Finite Group Databasebeta

← C11×#10275 #14587468

Subgroups — C11×#10275 #14587468

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C11×#474C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×#332C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#487—22no—
12C11×#487—22no—
13C11×#476—22no—
14C11×#476—22no—
15C11×#474—22no—
16C11×#474—22no—
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103—22no—
23C2×C11×#102—21no—
24C2×C11×#102—21no—
25C2×C11×C22⋊C8—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11D412yes—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D412yes—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#103—28no—
65C11×#102—24no—
66C11×#102—24no—
67C11×C22⋊C8—44no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#10275C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—82no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11Q1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—42no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C2×#487C2×C1111yescharacteristic, complemented
123C2×#476C2×C1111yescharacteristic
124C2×#474C2×C1111yescharacteristic
125#1954C2×C1111yescharacteristic
126C2×#333C2×C1111yescharacteristic, complemented
127C2×#332C2×C1111yescharacteristic, complemented
128#1277C2×C1111yescharacteristic, complemented
129C23×C11—22no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11#12111yescharacteristic
135Q8×C11—44no—
136Q8×C11—82no—
137Q8×C11—82no—
138Q8×C11—81no—
139Q8×C11—81no—
140D4×C11—22no—
141D4×C11—22no—
142D4×C11—41no—
143D4×C11—41no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×C4×C11C2×Q1611yescharacteristic
161C2×C4×C11#13512yes—
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11#13711yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×D4C22×C1111yescharacteristic
173#487—22no—
174#487—22no—
175#476—22no—
176#476—22no—
177#474—22no—
178#474—22no—
179C2×#107—21no—
180C2×#106—21no—
181C2×C4⋊C8C22×C1111yescharacteristic
182C2×C4⋊C8C22×C1111yescharacteristic
183C2×C4⋊C8C22×C1111yescharacteristic
184C2×#103—22no—
185C2×#102—21no—
186C2×#102—21no—
187C2×C22⋊C8—22no—
188C2×C4×C8C22×C1111yescharacteristic
189#333—22no—
190#332—22no—
191C22×C11—44no—
192C22×C11—42no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11#39211yescharacteristic
197C22×C11#46312yes—
198C22×C11#46711yescharacteristic
199C22×C11#47011yescharacteristic
200C22×C11#47112yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11—82no—
206C4×C11#44912yes—
207C4×C11#45111yescharacteristic
208C4×C11#45111yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#49511yescharacteristic
212C4×C11#49611yescharacteristic
213C22×Q8—21no—
214C22×Q8—21no—
215C22×D4D4×C1111yescharacteristic
216C23×C4—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8D4×C1112yes—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8D4×C1112yes—
228C4⋊Q8D4×C1112yes—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C23×C1111yescharacteristic
240#107—24no—
241#106—24no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C1112yes—
247C4⋊C8D4×C1112yes—
248#103—28no—
249#102—24no—
250#102—24no—
251C22⋊C8—44no—
252C4×C8—21no—
253C4×C8—21no—
254C2×C11—82no—
255C2×C11#168312yes—
256C2×C11#170312yes—
257C2×C11#200111yescharacteristic
258C2×C11#201211yescharacteristic
259C2×C11#201911yescharacteristic
260C24—21no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—82no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4C11×Q1612yes—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4C2×D4×C1111yescharacteristic
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C11×#4111yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—42no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42C2×D4×C1111yescharacteristic
308C42C2×D4×C1111yescharacteristic
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C11#1027511yescharacteristic, direct product factor, Sylow
312C23—22no—
313C23—41no—
314C23—42no—
315C23—41no—
316C23—42no—
317C23C11×#12111yescharacteristic
318Q8—44no—
319Q8—82no—
320Q8—82no—
321Q8—81no—
322Q8—81no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12711yescharacteristic
343C2×C4C2×C11×Q1611yescharacteristic
344C2×C4C11×#13512yes—
345C2×C4C11×#13511yescharacteristic
346C2×C4C11×AGL(1,ℤ/8)12yes—
347C2×C4C11×#13711yescharacteristic
348C2×C4C11×#13711yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—81no—
353C22—44no—
354C22—42no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22C11×#39211yescharacteristic
359C22C11×#46312yes—
360C22C11×#46711yescharacteristic
361C22C11×#47011yescharacteristic
362C22C11×#47112yes—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—82no—
367C4—82no—
368C4C11×#44912yes—
369C4C11×#45111yescharacteristic
370C4C11×#45111yescharacteristic
371C4C11×#45211yescharacteristic
372C4C11×#45211yescharacteristic
373C4C11×#49511yescharacteristic
374C4C11×#49611yescharacteristic
375C2—82no—
376C2C11×#168312yes—
377C2C11×#170312yes—
378C2C11×#200111yescharacteristic
379C2C11×#201211yescharacteristic
380C2C11×#201911yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#487C2semidirect
5. C2×C11×#333C2semidirect
6. C2×C11×#332C2semidirect
7. C11×#1277C2semidirect
70. #10275C11direct (N × H)
122. C2×#487C2×C11semidirect
126. C2×#333C2×C11semidirect
127. C2×#332C2×C11semidirect
128. #1277C2×C11semidirect
311. C11#10275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4762
C2×C11×#4742
C11×#19542
C2×C11×#3332
C2×C11×#3322
C11×#12772
#1027511