Finite Group Databasebeta

← #27183095

Subgroups — #27183095

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#20265831C211yesmaximal, characteristic, complemented
2#20265823C211yesmaximal, characteristic, complemented
3#20265537C211yesmaximal, characteristic, complemented
4#20265508C211yesmaximal, characteristic, complemented
5#20265496C211yesmaximal, characteristic, complemented
6#20265468C211yesmaximal, characteristic, complemented
7#20265430C211yesmaximal, characteristic, complemented
8#20265406C211yesmaximal, characteristic, complemented
9#20265393C211yesmaximal, characteristic, complemented
10#20265324C211yesmaximal, characteristic, complemented
11#20265313C211yesmaximal, characteristic, complemented
12#20265290C211yesmaximal, characteristic, complemented
13#20265179C211yesmaximal, characteristic, complemented
14C2×#15692177C211yesmaximal, characteristic, complemented
15#435×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108073—21no—
18C22×D404C2211yescharacteristic
19C2×#13108063C2211yescharacteristic, complemented
20C2×D808C2211yescharacteristic
21C2×D808C2211yescharacteristic
22#15692255C2211yescharacteristic, complemented
23#15692243C2211yescharacteristic
24#15692240—21no—
25#15692239—21no—
26#15692239—21no—
27#15692235—21no—
28#15692234C2211yescharacteristic
29#15692229C2211yescharacteristic
30#15692229C2211yescharacteristic
31#15692229C2211yescharacteristic, complemented
32#15692228—21no—
33#15692223—21no—
34C4×D404C2211yescharacteristic
35C4×D404C2211yescharacteristic, complemented
36C2×C4⋊Dic101C2211yescharacteristic
37C2×C4⋊Dic101C2211yescharacteristic, complemented
38C22⋊C4×D101—21no—
39#15692187C2211yescharacteristic, complemented
40#15692187C2211yescharacteristic, complemented
41#15692187C2211yescharacteristic, complemented
42#15692180C2211yescharacteristic, complemented
43#15692180C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, complemented
45#15692177C2211yescharacteristic
46#15692177C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic
51#15692177C2211yescharacteristic, complemented
52C2×M16×C101C2211yescharacteristic, complemented
53C22×C8×C101C2211yescharacteristic
54C4×D4×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic, complemented
56C22⋊C8×C101C2211yescharacteristic
57C22⋊C8×C101C2211yescharacteristic, complemented
58#97×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62#13108073—44no—
63C2×Dic202—21no—
64C2×Dic202C2311yescharacteristic
65C2×D404—22no—
66C2×D404—21no—
67C2×D404—41no—
68C2×D404C2311yescharacteristic
69C2×D404C2311yescharacteristic
70C2×D404C2311yescharacteristic
71C2×C22⋊D101—21no—
72C2×C22⋊D101—21no—
73C2×C22⋊D101—21no—
74C2×C22⋊D101—21no—
75C22×Dic101—21no—
76C22×Dic101—21no—
77C2×C4×D101—21no—
78C2×C4×D101—21no—
79C2×C4×D101—21no—
80#13108063—41no—
81D808—22no—
82D808—41no—
83C4⋊Dic101—21no—
84C4⋊Dic101—21no—
85C4⋊Dic101—21no—
86C4⋊Dic101C2311yescharacteristic
87C4⋊Dic101C2311yescharacteristic
88C4⋊Dic101C2311yescharacteristic
89C4⋊Dic101C2311yescharacteristic
90#13108053—21no—
91C22⋊Dic101—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95#13108051—21no—
96#13108051—21no—
97#13108051—21no—
98#13108051—21no—
99C2×D4×C101D411yescharacteristic
100C22×C4×C101C2311yescharacteristic
101C22×C4×C101C2311yescharacteristic
