Finite Group Databasebeta

← #27183091

Subgroups — #27183091

Order 12928.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265828C211yesmaximal, characteristic, complemented
2#20265818C211yesmaximal, characteristic, complemented
3#20265538C211yesmaximal, characteristic, complemented
4#20265497C211yesmaximal, characteristic, complemented
5#20265466C211yesmaximal, characteristic, complemented
6#20265431C211yesmaximal, characteristic, complemented
7#20265408C211yesmaximal, characteristic, complemented
8#20265395C211yesmaximal, characteristic, complemented
9#20265325C211yesmaximal, characteristic, complemented
10#20265313C211yesmaximal, characteristic, complemented
11#20265288C211yesmaximal, characteristic, complemented
12#20265245C211yesmaximal, characteristic, complemented
13#20265177C211yesmaximal, characteristic, complemented
14C2×#15692175C211yesmaximal, characteristic, complemented
15#483×C101C211yesmaximal, characteristic, complemented
16C2×#13108075C2211yescharacteristic
17C2×#13108074—21no—
18C22×D404C2211yescharacteristic
19C2×#13108061C2211yescharacteristic, complemented
20C2×D808C2211yescharacteristic
21C2×D808C2211yescharacteristic
22C2×#13108057C2211yescharacteristic, complemented
23C22×#11717579C2211yescharacteristic
24#15692254C2211yescharacteristic, complemented
25#15692244C2211yescharacteristic
26#15692240—21no—
27#15692240—21no—
28#15692238—21no—
29#15692233—21no—
30#15692230—21no—
31#15692230C2211yescharacteristic
32#15692230C2211yescharacteristic, complemented
33#15692229C2211yescharacteristic
34#15692225—21no—
35#15692217C2211yescharacteristic
36#15692217C2211yescharacteristic, complemented
37C4×C22⋊D101C2211yescharacteristic
38C4⋊C4×D101C2211yescharacteristic, complemented
39C22⋊C4×D101—21no—
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692179C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic
44#15692177C2211yescharacteristic
45#15692175C2211yescharacteristic
46#15692175C2211yescharacteristic
47#15692175C2211yescharacteristic
48#15692175C2211yescharacteristic
49#15692175C2211yescharacteristic, complemented
50#15692167C2211yescharacteristic, complemented
51#15692165C2211yescharacteristic, complemented
52C22⋊Q8×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic
54#106×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56#103×C101C2211yescharacteristic, complemented
57#103×C101C2211yescharacteristic, complemented
58C22⋊C8×C101C2211yescharacteristic
59C23×D101—21no—
60#13108075—22no—
61#13108075—41no—
62#13108074—44no—
63C2×Dic202—21no—
64C2×D404—22no—
65C2×D404—21no—
66C2×D404—21no—
67C2×D404—21no—
68C2×D404—21no—
69C2×D404—41no—
70C2×D404C2311yescharacteristic
71C2×D404C2311yescharacteristic
72C2×D404C2311yescharacteristic
73C2×C22⋊D101—21no—
74C2×C22⋊D101D411yescharacteristic
75C2×C4×D101—21no—
76C2×C4×D101—21no—
77C2×C4×D101—21no—
78C2×C4×D101—21no—
79C2×C4×D101C2311yescharacteristic
80#13108061—41no—
81D808—22no—
82D808—41no—
83#13108057—41no—
84C2×#11717579—41no—
85C2×#11717579C2311yescharacteristic
86C2×#11717579C2311yescharacteristic
87C4⋊Dic101C2311yescharacteristic
88#13108053—21no—
89#13108053—21no—
90#13108053D411yescharacteristic
91C22⋊Dic101D411yescharacteristic
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95#13108051—21no—
96#13108051—21no—
97#13108051—21no—
98#13108051—21no—
99#13108051D411yescharacteristic
100C4×Dic101C2311yescharacteristic
101C2×Q8×C101C2311yescharacteristic
