Finite Group Databasebeta

← #27183733

Subgroups — #27183733

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#20265879C211yesmaximal, characteristic, complemented
2#20265874C211yesmaximal, characteristic, complemented
3#20265577C211yesmaximal, characteristic, complemented
4#20265500C211yesmaximal, characteristic, complemented
5#20265498C211yesmaximal, characteristic, complemented
6#20265489C211yesmaximal, characteristic, complemented
7#20265488C211yesmaximal, characteristic, complemented
8#20265479C211yesmaximal, characteristic, complemented
9#20265475C211yesmaximal, characteristic, complemented
10#20265427C211yesmaximal, characteristic, complemented
11D8×Dic101C211yesmaximal, characteristic, complemented
12#20265253C211yesmaximal, characteristic, complemented
13#20265219C211yesmaximal, characteristic, complemented
14#20265216C211yesmaximal, characteristic, complemented
15#469×C101C211yesmaximal, characteristic, complemented
16C2×#13108057C2211yescharacteristic
17#15692248—21no—
18#15692248—21no—
19#15692246C2211yescharacteristic
20#15692246C2211yescharacteristic
21#15692239—21no—
22#15692236—21no—
23#15692227—21no—
24#15692226—21no—
25#15692226C2211yescharacteristic
26#15692226C2211yescharacteristic
27D4×Dic101—21no—
28D4×Dic101C2211yescharacteristic
29D4×Dic101C2211yescharacteristic
30C4×C22⋊D101C2211yescharacteristic
31#15692215—21no—
32#15692214C2211yescharacteristic
33#15692213C2211yescharacteristic
34C2×C4⋊Dic101C2211yescharacteristic
35C4⋊C4×D101C2211yescharacteristic
36#15692189C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692188C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692188C2211yescharacteristic
41#15692187C2211yescharacteristic
42#15692187C2211yescharacteristic
43#15692186C2211yescharacteristic
44#15692184C2211yescharacteristic
45#15692176C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692176C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692167C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C2×D8×C101C2211yescharacteristic
53C2×M16×C101C2211yescharacteristic
54#121×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56#106×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58#102×C101C2211yescharacteristic
59C2×C22⋊D101—21no—
60C2×C22⋊D101—21no—
61C2×C22⋊D101D411yescharacteristic
62C22×Dic101—21no—
63C22×Dic101—21no—
64C22×Dic101—21no—
65C2×C4×D101—21no—
66C2×C4×D101C2311yescharacteristic
67#13108057—22no—
68C2×#11717579C2311yescharacteristic
69C2×#11717579C2311yescharacteristic
70C4⋊Dic101—21no—
71C4⋊Dic101—21no—
72C4⋊Dic101—21no—
73C4⋊Dic101C2311yescharacteristic
74C4⋊Dic101C2311yescharacteristic
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79#13108053—21no—
80#13108053D411yescharacteristic
81C22⋊Dic101—21no—
82C22⋊Dic101—21no—
83C22⋊Dic101—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101D411yescharacteristic
87#13108051—21no—
88#13108051D411yescharacteristic
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101C2311yescharacteristic
92C2×D4×C101—21no—
93C2×D4×C101—21no—
94C2×D4×C101C2311yescharacteristic
95C2×D4×C101C2311yescharacteristic
96C22×C4×C101C2311yescharacteristic
97D8×C101—22no—
98M16×C101—22no—
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C22⋊C4×C101—21no—
104C22⋊C4×C101—21no—
105C23×C101—21no—
106C23×C101—21no—
107C23×C101C2×D411yescharacteristic
108C22×D101C2×D411yescharacteristic
109D4×C101—21no—
110D4×C101—21no—
111D4×C101—21no—
112D4×C101—21no—
113D4×C101—42no—
114D4×C101—81no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101C2×D411yescharacteristic
120C2×C4×C101C2411yescharacteristic
121C22⋊D101—41no—
122C22⋊D101—42no—
123C22⋊D101—81no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—81no—
129C2×Dic101—81no—
130C2×Dic101—81no—
131C2×Dic101C2×D411yescharacteristic
132C2×Dic101C2×D411yescharacteristic
133C2×Dic101C2×D411yescharacteristic
134C4×D101—21no—
135C4×D101—21no—
136C4×D101—81no—
137C8×C101—21no—
138C8×C101#4112yes—
