Finite Group Databasebeta

← C11×#10163 #14587356

Subgroups — C11×#10163 #14587356

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic
2C11×#3165C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic
5C11×#1548C211yesmaximal, characteristic
6C11×#1493C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#494—21no—
15C11×#487—21no—
16C11×#487—22no—
17C11×#487—22no—
18C11×#462—22no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21C11×#428—22no—
22C11×#423C2211yescharacteristic
23C2×C11×#103—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#333—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C2×C11×Q16—24no—
32C2×C11×M16—21no—
33C2×C11×M16D412yes—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×C4⋊Q8D412yes—
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#103—28no—
62C11×#103—24no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69#10163C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C11×Q16—84no—
84C11×M16—22no—
85C11×M16—42no—
86C11×M16Q1614yescomplemented
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—42no—
91C2×C8×C11—41no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#3209C2×C1111yescharacteristic
113#3165C2×C1111yescharacteristic
114C2×#487C2×C1111yescharacteristic
115#1997C2×C1111yescharacteristic
116#1548C2×C1111yescharacteristic
117#1493C2×C1111yescharacteristic
118#1278C2×C1111yescharacteristic
119C23×C11#12111yescharacteristic
120Q8×C11—44no—
121Q8×C11—42no—
122Q8×C11—44no—
123Q8×C11—42no—
124Q8×C11—82no—
125Q8×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—82no—
133C2×C4×C11—82no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11C2×Q1612yes—
141C2×C4×C11#13712yes—
142C8×C11—24no—
143C8×C11—42no—
144C8×C11—42no—
145C8×C11—81no—
146#533C22×C1111yescharacteristic
147C2×C4⋊Q8C22×C1111yescharacteristic
148C2×C4⋊Q8C22×C1111yescharacteristic
149#501—22no—
150#500—21no—
151#498—21no—
152#494—21no—
153#487—22no—
154#487—21no—
155#487—22no—
156#462—22no—
157#451—22no—
158#431C22×C1111yescharacteristic
159#428—22no—
160#423C22×C1111yescharacteristic
161C2×#103—22no—
162C4×M16C22×C1111yescharacteristic
163C2×C4×C8C22×C1111yescharacteristic
164#343—22no—
165#333—22no—
166Q8⋊C8—22no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39211yescharacteristic
170C22×C11#46212yes—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11—82no—
176C4×C11—81no—
177C4×C11#45112yes—
178C4×C11#45512yes—
179C4×C11#47112yes—
180C4×C11#49411yescharacteristic
181C4×C11#49711yescharacteristic
182C22×Q8—21no—
183C22×Q8D4×C1112yes—
184C2×Q16—24no—
185C2×M16—21no—
186C2×M16D4×C1112yes—
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⋊Q8D4×C1112yes—
196C4⋊Q8D4×C1111yescharacteristic
197C4⋊Q8D4×C1111yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203#117—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C42C23×C1111yescharacteristic
209#107—24no—
210#106—24no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8D4×C1112yes—
214#103—28no—
215#103—24no—
216C22⋊C8—21no—
217#97—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8D4×C1112yes—
222C2×C11—22no—
223C2×C11#200411yescharacteristic
224C2×C11#201611yescharacteristic
225C2×C11#201911yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—22no—
231C2×Q8—44no—
232C2×Q8—41no—
233C2×Q8—82no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4C2×D4×C1111yescharacteristic
237C22×C4C2×D4×C1111yescharacteristic
238C22×C4C11×#4111yescharacteristic
239Q16—84no—
240M16—22no—
241M16—42no—
242M16C11×Q1614yescomplemented
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—42no—
247C2×C8—41no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C42—41no—
264C42C2×D4×C1111yescharacteristic
265C42C2×D4×C1111yescharacteristic
266C42C2×D4×C1111yescharacteristic
267C42C2×D4×C1111yescharacteristic
268C11#1016311yescharacteristic, direct product factor, Sylow
269C23C11×#12111yescharacteristic
270Q8—44no—
271Q8—42no—
272Q8—44no—
273Q8—42no—
274Q8—82no—
275Q8—82no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4C11×#12011yescharacteristic
285C2×C4C11×#12011yescharacteristic
286C2×C4C11×#12011yescharacteristic
287C2×C4C11×#12111yescharacteristic
288C2×C4C11×#12111yescharacteristic
289C2×C4C11×#12711yescharacteristic
290C2×C4C2×C11×Q1612yes—
291C2×C4C11×#13712yes—
292C8—24no—
293C8—42no—
294C8—42no—
295C8—81no—
296C22—21no—
297C22—21no—
298C22C11×#39211yescharacteristic
299C22C11×#46212yes—
300C4—21no—
301C4—21no—
302C4—82no—
303C4—81no—
304C4—82no—
305C4—81no—
306C4C11×#45112yes—
307C4C11×#45512yes—
308C4C11×#47112yes—
309C4C11×#49411yescharacteristic
310C4C11×#49711yescharacteristic
311C2—22no—
312C2C11×#200411yescharacteristic
313C2C11×#201611yescharacteristic
314C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
69. #10163C11direct (N × H)
86. C11×M16Q16semidirect
242. M16C11×Q16semidirect
268. C11#10163direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#31652
C2×C11×#4872
C11×#19972
C11×#15482
C11×#14932
C11×#12782
#1016311