Finite Group Databasebeta

← #27181377

Subgroups — #27181377

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#20265783C211yesmaximal, characteristic, complemented
2#20265649C211yesmaximal, characteristic, complemented
3#20265504C211yesmaximal, characteristic, complemented
4#20265503C211yesmaximal, characteristic, complemented
5#20265474C211yesmaximal, characteristic, complemented
6#20265373C211yesmaximal, characteristic, complemented
7#20265372C211yesmaximal, characteristic, complemented
8#20265312C211yesmaximal, characteristic, complemented
9#20265312C211yesmaximal, characteristic, complemented
10#20265288C211yesmaximal, characteristic, complemented
11#20265286C211yesmaximal, characteristic, complemented
12#20265259C211yesmaximal, characteristic, complemented
13#20265257C211yesmaximal, characteristic, complemented
14#20265237C211yesmaximal, characteristic, complemented
15#478×C101C211yesmaximal, characteristic, complemented
16C2×D4×D101C2211yescharacteristic
17C2×D808C2211yescharacteristic
18C2×D808C2211yescharacteristic
19C2×#13108059C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21#15692252C2211yescharacteristic, complemented
22#15692240—21no—
23#15692240—21no—
24#15692230—21no—
25#15692230—21no—
26#15692230C2211yescharacteristic
27#15692230C2211yescharacteristic
28C4×D404C2211yescharacteristic
29D4×Dic101C2211yescharacteristic
30#15692217C2211yescharacteristic
31#15692217C2211yescharacteristic, complemented
32#15692217C2211yescharacteristic, complemented
33C4×C22⋊D101—21no—
34#15692215—21no—
35#15692213C2211yescharacteristic
36#15692212C2211yescharacteristic
37C2×#13108051—21no—
38C22⋊C4×D101—21no—
39#15692188C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41C4⋊#11717579C2211yescharacteristic, complemented
42#15692177C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic, complemented
44#15692175C2211yescharacteristic
45#15692175C2211yescharacteristic
46#15692175C2211yescharacteristic, complemented
47#15692175C2211yescharacteristic, complemented
48#15692167C2211yescharacteristic
49#15692167C2211yescharacteristic
50#15692165C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52#125×C101C2211yescharacteristic, complemented
53C4×D4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56C4⋊C8×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic
58#102×C101C2211yescharacteristic
59C23×D101—21no—
60C2×D404—21no—
61C2×D404—21no—
62C2×D404—21no—
63C2×D404—21no—
64C2×D404C2311yescharacteristic
65C2×D404C2311yescharacteristic
66C2×D404C2311yescharacteristic
67C2×C22⋊D101—21no—
68D4×D101—22no—
69D4×D101—22no—
70C22×Dic101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101—21no—
75C2×C4×D101C2311yescharacteristic
76D808—22no—
77D808—22no—
78#13108059—22no—
79#13108059—22no—
80C2×#11717579C2311yescharacteristic
81C2×#11717579C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83#13108053D411yescharacteristic
84#13108053D411yescharacteristic
85C22⋊Dic101—21no—
86#13108051—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051D411yescharacteristic
94#13108051D411yescharacteristic
95C4×Dic101—21no—
96C4×Dic101C2311yescharacteristic
97C2×D4×C101C2311yescharacteristic
98C22×C4×C101—21no—
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101—21no—
102C4⋊C4×C101—21no—
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C22⋊C4×C101—21no—
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C22×D101—21no—
110C22×D101—24no—
111C22×D101—21no—
112C22×D101—21no—
113C22×D101—81no—
114C22×D101—81no—
115C22×D101C2×D411yescharacteristic
116D4×C101—21no—
117D4×C101#4112yes—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—81no—
122C2×C4×C101C2×D411yescharacteristic
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2411yescharacteristic
125C22⋊D101—24no—
126C2×Dic101—21no—
127C2×Dic101—81no—
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131D404—21no—
132D404—21no—
133D404—21no—
134D404—21no—
135D404—21no—
136D404—81no—
137D404—81no—
138D404—81no—
139D404—81no—
140D404#4112yes—
141C4×D101—21no—
142C4×D101—21no—
143C4×D101—81no—
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×C101C22×D411yescharacteristic
155C2×D101—21no—
156C2×D101—22no—
157C2×D101—21no—
158C2×D101—21no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101—41no—
