
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C22⋊D101—21no—
69C2×C22⋊D101D411yescharacteristic
70C2×C22⋊D101D411yescharacteristic
71D4×D101—22no—
72D4×D101—22no—
73C2×C4×D101—21no—
74C2×C4×D101—21no—
75C2×C4×D101C2311yescharacteristic
76C2×C4×D101C2311yescharacteristic
77#13108057—22no—
78C2×#11717579C2311yescharacteristic
79C2×#11717579C2311yescharacteristic
80C8×D101—22no—
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101—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×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101—21no—
100C22×C4×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—21no—
111C22×D101—42no—
112C22×D101—81no—
113C22×D101—81no—
114C22×D101C2×D411yescharacteristic
115C22×D101C2×D411yescharacteristic
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—81no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—81no—
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2411yescharacteristic
127C22⋊D101—22no—
128C22⋊D101—22no—
129C22⋊D101—42no—
130C22⋊D101—81no—
131C22⋊D101—81no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137D404—22no—
138D404—21no—
139D404—21no—
140D404—81no—
141C4×D101—21no—
142C4×D101—21no—
143C4×D101—81no—
144C4×D101—81no—
145C4×D101#4112yes—
146C4×D101#4112yes—
147Dic202—22no—
148C8×C101—21no—
149C8×C101—21no—
150#11717579—21no—
151#11717579—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—21no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101—41no—
158C22×C101C22×D411yescharacteristic
159C2×D101—21no—
160C2×D101—21no—
161C2×D101—21no—
162C2×D101—21no—
163C2×D101—21no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—84no—
168C2×D101#12312yes—
169C4×C101—21no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101—41no—
173C4×C101C2×#4111yescharacteristic
174C4×C101C2×#4111yescharacteristic
175Dic101—21no—
176Dic101—41no—
177Dic101—41no—
178Dic101—41no—
179Dic101#12312yes—
180C2×C101—41no—
181C2×C101—81no—
182C2×C101C2×#12311yescharacteristic
183C2×C101#57611yescharacteristic
184C2×C101#57711yescharacteristic
185D101—22no—
186D101—41no—
187D101—81no—
188#3096—1011nomaximal, Sylow
189C101#309611yescharacteristic, complemented, Sylow
190#535—1011no—
191#520—1011no—
192#482—1011no—
193#482—1011no—
194#482—1011no—
195#482—1011no—
196#481—1011no—
197#481—1011no—
198#480—1011no—
199#480D10111yescharacteristic, complemented
200#428—1011no—
201#427—1011no—
202#418—1011no—
203C2×#102—1011no—
204#408—1011no—
205C2×#41—1011no—
206C22×D4—1011no—
207C2×M16—1011no—
208C22×C8—1011no—
209#127—2021no—
210#124—2021no—
211#121—1011no—
212#121—1011no—
213#121—1011no—
214#121C2×D10111yescharacteristic
215#120—2021no—
216#120—2021no—
217C4×Q8—2021no—
218C4×D4—2021no—
219C4×D4—2021no—
220C4×D4—2021no—
221#117—1011no—
222#117—1011no—
223#117—1011no—
224#117—1011no—
225C2×C4⋊C4—1011no—
226C2×C4⋊C4—1011no—
227C2×C4⋊C4C2×D10111yescharacteristic, complemented
228#107—1011no—
229#107—1011no—
230#107C2×D10111yescharacteristic, complemented
231#107C2×D10111yescharacteristic, complemented
232#106—1011no—
233#106—1011no—
234#106—1011no—
235#106—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102—1011no—
242#102C2×D10111yescharacteristic
243#102C2×D10111yescharacteristic
244C22⋊C8—1011no—
245C22⋊C8—1011no—
246C22⋊C8—1011no—
247C22⋊C8C2×D10111yescharacteristic, complemented
248C24—2021no—
249#41—2022no—
250#41—2022no—
251C2×Q8—1011no—
252C2×D4—21no—
