Finite Group Databasebeta

← #27182970

Subgroups — #27182970

Order 12928.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265866C211yesmaximal, characteristic, complemented
2#20265824C211yesmaximal, characteristic
3#20265530C211yesmaximal, characteristic, complemented
4#20265509C211yesmaximal, characteristic, complemented
5#20265480C211yesmaximal, characteristic, complemented
6#20265419C211yesmaximal, characteristic, complemented
7#20265404C211yesmaximal, characteristic, complemented
8#20265398C211yesmaximal, characteristic, complemented
9#20265341C211yesmaximal, characteristic, complemented
10#20265329C211yesmaximal, characteristic, complemented
11#20265264C211yesmaximal, characteristic, complemented
12#20265240C211yesmaximal, characteristic, complemented
13#20265171C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic, complemented
15#482×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C2×Dic404C2211yescharacteristic, complemented
19C2×#13108063C2211yescharacteristic
20C2×#13108062C2211yescharacteristic
21C22×#11717579C2211yescharacteristic, complemented
22C2×C8×D101C2211yescharacteristic
23#15692248—21no—
24#15692247—21no—
25#15692246C2211yescharacteristic, complemented
26#15692242C2211yescharacteristic
27#15692237—21no—
28#15692237—21no—
29#15692235C2211yescharacteristic
30#15692235C2211yescharacteristic
31#15692234C2211yescharacteristic, complemented
32#15692226—21no—
33#15692223—21no—
34#15692220C2211yescharacteristic, complemented
35#15692217C2211yescharacteristic
36C4×C22⋊D101C2211yescharacteristic
37#15692212—21no—
38C4⋊C4×D101C2211yescharacteristic
39C22⋊C4×D101—21no—
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692180C2211yescharacteristic, complemented
43#15692178C2211yescharacteristic, complemented
44#15692178C2211yescharacteristic, complemented
45#15692178C2211yescharacteristic, complemented
46#15692177C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692175C2211yescharacteristic
49#15692175C2211yescharacteristic
50#15692167C2211yescharacteristic
51C8×Dic101C2211yescharacteristic, complemented
52#121×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic, complemented
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62C2×Dic202C2311yescharacteristic
63C2×Dic202C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101D411yescharacteristic
68D4×D101—22no—
69D4×D101—41no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101C2311yescharacteristic
74Dic404—41no—
75#13108063—22no—
76#13108062—41no—
77C2×#11717579—41no—
78C2×#11717579C2311yescharacteristic
79C2×#11717579C2311yescharacteristic
80C8×D101—41no—
81C4⋊Dic101—21no—
82C4⋊Dic101—21no—
83C4⋊Dic101—21no—
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053—21no—
89#13108053D411yescharacteristic
90C22⋊Dic101—21no—
91C22⋊Dic101—21no—
92C22⋊Dic101—21no—
93C22⋊Dic101D411yescharacteristic
94#13108051—21no—
95#13108051—21no—
96#13108051—21no—
97#13108051D411yescharacteristic
98C4×Dic101—21no—
99C4×Dic101C2311yescharacteristic
100C2×D4×C101—21no—
101C2×D4×C101C2311yescharacteristic
102C22×C4×C101C2311yescharacteristic
103C2×C8×C101C2311yescharacteristic
104C2×C8×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C4⋊C4×C101C2311yescharacteristic
108C22⋊C4×C101—21no—
109C22⋊C4×C101—21no—
110C42×C101—21no—
111C23×C101—21no—
112C23×C101C2×D411yescharacteristic
113C22×D101—21no—
114C22×D101—42no—
115C22×D101—42no—
116C22×D101—81no—
117C22×D101C2×D411yescharacteristic
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—81no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2411yescharacteristic
128C22⋊D101—22no—
129C22⋊D101—42no—
130C22⋊D101—42no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101C2×D411yescharacteristic
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137D404—21no—
138D404#4112yes—
139C4×D101—21no—
140C4×D101—21no—
141C4×D101—42no—
142C4×D101—42no—
143C4×D101—81no—
144Dic202—21no—
145Dic202—21no—
146Dic202—21no—
147Dic202—21no—
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—22no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—84no—
165C2×D101#13512yes—
166C4×C101—21no—
167C4×C101—41no—
168C4×C101—41no—
169C4×C101—41no—
170C4×C101C2×#4111yescharacteristic
171C4×C101H(5,𝔽2)11yescharacteristic
172Dic101—21no—
173Dic101—21no—
174Dic101—21no—
175Dic101—41no—
176Dic101—41no—
177Dic101—41no—
178C2×C101—41no—
179C2×C101—81no—
180C2×C101#54611yescharacteristic
181C2×C101C2×#13511yescharacteristic
182C2×C101#57711yescharacteristic
183D101—22no—
184D101—42no—
185#3296—1011nomaximal, Sylow
186C101#329611yescharacteristic, complemented, Sylow
187#552—1011no—
188#546—1011no—
