Finite Group Databasebeta

← C11×#10186 #14587379

Subgroups — C11×#10186 #14587379

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4C11×#1546C211yesmaximal, characteristic, complemented
5C11×#1481C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C11×#533C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#487—21no—
14C11×#483—22no—
15C11×#478—22no—
16C11×#476—21no—
17C11×#475—22no—
18C11×#474—21no—
19C11×#461—22no—
20C11×#461—22no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C11×#428—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#418—21no—
27C2×C11×#103—21no—
28C11×#332—22no—
29C11×Q8⋊C8—22no—
30C11×#323—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×SD16—24no—
35C2×C11×SD16—42no—
36C2×C11×SD16—42no—
37C2×C11×M16—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C11×#117—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—22no—
61C11×#106—24no—
62C11×#106—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C11×#103—24no—
71C11×#102—22no—
72C11×#102—22no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10186C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11SD1612yes—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C11×SD16—48no—
102C11×M16—41no—
103C11×M16—41no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130#3229C2×C1111yescharacteristic, complemented
131#3077C2×C1111yescharacteristic
132C2×#461C2×C1111yescharacteristic
133#1546C2×C1111yescharacteristic, complemented
134#1481C2×C1111yescharacteristic, complemented
135#1460C2×C1111yescharacteristic
136#1301C2×C1111yescharacteristic, complemented
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11#12111yescharacteristic
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—81no—
148Q8×C11—81no—
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—41no—
152D4×C11—41no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C8×C11—42no—
175C8×C11—42no—
176C8×C11—42no—
177C8×C11—81no—
178C22×SD16—21no—
179#533C22×C1111yescharacteristic
180C2×C4⋊Q8C22×C1111yescharacteristic
181C2×C4×D4C22×C1111yescharacteristic
182#498—21no—
183#487—21no—
184#483—22no—
185#478—22no—
186#476—21no—
187#475—22no—
188#474—21no—
189#461—22no—
190#461—22no—
191#431C22×C1111yescharacteristic
192#431C22×C1111yescharacteristic
193#428—21no—
194#423C22×C1111yescharacteristic
195C2×C4⋊C8C22×C1111yescharacteristic
196#418—21no—
197C2×#103—21no—
198#332—22no—
199Q8⋊C8—22no—
200#323—22no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—42no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#46511yescharacteristic
210C22×C11#46811yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11#44811yescharacteristic
219C4×C11#44911yescharacteristic
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#47112yes—
223C22×Q8—21no—
224C22×D4D4×C1111yescharacteristic
225C23×C4—21no—
226C2×SD16—24no—
227C2×SD16—42no—
228C2×SD16—42no—
229C2×M16—21no—
230C22×C8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C1112yes—
235C4⋊Q8D4×C1111yescharacteristic
236C4⋊Q8D4×C1111yescharacteristic
237#125—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246#117—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C42C23×C1111yescharacteristic
252#107—22no—
253#106—22no—
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260C4⋊C8D4×C1112yes—
261#103—24no—
262#103—24no—
263#102—22no—
264#102—22no—
265C22⋊C8—21no—
266C22⋊C8D4×C1112yes—
267C4×C8—21no—
268C4×C8—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—82no—
272C2×C11#200011yescharacteristic
273C2×C11#200911yescharacteristic
274C2×C11#201911yescharacteristic
275C24—21no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4C11×SD1612yes—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—82no—
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C11×#4111yescharacteristic
298SD16—48no—
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—41no—
323C42C2×D4×C1111yescharacteristic
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C42C2×D4×C1111yescharacteristic
327C11#1018611yescharacteristic, direct product factor, Sylow
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23C11×#12111yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4C11×#12011yescharacteristic
356C2×C4C11×#12011yescharacteristic
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12111yescharacteristic
359C2×C4C11×#12111yescharacteristic
360C2×C4C11×#12711yescharacteristic
361C2×C4C2×C11×SD1611yescharacteristic
362C2×C4C11×#13511yescharacteristic
363C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
364C2×C4C11×#13711yescharacteristic
365C8—42no—
366C8—42no—
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22C11×#39211yescharacteristic
377C22C11×#46511yescharacteristic
378C22C11×#46811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4C11×#44811yescharacteristic
387C4C11×#44911yescharacteristic
388C4C11×#45011yescharacteristic
389C4C11×#45211yescharacteristic
390C4C11×#47112yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2C11×#200011yescharacteristic
395C2C11×#200911yescharacteristic
396C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
1. C11×#3229C2semidirect
4. C11×#1546C2semidirect
5. C11×#1481C2semidirect
7. C11×#1301C2semidirect
77. #10186C11direct (N × H)
130. #3229C2×C11semidirect
133. #1546C2×C11semidirect
134. #1481C2×C11semidirect
136. #1301C2×C11semidirect
327. C11#10186direct (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×#30772
C2×C11×#4612
C11×#15462
C11×#14812
C11×#14602
C11×#13012
#1018611