Finite Group Databasebeta

← #27182984

Subgroups — #27182984

Order 12928.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265873C211yesmaximal, characteristic, complemented
2#20265823C211yesmaximal, characteristic, complemented
3#20265532C211yesmaximal, characteristic, complemented
4#20265513C211yesmaximal, characteristic, complemented
5#20265502C211yesmaximal, characteristic, complemented
6#20265478C211yesmaximal, characteristic, complemented
7#20265413C211yesmaximal, characteristic, complemented
8#20265406C211yesmaximal, characteristic, complemented
9#20265393C211yesmaximal, characteristic, complemented
10#20265324C211yesmaximal, characteristic, complemented
11#20265313C211yesmaximal, characteristic, complemented
12C4×D808C211yesmaximal, characteristic, complemented
13#20265174C211yesmaximal, characteristic, complemented
14C2×#15692177C211yesmaximal, characteristic, complemented
15C8×D4×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C22×D404C2211yescharacteristic
18C2×#13108063C2211yescharacteristic, complemented
19C2×D808C2211yescharacteristic
20C2×D808C2211yescharacteristic
21#15692250—21no—
22#15692247C2211yescharacteristic, complemented
23#15692243C2211yescharacteristic
24#15692240—21no—
25#15692237—21no—
26#15692234C2211yescharacteristic
27#15692229C2211yescharacteristic
28#15692229C2211yescharacteristic
29#15692229C2211yescharacteristic, complemented
30#15692228—21no—
31#15692227—21no—
32#15692223—21no—
33C4×D404C2211yescharacteristic
34C4×D404C2211yescharacteristic, complemented
35#15692215—21no—
36#15692214C2211yescharacteristic, complemented
37C2×C4⋊Dic101C2211yescharacteristic
38C22⋊C4×D101—21no—
39#15692189C2211yescharacteristic, complemented
40#15692189C2211yescharacteristic, 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
52C22×C8×C101C2211yescharacteristic
53C22×C8×C101C2211yescharacteristic, complemented
54C4×D4×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic, complemented
56C22⋊C8×C101C2211yescharacteristic
57C22⋊C8×C101C2211yescharacteristic, complemented
58C4×C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62C2×Dic202C2311yescharacteristic
63C2×D404—22no—
64C2×D404—21no—
65C2×D404—41no—
66C2×D404C2311yescharacteristic
67C2×D404C2311yescharacteristic
68C2×D404C2311yescharacteristic
69C2×C22⋊D101—21no—
70C2×C22⋊D101—21no—
71C2×C22⋊D101—21no—
72C2×C22⋊D101—21no—
73C22×Dic101—21no—
74C2×C4×D101—21no—
75C2×C4×D101—21no—
76C2×C4×D101—21no—
77#13108063—41no—
78D808—22no—
79D808—41no—
80C4⋊Dic101—21no—
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95#13108051—21no—
96#13108051—21no—
97C4×Dic101—21no—
98C2×D4×C101D411yescharacteristic
99C22×C4×C101C2311yescharacteristic
100C22×C4×C101C2311yescharacteristic
101C2×C8×C101—41no—
102C2×C8×C101—41no—
103C2×C8×C101C2311yescharacteristic
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C4⋊C4×C101D411yescharacteristic
108C22⋊C4×C101D411yescharacteristic
109C22⋊C4×C101D411yescharacteristic
110C42×C101C2311yescharacteristic
111C23×C101C2×D411yescharacteristic
112C23×C101C2×D411yescharacteristic
113C22×D101—21no—
114C22×D101—21no—
115C22×D101—21no—
116C22×D101—42no—
117C22×D101—42no—
118C22×D101—81no—
119D4×C101—22no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2411yescharacteristic
129C22⋊D101—42no—
130C22⋊D101—42no—
131C22⋊D101—81no—
132C22⋊D101—81no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—81no—
139D404—21no—
140D404—21no—
141D404—21no—
142D404—21no—
143D404—21no—
144D404—42no—
145D404#4112yes—
146C4×D101—42no—
147C4×D101—81no—
148C4×D101—81no—
149Dic202—21no—
150Dic202—21no—
151C8×C101—21no—
152C8×C101—21no—
153C8×C101—21no—
154C8×C101—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101#13512yes—
161C22×C101C22×D411yescharacteristic
162C2×D101—22no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—41no—
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—41no—
171C2×D101—84no—
172C4×C101—21no—
173C4×C101—21no—
174C4×C101—21no—
175C4×C101—21no—
176C4×C101C2×#4111yescharacteristic
177C4×C101H(5,𝔽2)11yescharacteristic
178Dic101—41no—
179Dic101—41no—
180Dic101—41no—
181Dic101—41no—
182Dic101—41no—
183C2×C101—22no—
184C2×C101—41no—
185C2×C101#54611yescharacteristic
186C2×C101C2×#13511yescharacteristic
187C2×C101#57611yescharacteristic
188D101—42no—
189D101—81no—
190D101—81no—
191#3297—1011nomaximal, Sylow
192C101#329711yescharacteristic, complemented, Sylow
193#553—1011no—
194#546—1011no—
195#488—1011no—
196#484—1011no—
197#482—1011no—
198#478—1011no—
199#466—1011no—
200#465—1011no—
201#463—1011no—
202#449—1011no—
203#447—1011no—
204C4×D8—1011no—
205C8×D4D10111yescharacteristic, complemented
206#416—1011no—
207C2×#102—1011no—
