Finite Group Databasebeta

← C11×#62000 #14639193

Subgroups — C11×#62000 #14639193

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3482C211yesmaximal, characteristic
3C11×#3395C212yesmaximal, complemented
4C11×#3359C212yesmaximal, complemented
5C11×#3328C216yesmaximal, complemented
6C11×#3276C216yesmaximal, complemented
7C11×#3255C213yesmaximal, complemented
8C11×#3209C213yesmaximal, complemented
9C11×#3107C213yesmaximal, complemented
10C11×#3039C213yesmaximal, complemented
11C11×#2991C211yesmaximal, characteristic, complemented
12C2×C11×#137C2216yes—
13Q82×C11—21no—
14C11×#557C2211yescharacteristic
15C11×#557C2212yes—
16C11×#556C2213yes—
17C11×#554—23no—
18C11×#552—23no—
19D4×Q8×C11C2216yes—
20D4×Q8×C11C2211yescharacteristic
21C11×#548—21no—
22C11×#547C2213yes—
23C11×#544—23no—
24C11×#533C2213yes—
25C11×#533C2213yes—
26C2×C11×C4⋊Q8C2213yes—
27C11×#529—23no—
28C11×#520—21no—
29C4×C11×#41C2213yes—
30C4×C11×#41C2211yescharacteristic
31C2×C4×Q8×C11—21no—
32C11×#494C2216yes—
33C11×#487C2216yes—
34C11×#485C2216yes—
35C11×#475C2213yes—
36C11×#475C2216yes—
37C11×#474C2211yescharacteristic
38C11×#470C22112yes—
39C11×#462C2213yes—
40C11×#462C2216yes—
41C11×#462C2216yes—
42C11×#462C2216yes—
43C11×#461C2216yes—
44C11×#461C2213yes—
45C11×#452C2216yes—
46C11×#451C22112yes—
47C8×Q8×C11C2212yes—
48C4×C11×Q16C2216yes—
49C4×C11×SD16C2216yes—
50C11×#436C2216yes—
51C11×#431C2213yes—
52C11×#423C2213yes—
53C11×#419C2216yes—
54C2×C11×#41D411yescharacteristic
55C2×C11×#41C2313yes—
56C22×Q8×C11—21no—
57C22×Q8×C11C2316yes—
58C11×#137—412no—
59C2×C11×Q16C2316yes—
60C2×C11×Q16C23112yes—
61C2×C11×SD16C2316yes—
62C2×C11×M16C2316yes—
63C11×C4⋊Q8—26no—
64C11×C4⋊Q8—23no—
65C11×C4⋊Q8—23no—
66C11×C4⋊Q8C2313yes—
67C11×C4⋊Q8C2316yes—
68C11×C4⋊Q8C2313yes—
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2313yes—
71C11×#126—26no—
72C11×#125—23no—
73C11×#125—26no—
74C11×#125—23no—
75C11×#125—23no—
76C11×#124—23no—
77C11×#123—26no—
78C11×C22⋊Q8—23no—
79C11×C22⋊Q8—23no—
80C11×C22⋊Q8—23no—
81C11×C22⋊Q8—212no—
82C11×C22⋊Q8C2316yes—
83C11×C22⋊Q8C2316yes—
84C11×#121—23no—
85C4×Q8×C11—21no—
86C4×Q8×C11—22no—
87C4×Q8×C11—23no—
88C4×Q8×C11—23no—
89C4×Q8×C11—23no—
90C4×Q8×C11D411yescharacteristic
91C4×Q8×C11C2313yes—
92C4×Q8×C11C2313yes—
93C4×Q8×C11C2316yes—
94C4×Q8×C11C2311yescharacteristic
95C4×D4×C11—26no—
96C4×D4×C11—23no—
97C4×D4×C11—23no—
98C4×D4×C11D413yes—
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2313yes—
101C4×D4×C11C2313yes—
102C11×#117—23no—
103C11×#117—23no—
104C11×#117—23no—
105C11×#117D413yes—
106C11×#117C2313yes—
107C2×C11×C4⋊C4—23no—
108C2×C11×C4⋊C4—23no—
109C2×C11×C4⋊C4—23no—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2312yes—
113C11×#106C2316yes—
114C11×C4⋊C8C2313yes—
115C11×C4⋊C8C2316yes—
116C11×C4⋊C8C2311yescharacteristic
117C11×#103C2316yes—
118C11×#103C23112yes—