102C22×C4×C101—21no—
103C22×C4×C101C2311yescharacteristic
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C4⋊C4×C101—21no—
107C4⋊C4×C101—21no—
108C4⋊C4×C101C2311yescharacteristic
109C4⋊C4×C101C2311yescharacteristic
110C4⋊C4×C101C2311yescharacteristic
111C22⋊C4×C101—21no—
112C23×C101C2×D411yescharacteristic
113C22×D101—21no—
114C22×D101—21no—
115C22×D101—21no—
116C22×D101—42no—
117C22×D101—42no—
118C22×D101—81no—
119C22×D101C2×D411yescharacteristic
120Q8×C101—21no—
121Q8×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—42no—
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2411yescharacteristic
131C22⋊D101—22no—
132C22⋊D101—42no—
133C2×Dic101—21no—
134C2×Dic101C2×D411yescharacteristic
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137D404—21no—
138D404—21no—
139D404—21no—
140D404—21no—
141D404—21no—
142D404—42no—
143D404—42no—
144D404—42no—
145D404—81no—
146D404#4112yescomplemented
147C4×D101—21no—
148C4×D101—21no—
149C4×D101—42no—
150C4×D101—42no—
151C4×D101—42no—
152C4×D101—81no—
153Dic202—42no—
154C8×C101—21no—
155C8×C101—21no—
156#11717579—21no—
157#11717579—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101AGL(1,ℤ/8)12yes—
161C22×C101C22×D411yescharacteristic
162C2×D101—21no—
163C2×D101—22no—
164C2×D101—21no—
165C2×D101—21no—
166C2×D101—41no—
167C2×D101—41no—
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—41no—
171C2×D101—41no—
172C2×D101—41no—
173C2×D101—41no—
174C2×D101—84no—
175C4×C101—21no—
176C4×C101—41no—
177C4×C101—41no—
178C4×C101—41no—
179C4×C101—41no—
180C4×C101C2×#4111yescharacteristic
181C4×C101H(5,𝔽2)11yescharacteristic
182Dic101—21no—
183Dic101—21no—
184Dic101—21no—
185Dic101—41no—
186C2×C101—22no—
187C2×C101#54611yescharacteristic
188C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C101#57711yescharacteristic
190D101—41no—
191D101—42no—
192D101—81no—
193D101—81no—
194#3306—1011nomaximal, Sylow
195C101#330611yescharacteristic, complemented, Sylow
196#547—1011no—
197#546—1011no—
198#489—1011no—
199#483D10111yescharacteristic, complemented
200#481—1011no—
201#476—1011no—
202#469—1011no—
203#465—1011no—
204#463—1011no—
205#449—1011no—
206#447—1011no—
207#442—1011no—
208#435—1011no—
209#417—1011no—
210C2×#102—1011no—
211C2×#41—1011no—
212C2×#41—2021no—
213C22×D4—1011no—
214C2×SD16—1011no—
215C2×D8—1011no—
216C2×D8—1011no—
217C2×M16—1011no—
218C22×C8—1011no—
219C4⋊Q8—1011no—
220#124—1011no—
221#123—2021no—
222#123—2021no—
223#123—2021no—
224C22⋊Q8—2021no—
225C22⋊Q8C2×D10111yescharacteristic
226#121—1011no—
227#121—1011no—
228#121—1011no—
229#121—2021no—
230#120—2021no—
231C4×D4—1011no—
232C4×D4—1011no—
233C4×D4—1011no—
234C2×C4⋊C4—1011no—
235C2×C4⋊C4C2×D10111yescharacteristic
236C2×C22⋊C4—2021no—
237#106—1011no—
238#106C2×D10111yescharacteristic, complemented
239#106C2×D10111yescharacteristic, complemented
240C4⋊C8—1011no—
241#103—1011no—
242#103C2×D10111yescharacteristic, complemented
243#103C2×D10111yescharacteristic, complemented
244#102—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248#102—1011no—
249#102—1011no—
250#102—1011no—
251C22⋊C8—1011no—
252C22⋊C8C2×D10111yescharacteristic
253#97—1011no—
254C24—2021no—
255#41—4044no—
256#41—4041no—
257#41—2022no—
258C2×Q8—2021no—
259C2×Q8C22×D10111yescharacteristic
260C2×D4—1011no—
261C2×D4—1011no—
262C2×D4—1011no—
263C2×D4—1011no—
264C2×D4—4041no—
265C2×D4—2021no—
266C2×D4—2022no—
267C2×D4—2021no—
268C2×D4—2021no—