208C2×#41—1011no—
209C22×D4—1011no—
210C2×SD16—1011no—
211C2×D8—1011no—
212C2×D8—1011no—
213C22×C8C2×D10111yescharacteristic
214C22×C8C2×D10111yescharacteristic, complemented
215#126—2021no—
216#125—1011no—
217#124—1011no—
218#123—2021no—
219#123—2021no—
220C22⋊Q8—1011no—
221#121—1011no—
222#121—1011no—
223#121—1011no—
224#121—2021no—
225#121—2021no—
226#120—2021no—
227C4×D4—1011no—
228C4×D4—1011no—
229C4×D4—2021no—
230C4×D4C2×D10111yescharacteristic
231#117—1011no—
232C2×C4⋊C4—1011no—
233C2×C22⋊C4—2021no—
234#107—1011no—
235#107—1011no—
236#106—1011no—
237C4⋊C8C2×D10111yescharacteristic, complemented
238#103—1011no—
239#103—1011no—
240#103—1011no—
241#102—1011no—
242#102—1011no—
243#102—1011no—
244#102—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248C22⋊C8C2×D10111yescharacteristic
249C22⋊C8C2×D10111yescharacteristic, complemented
250C4×C8C2×D10111yescharacteristic, complemented
251C24—2021no—
252#41—4041no—
253#41—2022no—
254C2×Q8—1011no—
255C2×D4—1011no—
256C2×D4—1011no—
257C2×D4—1011no—
258C2×D4—4041no—
259C2×D4—2022no—
260C2×D4—2021no—
261C2×D4—2021no—
262C2×D4—2021no—
263C2×D4—2021no—
264C2×D4—2021no—
265C2×D4D40411yescharacteristic
266C22×C4—2021no—
267C22×C4—2021no—
268C22×C4—2021no—
269C22×C4—2021no—
270C22×C4C22×D10111yescharacteristic
271C22×C4C22×D10111yescharacteristic
272SD16—4041no—
273D8—4041no—
274D8—2022no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D10111yescharacteristic
278C2×C8C22×D10111yescharacteristic
279C2×C8C22×D10111yescharacteristic
280C2×C8C22×D10111yescharacteristic
281C4⋊C4—1011no—
282C4⋊C4—1011no—
283C4⋊C4—1011no—
284C4⋊C4—1011no—
285C4⋊C4—2021no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4—2021no—
289C4⋊C4D40411yescharacteristic
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C22⋊C4—2021no—
294C22⋊C4—2021no—
295C22⋊C4—2021no—
296C22⋊C4—2021no—
297C22⋊C4—2021no—
298C22⋊C4—2021no—
299C22⋊C4D40411yescharacteristic
300C22⋊C4D40411yescharacteristic
301C42—2021no—
302C42C22×D10111yescharacteristic
303C23—8081no—
304C23—4042no—
305C23—4042no—
306C23—2021no—
307C23—2021no—
308C23—2021no—
309C23C2×D40411yescharacteristic
310C23C2×D40411yescharacteristic
311Q8—2021no—
312Q8—2021no—
313D4—22no—
314D4—8081no—
315D4—8081no—
316D4—1012no—
317D4—4042no—
318D4—4042no—
319D4—4042no—
320D4—2021no—
321D4—2021no—
322D4—2021no—
323D4—2021no—
324D4—2021no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8081no—
330C2×C4—8081no—
331C2×C4—8081no—
332C2×C4—4042no—
333C2×C4—2021no—
334C2×C4—2021no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4C2×D40411yescharacteristic
339C2×C4C2×D40411yescharacteristic
340C2×C4C2×D40411yescharacteristic
341C2×C4C2×D40411yescharacteristic
342C2×C4C23×D10111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—8084no—
353C22—4041no—
354C22—4041no—
355C22—4041no—
356C22—4041no—
357C22—4041no—
358C22—4041no—
359C22—4041no—
360C22—4041no—
361C22—2022no—
362C22#1569227712yes—
363C22C22×D40411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—4041no—
369C4—4041no—
370C4—4041no—
371C4—4041no—
372C4—4041no—
373C4#41×D10111yescharacteristic
374C4#1569230011yescharacteristic
375C2—22no—
376C2—41no—
377C2—8081no—
378C2—8081no—
379C2—4042no—
380C2#2026582211yescharacteristic
381C2C2×#1569227711yescharacteristic
382C2#2026598211yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC8×D4×C101C2
socleC22×C101C22×D4
hypercenterC8×D4D101
hypocenterC101#3297
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20265873C2semidirect
2. #20265823C2semidirect
3. #20265532C2semidirect
4. #20265513C2semidirect
5. #20265502C2semidirect
6. #20265478C2semidirect
7. #20265413C2semidirect
8. #20265406C2semidirect
9. #20265393C2semidirect
10. #20265324C2semidirect
11. #20265313C2semidirect
12. C4×D808C2semidirect
13. #20265174C2semidirect
14. C2×#15692177C2semidirect
15. C8×D4×C101C2semidirect
18. C2×#13108063C22semidirect
22. #15692247C22semidirect
29. #15692229C22semidirect
34. C4×D404C22semidirect
36. #15692214C22semidirect
39. #15692189C22semidirect
40. #15692189C22semidirect
41. #15692187C22semidirect
42. #15692180C22semidirect
43. #15692180C22semidirect
44. #15692180C22semidirect
51. #15692177C22semidirect
53. C22×C8×C101C22semidirect
55. C4⋊C8×C101C22semidirect
57. C22⋊C8×C101C22semidirect
58. C4×C8×C101C22semidirect
192. C101#3297semidirect
205. C8×D4D101semidirect
214. C22×C8C2×D101semidirect
237. C4⋊C8C2×D101semidirect
249. C22⋊C8C2×D101semidirect
250. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658732
#202658232
#202655322
#202655132
#202655022
#202654782
#202654132
#202654062
#202653932
#202653242
#202653132
C4×D8082
#202651742
C2×#156921772
C8×D4×C1012
#3297101