Finite Group Databasebeta

← #27183732

Subgroups — #27183732

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#20265873C211yesmaximal, characteristic, complemented
2#20265576C211yesmaximal, characteristic, complemented
3#20265501C211yesmaximal, characteristic, complemented
4#20265498C211yesmaximal, characteristic, complemented
5#20265490C211yesmaximal, characteristic, complemented
6#20265488C211yesmaximal, characteristic, complemented
7#20265477C211yesmaximal, characteristic, complemented
8#20265474C211yesmaximal, characteristic, complemented
9#20265428C211yesmaximal, characteristic, complemented
10#20265428C211yesmaximal, characteristic, complemented
11C4×#13108059C211yesmaximal, characteristic, complemented
12#20265255C211yesmaximal, characteristic, complemented
13#20265220C211yesmaximal, characteristic, complemented
14#20265217C211yesmaximal, characteristic, complemented
15#553×C101C211yesmaximal, characteristic, complemented
16C2×#13108059C2211yescharacteristic
17C2×#13108058C2211yescharacteristic
18C2×#13108058C2211yescharacteristic
19#15692250—21no—
20#15692247C2211yescharacteristic
21#15692237—21no—
22#15692229C2211yescharacteristic
23#15692229C2211yescharacteristic
24#15692227—21no—
25C4×D404C2211yescharacteristic
26#15692215—21no—
27#15692214C2211yescharacteristic
28C2×C4⋊Dic101C2211yescharacteristic
29#15692188C2211yescharacteristic
30#15692188C2211yescharacteristic
31#15692188C2211yescharacteristic
32#15692188C2211yescharacteristic
33#15692188C2211yescharacteristic
34#15692186C2211yescharacteristic
35#15692186C2211yescharacteristic
36#15692186C2211yescharacteristic
37#15692186C2211yescharacteristic
38C4⋊#11717579C2211yescharacteristic
39#15692176C2211yescharacteristic
40#15692176C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692175C2211yescharacteristic
43#15692175C2211yescharacteristic
44#15692175C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic
47C4×#11717579C2211yescharacteristic
48#126×C101—21no—
49#125×C101C2211yescharacteristic
50#123×C101—21no—
51#121×C101—21no—
52#121×C101C2211yescharacteristic
53#121×C101C2211yescharacteristic
54C4×D4×C101—21no—
55C4×D4×C101C2211yescharacteristic
56C4×D4×C101C2211yescharacteristic
57#117×C101C2211yescharacteristic
58C2×C4⋊C4×C101C2211yescharacteristic
59C2×D404C2311yescharacteristic
60C2×C22⋊D101—21no—
61C2×C22⋊D101—21no—
62C22×Dic101—21no—
63C2×C4×D101—21no—
64#13108059—22no—
65#13108058—22no—
66#13108058—22no—
67C2×#11717579C2311yescharacteristic
68C2×#11717579C2311yescharacteristic
69C2×#11717579C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C4⋊Dic101—21no—
72C4⋊Dic101C2311yescharacteristic
73C4⋊Dic101C2311yescharacteristic
74C4⋊Dic101C2311yescharacteristic
75#13108053—21no—
76#13108053—21no—
77C22⋊Dic101—21no—
78#13108051—21no—
79#13108051—21no—
80#13108051—21no—
81C4×Dic101—21no—
82C2×D4×C101—21no—
83C2×D4×C101—21no—
84C2×D4×C101D411yescharacteristic
85C2×D4×C101C2311yescharacteristic
86C22×C4×C101—21no—
87C22×C4×C101—21no—
88C22×C4×C101C2311yescharacteristic
89C22×C4×C101C2311yescharacteristic
90C4⋊C4×C101—21no—
91C4⋊C4×C101—21no—
92C4⋊C4×C101—21no—
93C4⋊C4×C101D411yescharacteristic
94C4⋊C4×C101C2311yescharacteristic
95C4⋊C4×C101C2311yescharacteristic
96C4⋊C4×C101C2311yescharacteristic
97C22⋊C4×C101—21no—
98C22⋊C4×C101—21no—
99C22⋊C4×C101—21no—
100C22⋊C4×C101—21no—
101C22⋊C4×C101D411yescharacteristic
102C22⋊C4×C101D411yescharacteristic
103C42×C101—21no—
104C42×C101C2311yescharacteristic
105C23×C101—21no—
106C23×C101C2×D411yescharacteristic
107C23×C101C2×D411yescharacteristic
108C22×D101—21no—
109D4×C101—21no—
110D4×C101—21no—
111D4×C101—41no—
112D4×C101—42no—
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—21no—
120C2×C4×C101—21no—
121C2×C4×C101—81no—
122C2×C4×C101—81no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2411yescharacteristic
128C22⋊D101—42no—
129C22⋊D101—81no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—81no—
134D404—21no—
135D404—21no—
136C4×D101—81no—
137#11717579—21no—
138#11717579—21no—
139#11717579—21no—
140#11717579#4112yes—
141C22×C101—21no—
142C22×C101—21no—
143C22×C101—21no—