102M16×C101—41no—
103C2×C8×C101—41no—
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C2×C8×C101C2311yescharacteristic
108C4⋊C4×C101D411yescharacteristic
109C22⋊C4×C101D411yescharacteristic
110C22⋊C4×C101D411yescharacteristic
111C42×C101C2311yescharacteristic
112C23×C101C2×D411yescharacteristic
113C23×C101C2×D411yescharacteristic
114C22×D101—21no—
115C22×D101—21no—
116C22×D101—21no—
117C22×D101—42no—
118C22×D101—42no—
119C22×D101—81no—
120D4×C101—22no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2×D411yescharacteristic
129C2×C4×C101C2411yescharacteristic
130C22⋊D101—42no—
131C22⋊D101—42no—
132C22⋊D101—42no—
133C22⋊D101—81no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101—42no—
140C2×Dic101—42no—
141D404—21no—
142D404—21no—
143D404—21no—
144D404—21no—
145D404—21no—
146D404—42no—
147D404#4112yescomplemented
148C4×D101—42no—
149C4×D101—42no—
150C4×D101—81no—
151Dic202—21no—
152Dic202—21no—
153Dic202—42no—
154C8×C101—21no—
155C8×C101—21no—
156C8×C101—21no—
157C8×C101—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—21no—
163C22×C101AGL(1,ℤ/8)12yes—
164C22×C101C22×D411yescharacteristic
165C2×D101—22no—
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—21no—
177C4×C101—21no—
178C4×C101—21no—
179C4×C101C2×#4111yescharacteristic
180C4×C101H(5,𝔽2)11yescharacteristic
181Dic101—41no—
182Dic101—41no—
183Dic101—41no—
184Dic101—41no—
185Dic101—41no—
186C2×C101—22no—
187C2×C101—41no—
188C2×C101#54611yescharacteristic
189C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C101#57711yescharacteristic
191D101—42no—
192D101—81no—
193D101—81no—
194#3306—1011nomaximal, Sylow
195C101#330611yescharacteristic, complemented, Sylow
196#547—1011no—
197#546—1011no—
198#489—1011no—
199#483—1011no—
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#435D10111yescharacteristic, complemented
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×M16C2×D10111yescharacteristic, complemented
218C22×C8C2×D10111yescharacteristic
219C4⋊Q8—1011no—
220#124—1011no—
221#123—2021no—
222#123—2021no—
223#123—2021no—
224C22⋊Q8—1011no—
225C22⋊Q8—2021no—
226#121—1011no—
227#121—1011no—
228#121—1011no—
229#121—2021no—
230#120—2021no—
231C4×D4—1011no—
232C4×D4—1011no—
233C4×D4C2×D10111yescharacteristic
234C2×C4⋊C4—1011no—
235C2×C4⋊C4—1011no—
236C2×C22⋊C4—2021no—
237#106—1011no—
238#106—1011no—
239#106—1011no—
240C4⋊C8C2×D10111yescharacteristic, complemented
241#103—1011no—
242#103—1011no—
243#103—1011no—
244#102—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248#102—1011no—
249#102—1011no—
250#102—1011no—
251C22⋊C8C2×D10111yescharacteristic
252C22⋊C8C2×D10111yescharacteristic, complemented
253#97C2×D10111yescharacteristic, complemented
254C24—2021no—
255#41—4041no—
256#41—4044no—
257#41—2022no—
258C2×Q8—1011no—
259C2×Q8—2021no—
260C2×D4—1011no—
261C2×D4—1011no—
262C2×D4—1011no—
263C2×D4—4041no—
264C2×D4—2022no—
265C2×D4—2021no—
266C2×D4—2021no—
267C2×D4—2021no—
268C2×D4—2021no—
269C2×D4—2021no—
270C2×D4D40411yescharacteristic
271C22×C4—2021no—
272C22×C4—2021no—
273C22×C4—2021no—
274C22×C4—2021no—
275C22×C4—2021no—
276C22×C4C22×D10111yescharacteristic
277C22×C4C22×D10111yescharacteristic
278SD16—4041no—
279D8—4041no—
280D8—2022no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D10111yescharacteristic
