Finite Group Databasebeta

← #27183725

Subgroups — #27183725

Order 12928.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265890C211yesmaximal, characteristic, complemented
2#20265827C211yesmaximal, characteristic, complemented
3#20265574C211yesmaximal, characteristic, complemented
4#20265500C211yesmaximal, characteristic, complemented
5#20265497C211yesmaximal, characteristic, complemented
6#20265496C211yesmaximal, characteristic, complemented
7#20265465C211yesmaximal, characteristic, complemented
8#20265456C211yesmaximal, characteristic, complemented
9#20265429C211yesmaximal, characteristic, complemented
10#20265428C211yesmaximal, characteristic, complemented
11#20265257C211yesmaximal, characteristic, complemented
12#20265252C211yesmaximal, characteristic, complemented
13#20265220C211yesmaximal, characteristic, complemented
14#20265218C211yesmaximal, characteristic, complemented
15#482×C101C211yesmaximal, characteristic, complemented
16C2×#13108073—21no—
17C2×#13108059C2211yescharacteristic
18C2×#13108058C2211yescharacteristic
19C2×#13108057C2211yescharacteristic
20#15692254C2211yescharacteristic
21#15692254C2211yescharacteristic
22#15692243—21no—
23#15692241—21no—
24#15692237—21no—
25#15692236—21no—
26#15692232—21no—
27#15692230C2211yescharacteristic
28#15692229C2211yescharacteristic
29#15692228—21no—
30#15692226C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32#15692217C2211yescharacteristic
33C4×C22⋊D101C2211yescharacteristic
34#15692213C2211yescharacteristic
35#15692212—21no—
36C2×C4⋊Dic101C2211yescharacteristic
37C4⋊C4×D101C2211yescharacteristic
38#15692188C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692187C2211yescharacteristic
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
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108073—44no—
60C2×Dic202—21no—
61C2×Dic202—21no—
62C2×D404—21no—
63C2×D404C2311yescharacteristic
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101D411yescharacteristic
67C22×Dic101—21no—
68C22×Dic101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101C2311yescharacteristic
72#13108059—22no—
73#13108058—22no—
74#13108057—22no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C4⋊Dic101—21no—
78C4⋊Dic101C2311yescharacteristic
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053D411yescharacteristic
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101D411yescharacteristic
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051D411yescharacteristic
93C4×Dic101—21no—
94C4×Dic101C2311yescharacteristic
95C2×D4×C101—21no—
96C2×D4×C101C2311yescharacteristic
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C4⋊C4×C101C2311yescharacteristic
101C4⋊C4×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C22⋊C4×C101—21no—
104C22⋊C4×C101—21no—
105C42×C101—21no—
106C23×C101—21no—
107C23×C101C2×D411yescharacteristic
108C22×D101—21no—
109C22×D101C2×D411yescharacteristic
110D4×C101—21no—
111D4×C101—21no—
112D4×C101—42no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101C2×D411yescharacteristic
119C2×C4×C101C2411yescharacteristic
120C22⋊D101—22no—
121C22⋊D101—42no—
122C22⋊D101—81no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—42no—
127C2×Dic101—42no—
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131D404—21no—
132D404—21no—
133D404—81no—
134C4×D101—21no—
135C4×D101—21no—
136C4×D101—42no—
137C4×D101—42no—
138Dic202—42no—
139Dic202—81no—
140C8×C101—21no—
141C8×C101—21no—
142#11717579—21no—
143#11717579#4112yescomplemented
144C22×C101—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—41no—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101C22×D411yescharacteristic
151C2×D101—21no—
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—41no—
155C2×D101—41no—
156C2×D101—41no—
157C4×C101—21no—
158C4×C101—41no—
159C4×C101—41no—
160C4×C101—41no—
161C4×C101C2×#4111yescharacteristic
162C4×C1012−1+411yescharacteristic
163Dic101—21no—
164Dic101—21no—
165Dic101—41no—
166Dic101—41no—
167Dic101—41no—
168Dic101AGL(1,ℤ/8)12yes—
169C2×C101—41no—
170C2×C101—81no—
171C2×C101#54711yescharacteristic