119C11×#103C2316yes—
120C11×#103C2316yes—
121C11×#102C2312yes—
122C11×C22⋊C8C2316yes—
123C4×C8×C11C2316yes—
124#62000C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41—24no—
126C11×#41—26no—
127C11×#41—43no—
128C2×Q8×C11—21no—
129C2×Q8×C11—23no—
130C2×Q8×C11—26no—
131C2×Q8×C11—46no—
132C2×Q8×C11—46no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2×D411yescharacteristic
135C2×Q8×C11C2416yes—
136C2×Q8×C11C2413yes—
137C2×D4×C11—23no—
138C2×D4×C11C2×D413yes—
139C2×D4×C11C2411yescharacteristic
140C22×C4×C11—26no—
141C22×C4×C11—21no—
142C22×C4×C11—23no—
143C22×C4×C11—23no—
144C22×C4×C11C2×D413yes—
145C22×C4×C11C2×D413yes—
146C22×C4×C11C2413yes—
147C11×Q16—46no—
148C11×Q16—412no—
149C11×SD16—212no—
150C11×M16—46no—
151C2×C8×C11C2412yes—
152C2×C8×C11C2416yes—
153C11×C4⋊C4—23no—
154C11×C4⋊C4—23no—
155C11×C4⋊C4—26no—
156C11×C4⋊C4—23no—
157C11×C4⋊C4—26no—
158C11×C4⋊C4—26no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—23no—
161C11×C4⋊C4—23no—
162C11×C4⋊C4—23no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—26no—
165C11×C4⋊C4—26no—
166C11×C4⋊C4C2×D413yes—
167C11×C4⋊C4C2×D413yes—
168C11×C4⋊C4C2412yes—
169C11×C4⋊C4C2413yes—
170C11×C4⋊C4C2411yescharacteristic
171C11×C22⋊C4—26no—
172C11×C22⋊C4—26no—
173C11×C22⋊C4—23no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—23no—
176C11×C22⋊C4C2×D416yes—
177C42×C11—23no—
178C42×C11—23no—
179C42×C11—23no—
180C42×C11—26no—
181C42×C11C2×D413yes—
182C42×C11C2×D413yes—
183C42×C11C2413yes—
184C42×C11C2411yescharacteristic
185#3503C2×C1111yescharacteristic, complemented
186#3482C2×C1111yescharacteristic
187#3395C2×C1112yescomplemented
188#3359C2×C1112yescomplemented
189#3328C2×C1116yescomplemented
190#3276C2×C1116yescomplemented
191#3255C2×C1113yescomplemented
192#3209C2×C1113yescomplemented
193#3107C2×C1113yescomplemented
194#3039C2×C1113yescomplemented
195#2991C2×C1111yescharacteristic, complemented
196C23×C11—21no—
197C23×C11C22×D413yes—
198Q8×C11—26no—
199Q8×C11—23no—
200Q8×C11—23no—
201Q8×C11—26no—
202Q8×C11—46no—
203Q8×C11—42no—
204Q8×C11—86no—
205Q8×C11#13714yescomplemented
206D4×C11—26no—
207D4×C11—21no—
208D4×C11—46no—
209D4×C11H(5,𝔽2)12yes—
210C2×C4×C11—26no—
211C2×C4×C11—26no—
212C2×C4×C11—23no—
213C2×C4×C11—23no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—23no—
217C2×C4×C11—23no—
218C2×C4×C11—26no—
219C2×C4×C11—46no—
220C2×C4×C11—46no—
221C2×C4×C11—42no—
222C2×C4×C11—86no—
223C2×C4×C11C22×D413yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D413yes—
226C2×C4×C11C22×D413yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2511yescharacteristic
229C8×C11—26no—
230C8×C11—22no—
231C2×#137C22×C1116yes—
232Q82—21no—
233#557C22×C1112yes—
234#557C22×C1111yescharacteristic
235#556C22×C1113yes—
236#554—23no—
237#552—23no—
238D4×Q8C22×C1116yes—
239D4×Q8C22×C1111yescharacteristic
240#548—21no—
