Finite Group Databasebeta

← #27181318

Subgroups — #27181318

Order 12928.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265798C211yesmaximal, characteristic, complemented
2#20265651C211yesmaximal, characteristic, complemented
3#20265519C211yesmaximal, characteristic, complemented
4#20265502C211yesmaximal, characteristic, complemented
5#20265468C211yesmaximal, characteristic, complemented
6#20265458C211yesmaximal, characteristic, complemented
7#20265393C211yesmaximal, characteristic, complemented
8#20265393C211yesmaximal, characteristic, complemented
9#20265330C211yesmaximal, characteristic, complemented
10#20265313C211yesmaximal, characteristic
11#20265290C211yesmaximal, characteristic, complemented
12#20265279C211yesmaximal, characteristic, complemented
13C4×#13108063C211yesmaximal, characteristic, complemented
14C4×D808C211yesmaximal, characteristic, complemented
15#433×C101C211yesmaximal, characteristic, complemented
16C22×D404C2211yescharacteristic
17C2×#13108063C2211yescharacteristic
18C2×#13108063C2211yescharacteristic
19C2×D808C2211yescharacteristic
20C2×D808C2211yescharacteristic
21#15692255C2211yescharacteristic, complemented
22#15692250—21no—
23#15692243C2211yescharacteristic, complemented
24#15692241—21no—
25#15692237—21no—
26#15692234C2211yescharacteristic
27#15692233—21no—
28#15692229C2211yescharacteristic
29C4×Dic202C2211yescharacteristic, complemented
30C4×D404C2211yescharacteristic
31C4×D404C2211yescharacteristic
32C4×D404C2211yescharacteristic
33C4×D404C2211yescharacteristic
34C4×D404C2211yescharacteristic, complemented
35#15692217—21no—
36#15692217—21no—
37#15692214C2211yescharacteristic
38C22⋊C4×D101—21no—
39C22⋊C4×D101—21no—
40#15692189C2211yescharacteristic, complemented
41#15692189C2211yescharacteristic, complemented
42#15692187C2211yescharacteristic, complemented
43#15692187C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, complemented
45#15692180C2211yescharacteristic, complemented
46#15692177C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic, complemented
51#15692177C2211yescharacteristic, complemented
52#117×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic, complemented
54C4⋊C8×C101C2211yescharacteristic, complemented
55C22⋊C8×C101C2211yescharacteristic
56C22⋊C8×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic, complemented
58C4×C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60C2×Dic202—21no—
61C2×Dic202C2311yescharacteristic
62C2×D404—21no—
63C2×D404—22no—
64C2×D404—22no—
65C2×D404C2311yescharacteristic
66C2×D404C2311yescharacteristic
67C2×D404C2311yescharacteristic
68C2×C22⋊D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74#13108063—22no—
75#13108063—22no—
76D808—22no—
77D808—22no—
78C4⋊Dic101—21no—
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83#13108053—21no—
84#13108053—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101D411yescharacteristic
103C4⋊C4×C101D411yescharacteristic
104C22⋊C4×C101D411yescharacteristic
105C22⋊C4×C101D411yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101C2×D411yescharacteristic
109C22×D101—21no—
110C22×D101—21no—
111C22×D101—24no—
112C22×D101—21no—
113C22×D101—81no—
114C22×D101—81no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101C2×D411yescharacteristic
118C2×C4×C101C2×D411yescharacteristic
119C2×C4×C101C2×D411yescharacteristic
120C2×C4×C101C2×D411yescharacteristic
121C2×C4×C101C2×D411yescharacteristic
122C2×C4×C101C2411yescharacteristic
123C22⋊D101—81no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129D404—24no—
130D404—21no—
131D404—21no—
132D404—21no—
133D404—21no—
134D404#4112yes—
135D404#4112yes—
136C4×D101—81no—
137C4×D101—81no—
138C4×D101—81no—
139C4×D101—81no—
140C4×D101—81no—
141Dic202—21no—
142Dic202—21no—
143Dic202—81no—
144C8×C101—21no—
145C8×C101—21no—
146C8×C101—21no—
147C8×C101—21no—
148C22×C101—21no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101C22×D411yescharacteristic
152C2×D101—22no—
153C2×D101—22no—
154C2×D101—41no—
155C2×D101—41no—
156C2×D101—41no—
157C2×D101—41no—
158C2×D101—41no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101—84no—
162C4×C101—21no—
163C4×C101—21no—
164C4×C101—21no—
165C4×C101—21no—
166C4×C101—21no—
167C4×C101C2×#4111yescharacteristic
168C4×C101C2×#4111yescharacteristic
169Dic101—41no—
170Dic101—41no—
171Dic101—41no—
172Dic101—41no—
173Dic101—41no—
174C2×C101—41no—
175C2×C101#52511yescharacteristic
176C2×C101#57611yescharacteristic
177C2×C101#57711yescharacteristic
178D101—42no—
179D101—42no—
180D101—81no—
181#3118—1011nomaximal, Sylow
182C101#311811yescharacteristic, complemented, Sylow
183#542—1011no—
184#518—1011no—