253C2×D4—1011no—
254C2×D4—1011no—
255C2×D4—1011no—
256C2×D4—1011no—
257C2×D4—2021no—
258C2×D4—2022no—
259C2×D4—2022no—
260C2×D4—2021no—
261C2×D4—2021no—
262C2×D4—2021no—
263C2×D4C22×D10111yescharacteristic
264C22×C4—21no—
265C22×C4—1011no—
266C22×C4—1011no—
267C22×C4—2021no—
268C22×C4—2021no—
269C22×C4C22×D10111yescharacteristic
270M16—2022no—
271C2×C8—1011no—
272C2×C8—1011no—
273C2×C8—2022no—
274C2×C8C22×D10111yescharacteristic
275C2×C8C22×D10111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—1011no—
278C4⋊C4—1011no—
279C4⋊C4—1011no—
280C4⋊C4—2021no—
281C4⋊C4—2021no—
282C4⋊C4C22×D10111yescharacteristic
283C4⋊C4C22×D10111yescharacteristic
284C4⋊C4C22×D10111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C42—2021no—
294C42—2021no—
295C42—2021no—
296C42—2021no—
297C23—21no—
298C23—8081no—
299C23—8081no—
300C23—1011no—
301C23—1011no—
302C23—4042no—
303C23—2021no—
304C23D4×D10111yescharacteristic
305Q8—2022no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—8081no—
310D4—8081no—
311D4—8081no—
312D4—4042no—
313D4—2022no—
314D4—2022no—
315D4—2022no—
316D4—2021no—
317D4—2021no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—8081no—
325C2×C4—8081no—
326C2×C4—1011no—
327C2×C4—1012no—
328C2×C4—1012no—
329C2×C4—1011no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4—2021no—
333C2×C4—2021no—
334C2×C4—2021no—
335C2×C4D4×D10111yescharacteristic
336C2×C4C23×D10111yescharacteristic
337C8—21no—
338C8—21no—
339C8—2021no—
340C8—2021no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—8084no—
348C22—1012no—
349C22—4041no—
350C22—4041no—
351C22—4041no—
352C22—2021no—
353C22—2021no—
354C22—2021no—
355C22—2021no—
356C22—2021no—
357C22C2×D4×D10111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—1012no—
363C4—4041no—
364C4—4041no—
365C4—4041no—
366C4—2021no—
367C4#41×D10111yescharacteristic
368C4#41×D10111yescharacteristic
369C2—41no—
370C2—81no—
371C2—8081no—
372C2—4041no—
373C2—2022no—
374C2#123×D10111yescharacteristic
375C2#2026597811yescharacteristic
376C2#2026598611yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#480×C101C2
socleC22×C101C22×D4
prime radical#20265743C2
hypercenter#480D101
hypocenterC101#3096
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20265658C2semidirect
3. #20265504C2semidirect
4. #20265502C2semidirect
5. #20265499C2semidirect
6. #20265498C2semidirect
7. #20265495C2semidirect
8. #20265494C2semidirect
9. #20265492C2semidirect
10. #20265218C2semidirect
11. #20265214C2semidirect
12. #20265180C2semidirect
13. #102×D101C2semidirect
14. #20265142C2semidirect
15. #480×C101C2semidirect
31. #15692214C22semidirect
34. #15692213C22semidirect
36. C4⋊C4×D101C22semidirect
37. #15692189C22semidirect
38. #15692188C22semidirect
39. #15692187C22semidirect
40. #15692186C22semidirect
41. #15692186C22semidirect
42. #15692186C22semidirect
49. C22⋊#11717579C22semidirect
50. #15692167C22semidirect
51. #15692167C22semidirect
53. C2×C4⋊C4×C101C22semidirect
54. #107×C101C22semidirect
55. #107×C101C22semidirect
58. C22⋊C8×C101C22semidirect
189. C101#3096semidirect
199. #480D101semidirect
227. C2×C4⋊C4C2×D101semidirect
230. #107C2×D101semidirect
231. #107C2×D101semidirect
247. C22⋊C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657432
#202656582
#202655042
#202655022
#202654992
#202654982
#202654952
#202654942
#202654922
#202652182
#202652142
#202651802
#102×D1012
#202651422
#480×C1012
#3096101