241#547C22×C1113yes—
242#544—23no—
243#533C22×C1113yes—
244#533C22×C1113yes—
245C2×C4⋊Q8C22×C1113yes—
246#529—23no—
247#520—21no—
248C4×#41C22×C1113yes—
249C4×#41C22×C1111yescharacteristic
250C2×C4×Q8—21no—
251#494C22×C1116yes—
252#487C22×C1116yes—
253#485C22×C1116yes—
254#475C22×C1116yes—
255#475C22×C1113yes—
256#474C22×C1111yescharacteristic
257#470C22×C11112yes—
258#462C22×C1116yes—
259#462C22×C1113yes—
260#462C22×C1116yes—
261#462C22×C1116yes—
262#461C22×C1116yes—
263#461C22×C1113yes—
264#452C22×C1116yes—
265#451C22×C11112yes—
266C8×Q8C22×C1112yes—
267C4×Q16C22×C1116yes—
268C4×SD16C22×C1116yes—
269#436C22×C1116yes—
270#431C22×C1113yes—
271#423C22×C1113yes—
272#419C22×C1116yes—
273C22×C11—23no—
274C22×C11—22no—
275C22×C11—23no—
276C22×C11—23no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11C23×D411yescharacteristic
280C4×C11—23no—
281C4×C11—21no—
282C4×C11—23no—
283C4×C11—43no—
284C4×C11—46no—
285C4×C11—43no—
286C4×C11—41no—
287C4×C11—42no—
288C4×C11C2×#13716yes—
289C4×C11#57812yes—
290C4×C11C2×H(5,𝔽2)11yescharacteristic
291C4×C11#58511yescharacteristic
292C2×#41D4×C1111yescharacteristic
293C2×#41C23×C1113yes—
294C22×Q8—21no—
295C22×Q8C23×C1116yes—
296#137—412no—
297C2×Q16C23×C11112yes—
298C2×Q16C23×C1116yes—
299C2×SD16C23×C1116yes—
300C2×M16C23×C1116yes—
301C4⋊Q8—26no—
302C4⋊Q8—23no—
303C4⋊Q8—23no—
304C4⋊Q8C23×C1113yes—
305C4⋊Q8C23×C1116yes—
306C4⋊Q8C23×C1113yes—
307C4⋊Q8C23×C1111yescharacteristic
308C4⋊Q8C23×C1113yes—
309#126—26no—
310#125—23no—
311#125—26no—
312#125—23no—
313#125—23no—
314#124—23no—
315#123—26no—
316C22⋊Q8—23no—
317C22⋊Q8—23no—
318C22⋊Q8—23no—
319C22⋊Q8—212no—
320C22⋊Q8C23×C1116yes—
321C22⋊Q8C23×C1116yes—
322#121—23no—
323C4×Q8—21no—
324C4×Q8—22no—
325C4×Q8—23no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8D4×C1111yescharacteristic
329C4×Q8C23×C1113yes—
330C4×Q8C23×C1113yes—
331C4×Q8C23×C1116yes—
332C4×Q8C23×C1111yescharacteristic
333C4×D4—26no—
334C4×D4—23no—
335C4×D4—23no—
336C4×D4D4×C1113yes—
337C4×D4C23×C1111yescharacteristic
338C4×D4C23×C1113yes—
339C4×D4C23×C1113yes—
340#117—23no—
341#117—23no—
342#117—23no—
343#117D4×C1113yes—
344#117C23×C1113yes—
345C2×C4⋊C4—23no—
346C2×C4⋊C4—23no—
347C2×C4⋊C4—23no—
348C2×C42—23no—
349C2×C42C23×C1113yes—
350#107C23×C1112yes—
351#106C23×C1116yes—
352C4⋊C8C23×C1113yes—
353C4⋊C8C23×C1116yes—
354C4⋊C8C23×C1111yescharacteristic
355#103C23×C1116yes—
356#103C23×C11112yes—
357#103C23×C1116yes—
358#103C23×C1116yes—
359#102C23×C1112yes—
360C22⋊C8C23×C1116yes—
361C4×C8C23×C1116yes—
362C2×C11—43no—
363C2×C11—42no—
364C2×C11#348811yescharacteristic
365C2×C11C22×#13711yescharacteristic
366C2×C11C2×#57811yescharacteristic
367#41—24no—
368#41—26no—
369#41—43no—
370C2×Q8—21no—
371C2×Q8—23no—
372C2×Q8—26no—
373C2×Q8—46no—
374C2×Q8—46no—
375C2×Q8—44no—
376C2×Q8C2×D4×C1111yescharacteristic
