Finite Group Databasebeta

← #14735788

Subgroups — #14735788

Order 2816.

1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079076C211yesmaximal, characteristic, complemented
2#13079009C212yesmaximal, complemented
3#13067922C218yesmaximal, complemented
4#13067208C212yesmaximal, complemented
5#13067208C211yesmaximal, characteristic, complemented
6C11×#3549C211yesmaximal, characteristic
7C11×H(3,𝔽4)C2214yes—
8C11×#555—22no—
9C11×#555—21no—
10D42×C11—22no—
11D42×C11—21no—
12C11×#535—22no—
13C11×#535—24no—
14C11×#532C2211yescharacteristic
15C11×#532C2212yes—
16C2×#67004—22no—
17C2×#66922C2211yescharacteristic, complemented
18#10622845—24no—
19#10622705—21no—
20#10622694—22no—
21#10622689—21no—
22#10622683—22no—
23#10622673C2214yescomplemented
24#10622668C2218yescomplemented
25C4×#4318C2211yescharacteristic, complemented
26C4×#4318C2212yescomplemented
27#10622178C2214yescomplemented
28#10622178C2218yescomplemented
29C2×C11×#41D412yes—
30C2×C11×#41D414yes—
31C22×D4×C11—22no—
32C22×D4×C11—24no—
33C22×Dic22—21no—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127—24no—
37C11×#127D412yes—
38C11×#127D411yescharacteristic
39C11×#124—28no—
40C11×#124—24no—
41C11×#124C2314yes—
42C11×#124C2312yes—
43C11×#121—24no—
44C11×#121—24no—
45C11×#121—24no—
46C11×#121—22no—
47C11×#121—22no—
48C11×#121—22no—
49C11×#120—24no—
50C11×#120—28no—
51C11×#120—24no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C11×#117—22no—
56C11×#117—24no—
57C2×C42×C11C2311yescharacteristic
58#67004—48no—
59C2×#4326—24no—
60C2×#4324—24no—
61C2×C4⋊Dic11—22no—
62C2×#4318—21no—
63C2×#4318—22no—
64#66922—22no—
65#66922—21no—
66#66922C2312yes—
67#66899—28no—
68#66896—28no—
69#66867C2314yes—
70#66867C2312yes—
71C4×C11⋊C8—22no—
72C4×C11⋊C8—21no—
73#19074—111nomaximal, Sylow
74C24×C11—24no—
75C11×#41—44no—
76C11×#41—48no—
77C2×Q8×C11C2×D414yes—
78C2×Q8×C11C2×D412yes—
79C2×D4×C11—24no—
80C2×D4×C11—28no—
81C2×D4×C11—22no—
82C2×D4×C11—24no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—84no—
87C2×D4×C11—88no—
88C2×D4×C11C2×D414yes—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C2×Dic22—22no—
96C2×Dic22—44no—
97C2×Dic22—41no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C22⋊C4—28no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—24no—
106C42×C11—24no—
107C42×C11C2×D412yes—
108C42×C11C2×D411yescharacteristic
109C42×C11C2411yescharacteristic
110#4326—48no—
111#4324—48no—
112C4⋊Dic11—24no—
113C4⋊Dic11—42no—
114#4318—24no—
115#4318—44no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—24no—
118#3549D1111yescharacteristic
119#3152—111no—
120#3141—112no—
121#1659—118no—
122#1525—112no—
123#1525—111no—
124C23×C11—22no—
125C23×C11—24no—
126C23×C11—84no—
127C23×C11—88no—
128C23×C11#12011yescharacteristic
129Q8×C11—42no—
130Q8×C11—44no—
131D4×C11—42no—
132D4×C11—44no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—44no—
136D4×C11—82no—
137D4×C11—84no—
138D4×C11—84no—
139D4×C11—88no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—44no—
145C2×C4×C11—48no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12012yes—
148C2×C4×C11C22×D412yes—
149C2×C4×C11C22×D411yescharacteristic
150C2×Dic11—42no—
151C2×Dic11—82no—
152Dic22—44no—
153Dic22—82no—
154C11⋊C8—24no—
155C11⋊C8—44no—
156C2×#137—222no—
157H(3,𝔽4)C2×D1114yes—
158#555—22no—
159#555—21no—
160D42—22no—
161D42—21no—
162#535—22no—
163#535—24no—
164#532C2×D1112yes—
165#532C2×D1111yescharacteristic
166C2×C4⋊Q8—111no—
167#497—114no—
168#494—221no—
169#492—221no—
170#489—118no—
171#487—222no—
172#486—222no—
173#417—224no—
174C4×M16—112no—
175C4×M16—111no—
