Finite Group Databasebeta

← #14655218

Subgroups — #14655218

Order 2816.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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
2#13074567C211yesmaximal, characteristic
3#13067334C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic
5#13067128C211yesmaximal, characteristic
6#13066508C211yesmaximal, characteristic
7C11×#3236C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#484—21no—
14C11×#483—21no—
15C11×#479—22no—
16C11×#432C2211yescharacteristic
17#10622692—21no—
18#10622691—21no—
19#10622678—22no—
20#10622608—22no—
21#10622599—22no—
22#10622599—22no—
23#10622587—21no—
24#10622587—21no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622176—22no—
30#10622120—22no—
31C22×Dic22—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D412yes—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57C11×#107—22no—
58C11×#106—22no—
59C11×C4⋊C8D412yes—
60C11×#103—22no—
61C11×#103—22no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66C11⋊#95—21no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10103—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C2×Dic22—44no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×C8×C11—22no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4×Dic11—42no—
114#4318—24no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3236D1111yescharacteristic
118#3165—111no—
119#2642—111no—
120#1556—111no—
121#1528—111no—
122#1506—111no—
123#1300—111no—
124C23×C11#12011yescharacteristic
125Q8×C11—42no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—44no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147Dic22—82no—
148Dic22—82no—
149C8×C11—42no—
150C11⋊C8—24no—
151C11⋊C8—81no—
152#533C2×D1111yescharacteristic
153C2×C4⋊Q8—111no—
154C2×#125C2×D1111yescharacteristic
155#501—21no—
156#501—222no—
157#500—221no—
158#498—221no—
159#491—21no—
160#484—21no—
161#483—21no—
162#479—22no—
163#432—111no—
164#432C2×D1111yescharacteristic
165#428—222no—
166C4×M16—111no—
167#400—222no—
168#400—222no—
169#391—221no—
170#391—221no—
171#376—111no—
172#332—222no—
173#330—222no—
174#328—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39211yescharacteristic
178C22×C11#45612yes—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11#45412yes—
189Dic11—82no—
190Dic11—82no—
191C22×Q8—221no—
192C2×M16—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8C22⋊D1111yescharacteristic
198C4⋊Q8C22⋊D1111yescharacteristic
199#125—21no—
200#125—21no—
201#125—21no—
202#125—21no—
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208#117—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—112no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C42—221no—
216C2×C42C22×D1111yescharacteristic
217#107—22no—
218#107—224no—
219#106—22no—
220#106—224no—
221C4⋊C8—221no—
222C4⋊C8C22⋊D1112yes—
223#103—22no—
224#103—22no—
225C22⋊C8—21no—
226C22⋊C8—221no—
227#97—21no—
228#97—112no—
229#97—221no—
230C4×C8—221no—
231#95—112no—
232#95—224no—
233#95—224no—
234#95—221no—
235C2×C11—22no—
236C2×C11#200311yescharacteristic
237C2×C11#200511yescharacteristic
238C2×C11#200911yescharacteristic
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—444no—
242C2×Q8—441no—
243C2×Q8—441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4D4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251M16—224no—
252C2×C8—22no—
253C2×C8—222no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—41no—
274C42—41no—
275C42—442no—
276C42D4×D1111yescharacteristic
277C42#434111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#1010311yescharacteristic, complemented, Sylow
281C23#6699011yescharacteristic
282Q8—42no—
283Q8—81no—
284Q8—882no—
285Q8—882no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—442no—
296C2×C4—444no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4#6699011yescharacteristic
301C2×C4#6699111yescharacteristic
302C2×C4#6699211yescharacteristic
303C2×C4#6699211yescharacteristic
304C2×C4#6699311yescharacteristic
305C2×C4#6700611yescharacteristic
306C8—42no—
307C8—224no—
308C8—881no—
309C22—21no—
310C22—21no—
311C22#1062281812yes—
312C22#1062283611yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—882no—
323C4—882no—
324C4#1062285812yes—
325C2—22no—
326C2#1306963611yescharacteristic
327C2#1306964911yescharacteristic
328C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3236D11
hypocenterC11#10103
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
280. C11#10103semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130745672
#130673342
#130672182
#130671282
#130665082
C11×#32362
#1010311