Finite Group Databasebeta

← #14735621

Subgroups — #14735621

Order 2816.

992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079627C212yesmaximal, complemented
2#13078961C211yesmaximal, characteristic, complemented
3#13067922C218yesmaximal, complemented
4#13067251C211yesmaximal, characteristic, complemented
5#13067227C212yesmaximal, complemented
6C11×#3549C211yesmaximal, characteristic
7C11×H(3,𝔽4)C2214yes—
8C11×#555—21no—
9C11×#555—22no—
10D42×C11—21no—
11D42×C11—22no—
12C11×#535—22no—
13C11×#535—24no—
14C11×#532C2212yes—
15C11×#532C2211yescharacteristic
16#10623001C2211yescharacteristic, complemented
17#10622852—24no—
18#10622846—22no—
19#10622703—22no—
20#10622695—21no—
21#10622688—22no—
22#10622684—21no—
23#10622673C2214yescomplemented
24#10622668C2214yescomplemented
25#10622668C2214yescomplemented
26#10622539C2212yescomplemented
27C2×#66867C2211yescharacteristic, complemented
28#10622178C2218yescomplemented
29#10622178C2214yescomplemented
30C2×C11×#41D412yes—
31C2×C11×#41D414yes—
32C22×D4×C11—24no—
33C22×D4×C11—22no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D412yes—
36C11×#127—24no—
37C11×#127D411yescharacteristic
38C11×#127D412yes—
39C11×#124—24no—
40C11×#124—28no—
41C11×#124C2312yes—
42C11×#124C2314yes—
43C11×#121—24no—
44C11×#121—24no—
45C11×#121—24no—
46C11×#121—22no—
47C11×#121—22no—
48C11×#121—22no—
49C11×#120—24no—
50C11×#120—24no—
51C11×#120—28no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C11×#117—24no—
56C11×#117—22no—
57C2×C42×C11C2311yescharacteristic
58C2×#4326—24no—
59C2×#4324—24no—
60#66979—21no—
61#66977—22no—
62C22×C11⋊C8—21no—
63#66923—21no—
64#66922C2312yes—
65C4×Dic22—22no—
66#66899—24no—
67#66899—24no—
68#66896—24no—
69#66896—24no—
70C22⋊(C11⋊C8)—22no—
71C4⋊(C11⋊C8)—22no—
72#66867—21no—
73#66867C2312yes—
74#66867C2314yes—
75#19056—111nomaximal, Sylow
76C24×C11—24no—
77C11×#41—44no—
78C11×#41—84no—
79C2×Q8×C11C2×D412yes—
80C2×Q8×C11C2×D414yes—
81C2×D4×C11—24no—
82C2×D4×C11—28no—
83C2×D4×C11—22no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—88no—
89C2×D4×C11—84no—
90C2×D4×C11C2×D412yes—
91C2×D4×C11C2×D414yes—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C2×Dic22—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C42×C11—24no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D412yes—
108C42×C11C2411yescharacteristic
109C22⋊Dic11—41no—
110#4326—84no—
111#4324—84no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114Dic11⋊C4—42no—
115C4×Dic11—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—42no—
119#3549D1111yescharacteristic
120#3216—112no—
121#3135—111no—
122#1659—118no—
123#1536—111no—
124#1530—112no—
125C23×C11—22no—
126C23×C11—24no—
127C23×C11—84no—
128C23×C11—88no—
129C23×C11#12011yescharacteristic
130Q8×C11—44no—
131Q8×C11—42no—
132D4×C11—44no—
133D4×C11—42no—
134D4×C11—44no—
135D4×C11—44no—
136D4×C11—44no—
137D4×C11—82no—
138D4×C11—84no—
139D4×C11—84no—
140D4×C11—88no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—42no—
145C2×C4×C11—48no—
146C2×C4×C11—44no—
147C2×C4×C11#12012yes—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C22×D412yes—
151C2×Dic11—42no—
152Dic22—42no—
153Dic22—42no—
154C11⋊C8—42no—
155C11⋊C8—44no—
156H(3,𝔽4)C2×D1114yes—
157#555—22no—
158#555—21no—
159D42—22no—
160D42—21no—
161#535—22no—
162#535—24no—
163#533—111no—
164#532C2×D1111yescharacteristic
165#532C2×D1112yes—
166#497—114no—
167#491—221no—
168#490—221no—
169#489—114no—
