Finite Group Databasebeta

← #14655637

Subgroups — #14655637

Order 2816.

488 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079564C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic
5#13067072C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic
7C2×C11×#487C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#487—22no—
12C11×#487—22no—
13C2×C11×#103—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622841—22no—
16#10622705—21no—
17#10622703—22no—
18#10622694—21no—
19#10622693—22no—
20#10622692—21no—
21#10622691—21no—
22#10622577—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622184—22no—
27#10622168—22no—
28#10622094—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C22×C8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—24no—
46#66979—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51#66923—21no—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×#103—28no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66899—24no—
60C22⋊(C11⋊C8)—21no—
61#66872—24no—
62#66871—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10163—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—44no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×C8×C11—22no—
84C2×C8×C11—42no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C22⋊Dic11—41no—
98#4326—84no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—41no—
106#4318—22no—
107#4318—42no—
108#4318Q1614yescomplemented
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112#3209—111no—
113#3165—111no—
114C2×#487D1111yescharacteristic
115#1997—111no—
116#1548—111no—
117#1493—111no—
118#1278—111no—
119C23×C11#12111yescharacteristic
120Q8×C11—44no—
121Q8×C11—44no—
122Q8×C11—82no—
123Q8×C11—82no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12711yescharacteristic
136C2×C4×C11C2×Q1612yes—
137C2×C4×C11#13712yes—
138C2×Dic11—41no—
139C2×Dic11—41no—
140Dic22—42no—
141Dic22—42no—
142C8×C11—42no—
143C11⋊C8—24no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146#533—111no—
147C2×C4⋊Q8C2×D1111yescharacteristic
148C2×C4⋊Q8C2×D1111yescharacteristic
149#501—222no—
150#500—221no—
151#498—221no—
152#494—221no—
153#487—22no—
154#487—22no—
155#487—221no—
156#462—222no—
157#451—222no—
158#431—111no—
159#428—222no—
160#423—111no—
161C2×#103—22no—
162C4×M16—111no—
163C2×C4×C8C2×D1111yescharacteristic
164#343—222no—
165#333—222no—
166Q8⋊C8—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39211yescharacteristic
170C22×C11#46212yes—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11—82no—
175C4×C11#45112yes—
176C4×C11#45512yes—
177C4×C11#47112yes—
178C4×C11#49411yescharacteristic
179C4×C11#49711yescharacteristic
180Dic11—81no—
181Dic11—81no—
182C22×Q8—21no—
183C22×Q8C22⋊D1112yes—
184C2×Q16—224no—
185C2×M16—112no—
186C2×M16—221no—
187C22×C8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—111no—
196C4⋊Q8—111no—
197C4⋊Q8C22⋊D1112yes—
198#125—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203#117—221no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C42C22×D1111yescharacteristic
209#107—224no—
210#106—224no—
211C4⋊C8—112no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—28no—
215#103—224no—
216C22⋊C8—221no—
217#97—221no—
218C4×C8—21no—
219C4×C8—221no—
220C4×C8—221no—
221C4×C8C22⋊D1112yes—
222C2×C11—22no—
223C2×C11#200411yescharacteristic
224C2×C11#201611yescharacteristic
225C2×C11#201911yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—44no—
230C2×Q8—41no—
231C2×Q8—82no—
232C2×Q8—221no—
233C2×Q8—221no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4D4×D1111yescharacteristic
237C22×C4#434111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239Q16—884no—
240M16—114no—
241M16—222no—
242M16—442no—
243C2×C8—22no—
244C2×C8—42no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—441no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—441no—
263C42—441no—
264C42D4×D1111yescharacteristic
265C42D4×D1111yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1016311yescharacteristic, complemented, Sylow
269C23#6699211yescharacteristic
270Q8—44no—
271Q8—44no—
272Q8—82no—
273Q8—82no—
274Q8—442no—
275Q8—442no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4Q16×D1112yes—
285C2×C4#6697112yes—
286C2×C4#6699011yescharacteristic
287C2×C4#6699011yescharacteristic
288C2×C4#6699111yescharacteristic
289C2×C4#6699211yescharacteristic
290C2×C4#6699311yescharacteristic
291C2×C4#6700611yescharacteristic
292C8—42no—
293C8—224no—
294C8—442no—
295C8—881no—
296C22—21no—
297C22—21no—
298C22#1062279512yes—
299C22#1062283611yescharacteristic
300C4—21no—
301C4—21no—
302C4—82no—
303C4—82no—
304C4—881no—
305C4—881no—
306C4#1062267412yes—
307C4#1062279012yes—
308C4#1062279411yescharacteristic
309C4#1062279912yes—
310C4#1062280311yescharacteristic
311C2—22no—
312C2#1306964511yescharacteristic
313C2#1306971411yescharacteristic
314C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#487C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenterC2×#487D11
hypocenterC11#10163
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
108. #4318Q16semidirect
268. C11#10163semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130791582
#130696062
#130672972
#130670722
#130664532
C2×C11×#4872
#1016311