Finite Group Databasebeta

← #27181372

Subgroups — #27181372

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#20265778C211yesmaximal, characteristic, complemented
2#20265649C211yesmaximal, characteristic, complemented
3#20265504C211yesmaximal, characteristic, complemented
4#20265499C211yesmaximal, characteristic, complemented
5#20265480C211yesmaximal, characteristic, complemented
6#20265475C211yesmaximal, characteristic, complemented
7#20265371C211yesmaximal, characteristic, complemented
8#20265370C211yesmaximal, characteristic, complemented
9#20265312C211yesmaximal, characteristic, complemented
10#20265309C211yesmaximal, characteristic, complemented
11#20265287C211yesmaximal, characteristic, complemented
12#20265287C211yesmaximal, characteristic, complemented
13C4×D808C211yesmaximal, characteristic, complemented
14#20265236C211yesmaximal, characteristic, complemented
15C4×D8×C101C211yesmaximal, characteristic, complemented
16C2×D4×D101C2211yescharacteristic
17C2×D808C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19C2×#13108059C2211yescharacteristic
20#15692251C2211yescharacteristic, complemented
21#15692246C2211yescharacteristic, complemented
22#15692238—21no—
23#15692237—21no—
24#15692230C2211yescharacteristic
25#15692229—21no—
26#15692228—21no—
27#15692226C2211yescharacteristic
28C4×D404C2211yescharacteristic
29C4×D404C2211yescharacteristic, complemented
30D4×Dic101C2211yescharacteristic
31#15692217C2211yescharacteristic
32C4×C22⋊D101—21no—
33#15692215—21no—
34#15692213C2211yescharacteristic
35#15692212C2211yescharacteristic
36C2×#13108051—21no—
37C22⋊C4×D101—21no—
38#15692189C2211yescharacteristic, complemented
39#15692186C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692184C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic
44#15692177C2211yescharacteristic, complemented
45#15692176C2211yescharacteristic
46#15692176C2211yescharacteristic, complemented
47#15692175C2211yescharacteristic
48#15692175C2211yescharacteristic, complemented
49#15692167C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692166C2211yescharacteristic, complemented
52C2×D8×C101C2211yescharacteristic
53C4×D4×C101C2211yescharacteristic
54C4×D4×C101C2211yescharacteristic, complemented
55#107×C101C2211yescharacteristic, complemented
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic, complemented
58C4×C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60C2×D404—21no—
61C2×D404C2311yescharacteristic
62C2×D404C2311yescharacteristic
63C2×C22⋊D101—21no—
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67D4×D101—22no—
68D4×D101—22no—
69C22×Dic101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101C2311yescharacteristic
74D808—22no—
75#13108059—22no—
76#13108059—22no—
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C4⋊Dic101—21no—
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82#13108053—21no—
83#13108053D411yescharacteristic
84#13108053D411yescharacteristic
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051D411yescharacteristic
93#13108051D411yescharacteristic
94C4×Dic101—21no—
95C4×Dic101C2311yescharacteristic
96C2×D4×C101C2311yescharacteristic
97C2×D4×C101C2311yescharacteristic
98C22×C4×C101—21no—
99C22×C4×C101—21no—
100D8×C101—22no—
101C2×C8×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C23×C101—21no—
110C22×D101—21no—
111C22×D101—24no—
112C22×D101—21no—
113C22×D101—81no—
114C22×D101—81no—
115C22×D101C2×D411yescharacteristic
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—21no—
119D4×C101#4112yes—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—81no—
123C2×C4×C101—81no—
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2411yescharacteristic
127C22⋊D101—24no—
128C22⋊D101—81no—
129C22⋊D101—81no—
130C22⋊D101—81no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—81no—
134C2×Dic101C2×D411yescharacteristic
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137D404—21no—
138D404—21no—
139D404—21no—
140D404—81no—
141D404#4112yes—
142C4×D101—21no—
143C4×D101—21no—
144C4×D101—81no—
145C4×D101—81no—
146C4×D101—81no—
147C8×C101—21no—
148C8×C101—21no—
149#11717579—21no—
150#11717579—21no—
151C22×C101—22no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101C22×D411yescharacteristic
158C2×D101—21no—
159C2×D101—22no—
160C2×D101—21no—
161C2×D101—21no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—84no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101C2×#4111yescharacteristic
173C4×C101C2×#4111yescharacteristic
