Finite Group Databasebeta

← #27181481

Subgroups — #27181481

Order 12928.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265804C211yesmaximal, characteristic, complemented
2#20265740C211yesmaximal, characteristic
3#20265541C211yesmaximal, characteristic, complemented
4#20265540C211yesmaximal, characteristic, complemented
5#20265539C211yesmaximal, characteristic, complemented
6#20265535C211yesmaximal, characteristic, complemented
7#20265532C211yesmaximal, characteristic, complemented
8#20265530C211yesmaximal, characteristic, complemented
9#20265522C211yesmaximal, characteristic, complemented
10#20265180C211yesmaximal, characteristic, complemented
11#20265175C211yesmaximal, characteristic, complemented
12#20265170C211yesmaximal, characteristic, complemented
13#102×D101C211yesmaximal, characteristic, complemented
14#20265131C211yesmaximal, characteristic, complemented
15#486×C101C211yesmaximal, characteristic, complemented
16C2×#13108073C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692254C2211yescharacteristic, complemented
21#15692253—21no—
22#15692251C2211yescharacteristic
23#15692247C2211yescharacteristic, complemented
24#15692246C2211yescharacteristic, complemented
25#15692245—21no—
26#15692243C2211yescharacteristic
27#15692242C2211yescharacteristic
28#15692233—21no—
29#15692231—21no—
30#15692227—21no—
31#15692227—21no—
32#15692223—21no—
33#15692223—21no—
34#15692213C2211yescharacteristic
35#15692212C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic
37#15692180C2211yescharacteristic, complemented
38#15692180C2211yescharacteristic, complemented
39#15692178C2211yescharacteristic, complemented
40#15692178C2211yescharacteristic, complemented
41#15692177C2211yescharacteristic
42#15692177C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692176C2211yescharacteristic
45#15692176C2211yescharacteristic, complemented
46#15692176C2211yescharacteristic, complemented
47#15692175C2211yescharacteristic
48#15692175C2211yescharacteristic
49#15692166C2211yescharacteristic, complemented
50#15692165C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52C4⋊Q8×C101C2211yescharacteristic, complemented
53#127×C101C2211yescharacteristic
54#102×C101C2211yescharacteristic
55#102×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic, complemented
58C4×C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108073—22no—
61#13108073—22no—
62C2×Dic202—21no—
63C2×Dic202C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C22⋊D101—21no—
69D4×D101—22no—
70D4×D101—22no—
71C22×Dic101—21no—
72C2×C4×D101—21no—
73C2×C4×D101C2311yescharacteristic
74#13108057—22no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C8×D101—22no—
78C4⋊Dic101—21no—
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053D411yescharacteristic
87#13108053D411yescharacteristic
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051D411yescharacteristic
94#13108051D411yescharacteristic
95C4×Dic101—21no—
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101—21no—
98C2×D4×C101—21no—
99C2×D4×C101—21no—
100C2×D4×C101C2311yescharacteristic
101C2×D4×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C2×C8×C101C2311yescharacteristic
104C4⋊C4×C101—21no—
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C23×C101—21no—
110C22×D101—21no—
111C22×D101—42no—
112C22×D101—81no—
113C22×D101—81no—
114C22×D101C2×D411yescharacteristic
115Q8×C101—81no—
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—81no—
121D4×C101—81no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2411yescharacteristic
127C22⋊D101—42no—
128C22⋊D101—42no—
129C22⋊D101—81no—
130C22⋊D101—81no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—42no—
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137C2×Dic101C2×D411yescharacteristic
138D404—21no—
139D404—21no—
140C4×D101—81no—
141C4×D101#4112yes—
142C4×D101#4112yes—
143Dic202—21no—
144Dic202—21no—
145Dic202—81no—
146C8×C101—21no—
147C8×C101—21no—
148#11717579—21no—
149#11717579—21no—
150C22×C101—41no—
151C22×C101—41no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101C22×D411yescharacteristic
157C2×D101—21no—
158C2×D101—21no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101—41no—
162C2×D101—84no—
163C2×D101#12412yes—
164C4×C101—21no—
165C4×C101—21no—
166C4×C101—41no—
167C4×C101—41no—
168C4×C101C2×#4111yescharacteristic
169C4×C101C2×#4111yescharacteristic
170Dic101—21no—
171Dic101—21no—
172Dic101—41no—
173Dic101—41no—
174Dic101—41no—
175Dic101#12412yes—
176C2×C101—81no—
177C2×C101—81no—
178C2×C101C2×#12411yescharacteristic
179C2×C101#57611yescharacteristic
180C2×C101#57711yescharacteristic
181D101—22no—
182D101—81no—
