Finite Group Databasebeta

← C11×#10060 #14587253

Subgroups — C11×#10060 #14587253

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 396 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
3C11×#2542C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C22⋊Q8—22no—
11C2×C4×D4×C11C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C11×#476—22no—
15C11×#476—22no—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—22no—
20C2×C11×#102—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#399—22no—
23C11×#390—21no—
24C11×#384—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×D4⋊C8—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—
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⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×C22⋊Q8—44no—
45C11×C22⋊Q8—44no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#106—24no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—28no—
67C11×#102—24no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70C11×#95—21no—
71#10060C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11Q1612yes—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—42no—
103C2×C8×C11—41no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4SD1614yes—
117C11×C22⋊C4—48no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C2×#487C2×C1111yescharacteristic, complemented
127C2×#476C2×C1111yescharacteristic
128#2542C2×C1111yescharacteristic
129#1987C2×C1111yescharacteristic, complemented
130C2×#332C2×C1111yescharacteristic, complemented
131C2×D4⋊C8C2×C1111yescharacteristic
132#1279C2×C1111yescharacteristic, complemented
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11#12011yescharacteristic
139Q8×C11—44no—
140Q8×C11—82no—
141Q8×C11—82no—
142Q8×C11—81no—
143Q8×C11—81no—
144D4×C11—22no—
145D4×C11—22no—
146D4×C11—41no—
147D4×C11—41no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×SD1612yes—
168C2×C4×C11C2×Q1611yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)12yes—
171C2×C4×C11#13711yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—81no—
176C2×C4⋊Q8C22×C1111yescharacteristic
177C2×C4⋊Q8C22×C1111yescharacteristic
178C2×C22⋊Q8—22no—
179C2×C4×D4C22×C1111yescharacteristic
180#487—22no—
181#487—22no—
182#476—22no—
183#476—22no—
184C2×#106—21no—
185C2×C4⋊C8C22×C1111yescharacteristic
186C2×C4⋊C8C22×C1111yescharacteristic
187C2×#103—22no—
188C2×#102—21no—
189C2×C4×C8C22×C1111yescharacteristic
190#399—22no—
191#390—21no—
192#384—21no—
193C4×C4⋊C4C22×C1111yescharacteristic
194#340—22no—
195#332—22no—
196D4⋊C8—22no—
197C22×C11—44no—
198C22×C11—42no—
199C22×C11—82no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#39211yescharacteristic
203C22×C11#45012yes—
204C22×C11#45111yescharacteristic
205C22×C11#45211yescharacteristic
206C22×C11#45412yes—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—44no—
210C4×C11—82no—
211C4×C11—81no—
212C4×C11—82no—
213C4×C11#45111yescharacteristic
214C4×C11#45211yescharacteristic
215C4×C11#46012yes—
216C4×C11#46711yescharacteristic
217C4×C11#47011yescharacteristic
218C4×C11#49211yescharacteristic
219C4×C11#49611yescharacteristic
220C22×Q8—21no—
221C22×Q8—21no—
222C22×D4D4×C1111yescharacteristic
223C23×C4—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C1112yes—
235C22⋊Q8—44no—
236C22⋊Q8—44no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C1111yescharacteristic
246C2×C4⋊C4D4×C1112yes—
247C2×C4⋊C4D4×C1112yes—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—21no—
250C2×C42—21no—
251C2×C42C23×C1111yescharacteristic
252#106—24no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C1112yes—
257#103—28no—
258#102—24no—
259C4×C8—21no—
260C4×C8D4×C1112yes—
261#95—21no—
262C2×C11—82no—
263C2×C11#163512yes—
264C2×C11#163712yes—
265C2×C11#200111yescharacteristic
266C2×C11#200311yescharacteristic
267C2×C11#201411yescharacteristic
268C24—21no—
269C2×Q8—22no—
270C2×Q8—44no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4C11×Q1612yes—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—42no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—48no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C11×SD1614yes—
313C22⋊C4—48no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42C2×D4×C1111yescharacteristic
319C42C2×D4×C1111yescharacteristic
320C42C2×D4×C1111yescharacteristic
321C42C11×#4111yescharacteristic
322C11#1006011yescharacteristic, direct product factor, Sylow
323C23—22no—
324C23—41no—
325C23—42no—
326C23—41no—
327C23—42no—
328C23C11×#12011yescharacteristic
329Q8—44no—
330Q8—82no—
331Q8—81no—
332Q8—81no—
333Q8—82no—
334D4—22no—
335D4—22no—
336D4—41no—
337D4—41no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12111yescharacteristic
354C2×C4C11×#12111yescharacteristic
355C2×C4C11×#12111yescharacteristic
356C2×C4C11×#12711yescharacteristic
357C2×C4C2×C11×SD1612yes—
358C2×C4C2×C11×Q1611yescharacteristic
359C2×C4C11×#13511yescharacteristic
360C2×C4C11×AGL(1,ℤ/8)12yes—
361C2×C4C11×#13711yescharacteristic
362C2×C4C11×#13711yescharacteristic
363C8—42no—
364C8—42no—
365C8—81no—
366C22—44no—
367C22—42no—
368C22—82no—
369C22—81no—
370C22—81no—
371C22C11×#39211yescharacteristic
372C22C11×#45012yes—
373C22C11×#45111yescharacteristic
374C22C11×#45211yescharacteristic
375C22C11×#45412yes—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—82no—
380C4—81no—
381C4—82no—
382C4C11×#45111yescharacteristic
383C4C11×#45211yescharacteristic
384C4C11×#46012yes—
385C4C11×#46711yescharacteristic
386C4C11×#47011yescharacteristic
387C4C11×#49211yescharacteristic
388C4C11×#49611yescharacteristic
389C2—82no—
390C2C11×#163512yes—
391C2C11×#163712yes—
392C2C11×#200111yescharacteristic
393C2C11×#200311yescharacteristic
394C2C11×#201411yescharacteristic
subgroupG/H
center, socleC23×C11#120
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
4. C11×#1987C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1279C2semidirect
71. #10060C11direct (N × H)
126. C2×#487C2×C11semidirect
129. #1987C2×C11semidirect
130. C2×#332C2×C11semidirect
132. #1279C2×C11semidirect
322. C11#10060direct (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
C11×#25422
C11×#19872
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1006011