284C2×C8C22×D10111yescharacteristic
285C2×C8C22×D10111yescharacteristic
286C2×C8C22×D10111yescharacteristic
287C4⋊C4—1011no—
288C4⋊C4—1011no—
289C4⋊C4—1011no—
290C4⋊C4—1011no—
291C4⋊C4—2021no—
292C4⋊C4—2021no—
293C4⋊C4—2021no—
294C4⋊C4—2021no—
295C4⋊C4D40411yescharacteristic
296C22⋊C4—2021no—
297C22⋊C4—2021no—
298C22⋊C4—2021no—
299C22⋊C4—2021no—
300C22⋊C4—2021no—
301C22⋊C4—2021no—
302C22⋊C4—2021no—
303C22⋊C4—2021no—
304C22⋊C4D40411yescharacteristic
305C22⋊C4D40411yescharacteristic
306C42C22×D10111yescharacteristic
307C23—8081no—
308C23—4042no—
309C23—4042no—
310C23—2021no—
311C23—2021no—
312C23—2021no—
313C23C2×D40411yescharacteristic
314C23C2×D40411yescharacteristic
315Q8—4042no—
316Q8—2021no—
317Q8—2021no—
318D4—22no—
319D4—8081no—
320D4—1012no—
321D4—4042no—
322D4—4042no—
323D4—4042no—
324D4—4042no—
325D4—2021no—
326D4—2021no—
327D4—2021no—
328D4—2021no—
329D4—2021no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—8081no—
335C2×C4—4042no—
336C2×C4—4042no—
337C2×C4—4042no—
338C2×C4—4042no—
339C2×C4—2021no—
340C2×C4—2021no—
341C2×C4—2021no—
342C2×C4—2021no—
343C2×C4—2021no—
344C2×C4C2×D40411yescharacteristic
345C2×C4C2×D40411yescharacteristic
346C2×C4C2×D40411yescharacteristic
347C2×C4C2×D40411yescharacteristic
348C2×C4C23×D10111yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—8084no—
359C22—4041no—
360C22—4041no—
361C22—4041no—
362C22—4041no—
363C22—4041no—
364C22—4041no—
365C22—4041no—
366C22—4041no—
367C22—2022no—
368C22#1569228312yes—
369C22C22×D40411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—4041no—
375C4—4041no—
376C4—4041no—
377C4—4041no—
378C4—4041no—
379C4#41×D10111yescharacteristic
380C4#1569230011yescharacteristic
381C2—22no—
382C2—41no—
383C2—8081no—
384C2—8081no—
385C2—4042no—
386C2#2026582211yescharacteristic
387C2C2×#1569228311yescharacteristic
388C2#2026598911yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#435×C101C2
socleC22×C101C22×D4
hypercenter#435D101
hypocenterC101#3306
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20265831C2semidirect
2. #20265823C2semidirect
3. #20265537C2semidirect
4. #20265508C2semidirect
5. #20265496C2semidirect
6. #20265468C2semidirect
7. #20265430C2semidirect
8. #20265406C2semidirect
9. #20265393C2semidirect
10. #20265324C2semidirect
11. #20265313C2semidirect
12. #20265290C2semidirect
13. #20265179C2semidirect
14. C2×#15692177C2semidirect
15. #435×C101C2semidirect
19. C2×#13108063C22semidirect
22. #15692255C22semidirect
31. #15692229C22semidirect
35. C4×D404C22semidirect
37. C2×C4⋊Dic101C22semidirect
39. #15692187C22semidirect
40. #15692187C22semidirect
41. #15692187C22semidirect
42. #15692180C22semidirect
43. #15692180C22semidirect
44. #15692180C22semidirect
51. #15692177C22semidirect
52. C2×M16×C101C22semidirect
55. C4⋊C8×C101C22semidirect
57. C22⋊C8×C101C22semidirect
58. #97×C101C22semidirect
147. D404#41semidirect
195. C101#3306semidirect
208. #435D101semidirect
217. C2×M16C2×D101semidirect
240. C4⋊C8C2×D101semidirect
252. C22⋊C8C2×D101semidirect
253. #97C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658312
#202658232
#202655372
#202655082
#202654962
#202654682
#202654302
#202654062
#202653932
#202653242
#202653132
#202652902
#202651792
C2×#156921772
#435×C1012
#3306101