144C22×C101—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—41no—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101C22×D411yescharacteristic
151C2×D101—41no—
152C2×D101—41no—
153C2×D101—41no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—21no—
158C4×C101—41no—
159C4×C101—41no—
160C4×C101—41no—
161C4×C101C2×#4111yescharacteristic
162C4×C1012−1+411yescharacteristic
163Dic101—41no—
164Dic101—41no—
165Dic101—41no—
166C2×C101—41no—
167C2×C101—41no—
168C2×C101—81no—
169C2×C101#54711yescharacteristic
170C2×C101#57511yescharacteristic
171C2×C101#57611yescharacteristic
172D101—81no—
173#3355—1011nomaximal, Sylow
174C101#335511yescharacteristic, complemented, Sylow
175#553—1011no—
176#553D10111yescharacteristic, complemented
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#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—21no—
194#126—2021no—
195#125—1011no—
196#125C2×D10111yescharacteristic
197#123—21no—
198#123—2021no—
199#121—21no—
200#121—1011no—
201#121—1011no—
202#121—2021no—
203#121C2×D10111yescharacteristic
204#121C2×D10111yescharacteristic
205C4×D4—21no—
206C4×D4—1011no—
207C4×D4—2021no—
208C4×D4C2×D10111yescharacteristic
209C4×D4C2×D10111yescharacteristic
210#117—1011no—
211#117C2×D10111yescharacteristic
212C2×C4⋊C4—1011no—
213C2×C4⋊C4C2×D10111yescharacteristic
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#106—1011no—
223C4⋊C8—1011no—
224#102—1011no—
225#102—1011no—
226#102—1011no—
227#102—1011no—
228#102—1011no—
229#102—1011no—
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—21no—
241C22×C4—21no—
242C22×C4—2021no—
243C22×C4—2021no—
244C22×C4C22×D10111yescharacteristic
245C22×C4C22×D10111yescharacteristic
246D8—2022no—
247M16—2022no—
248M16—2022no—
249C2×C8—1011no—
250C2×C8—1011no—
251C2×C8—1011no—
252C2×C8—1011no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1011no—
257C4⋊C4—1011no—
258C4⋊C4—1011no—
259C4⋊C4—2021no—
260C4⋊C4—2021no—
261C4⋊C4—2021no—
262C4⋊C4C22⋊D10111yescharacteristic
263C4⋊C4C22×D10111yescharacteristic
264C4⋊C4C22×D10111yescharacteristic
265C4⋊C4C22×D10111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2021no—
271C22⋊C4—2021no—
272C22⋊C4—2021no—
273C22⋊C4—2021no—
274C22⋊C4C22⋊D10111yescharacteristic
275C22⋊C4C22⋊D10111yescharacteristic
276C42—21no—
277C42—2021no—
278C42C22×D10111yescharacteristic
279C23—21no—
280C23—2021no—
281C23C2×C22⋊D10111yescharacteristic
282C23C2×C22⋊D10111yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—8081no—
289D4—4042no—
290D4—2021no—
291D4—2021no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—8081no—
302C2×C4—8081no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4C2×C22⋊D10111yescharacteristic
307C2×C4C2×C22⋊D10111yescharacteristic
308C2×C4C2×C22⋊D10111yescharacteristic
309C2×C4C2×C22⋊D10111yescharacteristic
310C2×C4C23×D10111yescharacteristic
311C8—1012no—
312C8—2021no—
313C8—2021no—
314C8—2021no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—4041no—
325C22—4041no—
326C22—4041no—
327C22C22×C22⋊D10111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—4041no—
336C4—4041no—
337C4—4041no—
338C4#41×D10111yescharacteristic
339C4#1569230211yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—8081no—
344C2#2026582611yescharacteristic
345C2#2026597511yescharacteristic
346C2#2026598011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#553×C101C2
socleC22×C101C22×D4
hypercenter#553D101
hypocenterC101#3355
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20265873C2semidirect
2. #20265576C2semidirect
3. #20265501C2semidirect
4. #20265498C2semidirect
5. #20265490C2semidirect
6. #20265488C2semidirect
7. #20265477C2semidirect
8. #20265474C2semidirect
9. #20265428C2semidirect
10. #20265428C2semidirect
11. C4×#13108059C2semidirect
12. #20265255C2semidirect
13. #20265220C2semidirect
14. #20265217C2semidirect
15. #553×C101C2semidirect
174. C101#3355semidirect
176. #553D101semidirect

Maximal subgroups

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

subgroupindex
#202658732
#202655762
#202655012
#202654982
#202654902
#202654882
#202654772
#202654742
#202654282
C4×#131080592
#202652552
#202652202
#202652172
#553×C1012
#3355101