Finite Group Databasebeta

← #14655612

Subgroups — #14655612

Order 2816.

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

normal subgroups only

This group has 492 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#13079163C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#3229C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#498—21no—
12C11×#487—21no—
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16C2×#66900—22no—
17#10622706—22no—
18#10622706—22no—
19#10622692—21no—
20#10622691—21no—
21#10622678—22no—
22#10622608—22no—
23C2×#66874—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27Q8⋊(C11⋊C8)—22no—
28#10622120—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×#106—24no—
56C11×C4⋊C8D412yes—
57C11×#103—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66900—44no—
61#66874—28no—
62#66872—24no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10159—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—41no—
82C2×Dic22—22no—
83C2×Dic22—44no—
84C2×Dic22—41no—
85C2×C8×C11—22no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106#4318—22no—
107#4318—42no—
108#4318SD1614yes—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—41no—
113#3229D1111yescharacteristic
114#3165—111no—
115C2×#487—111no—
116#1966—111no—
117#1549—111no—
118#1493—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121Q8×C11—42no—
122Q8×C11—42no—
123Q8×C11—82no—
124Q8×C11—81no—
125Q8×C11—81no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—44no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×SD1612yes—
139C2×C4×C11#13712yes—
140C2×Dic11—42no—
141C2×Dic11—82no—
142Dic22—44no—
143Dic22—82no—
144C8×C11—42no—
145C11⋊C8—24no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148#533C2×D1111yescharacteristic
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#501—222no—
152#500—221no—
153#498—21no—
154#498—221no—
155#487—21no—
156#487—222no—
157#487—222no—
158#483—22no—
159#475—22no—
160#431C2×D1111yescharacteristic
161#428—222no—
162#423—111no—
163C2×#103—222no—
164C2×#101—222no—
165C4×M16—111no—
166C2×C4×C8—111no—
167#332—222no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46112yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—81no—
176C4×C11—82no—
177C4×C11—81no—
178C4×C11#44812yes—
179C4×C11#45412yes—
180C4×C11#47312yes—
181C4×C11#49211yescharacteristic
182C4×C11#49711yescharacteristic
183Dic11—82no—
184C22×Q8—21no—
185C22×Q8—221no—
186C2×M16—112no—
187C2×M16—221no—
188C22×C8—221no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—112no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8C22⋊D1111yescharacteristic
198C4⋊Q8C22⋊D1111yescharacteristic
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22⋊D1112yes—
209C2×C42C22×D1111yescharacteristic
210#107—224no—
211#106—24no—
212#106—224no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215C4⋊C8C22⋊D1112yes—
216#103—24no—
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—21no—
230C2×Q8—21no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—222no—
236C2×Q8—444no—
237C2×Q8—441no—
238C22×C4—22no—
239C22×C4—441no—
240C22×C4D4×D1111yescharacteristic
241C22×C4#434111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243M16—114no—
244M16—222no—
245M16—442no—
246C2×C8—22no—
247C2×C8—222no—
248C2×C8—222no—
249C2×C8—442no—
250C2×C8—441no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—222no—
262C4⋊C4—222no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—41no—
266C42—41no—
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C42C2×C22⋊D1111yescharacteristic
271C11#1015911yescharacteristic, complemented, Sylow
272C23#6699211yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—82no—
277Q8—81no—
278Q8—444no—
279Q8—882no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—44no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—442no—
287C2×C4—882no—
288C2×C4SD16×D1112yes—
289C2×C4#6696812yes—
290C2×C4#6699011yescharacteristic
291C2×C4#6699011yescharacteristic
292C2×C4#6699111yescharacteristic
293C2×C4#6699211yescharacteristic
294C2×C4#6699311yescharacteristic
295C2×C4#6700611yescharacteristic
296C8—42no—
297C8—224no—
298C8—442no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062277512yes—
303C22#1062283611yescharacteristic
304C4—21no—
305C4—21no—
306C4—81no—
307C4—82no—
308C4—81no—
309C4—882no—
310C4#1062278011yescharacteristic
311C4#1062278312yes—
312C4#1062278811yescharacteristic
313C4#1062281712yes—
314C4#1062285812yes—
315C2—22no—
316C2#1306963611yescharacteristic
317C2#1306969711yescharacteristic
318C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3229D11
hypocenterC11#10159
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

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
#130791632
C2×#106227062
#130694612
#130673002
#130670712
#130664522
C11×#32292
#1015911