189#488—1011no—
190#483—1011no—
191#482D10111yescharacteristic, complemented
192#478—1011no—
193#467—1011no—
194#465—1011no—
195#464—1011no—
196#452—1011no—
197#450—1011no—
198C4×SD16—1011no—
199C8×D4—1011no—
200#416—1011no—
201C2×#102—1011no—
202C2×#41—1011no—
203C22×D4—1011no—
204C2×Q16—1011no—
205C2×SD16—1011no—
206C2×SD16—1011no—
207C22×C8—1011no—
208C22×C8—1011no—
209#126—2021no—
210#125—1011no—
211#125—2021no—
212#124—1011no—
213#123—2021no—
214#123—2021no—
215C22⋊Q8—1011no—
216C22⋊Q8—1011no—
217C22⋊Q8—1011no—
218#121—2021no—
219#121C2×D10111yescharacteristic
220#120—2021no—
221C4×Q8—1011no—
222C4×D4—1011no—
223C4×D4—1011no—
224#117—2021no—
225#117C2×D10111yescharacteristic, complemented
226C2×C4⋊C4—1011no—
227C2×C22⋊C4—2021no—
228#107C2×D10111yescharacteristic, complemented
229#106—1011no—
230#106C2×D10111yescharacteristic, complemented
231C4⋊C8—1011no—
232#103—1011no—
233#103—1011no—
234#103—1011no—
235#103—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102C2×D10111yescharacteristic
241#102C2×D10111yescharacteristic
242C22⋊C8—1011no—
243C22⋊C8C2×D10111yescharacteristic, complemented
244C4×C8—1011no—
245C24—2021no—
246#41—4041no—
247#41—2022no—
248C2×Q8—1011no—
249C2×Q8—1011no—
250C2×D4—21no—
251C2×D4—1011no—
252C2×D4—1011no—
253C2×D4—4041no—
254C2×D4—2021no—
255C2×D4—2022no—
256C2×D4—2021no—
257C2×D4C22×D10111yescharacteristic
258C22×C4—1011no—
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4—2021no—
262C22×C4C22×D10111yescharacteristic
263Q16—4041no—
264SD16—4041no—
265SD16—2022no—
266C2×C8—1011no—
267C2×C8—1011no—
268C2×C8—4041no—
269C2×C8—4041no—
270C2×C8C22×D10111yescharacteristic
271C2×C8C22×D10111yescharacteristic
272C4⋊C4—1011no—
273C4⋊C4—1011no—
274C4⋊C4—2021no—
275C4⋊C4—2021no—
276C4⋊C4—2021no—
277C4⋊C4—2021no—
278C4⋊C4—2021no—
279C4⋊C4—2021no—
280C4⋊C4—2021no—
281C4⋊C4C22×D10111yescharacteristic
282C4⋊C4C22×D10111yescharacteristic
283C4⋊C4C22×D10111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1011no—
287C22⋊C4—1011no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C22⋊C4—2021no—
294C42—21no—
295C42—1011no—
296C42—2021no—
297C23—21no—
298C23—8081no—
299C23—1011no—
300C23—4042no—
301C23—4042no—
302C23—2021no—
303C23D4×D10111yescharacteristic
304Q8—2021no—
305Q8—2021no—
306Q8—2021no—
307Q8—2021no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—1012no—
312D4—4042no—
313D4—4042no—
314D4—2022no—
315D4—2021no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—8081no—
322C2×C4—1011no—
323C2×C4—1011no—
324C2×C4—1011no—
325C2×C4—4042no—
326C2×C4—4042no—
327C2×C4—2021no—
328C2×C4—2021no—
329C2×C4—2021no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4D4×D10111yescharacteristic
333C2×C4C23×D10111yescharacteristic
334C8—21no—
335C8—21no—
336C8—2021no—
337C8—2021no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—8084no—
345C22—1012no—
346C22—4041no—
347C22—4041no—
348C22—2022no—
349C22—2021no—
350C22—2021no—
351C22C2×D4×D10111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—4041no—
357C4—4041no—
358C4—4041no—
359C4—2021no—
360C4—2021no—
361C4—2021no—
362C4#41×D10111yescharacteristic
363C4#1569230111yescharacteristic
364C2—41no—
365C2—81no—
366C2—4042no—
367C2—2022no—
368C2#2026581911yescharacteristic
369C2#135×D10111yescharacteristic
370C2#2026598711yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#482×C101C2
socleC22×C101C22×D4
prime radical#20265824C2
hypercenter#482D101
hypocenterC101#3296
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20265866C2semidirect
3. #20265530C2semidirect
4. #20265509C2semidirect
5. #20265480C2semidirect
6. #20265419C2semidirect
7. #20265404C2semidirect
8. #20265398C2semidirect
9. #20265341C2semidirect
10. #20265329C2semidirect
11. #20265264C2semidirect
12. #20265240C2semidirect
13. #20265171C2semidirect
14. #102×D101C2semidirect
15. #482×C101C2semidirect
18. C2×Dic404C22semidirect
21. C22×#11717579C22semidirect
25. #15692246C22semidirect
31. #15692234C22semidirect
34. #15692220C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692180C22semidirect
43. #15692178C22semidirect
44. #15692178C22semidirect
45. #15692178C22semidirect
51. C8×Dic101C22semidirect
53. #117×C101C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
58. C22⋊C8×C101C22semidirect
186. C101#3296semidirect
191. #482D101semidirect
225. #117C2×D101semidirect
228. #107C2×D101semidirect
230. #106C2×D101semidirect
243. C22⋊C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658662
#202658242
#202655302
#202655092
#202654802
#202654192
#202654042
#202653982
#202653412
#202653292
#202652642
#202652402
#202651712
#102×D1012
#482×C1012
#3296101