Finite Group Databasebeta

← #27181389

Subgroups — #27181389

Order 12928.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265794C211yesmaximal, characteristic, complemented
2#20265658C211yesmaximal, characteristic, complemented
3#20265512C211yesmaximal, characteristic, complemented
4#20265471C211yesmaximal, characteristic, complemented
5#20265456C211yesmaximal, characteristic, complemented
6#20265398C211yesmaximal, characteristic, complemented
7#20265391C211yesmaximal, characteristic, complemented
8#20265341C211yesmaximal, characteristic, complemented
9#20265320C211yesmaximal, characteristic
10#20265276C211yesmaximal, characteristic, complemented
11#20265274C211yesmaximal, characteristic, complemented
12#20265271C211yesmaximal, characteristic, complemented
13#20265257C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#480×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×Dic404C2211yescharacteristic
18C2×#13108063C2211yescharacteristic
19C2×#13108062C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21#15692254C2211yescharacteristic
22#15692248—21no—
23#15692242—21no—
24#15692242C2211yescharacteristic
25#15692236—21no—
26#15692234C2211yescharacteristic
27#15692232—21no—
28#15692220C2211yescharacteristic
29#15692220C2211yescharacteristic
30#15692220C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32#15692217C2211yescharacteristic
33#15692217C2211yescharacteristic
34C4×C22⋊D101—21no—
35C4×C22⋊D101—21no—
36#15692214C2211yescharacteristic
37#15692213—21no—
38C4⋊C4×D101—21no—
39#15692188C2211yescharacteristic
40#15692188C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692178C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692175C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52#121×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#107×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202—21no—
62C2×Dic202C2311yescharacteristic
63C2×Dic202C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×C22⋊D101—21no—
66C22×Dic101—21no—
67C2×C4×D101—21no—
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70Dic404—22no—
71#13108063—22no—
72#13108062—22no—
73#13108059—22no—
74C2×#11717579C2311yescharacteristic
75C2×#11717579C2311yescharacteristic
76C4⋊Dic101D411yescharacteristic
77C4⋊Dic101D411yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101—21no—
88C22⋊Dic101D411yescharacteristic
89C22⋊Dic101D411yescharacteristic
90#13108051—21no—
91#13108051—21no—
92C4×Dic101—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101—21no—
100C22×C4×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—21no—
111D4×C101—21no—
112D4×C101—21no—
113D4×C101—81no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—81no—
120C2×C4×C101C2×D411yescharacteristic
121C2×C4×C101C2411yescharacteristic
122C22⋊D101—24no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—81no—
127C2×Dic101C2×D411yescharacteristic
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131D404—21no—
132D404#4112yes—
133C4×D101—24no—
134C4×D101—81no—
135C4×D101—81no—
136Dic202—21no—
137Dic202—21no—
138Dic202—21no—
139Dic202—81no—
140Dic202#4112yes—
141C8×C101—21no—
142C8×C101—21no—
143#11717579—21no—
144#11717579—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101C22×D411yescharacteristic
152C2×D101—22no—
153C2×D101—41no—
154C2×D101—41no—
155C4×C101—21no—
156C4×C101—41no—
157C4×C101—41no—
158C4×C101—41no—
159C4×C101C2×#4111yescharacteristic
160C4×C101C2×#4111yescharacteristic
161Dic101—22no—
162Dic101—21no—
163Dic101—21no—
164Dic101—21no—
165Dic101—21no—
166Dic101—41no—
167Dic101—41no—
168C2×C101—41no—
169C2×C101—81no—
170C2×C101#52511yescharacteristic
171C2×C101#57611yescharacteristic
172C2×C101#57811yescharacteristic
173D101—42no—
174#3124—1011nomaximal, Sylow
175C101#312411yescharacteristic, complemented, Sylow
176#542—1011no—
177#520—1011no—
178#484—1011no—
179#480D10111yescharacteristic, complemented
