Finite Group Databasebeta

← C11×#10251 #14587444

Subgroups — C11×#10251 #14587444

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic
4C11×#1546C211yesmaximal, characteristic
5C11×#1503C211yesmaximal, characteristic
6C11×#1479C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#487—21no—
14C11×#483—22no—
15C11×#479—22no—
16C11×#477—21no—
17C11×#475—21no—
18C11×#475—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#428—21no—
22C11×#423C2211yescharacteristic
23C11×#419—21no—
24C11×#398—22no—
25C11×#391—21no—
26C11×#389—22no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#332—22no—
29C11×#328—22no—
30C11×Q8⋊C8—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—42no—
39C11×C4⋊Q8—42no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D412yes—
58C2×C42×C11—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—22no—
62C11×#106—24no—
63C11×#106—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—22no—
69C11×#103—22no—
70C11×#103—24no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C11×#95—24no—
76C11×#95D412yes—
77#10251C1111yesmaximal, characteristic, direct product factor, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11SD1612yes—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—48no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130#3229C2×C1111yescharacteristic
131#3078C2×C1111yescharacteristic
132#2546C2×C1111yescharacteristic
133#1546C2×C1111yescharacteristic
134#1503C2×C1111yescharacteristic
135#1479C2×C1111yescharacteristic
136#1303C2×C1111yescharacteristic
137C23×C11#12011yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—41no—
141Q8×C11—41no—
142Q8×C11—42no—
143Q8×C11—81no—
144Q8×C11—81no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—81no—
176#533C22×C1111yescharacteristic
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8C22×C1111yescharacteristic
179C2×C4×Q8C22×C1111yescharacteristic
180#498—21no—
181#487—21no—
182#483—22no—
183#479—22no—
184#477—21no—
185#475—21no—
186#475—22no—
187#431C22×C1111yescharacteristic
188#431C22×C1111yescharacteristic
189#428—21no—
190#423C22×C1111yescharacteristic
191#419—21no—
192#398—22no—
193#391—21no—
194#389—22no—
195C4×C4⋊C4C22×C1111yescharacteristic
196#332—22no—
197#328—22no—
198Q8⋊C8—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#39211yescharacteristic
202C22×C11#45011yescharacteristic
203C22×C11#45211yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—44no—
208C4×C11—42no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11#44811yescharacteristic
214C4×C11#44911yescharacteristic
215C4×C11#45612yes—
216C4×C11#46511yescharacteristic
217C4×C11#46811yescharacteristic
218C22×Q8—21no—
219C22×Q8D4×C1111yescharacteristic
220C2×M16—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—42no—
226C4⋊Q8—42no—
227C4⋊Q8D4×C1111yescharacteristic
228C4⋊Q8D4×C1111yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C1111yescharacteristic
244C2×C4⋊C4D4×C1112yes—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C23×C1111yescharacteristic
248#107—22no—
249#106—22no—
250#106—24no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8D4×C1112yes—
254C4⋊C8D4×C1112yes—
255#103—22no—
256#103—22no—
257#103—24no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—24no—
263#95D4×C1112yes—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#200011yescharacteristic
267C2×C11#200511yescharacteristic
268C2×C11#200911yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8C11×SD1612yes—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4C2×D4×C1111yescharacteristic
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C4⋊C4—24no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—48no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42C2×D4×C1111yescharacteristic
318C42C2×D4×C1111yescharacteristic
319C42C2×D4×C1111yescharacteristic
320C42C11×#4111yescharacteristic
321C11#1025111yescharacteristic, direct product factor, Sylow
322C23C11×#12011yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332Q8—81no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4C11×#12011yescharacteristic
349C2×C4C11×#12011yescharacteristic
350C2×C4C11×#12111yescharacteristic
351C2×C4C11×#12111yescharacteristic
352C2×C4C11×#12111yescharacteristic
353C2×C4C11×#12711yescharacteristic
354C2×C4C2×C11×SD1611yescharacteristic
355C2×C4C11×#13511yescharacteristic
356C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
357C2×C4C11×#13711yescharacteristic
358C8—42no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22C11×#39211yescharacteristic
364C22C11×#45011yescharacteristic
365C22C11×#45211yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4C11×#44811yescharacteristic
376C4C11×#44911yescharacteristic
377C4C11×#45612yes—
378C4C11×#46511yescharacteristic
379C4C11×#46811yescharacteristic
380C2—21no—
381C2—21no—
382C2C11×#200011yescharacteristic
383C2C11×#200511yescharacteristic
384C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#120
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
77. #10251C11direct (N × H)
321. C11#10251direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#30782
C11×#25462
C11×#15462
C11×#15032
C11×#14792
C11×#13032
#1025111