269C2×D4—2021no—
270C2×D4—2021no—
271C22×C4—21no—
272C22×C4—1011no—
273C22×C4—2021no—
274C22×C4—2021no—
275C22×C4—2021no—
276C22×C4—2021no—
277C22×C4C22×D10111yescharacteristic
278SD16—4041no—
279D8—4041no—
280D8—2022no—
281M16—4041no—
282C2×C8—1011no—
283C2×C8—1011no—
284C2×C8—4041no—
285C2×C8C22×D10111yescharacteristic
286C2×C8C22×D10111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—1011no—
290C4⋊C4—1011no—
291C4⋊C4—2021no—
292C4⋊C4—2021no—
293C4⋊C4C22×D10111yescharacteristic
294C4⋊C4C22×D10111yescharacteristic
295C4⋊C4C22×D10111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—1011no—
298C22⋊C4—1011no—
299C22⋊C4—2021no—
300C22⋊C4—2021no—
301C22⋊C4—2021no—
302C22⋊C4—2021no—
303C22⋊C4—2021no—
304C22⋊C4—2021no—
305C22⋊C4—2021no—
306C42—1011no—
307C23—8081no—
308C23—1011no—
309C23—4042no—
310C23—4042no—
311C23—2021no—
312C23—2021no—
313C23—2021no—
314C23D4×D10111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4042no—
318D4—8081no—
319D4—1012no—
320D4—4042no—
321D4—4042no—
322D4—4042no—
323D4—4042no—
324D4—2022no—
325D4—2021no—
326D4—2021no—
327D4—2021no—
328D4—2021no—
329D4—2021no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—8081no—
338C2×C4—1011no—
339C2×C4—1011no—
340C2×C4—1011no—
341C2×C4—4042no—
342C2×C4—4042no—
343C2×C4—4042no—
344C2×C4—2021no—
345C2×C4—2021no—
346C2×C4—2021no—
347C2×C4D4×D10111yescharacteristic
348C2×C4C23×D10111yescharacteristic
349C8—21no—
350C8—21no—
351C8—2021no—
352C8—2021no—
353C22—21no—
354C22—21no—
355C22—8084no—
356C22—4041no—
357C22—4041no—
358C22—4041no—
359C22—4041no—
360C22—4041no—
361C22—4041no—
362C22—4041no—
363C22—4041no—
364C22—2021no—
365C22—2022no—
366C22—2021no—
367C22—2021no—
368C22#1569228212yes—
369C22C2×D4×D10111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—4041no—
376C4—2021no—
377C4—2021no—
378C4—2021no—
379C4#41×D10111yescharacteristic
380C4#1569230111yescharacteristic
381C2—22no—
382C2—8081no—
383C2—8081no—
384C2—4042no—
385C2—4041no—
386C2#2026581911yescharacteristic
387C2C2×#1569228211yescharacteristic
388C2#2026598611yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#483×C101C2
socleC22×C101C22×D4
hypercenter#483D101
hypocenterC101#3306
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #20265828C2semidirect
2. #20265818C2semidirect
3. #20265538C2semidirect
4. #20265497C2semidirect
5. #20265466C2semidirect
6. #20265431C2semidirect
7. #20265408C2semidirect
8. #20265395C2semidirect
9. #20265325C2semidirect
10. #20265313C2semidirect
11. #20265288C2semidirect
12. #20265245C2semidirect
13. #20265177C2semidirect
14. C2×#15692175C2semidirect
15. #483×C101C2semidirect
19. C2×#13108061C22semidirect
22. C2×#13108057C22semidirect
24. #15692254C22semidirect
32. #15692230C22semidirect
36. #15692217C22semidirect
38. C4⋊C4×D101C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692179C22semidirect
49. #15692175C22semidirect
50. #15692167C22semidirect
51. #15692165C22semidirect
54. #106×C101C22semidirect
55. #106×C101C22semidirect
56. #103×C101C22semidirect
57. #103×C101C22semidirect
146. D404#41semidirect
195. C101#3306semidirect
199. #483D101semidirect
238. #106C2×D101semidirect
239. #106C2×D101semidirect
242. #103C2×D101semidirect
243. #103C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658282
#202658182
#202655382
#202654972
#202654662
#202654312
#202654082
#202653952
#202653252
#202653132
#202652882
#202652452
#202651772
C2×#156921752
#483×C1012
#3306101