170#489—114no—
171#462—222no—
172#460—222no—
173#452—224no—
174#432—112no—
175#416—222no—
176C2×#97—111no—
177#329—114no—
178#329—118no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—44no—
183C22×C11—44no—
184C22×C11—44no—
185C22×C11—44no—
186C22×C11—168no—
187C22×C11C2×#12011yescharacteristic
188C4×C11—21no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—42no—
192C4×C11—44no—
193C4×C11#45512yes—
194Dic11—82no—
195C2×#41C22⋊D1112yes—
196C2×#41C22⋊D1114yes—
197C22×D4—24no—
198C22×D4—22no—
199C2×Q16—224no—
200C2×SD16—224no—
201C22×C8—221no—
202C4⋊Q8—112no—
203C4⋊Q8C22⋊D1112yes—
204C4⋊Q8C22⋊D1111yescharacteristic
205#127—24no—
206#127C22⋊D1112yes—
207#127C22⋊D1111yescharacteristic
208#125—221no—
209#124—24no—
210#124—28no—
211#124C22×D1112yes—
212#124C22×D1114yes—
213C22⋊Q8—222no—
214#121—24no—
215#121—24no—
216#121—24no—
217#121—22no—
218#121—22no—
219#121—22no—
220#120—24no—
221#120—24no—
222#120—28no—
223C4×Q8—222no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227#117—24no—
228#117—22no—
229#117—221no—
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—222no—
232#103—224no—
233#103—224no—
234#102—224no—
235#102—224no—
236C22⋊C8—222no—
237#97—112no—
238#97—114no—
239#97—221no—
240C2×C11—41no—
241C2×C11—82no—
242C2×C11—84no—
243C2×C11C2×#45511yescharacteristic
244C2×C11#301912yes—
245C24—24no—
246#41—44no—
247#41—84no—
248C2×Q8—222no—
249C2×Q8C2×C22⋊D1112yes—
250C2×Q8C2×C22⋊D1114yes—
251C2×D4—24no—
252C2×D4—28no—
253C2×D4—22no—
254C2×D4—24no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—88no—
259C2×D4—84no—
260C2×D4C2×C22⋊D1112yes—
261C2×D4C2×C22⋊D1114yes—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1112yes—
266Q16—884no—
267SD16—884no—
268C2×C8—222no—
269C2×C8—224no—
270C2×C8—442no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—442no—
277C22⋊C4—28no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—441no—
283C42—24no—
284C42—441no—
285C42C2×C22⋊D1111yescharacteristic
286C42C2×C22⋊D1112yes—
287C42C23×D1111yescharacteristic
288C11#1905611yescharacteristic, complemented, Sylow
289C23—22no—
290C23—24no—
291C23—84no—
292C23—88no—
293C23#6700611yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—442no—
297Q8—442no—
298D4—44no—
299D4—42no—
300D4—44no—
301D4—44no—
302D4—44no—
303D4—82no—
304D4—84no—
305D4—84no—
306D4—88no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—442no—
314C2×C4#6700612yes—
315C2×C4#6700611yescharacteristic
316C2×C4C22×C22⋊D1111yescharacteristic
317C2×C4C22×C22⋊D1112yes—
318C8—442no—
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—22no—
332C4—42no—
333C4—44no—
334C4—882no—
335C4#1062285512yes—
336C2—41no—
337C2—82no—
338C2—84no—
339C2C2×#1062285511yescharacteristic
340C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3549C2
socleC22×C11C2×#120
hypercenter#3549D11
hypocenterC11#19056
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. #13079627C2semidirect
2. #13078961C2semidirect
3. #13067922C2semidirect
4. #13067251C2semidirect
5. #13067227C2semidirect
16. #10623001C22semidirect
23. #10622673C22semidirect
24. #10622668C22semidirect
25. #10622668C22semidirect
26. #10622539C22semidirect
27. C2×#66867C22semidirect
28. #10622178C22semidirect
29. #10622178C22semidirect
288. C11#19056semidirect

Maximal subgroups

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

subgroupindex
#130796272
#130789612
#130679222
#130672512
#130672272
C11×#35492
#1905611