183#3136—1011nomaximal, Sylow
184C101#313611yescharacteristic, complemented, Sylow
185#544—1011no—
186#535—1011no—
187#490—1011no—
188#490—1011no—
189#489—1011no—
190#489—1011no—
191#488—1011no—
192#488—1011no—
193#486—1011no—
194#486D10111yescharacteristic, complemented
195#418—1011no—
196#417—1011no—
197#416—1011no—
198C2×#102—1011no—
199#405—1011no—
200C2×#41—1011no—
201C22×D4—1011no—
202C2×M16—1011no—
203C22×C8—1011no—
204C4⋊Q8—1011no—
205C4⋊Q8—2021no—
206C4⋊Q8C2×D10111yescharacteristic, complemented
207#127—1011no—
208#127C2×D10111yescharacteristic
209#125—1011no—
210#125—1011no—
211#125—2021no—
212#124—1011no—
213#124—1011no—
214C22⋊Q8—2021no—
215C22⋊Q8—2021no—
216#121—2021no—
217#121—2021no—
218#120—2021no—
219#120—2021no—
220#117—1011no—
221#117—1011no—
222C2×C4⋊C4—1011no—
223#103—1011no—
224#103—1011no—
225#103—1011no—
226#103—1011no—
227#102—1011no—
228#102—1011no—
229#102—1011no—
230#102—1011no—
231#102—1011no—
232#102—1011no—
233#102—1011no—
234#102—1011no—
235#102C2×D10111yescharacteristic
236#102C2×D10111yescharacteristic
237#102C2×D10111yescharacteristic, complemented
238#102C2×D10111yescharacteristic, complemented
239#97—1011no—
240#97—1011no—
241C4×C8—1011no—
242C4×C8C2×D10111yescharacteristic, complemented
243C24—2021no—
244#41—2022no—
245#41—2022no—
246C2×Q8—21no—
247C2×Q8—1011no—
248C2×Q8—2021no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—1011no—
252C2×D4—2022no—
253C2×D4—2022no—
254C2×D4—2021no—
255C2×D4—2021no—
256C2×D4—2021no—
257C2×D4—2021no—
258C2×D4C22×D10111yescharacteristic
259C2×D4C22×D10111yescharacteristic
260C22×C4—1011no—
261C22×C4—2021no—
262C22×C4—2021no—
263M16—2022no—
264C2×C8—1011no—
265C2×C8—1011no—
266C2×C8—2022no—
267C2×C8C22×D10111yescharacteristic
268C2×C8C22×D10111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—1011no—
271C4⋊C4—1011no—
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⋊C4C22×D10111yescharacteristic
281C4⋊C4C22×D10111yescharacteristic
282C22⋊C4—1011no—
283C22⋊C4—1011no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C42—1011no—
290C42—2021no—
291C42C22×D10111yescharacteristic
292C23—21no—
293C23—21no—
294C23—8081no—
295C23—8081no—
296C23—1011no—
297C23—4042no—
298C23—2021no—
299Q8—81no—
300Q8—8081no—
301Q8—2021no—
302Q8—2021no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—8081no—
310D4—8081no—
311D4—4042no—
312D4—4042no—
313D4—2021no—
314D4—2021no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—8081no—
318C2×C4—1011no—
319C2×C4—1012no—
320C2×C4—1012no—
321C2×C4—1011no—
322C2×C4—1011no—
323C2×C4—4042no—
324C2×C4—2021no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4D4×D10111yescharacteristic
328C2×C4D4×D10111yescharacteristic
329C2×C4C23×D10111yescharacteristic
330C8—21no—
331C8—21no—
332C8—2021no—
333C8—2021no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—8084no—
341C22—1012no—
342C22—4041no—
343C22—4041no—
344C22—4041no—
345C22—2021no—
346C22—2021no—
347C22C2×D4×D10111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—1012no—
353C4—4041no—
354C4—4041no—
355C4—4041no—
356C4—2021no—
357C4—2021no—
358C4#41×D10111yescharacteristic
359C4#41×D10111yescharacteristic
360C2—81no—
361C2—81no—
362C2—8081no—
363C2—2022no—
364C2#124×D10111yescharacteristic
365C2#2026597811yescharacteristic
366C2#2026598311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#486×C101C2
socleC22×C101C22×D4
prime radical#20265740C2
hypercenter#486D101
hypocenterC101#3136
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20265804C2semidirect
3. #20265541C2semidirect
4. #20265540C2semidirect
5. #20265539C2semidirect
6. #20265535C2semidirect
7. #20265532C2semidirect
8. #20265530C2semidirect
9. #20265522C2semidirect
10. #20265180C2semidirect
11. #20265175C2semidirect
12. #20265170C2semidirect
13. #102×D101C2semidirect
14. #20265131C2semidirect
15. #486×C101C2semidirect
20. #15692254C22semidirect
23. #15692247C22semidirect
24. #15692246C22semidirect
37. #15692180C22semidirect
38. #15692180C22semidirect
39. #15692178C22semidirect
40. #15692178C22semidirect
45. #15692176C22semidirect
46. #15692176C22semidirect
49. #15692166C22semidirect
50. #15692165C22semidirect
51. C8×Dic101C22semidirect
52. C4⋊Q8×C101C22semidirect
56. #102×C101C22semidirect
57. #102×C101C22semidirect
58. C4×C8×C101C22semidirect
184. C101#3136semidirect
194. #486D101semidirect
206. C4⋊Q8C2×D101semidirect
237. #102C2×D101semidirect
238. #102C2×D101semidirect
242. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658042
#202657402
#202655412
#202655402
#202655392
#202655352
#202655322
#202655302
#202655222
#202651802
#202651752
#202651702
#102×D1012
#202651312
#486×C1012
#3136101