Finite Group Databasebeta

← #27183738

Subgroups — #27183738

Order 12928.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265875C211yesmaximal, characteristic, complemented
2#20265874C211yesmaximal, characteristic, complemented
3#20265578C211yesmaximal, characteristic, complemented
4#20265502C211yesmaximal, characteristic, complemented
5#20265499C211yesmaximal, characteristic, complemented
6#20265492C211yesmaximal, characteristic, complemented
7#20265480C211yesmaximal, characteristic, complemented
8#20265479C211yesmaximal, characteristic, complemented
9#20265429C211yesmaximal, characteristic, complemented
10#20265428C211yesmaximal, characteristic, complemented
11#20265257C211yesmaximal, characteristic, complemented
12#20265252C211yesmaximal, characteristic, complemented
13#20265218C211yesmaximal, characteristic, complemented
14#20265217C211yesmaximal, characteristic, complemented
15#480×C101C211yesmaximal, characteristic, complemented
16C2×#13108059C2211yescharacteristic
17C2×#13108058C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19#15692250—21no—
20#15692248—21no—
21#15692246C2211yescharacteristic
22#15692246C2211yescharacteristic
23#15692240—21no—
24#15692236—21no—
25#15692230C2211yescharacteristic
26#15692229—21no—
27#15692229C2211yescharacteristic
28#15692226—21no—
29#15692226C2211yescharacteristic
30D4×Dic101C2211yescharacteristic
31#15692217C2211yescharacteristic
32C4×C22⋊D101—21no—
33C4×C22⋊D101C2211yescharacteristic
34#15692215—21no—
35#15692214C2211yescharacteristic
36#15692213C2211yescharacteristic
37C4⋊C4×D101C2211yescharacteristic
38#15692189C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692188C2211yescharacteristic
41#15692187C2211yescharacteristic
42#15692186C2211yescharacteristic
43#15692186C2211yescharacteristic
44#15692186C2211yescharacteristic
45#15692184C2211yescharacteristic
46#15692177C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692176C2211yescharacteristic
49#15692175C2211yescharacteristic
50#15692167C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52#121×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#107×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59C2×D404—21no—
60C2×D404C2311yescharacteristic
61C2×C22⋊D101—21no—
62C2×C22⋊D101—21no—
63C2×C22⋊D101D411yescharacteristic
64C22×Dic101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101C2311yescharacteristic
68#13108059—22no—
69#13108058—22no—
70#13108057—22no—
71C2×#11717579C2311yescharacteristic
72C2×#11717579C2311yescharacteristic
73C4⋊Dic101—21no—
74C4⋊Dic101—21no—
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77C4⋊Dic101C2311yescharacteristic
78#13108053—21no—
79#13108053—21no—
80#13108053—21no—
81#13108053D411yescharacteristic
82C22⋊Dic101—21no—
83C22⋊Dic101—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101D411yescharacteristic
86#13108051—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051D411yescharacteristic
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101C2311yescharacteristic
94C2×D4×C101—21no—
95C2×D4×C101C2311yescharacteristic
96C22×C4×C101—21no—
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C4⋊C4×C101—21no—
101C4⋊C4×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C22⋊C4×C101—21no—
105C23×C101—21no—
106C23×C101C2×D411yescharacteristic
107C22×D101—21no—
108C22×D101C2×D411yescharacteristic
109D4×C101—21no—
110D4×C101—21no—
111D4×C101—81no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—81no—
118C2×C4×C101C2×D411yescharacteristic
119C2×C4×C101C2411yescharacteristic
120C22⋊D101—41no—
121C22⋊D101—42no—
122C22⋊D101—42no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—81no—
127C2×Dic101C2×D411yescharacteristic
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130D404—21no—
131D404—21no—
132D404—81no—
133C4×D101—21no—
134C4×D101—21no—
135C4×D101—81no—
136C4×D101—81no—
137C8×C101—21no—
138C8×C101—21no—
139#11717579—21no—
140#11717579#4112yes—
141C22×C101—21no—
142C22×C101—21no—
143C22×C101—21no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101C22×D411yescharacteristic
148C2×D101—21no—
149C2×D101—21no—
150C2×D101—21no—
151C2×D101—41no—
152C2×D101—41no—
153C2×D101—41no—
154C4×C101—21no—
155C4×C101—41no—
156C4×C101—41no—
157C4×C101—41no—
158C4×C101C2×#4111yescharacteristic
159C4×C1012−1+411yescharacteristic