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×C101—41no—
173C4×C101C2×#4111yescharacteristic
174C4×C101C2×#4111yescharacteristic
175Dic101—21no—
176Dic101—21no—
177Dic101—21no—
178Dic101—41no—
179C2×C101—42no—
180C2×C101#52511yescharacteristic
181C2×C101#57611yescharacteristic
182C2×C101#57611yescharacteristic
183D101—41no—
184D101—42no—
185D101—81no—
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#478D10111yescharacteristic, complemented
195#459—1011no—
196#459—1011no—
197#447—1011no—
198#447—1011no—
199#442—1011no—
200#442—1011no—
201C4×D8—1011no—
202C4×D8—1011no—
203#433—1011no—
204C22×D4—1011no—
205C2×D8—1011no—
206C2×D8—1011no—
207C2×D8—1011no—
208C2×D8—1011no—
209#127—1011no—
210#125C2×D10111yescharacteristic, complemented
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—1011no—
222C4×D4—2021no—
223C4×D4—2021no—
224C4×D4C2×D10111yescharacteristic
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#106C2×D10111yescharacteristic, complemented
233C4⋊C8—1011no—
234C4⋊C8C2×D10111yescharacteristic, complemented
235#102—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102C2×D10111yescharacteristic
242#102C2×D10111yescharacteristic
243C22⋊C8—1011no—
244C22⋊C8—1011no—
245#97—1011no—
246C4×C8—1011no—
247C24—2021no—
248C2×D4—1011no—
249C2×D4—1011no—
250C2×D4—1011no—
251C2×D4—2021no—
252C2×D4—2021no—
253C2×D4—2021no—
254C2×D4—2022no—
255C2×D4—2022no—
256C2×D4—2021no—
257C2×D4—2021no—
258C2×D4C22×D10111yescharacteristic
259C22×C4—21no—
260C22×C4—1011no—
261C22×C4—2021no—
262C22×C4—2021no—
263C22×C4—2021no—
264C22×C4—2021no—
265C22×C4—2021no—
266D8—2022no—
267D8—2022no—
268D8—2022no—
269D8—2022no—
270C2×C8—1011no—
271C2×C8—1011no—
272C2×C8C22×D10111yescharacteristic
273C2×C8C22×D10111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1011no—
277C4⋊C4—1011no—
278C4⋊C4—1011no—
279C4⋊C4C22×D10111yescharacteristic
280C4⋊C4C22×D10111yescharacteristic
281C4⋊C4C22×D10111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—1011no—
284C22⋊C4—1011no—
285C22⋊C4—2021no—
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—8081no—
298C23—8081no—
299C23—1011no—
300C23—2024no—
301C23—2021no—
302C23—2021no—
303C23—2021no—
304D4—21no—
305D4—8081no—
306D4—8081no—
307D4—8081no—
308D4—8081no—
309D4—1012no—
310D4—2024no—
311D4—2021no—
312D4—2021no—
313D4—2021no—
314D4—2021no—
315D4—2021no—
316D4#1310807512yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—8081no—
322C2×C4—8081no—
323C2×C4—8081no—
324C2×C4—8081no—
325C2×C4—8081no—
326C2×C4—1011no—
327C2×C4—1011no—
328C2×C4—1011no—
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—8084no—
343C22—4041no—
344C22—4041no—
345C22—4041no—
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—41no—
361C4—4041no—
362C4—2021no—
363C4—2021no—
364C4—2021no—
365C4#41×D10111yescharacteristic
366C4C2×#1310807511yescharacteristic
367C2—42no—
368C2—8081no—
369C2—8081no—
370C2—4041no—
371C2—4042no—
372C2#2026569011yescharacteristic
373C2#2026597911yescharacteristic
374C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#478×C101C2
socleC22×C101C22×D4
hypercenter#478D101
hypocenterC101#3122
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20265783C2semidirect
2. #20265649C2semidirect
3. #20265504C2semidirect
4. #20265503C2semidirect
5. #20265474C2semidirect
6. #20265373C2semidirect
7. #20265372C2semidirect
8. #20265312C2semidirect
9. #20265312C2semidirect
10. #20265288C2semidirect
11. #20265286C2semidirect
12. #20265259C2semidirect
13. #20265257C2semidirect
14. #20265237C2semidirect
15. #478×C101C2semidirect
21. #15692252C22semidirect
31. #15692217C22semidirect
32. #15692217C22semidirect
39. #15692188C22semidirect
40. #15692186C22semidirect
41. C4⋊#11717579C22semidirect
42. #15692177C22semidirect
43. #15692177C22semidirect
46. #15692175C22semidirect
47. #15692175C22semidirect
50. #15692165C22semidirect
51. C8×Dic101C22semidirect
52. #125×C101C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
56. C4⋊C8×C101C22semidirect
188. C101#3122semidirect
194. #478D101semidirect
210. #125C2×D101semidirect
230. #107C2×D101semidirect
232. #106C2×D101semidirect
234. C4⋊C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657832
#202656492
#202655042
#202655032
#202654742
#202653732
#202653722
#202653122
#202652882
#202652862
#202652592
#202652572
#202652372
#478×C1012
#3122101