Finite Group Databasebeta

← #14908697

Subgroups — #14908697

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2#13070796C212yesmaximal, complemented
3#13070753C212yesmaximal, complemented
4#13070651C212yesmaximal, complemented
5#13070528C212yesmaximal, complemented
6C4×#66890C214yesmaximal, complemented
7#13070415C211yesmaximal, characteristic, complemented
8C2×C4×C11×D8C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C2×C4×D4×C11—21no—
11#10623008—21no—
12C4×C11×D8—21no—
13C4×C11×D8—21no—
14C4×C11×D8C2212yes—
15C4×C11×D8C2212yes—
16C2×C11×#107C2211yescharacteristic
17C2×C11×#102—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66890C2214yes—
20#10622728—21no—
21#10622728C2212yes—
22#10622308C2211yescharacteristic, complemented
23#10622307—21no—
24C4×D88—21no—
25C4×D88C2212yescomplemented
26#10622295C2211yescharacteristic, complemented
27#10622200C2214yes—
28C22⋊(C11⋊C16)C2212yes—
29#10622129C2214yescomplemented
30#10622127C2214yescomplemented
31C4⋊(C11⋊C16)C2212yescomplemented
32C4×C11⋊C16C2212yescomplemented
33C22×D4×C11—21no—
34C23×C4×C11—41no—
35C2×#4339—41no—
36C2×C11×D8—24no—
37C2×C11×D8—21no—
38C2×C11×D8C2312yes—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C4×D4×C11—22no—
42C4×D4×C11—22no—
43C4×D4×C11—41no—
44C4×D4×C11—41no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C22⋊C4—41no—
47C2×C42×C11D411yescharacteristic
48#66983—22no—
49#66983—41no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66928—41no—
53#66927—21no—
54C4×D44—22no—
55C4×D44—41no—
56#66922—21no—
57C11×#107—21no—
58C11×#107C2312yes—
59C11×#102—22no—
60C11×#102—22no—
61C4×C8×C11D411yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C4×C8×C11C2311yescharacteristic
65#66890—28no—
66#66885—22no—
67#66885—22no—
68#66882—21no—
69#66882C2312yes—
70C2×C11⋊C16C2314yes—
71#33660—111nomaximal, Sylow
72C24×C11—41no—
73C2×D4×C11—24no—
74C2×D4×C11—22no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—84no—
81C22×C4×C11D811yescharacteristic
82C22×C4×C11D811yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—42no—
85#4339—84no—
86C2×D44—22no—
87C2×D44—41no—
88C2×D44—41no—
89C2×C4×D11—42no—
90C2×Dic22—41no—
91C11×D8—24no—
92C11×D8—22no—
93C11×D8#4114yescomplemented
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C42×C11D811yescharacteristic
105C42×C11D811yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112D88—24no—
113D88—42no—
114C11⋊C16—24no—
115#3169—111no—
116C2×C4×D8D1111yescharacteristic, complemented
117#2232—112no—
118#2224—112no—
119#2206—112no—
120#2184—112no—
121C4×D16—114no—
122#2162—111no—
123C23×C11—44no—
124C23×C11—42no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11C2×D811yescharacteristic
128C22×D11—42no—
129D4×C11—24no—
130D4×C11—44no—
131D4×C11—42no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—82no—
137C2×C4×C11—84no—
138C2×C4×C11—84no—
139C2×C4×C11D1614yescomplemented
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—84no—
147C2×Dic11—42no—
148D44—42no—
149D44—42no—
150D44—82no—
151D44—82no—
152C4×D11—84no—
153Dic22—82no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11C2×#4112yes—
158C22×D8C2×D1111yescharacteristic
159#532—221no—
160C2×C4×D4—21no—
161C2×D16—114no—
162#500—111no—
163#493—111no—
164#486—221no—
165#466—112no—
166#466—221no—
167C4×D8—21no—
168C4×D8—21no—
169C4×D8—112no—
170C4×D8—221no—
171C4×D8C2×D1112yes—
172C4×D8C2×D1112yes—
173C2×#107C2×D1111yescharacteristic
174C2×#102—21no—
175C2×C4×C8C2×D1111yescharacteristic
176#366—114no—
177C4⋊C16—112no—
178#357—114no—
179#357—114no—
180C22⋊C16—112no—
181C4×C16—112no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—44no—
185C22×C11—88no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11C2×D1612yes—