176#329—114no—
177#329—118no—
178C22×C11—21no—
179C22×C11—22no—
180C22×C11—42no—
181C22×C11—44no—
182C22×C11—44no—
183C22×C11—44no—
184C22×C11—44no—
185C22×C11—168no—
186C22×C11C2×#12011yescharacteristic
187C4×C11—21no—
188C4×C11—22no—
189C4×C11—42no—
190C4×C11—44no—
191C4×C11#45312yes—
192C4×C11#45514yes—
193Dic11—82no—
194C2×#41C22⋊D1112yes—
195C2×#41C22⋊D1114yes—
196C22×Q8—221no—
197C22×D4—22no—
198C22×D4—24no—
199#137—448no—
200C2×Q16—224no—
201C2×SD16—224no—
202C2×M16—221no—
203C2×M16—222no—
204C4⋊Q8—112no—
205C4⋊Q8—222no—
206C4⋊Q8—221no—
207C4⋊Q8C22⋊D1112yes—
208C4⋊Q8C22⋊D1111yescharacteristic
209#127—24no—
210#127C22⋊D1112yes—
211#127C22⋊D1111yescharacteristic
212#124—28no—
213#124—24no—
214#124C22×D1114yes—
215#124C22×D1112yes—
216#121—24no—
217#121—24no—
218#121—24no—
219#121—22no—
220#121—22no—
221#121—22no—
222#120—24no—
223#120—28no—
224#120—24no—
225C4×D4—22no—
226C4×D4—22no—
227C4×D4—22no—
228#117—22no—
229#117—24no—
230C2×C4⋊C4—222no—
231C2×C42C22×D1111yescharacteristic
232#103—228no—
233#102—228no—
234#97—114no—
235#97—112no—
236C4×C8—222no—
237C4×C8—221no—
238C2×C11—41no—
239C2×C11—82no—
240C2×C11—84no—
241C2×C11C2×#45311yescharacteristic
242C2×C11C2×#45512yes—
243C24—24no—
244#41—44no—
245#41—48no—
246C2×Q8—222no—
247C2×Q8—444no—
248C2×Q8—441no—
249C2×Q8C2×C22⋊D1114yes—
250C2×Q8C2×C22⋊D1112yes—
251C2×D4—24no—
252C2×D4—28no—
253C2×D4—22no—
254C2×D4—24no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—84no—
259C2×D4—88no—
260C2×D4C2×C22⋊D1114yes—
261C2×D4C2×C22⋊D1112yes—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—441no—
265C22×C4C2×C22⋊D1112yes—
266C22×C4C2×C22⋊D1111yescharacteristic
267Q16—448no—
268SD16—448no—
269M16—224no—
270M16—444no—
271C2×C8—222no—
272C2×C8—224no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—224no—
277C4⋊C4—442no—
278C22⋊C4—28no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C42—24no—
284C42C2×C22⋊D1112yes—
285C42C2×C22⋊D1111yescharacteristic
286C42C23×D1111yescharacteristic
287C11#1907411yescharacteristic, complemented, Sylow
288C23—22no—
289C23—24no—
290C23—84no—
291C23—88no—
292C23#6700611yescharacteristic
293Q8—42no—
294Q8—44no—
295Q8—444no—
296Q8—882no—
297D4—42no—
298D4—44no—
299D4—44no—
300D4—44no—
301D4—44no—
302D4—82no—
303D4—84no—
304D4—84no—
305D4—88no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—44no—
311C2×C4—48no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4#6700611yescharacteristic
315C2×C4#6700612yes—
316C2×C4C22×C22⋊D1112yes—
317C2×C4C22×C22⋊D1111yescharacteristic
318C8—224no—
319C8—444no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—44no—
324C22—44no—
325C22—44no—
326C22—44no—
327C22—168no—
328C22C2×#6700611yescharacteristic
329C4—21no—
330C4—22no—
331C4—42no—
332C4—44no—
333C4—882no—
334C4#1062285412yes—
335C4#1062285514yes—
336C2—41no—
337C2—82no—
338C2—84no—
339C2C2×#1062285411yescharacteristic
340C2C2×#1062285512yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3549C2
socleC22×C11C2×#120
hypercenter#3549D11
hypocenterC11#19074
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #13079076C2semidirect
2. #13079009C2semidirect
3. #13067922C2semidirect
4. #13067208C2semidirect
5. #13067208C2semidirect
17. C2×#66922C22semidirect
23. #10622673C22semidirect
24. #10622668C22semidirect
25. C4×#4318C22semidirect
26. C4×#4318C22semidirect
27. #10622178C22semidirect
28. #10622178C22semidirect
287. C11#19074semidirect

Maximal subgroups

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

subgroupindex
#130790762
#130790092
#130679222
#130672082
C11×#35492
#1907411