160Dic101—21no—
161Dic101—21no—
162Dic101—21no—
163Dic101—41no—
164Dic101—41no—
165Dic101—41no—
166C2×C101—41no—
167C2×C101—81no—
168C2×C101#54711yescharacteristic
169C2×C101#57511yescharacteristic
170C2×C101#57611yescharacteristic
171D101—41no—
172D101—81no—
173#3355—1011nomaximal, Sylow
174C101#335511yescharacteristic, complemented, Sylow
175#553—1011no—
176#553—1011no—
177#499—1011no—
178#482—1011no—
179#482—1011no—
180#480—1011no—
181#480D10111yescharacteristic, complemented
182#478—1011no—
183#478—1011no—
184#469—1011no—
185#469—1011no—
186C4×D8—1011no—
187#436—1011no—
188#428—1011no—
189#428—1011no—
190C2×D8—1011no—
191C2×M16—1011no—
192C2×M16—1011no—
193#126—2021no—
194#126—2021no—
195#125—1011no—
196#125—1011no—
197#123—2021no—
198#123—2021no—
199#121—1011no—
200#121—1011no—
201#121—1011no—
202#121—2021no—
203#121—2021no—
204#121C2×D10111yescharacteristic
205C4×D4—1011no—
206C4×D4—1011no—
207C4×D4—1011no—
208C4×D4—2021no—
209C4×D4—2021no—
210#117—1011no—
211#117—1011no—
212C2×C4⋊C4—1011no—
213C2×C4⋊C4C2×D10111yescharacteristic
214#107—1011no—
215#107—1011no—
216#107—1011no—
217#107C2×D10111yescharacteristic
218#107C2×D10111yescharacteristic
219#106—1011no—
220#106—1011no—
221#106—1011no—
222#106—1011no—
223C4⋊C8—1011no—
224#102—1011no—
225#102—1011no—
226#102—1011no—
227#102—1011no—
228#102C2×D10111yescharacteristic
229#102C2×D10111yescharacteristic
230C22⋊C8—1011no—
231C22⋊C8C2×D10111yescharacteristic
232C4×C8—1011no—
233C2×D4—21no—
234C2×D4—1011no—
235C2×D4—1011no—
236C2×D4—2021no—
237C2×D4—2021no—
238C2×D4—2021no—
239C2×D4C22×D10111yescharacteristic
240C22×C4—21no—
241C22×C4—1011no—
242C22×C4—2021no—
243C22×C4—2021no—
244C22×C4—2021no—
245C22×C4C22×D10111yescharacteristic
246D8—2022no—
247M16—2022no—
248M16—2022no—
249C2×C8—1011no—
250C2×C8—1011no—
251C2×C8C22×D10111yescharacteristic
252C2×C8C22×D10111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—1011no—
255C4⋊C4—1011no—
256C4⋊C4—1011no—
257C4⋊C4—1011no—
258C4⋊C4—2021no—
259C4⋊C4—2021no—
260C4⋊C4—2021no—
261C4⋊C4—2021no—
262C4⋊C4—2021no—
263C4⋊C4C22×D10111yescharacteristic
264C4⋊C4C22×D10111yescharacteristic
265C4⋊C4C22×D10111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—1011no—
268C22⋊C4—1011no—
269C22⋊C4—2021no—
270C22⋊C4—2021no—
271C22⋊C4—2021no—
272C22⋊C4—2021no—
273C22⋊C4—2021no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C42—1011no—
277C42—2021no—
278C42—2021no—
279C23—21no—
280C23—1011no—
281C23—2021no—
282C23D4×D10111yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—8081no—
287D4—4042no—
288D4—4042no—
289D4—4041no—
290D4—2021no—
291D4—2021no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—8081no—
299C2×C4—8081no—
300C2×C4—8081no—
301C2×C4—1011no—
302C2×C4—1011no—
303C2×C4—1011no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4D4×D10111yescharacteristic
310C2×C4C23×D10111yescharacteristic
311C8—21no—
312C8—21no—
313C8—1012no—
314C8—2021no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4041no—
322C22—4041no—
323C22—4041no—
324C22—2021no—
325C22—2021no—
326C22—2021no—
327C22C2×D4×D10111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—4041no—
333C4—4041no—
334C4—4041no—
335C4—2021no—
336C4—2021no—
337C4—2021no—
338C4#41×D10111yescharacteristic
339C4#1569230211yescharacteristic
340C2—41no—
341C2—81no—
342C2—8081no—
343C2—4041no—
344C2#2026582511yescharacteristic
345C2#2026597611yescharacteristic
346C2#2026597811yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#480×C101C2
socleC22×C101C22×D4
hypercenter#480D101
hypocenterC101#3355
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #20265875C2semidirect
2. #20265874C2semidirect
3. #20265578C2semidirect
4. #20265502C2semidirect
5. #20265499C2semidirect
6. #20265492C2semidirect
7. #20265480C2semidirect
8. #20265479C2semidirect
9. #20265429C2semidirect
10. #20265428C2semidirect
11. #20265257C2semidirect
12. #20265252C2semidirect
13. #20265218C2semidirect
14. #20265217C2semidirect
15. #480×C101C2semidirect
174. C101#3355semidirect
181. #480D101semidirect

Maximal subgroups

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

subgroupindex
#202658752
#202658742
#202655782
#202655022
#202654992
#202654922
#202654802
#202654792
#202654292
#202654282
#202652572
#202652522
#202652182
#202652172
#480×C1012
#3355101