Finite Group Databasebeta

← #27181371

Subgroups — #27181371

Order 12928.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265780C211yesmaximal, characteristic, complemented
2#20265651C211yesmaximal, characteristic, complemented
3#20265501C211yesmaximal, characteristic, complemented
4#20265480C211yesmaximal, characteristic, complemented
5#20265476C211yesmaximal, characteristic, complemented
6#20265371C211yesmaximal, characteristic, complemented
7#20265371C211yesmaximal, characteristic, complemented
8#20265313C211yesmaximal, characteristic, complemented
9#20265310C211yesmaximal, characteristic, complemented
10#20265288C211yesmaximal, characteristic, complemented
11#20265286C211yesmaximal, characteristic, complemented
12#20265259C211yesmaximal, characteristic, complemented
13#20265257C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#482×C101C211yesmaximal, characteristic, complemented
16C22×D404C2211yescharacteristic
17C2×D808C2211yescharacteristic
18C2×D808C2211yescharacteristic
19C2×#13108059C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21#15692251C2211yescharacteristic, complemented
22#15692246C2211yescharacteristic, complemented
23#15692239—21no—
24#15692237—21no—
25#15692229C2211yescharacteristic
26#15692227—21no—
27#15692226—21no—
28C4×D404—21no—
29C4×D404—21no—
30D4×Dic101C2211yescharacteristic, complemented
31#15692217C2211yescharacteristic
32#15692217C2211yescharacteristic
33#15692217C2211yescharacteristic
34#15692217C2211yescharacteristic
35#15692217C2211yescharacteristic, complemented
36#15692214C2211yescharacteristic
37C22⋊C4×D101—21no—
38C22⋊C4×D101—21no—
39#15692188C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692184C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic
44#15692177C2211yescharacteristic
45#15692175C2211yescharacteristic
46#15692175C2211yescharacteristic
47#15692175C2211yescharacteristic, complemented
48#15692175C2211yescharacteristic, complemented
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52#121×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56#102×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic, complemented
58C22⋊C8×C101C2211yescharacteristic
59C23×D101—21no—
60C2×D404—21no—
61C2×D404—22no—
62C2×D404—22no—
63C2×D404C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×D404C2311yescharacteristic
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C22⋊D101—21no—
69C22×Dic101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101—21no—
75D808—22no—
76D808—22no—
77#13108059—22no—
78#13108059—22no—
79C2×#11717579C2311yescharacteristic
80C2×#11717579C2311yescharacteristic
81C4⋊Dic101—21no—
82C4⋊Dic101D411yescharacteristic
83C4⋊Dic101D411yescharacteristic
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101D411yescharacteristic
88C22⋊Dic101D411yescharacteristic
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—21no—
111C22×D101—21no—
112C22×D101—24no—
113C22×D101—21no—
114C22×D101—81no—
115C22×D101—81no—
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×C101C2×D411yescharacteristic
125C2×C4×C101C2411yescharacteristic
126C22⋊D101—81no—
127C22⋊D101—81no—
128C22⋊D101—81no—
129C2×Dic101—21no—
130C2×Dic101—81no—
131C2×Dic101C2×D411yescharacteristic
132C2×Dic101C2×D411yescharacteristic
133C2×Dic101C2×D411yescharacteristic
134C2×Dic101C2×D411yescharacteristic
135D404—24no—
136D404—21no—
137D404—21no—
138D404—21no—
139D404—21no—
140D404#4112yes—
141D404#4112yes—
142C4×D101—81no—
143C4×D101—81no—
144C4×D101—81no—
145C4×D101—81no—
146C4×D101—81no—
147C8×C101—21no—
148C8×C101—21no—
149#11717579—21no—
150#11717579—21no—
151C22×C101—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101C22×D411yescharacteristic
158C2×D101—22no—
159C2×D101—22no—
160C2×D101—41no—
161C2×D101—41no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—84no—
168C4×C101—21no—
169C4×C101—41no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101C2×#4111yescharacteristic
173C4×C101C2×#4111yescharacteristic
174Dic101—21no—
175Dic101—21no—
176Dic101—21no—
177Dic101—21no—
178Dic101—41no—
179C2×C101—41no—
180C2×C101—81no—
181C2×C101#52511yescharacteristic
182C2×C101#57611yescharacteristic
183C2×C101#57611yescharacteristic
184D101—42no—
185D101—42no—
186D101—81no—
187#3122—1011nomaximal, Sylow
188C101#312211yescharacteristic, complemented, Sylow
189#540—1011no—
190#518—1011no—
191#482—1011no—
192#482D10111yescharacteristic, complemented
193#478—1011no—
194#478—1011no—
