Finite Group Databasebeta

← C11×#10166 #14587359

Subgroups — C11×#10166 #14587359

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic
2C2×C11×#498C211yesmaximal, characteristic, complemented
3C11×#3141C211yesmaximal, characteristic
4C11×#1966C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#500—21no—
12C11×#498—22no—
13C11×#498—22no—
14C11×#489—22no—
15C11×#487—21no—
16C11×#486—21no—
17C11×#486—21no—
18C11×#480—22no—
19C11×#474—22no—
20C11×#431C2211yescharacteristic
21C2×C11×#106—22no—
22C11×#423C2211yescharacteristic
23C11×#417—22no—
24C2×C11×#101—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
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×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11C2311yescharacteristic
55C11×#107—24no—
56C11×#106—28no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×#103—24no—
61C11×#102—24no—
62C11×#102—24no—
63C11×#101—44no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70#10166C1111yesmaximal, characteristic, direct product factor, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—82no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—42no—
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#3226C2×C1111yescharacteristic
116C2×#498C2×C1111yescharacteristic, complemented
117#3141C2×C1111yescharacteristic
118#1966C2×C1111yescharacteristic, complemented
119#1548C2×C1111yescharacteristic, complemented
120#1492C2×C1111yescharacteristic
121#1278C2×C1111yescharacteristic, complemented
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—42no—
125Q8×C11—82no—
126Q8×C11—82no—
127Q8×C11—82no—
128Q8×C11—81no—
129Q8×C11—81no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11—82no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11#13512yes—
150C2×C4×C11AGL(1,ℤ/8)12yes—
151C8×C11—24no—
152C8×C11—42no—
153C8×C11—42no—
154C8×C11—81no—
155#532C22×C1111yescharacteristic
156C2×C4⋊Q8C22×C1111yescharacteristic
157C2×C4⋊Q8C22×C1111yescharacteristic
158#500—21no—
159#498—22no—
160#498—22no—
161#489—22no—
162#487—21no—
163#486—21no—
164#486—21no—
165#480—22no—
166#474—22no—
167#431C22×C1111yescharacteristic
168C2×#106—22no—
169#423C22×C1111yescharacteristic
170#417—22no—
171C2×#101—22no—
172C4×M16C22×C1111yescharacteristic
173C2×C4×C8C22×C1111yescharacteristic
174#333—22no—
175D4⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#39211yescharacteristic
182C22×C11#46312yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11—81no—
187C4×C11—82no—
188C4×C11#44912yes—
189C4×C11#45612yes—
190C4×C11#47112yes—
191C4×C11#49511yescharacteristic
192C4×C11#49611yescharacteristic
193C2×#41—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C2×M16—21no—
197C2×M16D4×C1112yes—
198C22×C8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8D4×C1112yes—
207C4⋊Q8D4×C1111yescharacteristic
208#127D4×C1111yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×D4—21no—
213C4×D4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C1112yes—
218C2×C42C23×C1111yescharacteristic
219#107—24no—
220#106—28no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8D4×C1112yes—
224#103—24no—
225#102—24no—
226#102—24no—
227#101—44no—
228C22⋊C8—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8D4×C1112yes—
234C2×C11—22no—
235C2×C11—161no—
236C2×C11#200511yescharacteristic
237C2×C11#201211yescharacteristic
238C2×C11#201911yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—82no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C22×C4C11×#4111yescharacteristic
259M16—22no—
260M16—22no—
261M16—42no—
262C2×C8—24no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—41no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42C2×D4×C1111yescharacteristic
280C42C2×D4×C1111yescharacteristic
281C42C2×D4×C1111yescharacteristic
282C42C2×D4×C1111yescharacteristic
283C11#1016611yescharacteristic, direct product factor, Sylow
284C23—41no—
285C23C11×#12111yescharacteristic
286Q8—42no—
287Q8—82no—
288Q8—81no—
289Q8—81no—
290Q8—82no—
291Q8—82no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4C11×#12011yescharacteristic
306C2×C4C11×#12011yescharacteristic
307C2×C4C11×#12011yescharacteristic
308C2×C4C11×#12111yescharacteristic
309C2×C4C11×#12111yescharacteristic
310C2×C4C11×#12711yescharacteristic
311C2×C4C11×#13512yes—
312C2×C4C11×AGL(1,ℤ/8)12yes—
313C8—24no—
314C8—42no—
315C8—42no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C11×#39211yescharacteristic
323C22C11×#46312yes—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—82no—
329C4C11×#44912yes—
330C4C11×#45612yes—
331C4C11×#47112yes—
332C4C11×#49511yescharacteristic
333C4C11×#49611yescharacteristic
334C2—22no—
335C2—161no—
336C2C11×#200511yescharacteristic
337C2C11×#201211yescharacteristic
338C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C2×C11×#498C2semidirect
4. C11×#1966C2semidirect
5. C11×#1548C2semidirect
7. C11×#1278C2semidirect
70. #10166C11direct (N × H)
116. C2×#498C2×C11semidirect
118. #1966C2×C11semidirect
119. #1548C2×C11semidirect
121. #1278C2×C11semidirect
283. C11#10166direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C2×C11×#4982
C11×#31412
C11×#19662
C11×#15482
C11×#14922
C11×#12782
#1016611