377C2×Q8C24×C1116yes—
378C2×Q8C24×C1113yes—
379C2×D4—23no—
380C2×D4C2×D4×C1113yes—
381C2×D4C24×C1111yescharacteristic
382C22×C4—26no—
383C22×C4—21no—
384C22×C4—23no—
385C22×C4—23no—
386C22×C4C2×D4×C1113yes—
387C22×C4C2×D4×C1113yes—
388C22×C4C24×C1113yes—
389Q16—412no—
390Q16—46no—
391SD16—212no—
392M16—46no—
393C2×C8C24×C1112yes—
394C2×C8C24×C1116yes—
395C4⋊C4—23no—
396C4⋊C4—23no—
397C4⋊C4—26no—
398C4⋊C4—23no—
399C4⋊C4—26no—
400C4⋊C4—26no—
401C4⋊C4—21no—
402C4⋊C4—23no—
403C4⋊C4—23no—
404C4⋊C4—23no—
405C4⋊C4—23no—
406C4⋊C4—26no—
407C4⋊C4—26no—
408C4⋊C4C2×D4×C1113yes—
409C4⋊C4C2×D4×C1113yes—
410C4⋊C4C24×C1112yes—
411C4⋊C4C24×C1113yes—
412C4⋊C4C24×C1111yescharacteristic
413C22⋊C4—26no—
414C22⋊C4—26no—
415C22⋊C4—23no—
416C22⋊C4—21no—
417C22⋊C4—23no—
418C22⋊C4C2×D4×C1116yes—
419C42—23no—
420C42—23no—
421C42—23no—
422C42—26no—
423C42C2×D4×C1113yes—
424C42C2×D4×C1113yes—
425C42C24×C1113yes—
426C42C24×C1111yescharacteristic
427C11#6200011yescharacteristic, direct product factor, Sylow
428C23—21no—
429C23C22×D4×C1113yes—
430Q8—26no—
431Q8—23no—
432Q8—23no—
433Q8—26no—
434Q8—46no—
435Q8—42no—
436Q8—86no—
437Q8C11×#13714yescomplemented
438D4—26no—
439D4—21no—
440D4—46no—
441D4C11×H(5,𝔽2)12yes—
442C2×C4—26no—
443C2×C4—26no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—26no—
451C2×C4—46no—
452C2×C4—46no—
453C2×C4—42no—
454C2×C4—86no—
455C2×C4C22×D4×C1113yes—
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C22×D4×C1113yes—
458C2×C4C22×D4×C1113yes—
459C2×C4C22×D4×C1111yescharacteristic
460C2×C4C25×C1111yescharacteristic
461C8—26no—
462C8—22no—
463C22—23no—
464C22—22no—
465C22—23no—
466C22—23no—
467C22—41no—
468C22—41no—
469C22C23×D4×C1111yescharacteristic
470C4—23no—
471C4—21no—
472C4—23no—
473C4—43no—
474C4—46no—
475C4—43no—
476C4—41no—
477C4—42no—
478C4C2×C11×#13716yes—
479C4C11×#57812yes—
480C4C2×C11×H(5,𝔽2)11yescharacteristic
481C4C11×#58511yescharacteristic
482C2—43no—
483C2—42no—
484C2C11×#348811yescharacteristic
485C2C22×C11×#13711yescharacteristic
486C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3503C2semidirect
3. C11×#3395C2semidirect
4. C11×#3359C2semidirect
5. C11×#3328C2semidirect
6. C11×#3276C2semidirect
7. C11×#3255C2semidirect
8. C11×#3209C2semidirect
9. C11×#3107C2semidirect
10. C11×#3039C2semidirect
11. C11×#2991C2semidirect
124. #62000C11direct (N × H)
185. #3503C2×C11semidirect
187. #3395C2×C11semidirect
188. #3359C2×C11semidirect
189. #3328C2×C11semidirect
190. #3276C2×C11semidirect
191. #3255C2×C11semidirect
192. #3209C2×C11semidirect
193. #3107C2×C11semidirect
194. #3039C2×C11semidirect
195. #2991C2×C11semidirect
205. Q8×C11#137semidirect
427. C11#62000direct (N × H)
437. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#34822
C11×#33952
C11×#33592
C11×#33282
C11×#32762
C11×#32552
C11×#32092
C11×#31072
C11×#30392
C11×#29912
#6200011