195#459—1011no—
196#459—1011no—
197#447—1011no—
198#447—1011no—
199#442—1011no—
200#442—1011no—
201C4×D8—1011no—
202C4×D8—1011no—
203#433—1011no—
204C22×D4—1011no—
205C2×D8—1011no—
206C2×D8—1011no—
207C2×D8—1011no—
208C2×D8—1011no—
209#127—1011no—
210#125—1011no—
211#123—2021no—
212#123—2021no—
213#121—1011no—
214#121—2021no—
215#121—2021no—
216#121C2×D10111yescharacteristic
217C4×D4—1011no—
218C4×D4—1011no—
219C4×D4—1011no—
220C4×D4—1011no—
221C4×D4—1011no—
222C4×D4—1011no—
223C4×D4—2021no—
224C4×D4—2021no—
225#117—1011no—
226#117C2×D10111yescharacteristic
227C2×C22⋊C4—2021no—
228C2×C22⋊C4—2021no—
229#107—1011no—
230#107C2×D10111yescharacteristic, complemented
231#106—1011no—
232#106C2×D10111yescharacteristic, complemented
233C4⋊C8—1011no—
234C4⋊C8—1011no—
235#102—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102C2×D10111yescharacteristic, complemented
242#102C2×D10111yescharacteristic, complemented
243C22⋊C8—1011no—
244C22⋊C8C2×D10111yescharacteristic
245#97—1011no—
246C4×C8—1011no—
247C24—2021no—
248C2×D4—21no—
249C2×D4—1011no—
250C2×D4—1011no—
251C2×D4—1011no—
252C2×D4—2022no—
253C2×D4—2022no—
254C2×D4—2021no—
255C2×D4—2021no—
256C2×D4—2021no—
257C2×D4—2021no—
258C2×D4C22×D10111yescharacteristic
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4—2021no—
262C22×C4—2021no—
263C22×C4—2021no—
264C22×C4—2021no—
265C22×C4C22×D10111yescharacteristic
266D8—2022no—
267D8—2022no—
268D8—2022no—
269D8—2022no—
270C2×C8—1011no—
271C2×C8—1011no—
272C2×C8C22×D10111yescharacteristic
273C2×C8C22×D10111yescharacteristic
274C4⋊C4—1011no—
275C4⋊C4—1011no—
276C4⋊C4—1011no—
277C4⋊C4—2021no—
278C4⋊C4—2021no—
279C4⋊C4C22×D10111yescharacteristic
280C4⋊C4C22×D10111yescharacteristic
281C4⋊C4C22×D10111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1011no—
285C22⋊C4—1011no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C42—21no—
294C42—1011no—
295C42—1011no—
296C23—21no—
297C23—8081no—
298C23—8081no—
299C23—2024no—
300C23—2021no—
301C23—2021no—
302C23—2021no—
303C23D4×D10111yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—8081no—
308D4—8081no—
309D4—8081no—
310D4—1012no—
311D4—1012no—
312D4—2024no—
313D4—2021no—
314D4—2021no—
315D4—2021no—
316D4—2021no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—8081no—
323C2×C4—8081no—
324C2×C4—8081no—
325C2×C4—8081no—
326C2×C4—8081no—
327C2×C4—8081no—
328C2×C4—1011no—
329C2×C4—1011no—
330C2×C4—1011no—
331C2×C4—1011no—
332C2×C4—2021no—
333C2×C4D4×D10111yescharacteristic
334C2×C4C23×D10111yescharacteristic
335C8—21no—
336C8—21no—
337C8—2021no—
338C8—2021no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—8084no—
346C22—4041no—
347C22—4041no—
348C22—4041no—
349C22—4041no—
350C22—4041no—
351C22—4041no—
352C22—4041no—
353C22—2022no—
354C22—2022no—
355C22C2×D4×D10111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—4041no—
361C4—2021no—
362C4—2021no—
363C4—2021no—
364C4—2021no—
365C4#41×D10111yescharacteristic
366C4#41×D10111yescharacteristic
367C2—41no—
368C2—81no—
369C2—8081no—
370C2—4042no—
371C2—4042no—
372C2#2026568511yescharacteristic
373C2#2026597911yescharacteristic
374C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#482×C101C2
socleC22×C101C22×D4
hypercenter#482D101
hypocenterC101#3122
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. #20265780C2semidirect
2. #20265651C2semidirect
3. #20265501C2semidirect
4. #20265480C2semidirect
5. #20265476C2semidirect
6. #20265371C2semidirect
7. #20265371C2semidirect
8. #20265313C2semidirect
9. #20265310C2semidirect
10. #20265288C2semidirect
11. #20265286C2semidirect
12. #20265259C2semidirect
13. #20265257C2semidirect
14. #20265235C2semidirect
15. #482×C101C2semidirect
21. #15692251C22semidirect
22. #15692246C22semidirect
30. D4×Dic101C22semidirect
35. #15692217C22semidirect
39. #15692188C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692184C22semidirect
47. #15692175C22semidirect
48. #15692175C22semidirect
50. #15692165C22semidirect
51. C8×Dic101C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
56. #102×C101C22semidirect
57. #102×C101C22semidirect
188. C101#3122semidirect
192. #482D101semidirect
230. #107C2×D101semidirect
232. #106C2×D101semidirect
241. #102C2×D101semidirect
242. #102C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657802
#202656512
#202655012
#202654802
#202654762
#202653712
#202653132
#202653102
#202652882
#202652862
#202652592
#202652572
#202652352
#482×C1012
#3122101