172C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C101#57711yescharacteristic
174D101—41no—
175D101—81no—
176#3354—1011nomaximal, Sylow
177C101#335411yescharacteristic, complemented, Sylow
178#555—1011no—
179#547—1011no—
180#498—1011no—
181#482—1011no—
182#482D10111yescharacteristic, complemented
183#481—1011no—
184#481—1011no—
185#476—1011no—
186#474—1011no—
187#469—1011no—
188#469—1011no—
189C4×D8—1011no—
190#436—1011no—
191#428—1011no—
192#428—1011no—
193C2×#41—2021no—
194C2×D8—1011no—
195C2×M16—1011no—
196C2×M16—1011no—
197C4⋊Q8—1011no—
198C4⋊Q8—1011no—
199#124—2021no—
200#124—2021no—
201#123—2021no—
202#123—2021no—
203C22⋊Q8—2021no—
204#121—1011no—
205#121—1011no—
206#121—1011no—
207#121—2021no—
208#121C2×D10111yescharacteristic
209C4×D4—1011no—
210C4×D4—1011no—
211C4×D4—1011no—
212#117—1011no—
213#117—2021no—
214#117C2×D10111yescharacteristic
215C2×C4⋊C4—1011no—
216C2×C4⋊C4—1011no—
217#107—1011no—
218#107—1011no—
219#107C2×D10111yescharacteristic
220#106—1011no—
221#106—1011no—
222#106—1011no—
223#106—1011no—
224#106—1011no—
225#106C2×D10111yescharacteristic
226C4⋊C8—1011no—
227#102—1011no—
228#102—1011no—
229#102—1011no—
230#102—1011no—
231#102C2×D10111yescharacteristic
232#102C2×D10111yescharacteristic
233C22⋊C8—1011no—
234C22⋊C8C2×D10111yescharacteristic
235C4×C8—1011no—
236#41—4044no—
237C2×Q8—2021no—
238C2×Q8—2021no—
239C2×D4—21no—
240C2×D4—1011no—
241C2×D4—1011no—
242C2×D4—2021no—
243C2×D4—2021no—
244C2×D4—2021no—
245C2×D4C22×D10111yescharacteristic
246C22×C4—1011no—
247C22×C4—2021no—
248C22×C4—2021no—
249C22×C4—2021no—
250C22×C4—2021no—
251C22×C4C22×D10111yescharacteristic
252D8—2022no—
253M16—2022no—
254M16—2022no—
255C2×C8—1011no—
256C2×C8—1011no—
257C2×C8C22×D10111yescharacteristic
258C2×C8C22×D10111yescharacteristic
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4—1011no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4—2021no—
267C4⋊C4C22×D10111yescharacteristic
268C4⋊C4C22×D10111yescharacteristic
269C4⋊C4C22×D10111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1011no—
273C22⋊C4—1011no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C42—21no—
281C42—1011no—
282C42—2021no—
283C23—21no—
284C23—1011no—
285C23—2021no—
286C23D4×D10111yescharacteristic
287Q8—8081no—
288Q8—4042no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—8081no—
293D4—8081no—
294D4—4042no—
295D4—2022no—
296D4—2021no—
297D4—2021no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—1011no—
304C2×C4—1011no—
305C2×C4—1011no—
306C2×C4—4042no—
307C2×C4—4042no—
308C2×C4—4042no—
309C2×C4—4042no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4—2021no—
315C2×C4D4×D10111yescharacteristic
316C2×C4C23×D10111yescharacteristic
317C8—21no—
318C8—21no—
319C8—1012no—
320C8—2021no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—4041no—
328C22—4041no—
329C22—4041no—
330C22—2021no—
331C22—2021no—
332C22—2021no—
333C22C2×D4×D10111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1012no—
339C4—4041no—
340C4—4041no—
341C4—4041no—
342C4—2021no—
343C4—2021no—
344C4#41×D10111yescharacteristic
345C4#1569230211yescharacteristic
346C2—41no—
347C2—81no—
348C2—8081no—
349C2—4041no—
350C2#2026582511yescharacteristic
351C2AGL(1,ℤ/8)×D10111yescharacteristic
352C2#2026598411yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#482×C101C2
socleC22×C101C22×D4
hypercenter#482D101
hypocenterC101#3354
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20265890C2semidirect
2. #20265827C2semidirect
3. #20265574C2semidirect
4. #20265500C2semidirect
5. #20265497C2semidirect
6. #20265496C2semidirect
7. #20265465C2semidirect
8. #20265456C2semidirect
9. #20265429C2semidirect
10. #20265428C2semidirect
11. #20265257C2semidirect
12. #20265252C2semidirect
13. #20265220C2semidirect
14. #20265218C2semidirect
15. #482×C101C2semidirect
143. #11717579#41semidirect
177. C101#3354semidirect
182. #482D101semidirect

Maximal subgroups

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

subgroupindex
#202658902
#202658272
#202655742
#202655002
#202654972
#202654962
#202654652
#202654562
#202654292
#202654282
#202652572
#202652522
#202652202
#202652182
#482×C1012
#3354101