Finite Group Databasebeta

← C11×#10171 #14587364

Subgroups — C11×#10171 #14587364

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic
2C11×#3139C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic
5C11×#1546C211yesmaximal, characteristic
6C11×#1493C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#494—21no—
12C11×#491—22no—
13C11×#487—21no—
14C11×#487—22no—
15C11×#487—21no—
16C11×#487—21no—
17C11×#487—22no—
18C11×#462—22no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#419—22no—
23C2×C11×#103—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#332—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⋊Q8D412yes—
43C11×C4⋊Q8D411yescharacteristic
44C11×C4⋊Q8D411yescharacteristic
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×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×#103—24no—
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#10171C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—44no—
76C2×Q8×C11—41no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C11×Q16—84no—
85C11×M16—22no—
86C11×M16—22no—
87C11×M16—42no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—42no—
92C2×C8×C11—41no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
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×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113#3209C2×C1111yescharacteristic
114#3139C2×C1111yescharacteristic
115C2×#487C2×C1111yescharacteristic
116#1997C2×C1111yescharacteristic
117#1546C2×C1111yescharacteristic
118#1493C2×C1111yescharacteristic
119#1278C2×C1111yescharacteristic
120C23×C11#12111yescharacteristic
121Q8×C11—44no—
122Q8×C11—44no—
123Q8×C11—42no—
124Q8×C11—44no—
125Q8×C11—42no—
126Q8×C11—81no—
127Q8×C11—81no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—82no—
135C2×C4×C11—82no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×C4×C11#13512yes—
143C2×C4×C11#13712yes—
144C8×C11—42no—
145C8×C11—42no—
146C8×C11—42no—
147C8×C11—81no—
148#533C22×C1111yescharacteristic
149C2×C4⋊Q8C22×C1111yescharacteristic
150C2×C4⋊Q8C22×C1111yescharacteristic
151#494—21no—
152#491—22no—
153#487—22no—
154#487—21no—
155#487—21no—
156#487—21no—
157#487—22no—
158#462—22no—
159#451—22no—
160#431C22×C1111yescharacteristic
161#423C22×C1111yescharacteristic
162#419—22no—
163C2×#103—22no—
164C4×M16C22×C1111yescharacteristic
165C2×C4×C8C22×C1111yescharacteristic
166#343—22no—
167#332—22no—
168Q8⋊C8—22no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46412yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11—81no—
177C4×C11—82no—
178C4×C11—81no—
179C4×C11#45212yes—
180C4×C11#45512yes—
181C4×C11#47312yes—
182C4×C11#49511yescharacteristic
183C4×C11#49711yescharacteristic
184C22×Q8—21no—
185C22×Q8D4×C1112yes—
186C2×Q16—24no—
187C2×M16—21no—
188C2×M16D4×C1112yes—
189C22×C8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8D4×C1112yes—
198C4⋊Q8D4×C1111yescharacteristic
199C4⋊Q8D4×C1111yescharacteristic
200#125—21no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205#117—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C42C23×C1111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8D4×C1112yes—
214#103—28no—
215#103—24no—
216#103—24no—
217#103—24no—
218C22⋊C8—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8D4×C1112yes—
224C2×C11—22no—
225C2×C11#200411yescharacteristic
226C2×C11#201511yescharacteristic
227C2×C11#202011yescharacteristic
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—44no—
234C2×Q8—41no—
235C2×Q8—42no—
236C2×Q8—42no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4C2×D4×C1111yescharacteristic
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C11×#4111yescharacteristic
242Q16—84no—
243M16—22no—
244M16—22no—
245M16—42no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—42no—
250C2×C8—41no—
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—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C22⋊C4—41no—
266C42—41no—
267C42C2×D4×C1111yescharacteristic
268C42C2×D4×C1111yescharacteristic
269C42C2×D4×C1111yescharacteristic
270C42C2×D4×C1111yescharacteristic
271C11#1017111yescharacteristic, direct product factor, Sylow
272C23C11×#12111yescharacteristic
273Q8—44no—
274Q8—44no—
275Q8—42no—
276Q8—44no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4C11×#12011yescharacteristic
289C2×C4C11×#12011yescharacteristic
290C2×C4C11×#12011yescharacteristic
291C2×C4C11×#12111yescharacteristic
292C2×C4C11×#12111yescharacteristic
293C2×C4C11×#12711yescharacteristic
294C2×C4C11×#13512yes—
295C2×C4C11×#13712yes—
296C8—42no—
297C8—42no—
298C8—42no—
299C8—81no—
300C22—21no—
301C22—21no—
302C22C11×#39211yescharacteristic
303C22C11×#46412yes—
304C4—21no—
305C4—21no—
306C4—82no—
307C4—81no—
308C4—82no—
309C4—81no—
310C4C11×#45212yes—
311C4C11×#45512yes—
312C4C11×#47312yes—
313C4C11×#49511yescharacteristic
314C4C11×#49711yescharacteristic
315C2—22no—
316C2C11×#200411yescharacteristic
317C2C11×#201511yescharacteristic
318C2C11×#202011yescharacteristic
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. #10171C11direct (N × H)
271. C11#10171direct (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×#31392
C2×C11×#4872
C11×#19972
C11×#15462
C11×#14932
C11×#12782
#1017111