139#11717579—21no—
140#11717579—21no—
141C22×C101—21no—
142C22×C101—21no—
143C22×C101—21no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101—41no—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101C22×D411yescharacteristic
151C2×D101—21no—
152C2×D101—21no—
153C2×D101—21no—
154C4×C101—21no—
155C4×C101—41no—
156C4×C101—41no—
157C4×C101C2×#4111yescharacteristic
158C4×C1012−1+411yescharacteristic
159Dic101—21no—
160Dic101—21no—
161Dic101—21no—
162Dic101—41no—
163Dic101—41no—
164Dic101—41no—
165Dic101—41no—
166C2×C101—41no—
167C2×C101—81no—
168C2×C101—81no—
169C2×C101#54711yescharacteristic
170C2×C101#57511yescharacteristic
171C2×C101#57611yescharacteristic
172D101—41no—
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#480—1011no—
182#478—1011no—
183#478—1011no—
184#469—1011no—
185#469D10111yescharacteristic, complemented
186C4×D8—1011no—
187#436—1011no—
188#428—1011no—
189#428—1011no—
190C2×D8C2×D10111yescharacteristic
191C2×M16—1011no—
192C2×M16C2×D10111yescharacteristic
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—2021no—
202#121—2021no—
203#121C2×D10111yescharacteristic
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⋊C4—1011no—
214#107—1011no—
215#107—1011no—
216#107—1011no—
217#107—1011no—
218#107—1011no—
219#106—1011no—
220#106—1011no—
221#106—1011no—
222#106C2×D10111yescharacteristic
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⋊C8—1011no—
232C4×C8—1011no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1011no—
236C2×D4—2021no—
237C2×D4—2021no—
238C2×D4C22×D10111yescharacteristic
239C2×D4C22×D10111yescharacteristic
240C22×C4—1011no—
241C22×C4—2021no—
242C22×C4—2021no—
243C22×C4—2021no—
244C22×C4—2021no—
245C22×C4C22×D10111yescharacteristic
246D8—22no—
247M16—22no—
248M16—2022no—
249C2×C8—1011no—
250C2×C8—1011no—
251C2×C8C22×D10111yescharacteristic
252C2×C8C22×D10111yescharacteristic
253C4⋊C4—1011no—
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⋊C4—2021no—
264C4⋊C4C22×D10111yescharacteristic
265C4⋊C4C22×D10111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1011no—
269C22⋊C4—1011no—
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—21no—
281C23—1011no—
282C23D4×D10111yescharacteristic
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—8081no—
290D4—4042no—
291D4—4041no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—8081no—
297C2×C4—8081no—
298C2×C4—8081no—
299C2×C4—8081no—
300C2×C4—1011no—
301C2×C4—1011no—
302C2×C4—1011no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4D4×D10111yescharacteristic
310C2×C4C23×D10111yescharacteristic
311C8—21no—
312C8—2021no—
313C8—2021no—
314C8#1310807312yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2021no—
325C22—2021no—
326C22—2021no—
327C22C2×D4×D10111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—4041no—
332C4—4041no—
333C4—4041no—
334C4—4041no—
335C4—2021no—
336C4—2021no—
337C4—2021no—
338C4C2×#1310807311yescharacteristic
339C4#1569230211yescharacteristic
340C2—41no—
341C2—81no—
342C2—81no—
343C2—4041no—
344C2#2026582711yescharacteristic
345C2#2026597311yescharacteristic
346C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#469×C101C2
socleC22×C101C22×D4
hypercenter#469D101
hypocenterC101#3355
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20265879C2semidirect
2. #20265874C2semidirect
3. #20265577C2semidirect
4. #20265500C2semidirect
5. #20265498C2semidirect
6. #20265489C2semidirect
7. #20265488C2semidirect
8. #20265479C2semidirect
9. #20265475C2semidirect
10. #20265427C2semidirect
11. D8×Dic101C2semidirect
12. #20265253C2semidirect
13. #20265219C2semidirect
14. #20265216C2semidirect
15. #469×C101C2semidirect
174. C101#3355semidirect
185. #469D101semidirect

Maximal subgroups

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

subgroupindex
#202658792
#202658742
#202655772
#202655002
#202654982
#202654892
#202654882
#202654792
#202654752
#202654272
D8×Dic1012
#202652532
#202652192
#202652162
#469×C1012
#3355101