174Dic101—21no—
175Dic101—21no—
176Dic101—21no—
177Dic101—41no—
178Dic101—41no—
179C2×C101—42no—
180C2×C101—81no—
181C2×C101#52511yescharacteristic
182C2×C101#57611yescharacteristic
183C2×C101#57611yescharacteristic
184D101—41no—
185D101—42no—
186D101—81no—
187#3122—1011nomaximal, Sylow
188C101#312211yescharacteristic, complemented, Sylow
189#540—1011no—
190#518—1011no—
191#482—1011no—
192#482—1011no—
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×D8D10111yescharacteristic, complemented
203#433—1011no—
204C22×D4—1011no—
205C2×D8—1011no—
206C2×D8—1011no—
207C2×D8—1011no—
208C2×D8C2×D10111yescharacteristic
209#127—1011no—
210#125—1011no—
211#123—2021no—
212#123—2021no—
213#121—1011no—
214#121—1011no—
215#121—2021no—
216#121—2021no—
217C4×D4—1011no—
218C4×D4—1011no—
219C4×D4—1011no—
220C4×D4—1011no—
221C4×D4—2021no—
222C4×D4—2021no—
223C4×D4C2×D10111yescharacteristic
224C4×D4C2×D10111yescharacteristic, complemented
225#117—1011no—
226#117—1011no—
227C2×C22⋊C4—2021no—
228C2×C22⋊C4—2021no—
229#107—1011no—
230#107C2×D10111yescharacteristic, complemented
231#106—1011no—
232#106—1011no—
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
242#102C2×D10111yescharacteristic, complemented
243C22⋊C8—1011no—
244C22⋊C8—1011no—
245#97—1011no—
246C4×C8C2×D10111yescharacteristic, complemented
247C24—2021no—
248C2×D4—1011no—
249C2×D4—1011no—
250C2×D4—2021no—
251C2×D4—2021no—
252C2×D4—2021no—
253C2×D4—2021no—
254C2×D4—2022no—
255C2×D4—2021no—
256C2×D4—2022no—
257C2×D4C22×D10111yescharacteristic
258C2×D4C22×D10111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1011no—
262C22×C4—2021no—
263C22×C4—2021no—
264C22×C4—2021no—
265C22×C4—2021no—
266D8—22no—
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—1011no—
278C4⋊C4—2021no—
279C4⋊C4—2021no—
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—1011no—
294C42—2021no—
295C42C22×D10111yescharacteristic
296C23—21no—
297C23—21no—
298C23—8081no—
299C23—8081no—
300C23—1011no—
301C23—2024no—
302C23—2021no—
303C23—2021no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—8081no—
308D4—8081no—
309D4—8081no—
310D4—8081no—
311D4—1012no—
312D4—2024no—
313D4—2021no—
314D4—2021no—
315D4—2021no—
316D4#1310807412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—8081no—
322C2×C4—8081no—
323C2×C4—8081no—
324C2×C4—8081no—
325C2×C4—1011no—
326C2×C4—1011no—
327C2×C4—1011no—
328C2×C4—2021no—
329C2×C4—2021no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4D4×D10111yescharacteristic
333C2×C4D4×D10111yescharacteristic
334C2×C4C23×D10111yescharacteristic
335C8—21no—
336C8—21no—
337C8—2021no—
338C8—2021no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—8084no—
346C22—4041no—
347C22—4041no—
348C22—4041no—
349C22—4041no—
350C22—4041no—
351C22—2021no—
352C22—2022no—
353C22—2021no—
354C22—2021no—
355C22C2×D4×D10111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—4041no—
361C4—4041no—
362C4—2021no—
363C4—2021no—
364C4—2021no—
365C4#41×D10111yescharacteristic
366C4C2×#1310807411yescharacteristic
367C2—42no—
368C2—81no—
369C2—8081no—
370C2—4041no—
371C2—4042no—
372C2#2026568611yescharacteristic
373C2#2026597811yescharacteristic
374C2#2026597911yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC4×D8×C101C2
socleC22×C101C22×D4
hypercenterC4×D8D101
hypocenterC101#3122
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20265778C2semidirect
2. #20265649C2semidirect
3. #20265504C2semidirect
4. #20265499C2semidirect
5. #20265480C2semidirect
6. #20265475C2semidirect
7. #20265371C2semidirect
8. #20265370C2semidirect
9. #20265312C2semidirect
10. #20265309C2semidirect
11. #20265287C2semidirect
12. #20265287C2semidirect
13. C4×D808C2semidirect
14. #20265236C2semidirect
15. C4×D8×C101C2semidirect
20. #15692251C22semidirect
21. #15692246C22semidirect
29. C4×D404C22semidirect
38. #15692189C22semidirect
39. #15692186C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692184C22semidirect
44. #15692177C22semidirect
46. #15692176C22semidirect
48. #15692175C22semidirect
51. #15692166C22semidirect
54. C4×D4×C101C22semidirect
55. #107×C101C22semidirect
57. #102×C101C22semidirect
58. C4×C8×C101C22semidirect
188. C101#3122semidirect
202. C4×D8D101semidirect
224. C4×D4C2×D101semidirect
230. #107C2×D101semidirect
242. #102C2×D101semidirect
246. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657782
#202656492
#202655042
#202654992
#202654802
#202654752
#202653712
#202653702
#202653122
#202653092
#202652872
C4×D8082
#202652362
C4×D8×C1012
#3122101