185#485—1011no—
186#482—1011no—
187#476—1011no—
188#474—1011no—
189#463—1011no—
190#463—1011no—
191#450—1011no—
192#447—1011no—
193#442—1011no—
194#440—1011no—
195C4×SD16—1011no—
196C4×D8—1011no—
197#433D10111yescharacteristic, complemented
198C22×D4—1011no—
199C2×SD16—1011no—
200C2×SD16—1011no—
201C2×D8—1011no—
202C2×D8—1011no—
203C4⋊Q8—1011no—
204#126—2021no—
205#124—1011no—
206#124—2021no—
207#123—2021no—
208C22⋊Q8—1011no—
209C22⋊Q8—2021no—
210#121—1011no—
211C4×Q8—1011no—
212C4×D4—1011no—
213C4×D4—1011no—
214C4×D4—1011no—
215C4×D4—1011no—
216C4×D4—1011no—
217C4×D4—2021no—
218C4×D4—2021no—
219#117—1011no—
220#117C2×D10111yescharacteristic
221C2×C22⋊C4—2021no—
222C2×C22⋊C4—2021no—
223#107—1011no—
224#107—1011no—
225#106—1011no—
226#106—1011no—
227C4⋊C8C2×D10111yescharacteristic, complemented
228C4⋊C8C2×D10111yescharacteristic, complemented
229#103—1011no—
230#103—1011no—
231#102—1011no—
232#102—1011no—
233#102—1011no—
234#102—1011no—
235#102—1011no—
236#102—1011no—
237C22⋊C8C2×D10111yescharacteristic
238C22⋊C8C2×D10111yescharacteristic
239#97C2×D10111yescharacteristic, complemented
240C4×C8C2×D10111yescharacteristic, complemented
241C24—2021no—
242C2×Q8—1011no—
243C2×Q8—2021no—
244C2×D4—1011no—
245C2×D4—1011no—
246C2×D4—1011no—
247C2×D4—2022no—
248C2×D4—2022no—
249C2×D4—2021no—
250C2×D4—2021no—
251C22×C4—2021no—
252C22×C4—2021no—
253C22×C4—2021no—
254C22×C4—2021no—
255C22×C4—2021no—
256C22×C4C22×D10111yescharacteristic
257SD16—2022no—
258SD16—2022no—
259D8—2022no—
260D8—2022no—
261C2×C8C22×D10111yescharacteristic
262C2×C8C22×D10111yescharacteristic
263C2×C8C22×D10111yescharacteristic
264C2×C8C22×D10111yescharacteristic
265C4⋊C4—1011no—
266C4⋊C4—1011no—
267C4⋊C4—1011no—
268C4⋊C4—1011no—
269C4⋊C4—2021no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4D40411yescharacteristic
273C4⋊C4D40411yescharacteristic
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4D40411yescharacteristic
285C22⋊C4D40411yescharacteristic
286C42—2021no—
287C42—2021no—
288C42C22×D10111yescharacteristic
289C42C22×D10111yescharacteristic
290C23—8081no—
291C23—8081no—
292C23—2024no—
293C23—2021no—
294C23—2021no—
295C23—2021no—
296C23C2×D40411yescharacteristic
297Q8—8081no—
298Q8—2021no—
299Q8—2021no—
300D4—8081no—
301D4—1012no—
302D4—1012no—
303D4—2024no—
304D4—2021no—
305D4—2021no—
306D4—2021no—
307D4—2021no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—8081no—
311C2×C4—8081no—
312C2×C4—8081no—
313C2×C4—8081no—
314C2×C4—8081no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2021no—
319C2×C4—2021no—
320C2×C4C2×D40411yescharacteristic
321C2×C4C2×D40411yescharacteristic
322C2×C4C2×D40411yescharacteristic
323C2×C4C2×D40411yescharacteristic
324C2×C4C2×D40411yescharacteristic
325C2×C4C23×D10111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—8084no—
334C22—4041no—
335C22—4041no—
336C22—4041no—
337C22—4041no—
338C22—4041no—
339C22—4041no—
340C22—4041no—
341C22—2022no—
342C22—2022no—
343C22C22×D40411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—4041no—
350C4—4041no—
351C4—4041no—
352C4—4041no—
353C4—4041no—
354C4#41×D10111yescharacteristic
355C4#41×D10111yescharacteristic
356C2—41no—
357C2—8081no—
358C2—4042no—
359C2—4042no—
360C2#2026568911yescharacteristic
361C2#2026598211yescharacteristic
362C2#2026598911yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#433×C101C2
socleC22×C101C22×D4
prime radical#20265313C2
hypercenter#433D101
hypocenterC101#3118
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20265798C2semidirect
2. #20265651C2semidirect
3. #20265519C2semidirect
4. #20265502C2semidirect
5. #20265468C2semidirect
6. #20265458C2semidirect
7. #20265393C2semidirect
8. #20265393C2semidirect
9. #20265330C2semidirect
11. #20265290C2semidirect
12. #20265279C2semidirect
13. C4×#13108063C2semidirect
14. C4×D808C2semidirect
15. #433×C101C2semidirect
21. #15692255C22semidirect
23. #15692243C22semidirect
29. C4×Dic202C22semidirect
34. C4×D404C22semidirect
40. #15692189C22semidirect
41. #15692189C22semidirect
42. #15692187C22semidirect
43. #15692187C22semidirect
44. #15692180C22semidirect
45. #15692180C22semidirect
50. #15692177C22semidirect
51. #15692177C22semidirect
53. C4⋊C8×C101C22semidirect
54. C4⋊C8×C101C22semidirect
57. #97×C101C22semidirect
58. C4×C8×C101C22semidirect
182. C101#3118semidirect
197. #433D101semidirect
227. C4⋊C8C2×D101semidirect
228. C4⋊C8C2×D101semidirect
239. #97C2×D101semidirect
240. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657982
#202656512
#202655192
#202655022
#202654682
#202654582
#202653932
#202653302
#202653132
#202652902
#202652792
C4×#131080632
C4×D8082
#433×C1012
#3118101