189C22×C11C22×D811yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11C2×D1612yes—
198C4×C11C2×D1612yes—
199C4×C11#52511yescharacteristic
200C4×C11#57511yescharacteristic
201Dic11—82no—
202C2×#41—441no—
203C22×D4—21no—
204C23×C4—41no—
205C2×D8—24no—
206C2×D8—21no—
207C2×D8—112no—
208C2×D8—221no—
209C2×D8C22×D1112yes—
210C22×C8C22⋊D1111yescharacteristic
211C22×C8C22×D1111yescharacteristic
212C4⋊Q8—221no—
213#127—221no—
214#124—441no—
215#121—222no—
216#121—441no—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4—41no—
220C4×D4—41no—
221C4×D4—222no—
222C4×D4—441no—
223C2×C4⋊C4—21no—
224C2×C22⋊C4—41no—
225C2×C42C22⋊D1111yescharacteristic
226D16—228no—
227C2×C16—114no—
228#107—21no—
229#107—112no—
230#107—221no—
231#107C22×D1112yes—
232#102—22no—
233#102—22no—
234#102—222no—
235#102—222no—
236C4×C8C22⋊D1111yescharacteristic
237C4×C8C22⋊D1111yescharacteristic
238C4×C8C22×D1111yescharacteristic
239C4×C8C22×D1111yescharacteristic
240C2×C11—22no—
241C2×C11—84no—
242C2×C11#310011yescharacteristic
243C2×C11C22×D1611yescharacteristic
244C2×C11#341411yescharacteristic
245D11—162no—
246C24—41no—
247#41—884no—
248C2×Q8—441no—
249C2×D4—24no—
250C2×D4—22no—
251C2×D4—42no—
252C2×D4—41no—
253C2×D4—222no—
254C2×D4—442no—
255C2×D4—441no—
256C2×D4—441no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—84no—
261C22×C4—442no—
262C22×C4#432311yescharacteristic
263C22×C4#432311yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265D8—24no—
266D8—22no—
267D8—224no—
268D8—442no—
269D8#433914yescomplemented
270C2×C8—22no—
271C2×C8—41no—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—222no—
279C4⋊C4—441no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C42#432311yescharacteristic
285C42#432311yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C16—224no—
289C11#3366011yescharacteristic, complemented, Sylow
290C23—44no—
291C23—42no—
292C23—82no—
293C23—82no—
294C23—442no—
295C23C2×#432311yescharacteristic
296Q8—882no—
297D4—24no—
298D4—44no—
299D4—42no—
300D4—442no—
301D4—442no—
302D4—882no—
303D4—884no—
304D4—882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—84no—
311C2×C4—84no—
312C2×C4—442no—
313C2×C4—884no—
314C2×C4#6689014yescomplemented
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432311yescharacteristic
317C2×C4C2×#432311yescharacteristic
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432311yescharacteristic
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8C2×#433912yes—
325C22—21no—
326C22—21no—
327C22—44no—
328C22—88no—
329C22—82no—
330C22—82no—
331C22—882no—
332C22—882no—
333C22—882no—
334C22C2×#6689012yes—
335C22C22×#432311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—82no—
340C4—882no—
341C4C2×#6689012yes—
342C4C2×#6689012yes—
343C4#1062332211yescharacteristic
344C4#1062335311yescharacteristic
345C2—22no—
346C2—84no—
347C2—1762no—
348C2#1307861611yescharacteristic
349C2C22×#6689011yescharacteristic
350C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×D8C2
socleC22×C11C22×D8
hypercenterC2×C4×D8D11
hypocenterC11#33660
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13070796C2semidirect
3. #13070753C2semidirect
4. #13070651C2semidirect
5. #13070528C2semidirect
6. C4×#66890C2semidirect
7. #13070415C2semidirect
8. C2×C4×C11×D8C2semidirect
22. #10622308C22semidirect
25. C4×D88C22semidirect
26. #10622295C22semidirect
29. #10622129C22semidirect
30. #10622127C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. C4×C11⋊C16C22semidirect
93. C11×D8#41semidirect
116. C2×C4×D8D11semidirect
139. C2×C4×C11D16semidirect
269. D8#4339semidirect
289. C11#33660semidirect
314. C2×C4#66890semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130707962
#130707532
#130706512
#130705282
C4×#668902
#130704152
C2×C4×C11×D82
#3366011