180#477—1011no—
181#474—1011no—
182#464—1011no—
183#463—1011no—
184#452—1011no—
185#449—1011no—
186#440—1011no—
187#440—1011no—
188C4×Q16—1011no—
189C4×D8—1011no—
190#433—1011no—
191C2×#41—1011no—
192C2×Q16—1011no—
193C2×SD16—1011no—
194C2×SD16—1011no—
195C2×D8—1011no—
196C4⋊Q8—1011no—
197#126—2021no—
198#124—1011no—
199#124—2021no—
200#123—2021no—
201C22⋊Q8—1011no—
202C22⋊Q8—2021no—
203#121C2×D10111yescharacteristic
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8—1011no—
207C4×D4—1011no—
208C4×D4—1011no—
209C4×D4—1011no—
210C4×D4—2021no—
211C4×D4—2021no—
212#117—1011no—
213#117—2021no—
214C2×C4⋊C4—2021no—
215C2×C4⋊C4C2×D10111yescharacteristic
216#107—1011no—
217#107—1011no—
218#107C2×D10111yescharacteristic
219#107C2×D10111yescharacteristic
220C4⋊C8—1011no—
221C4⋊C8—1011no—
222#103—1011no—
223#103—1011no—
224#103—1011no—
225#103—1011no—
226#102—1011no—
227#102—1011no—
228#102C2×D10111yescharacteristic
229#102C2×D10111yescharacteristic
230C22⋊C8—1011no—
231C22⋊C8C2×D10111yescharacteristic
232#97—1011no—
233C4×C8—1011no—
234#41—2022no—
235#41—2022no—
236C2×Q8—1011no—
237C2×Q8—1011no—
238C2×Q8—2021no—
239C2×D4—21no—
240C2×D4—1011no—
241C2×D4—2021no—
242C2×D4C22×D10111yescharacteristic
243C22×C4—21no—
244C22×C4—2021no—
245C22×C4—2021no—
246C22×C4—2021no—
247C22×C4—2021no—
248C22×C4C22×D10111yescharacteristic
249Q16—2022no—
250SD16—2022no—
251SD16—2022no—
252D8—2022no—
253C2×C8—1011no—
254C2×C8—1011no—
255C2×C8C22×D10111yescharacteristic
256C2×C8C22×D10111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—1011no—
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—2021no—
262C4⋊C4—2021no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4C22×D10111yescharacteristic
267C4⋊C4C22×D10111yescharacteristic
268C4⋊C4C22×D10111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4—2021no—
273C22⋊C4—2021no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C42—1011no—
279C42—1011no—
280C42—2021no—
281C42—2021no—
282C42—2021no—
283C23—21no—
284C23—2021no—
285C23D4×D10111yescharacteristic
286Q8—8081no—
287Q8—1012no—
288Q8—2021no—
289Q8—2021no—
290Q8—2021no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—1012no—
295D4—2024no—
296D4—2021no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—8081no—
304C2×C4—8081no—
305C2×C4—8081no—
306C2×C4—1011no—
307C2×C4—1011no—
308C2×C4—1011no—
309C2×C4—1011no—
310C2×C4—2024no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4D4×D10111yescharacteristic
315C2×C4C23×D10111yescharacteristic
316C8—21no—
317C8—21no—
318C8—2021no—
319C8—2021no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—4041no—
327C22—4041no—
328C22—2022no—
329C22C2×D4×D10111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—4041no—
335C4—4041no—
336C4—2021no—
337C4—2021no—
338C4—2022no—
339C4—2021no—
340C4—2021no—
341C4#41×D10111yescharacteristic
342C4#41×D10111yescharacteristic
343C2—41no—
344C2—81no—
345C2—4042no—
346C2#2026568511yescharacteristic
347C2#2026597811yescharacteristic
348C2#2026599311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#480×C101C2
socleC22×C101C22×D4
prime radical#20265320C2
hypercenter#480D101
hypocenterC101#3124
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. #20265794C2semidirect
2. #20265658C2semidirect
3. #20265512C2semidirect
4. #20265471C2semidirect
5. #20265456C2semidirect
6. #20265398C2semidirect
7. #20265391C2semidirect
8. #20265341C2semidirect
10. #20265276C2semidirect
11. #20265274C2semidirect
12. #20265271C2semidirect
13. #20265257C2semidirect
14. #20265235C2semidirect
15. #480×C101C2semidirect
175. C101#3124semidirect
179. #480D101semidirect

Maximal subgroups

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

subgroupindex
#202657942
#202656582
#202655122
#202654712
#202654562
#202653982
#202653912
#202653412
#202653202
#202652762
#202652742
#202652712
#202652572
#202652352
#480×C1012
#3124101