Finite Group Databasebeta

← #14655611

Subgroups — #14655611

Order 2816.

492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079762C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic
3C2×#10622694C211yesmaximal, characteristic
4#13069459C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#1549C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66899—22no—
14C2×#66888—22no—
15#10622694—22no—
16#10622694—22no—
17#10622693—22no—
18#10622692—21no—
19#10622691—21no—
20#10622577—22no—
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622464—22no—
24#10622334—22no—
25#10622294—21no—
26#10622293—21no—
27C11×#332—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D412yes—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66899—28no—
61#66888—44no—
62#66881—24no—
63#66880—24no—
64#66872—24no—
65#66871—24no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10159—111nomaximal, Sylow
71C2×Q8×C11—22no—
72C2×Q8×C11—44no—
73C2×Q8×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—22no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—42no—
84C2×Dic22—42no—
85C11×M16—42no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C22⋊Dic11—41no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108#4318—22no—
109#4318SD1614yes—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—42no—
113#3229—111no—
114#3165—111no—
115C2×#487—111no—
116#1966—111no—
117#1549D1111yescharacteristic
118#1493—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121Q8×C11—44no—
122Q8×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—42no—
126C2×C4×C11—82no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12711yescharacteristic
133C2×C4×C11C2×SD1612yes—
134C2×C4×C11#13712yes—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—44no—
139Dic22—42no—
140Dic22—42no—
141Dic22—82no—
142Dic22—81no—
143Dic22—81no—
144C8×C11—42no—
145C8×C11—81no—
146C11⋊C8—24no—
147C11⋊C8—42no—
148#533—111no—
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#501—222no—
152#500—221no—
153#498—221no—
154#498—221no—
155#487—221no—
156#487—222no—
157#487—222no—
158#483—222no—
159#475—222no—
160#431C2×D1111yescharacteristic
161#428—222no—
162#423C2×D1111yescharacteristic
163C2×#103—222no—
164C2×#101—222no—
165C4×M16—111no—
166C2×C4×C8—111no—
167#332—22no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46112yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11#44812yes—
177C4×C11#45412yes—
178C4×C11#47312yes—
179C4×C11#49211yescharacteristic
180C4×C11#49711yescharacteristic
181Dic11—81no—
182Dic11—82no—
183Dic11—81no—
184C22×Q8—21no—
185C22×Q8—221no—
186C2×M16—21no—
187C2×M16—112no—
188C22×C8—221no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8D4412yes—
199#125—221no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204#117—221no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—221no—
209C2×C42C22×D1111yescharacteristic
210#107—224no—
211#106—224no—
212#106—224no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8C22⋊D1112yes—
216#103—224no—
217#103—228no—
218#101—444no—
219C22⋊C8—21no—
220#97—221no—
221C4×C8—21no—
222C4×C8—112no—
223C4×C8—221no—
224C4×C8—221no—
225C2×C11—22no—
226C2×C11#200311yescharacteristic
227C2×C11#201311yescharacteristic
228C2×C11#202011yescharacteristic
229C2×Q8—22no—
230C2×Q8—44no—
231C2×Q8—41no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8—441no—
235C2×Q8—442no—
236C2×Q8—442no—
237C2×Q8—441no—
238C22×C4—41no—
239C22×C4—222no—
240C22×C4#433911yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243M16—42no—
244M16—114no—
245M16—222no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—222no—
249C2×C8—222no—
250C2×C8—442no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—222no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—441no—
266C42—441no—
267C42C2×D4411yescharacteristic
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42C2×C22⋊D1111yescharacteristic
271C11#1015911yescharacteristic, complemented, Sylow
272C23#6693711yescharacteristic
273Q8—44no—
274Q8—82no—
275Q8—442no—
276Q8—442no—
277Q8—881no—
278Q8—881no—
279Q8—882no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—442no—
287C2×C4—444no—
288C2×C4#6693511yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4#6693711yescharacteristic
291C2×C4SD16×D1112yes—
292C2×C4#6697112yes—
293C2×C4#6698311yescharacteristic
294C2×C4#6699011yescharacteristic
295C2×C4#6699311yescharacteristic
296C8—42no—
297C8—81no—
298C8—224no—
299C8—442no—
300C22—21no—
301C22—21no—
302C22#1062243112yes—
303C22#1062257311yescharacteristic
304C4—21no—
305C4—21no—
306C4—82no—
307C4—881no—
308C4—882no—
309C4—881no—
310C4#1062236812yes—
311C4#1062241912yes—
312C4#1062278811yescharacteristic
313C4#1062280311yescharacteristic
314C4#1062281412yes—
315C2—22no—
316C2#1306963911yescharacteristic
317C2#1306970011yescharacteristic
318C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1549D11
hypocenterC11#10159
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
271. C11#10159semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130791582
C2×#106226942
#130694592
#130670702
#130664522
C11×#15492
#1015911