Finite Group Databasebeta

← C11×#62002 #14639195

Subgroups — C11×#62002 #14639195

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3483C211yesmaximal, characteristic
3C11×#3392C212yesmaximal, complemented
4C11×#3363C212yesmaximal, complemented
5C11×#3329C216yesmaximal, complemented
6C11×#3278C216yesmaximal, complemented
7C11×#3254C213yesmaximal, complemented
8C11×#3206C213yesmaximal, complemented
9C11×#3107C213yesmaximal, complemented
10C11×#3039C213yesmaximal, complemented
11C11×#2991C211yesmaximal, characteristic, complemented
12C2×C11×#137C2216yes—
13Q82×C11—21no—
14Q82×C11C2211yescharacteristic
15C11×#557C2212yes—
16C11×#555—23no—
17C11×#555C2213yes—
18C11×#554—23no—
19C11×#550—21no—
20C11×#550C2213yes—
21C11×#550C2211yescharacteristic
22D4×Q8×C11C2216yes—
23C11×#544—23no—
24C11×#533C2213yes—
25C11×#532—23no—
26C11×#532C2213yes—
27C2×C11×C4⋊Q8C2213yes—
28C11×#520—21no—
29C4×C11×#41—21no—
30C4×C11×#41C2213yes—
31C4×C11×#41C2211yescharacteristic
32C11×#492C2216yes—
33C11×#487C2216yes—
34C11×#485C2216yes—
35C11×#477C2216yes—
36C11×#475C2211yescharacteristic
37C11×#474C2213yes—
38C11×#468C22112yes—
39C11×#462C2216yes—
40C11×#462C2213yes—
41C11×#461C2213yes—
42C11×#461C2216yes—
43C11×#461C2216yes—
44C11×#460C2216yes—
45C11×#452C2216yes—
46C11×#448C22112yes—
47C8×Q8×C11C2212yes—
48C4×C11×Q16C2216yes—
49C4×C11×SD16C2216yes—
50C11×#436C2216yes—
51C11×#431C2213yes—
52C11×#423C2213yes—
53C11×#419C2216yes—
54C2×C11×#41—21no—
55C2×C11×#41—23no—
56C2×C11×#41D411yescharacteristic
57C2×C11×#41C2313yes—
58C22×Q8×C11C2316yes—
59C11×#137—412no—
60C2×C11×Q16C2316yes—
61C2×C11×SD16C2316yes—
62C2×C11×SD16C23112yes—
63C2×C11×M16C2316yes—
64C11×C4⋊Q8—23no—
65C11×C4⋊Q8—26no—
66C11×C4⋊Q8—23no—
67C11×C4⋊Q8—23no—
68C11×C4⋊Q8C2316yes—
69C11×C4⋊Q8C2313yes—
70C11×C4⋊Q8C2313yes—
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127—23no—
73C11×#127C2313yes—
74C11×#125—26no—
75C11×#125—23no—
76C11×#124—26no—
77C11×#124—23no—
78C11×C22⋊Q8—23no—
79C11×C22⋊Q8—212no—
80C11×C22⋊Q8C2316yes—
81C11×#121—23no—
82C11×#121—23no—
83C11×#121—23no—
84C11×#121—26no—
85C11×#121C2316yes—
86C4×Q8×C11—21no—
87C4×Q8×C11—22no—
88C4×Q8×C11—23no—
89C4×Q8×C11D411yescharacteristic
90C4×Q8×C11C2311yescharacteristic
91C4×Q8×C11C2313yes—
92C4×Q8×C11C2316yes—
93C4×Q8×C11C2311yescharacteristic
94C4×D4×C11—26no—
95C4×D4×C11—23no—
96C4×D4×C11—23no—
97C4×D4×C11—23no—
98C4×D4×C11—23no—
99C4×D4×C11D413yes—
100C4×D4×C11C2313yes—
101C4×D4×C11C2313yes—
102C4×D4×C11C2313yes—
103C11×#117—23no—
104C11×#117—23no—
105C11×#117—23no—
106C11×#117D413yes—
107C11×#117C2313yes—
108C2×C11×C4⋊C4—23no—
109C2×C11×C4⋊C4—23no—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2316yes—
113C11×#106C2312yes—
114C11×C4⋊C8C2313yes—
115C11×C4⋊C8C2316yes—
116C11×C4⋊C8C2311yescharacteristic
117C11×#103C2316yes—
118C11×#103C23112yes—
119C11×#103C2312yes—
120C11×#103C2316yes—
121C11×#102C2316yes—
122C11×C22⋊C8C2316yes—
123C4×C8×C11C2316yes—
124#62002C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41—24no—
126C11×#41—26no—
127C11×#41—43no—
128C11×#41—44no—
129C11×#41—86no—
130C2×Q8×C11—21no—
131C2×Q8×C11—26no—
132C2×Q8×C11—23no—
133C2×Q8×C11—46no—
134C2×Q8×C11—46no—
135C2×Q8×C11C2×D411yescharacteristic
136C2×Q8×C11C2416yes—
137C2×Q8×C11C2411yescharacteristic
138C2×D4×C11—23no—
139C2×D4×C11—26no—
140C2×D4×C11—23no—
141C2×D4×C11—23no—
142C2×D4×C11C2×D413yes—
143C2×D4×C11C2413yes—
144C22×C4×C11—26no—
145C22×C4×C11—23no—
146C22×C4×C11—23no—
147C22×C4×C11—23no—
148C22×C4×C11C2×D413yes—
149C22×C4×C11C2×D413yes—
150C22×C4×C11C2413yes—
151C11×Q16—212no—
152C11×SD16—46no—
153C11×SD16—412no—
154C11×M16—46no—
155C2×C8×C11C2412yes—
156C2×C8×C11C2416yes—
157C11×C4⋊C4—23no—
158C11×C4⋊C4—23no—
159C11×C4⋊C4—26no—
160C11×C4⋊C4—26no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—23no—
165C11×C4⋊C4—26no—
166C11×C4⋊C4—26no—
167C11×C4⋊C4C2×D413yes—
168C11×C4⋊C4C2×D413yes—
169C11×C4⋊C4C2412yes—
170C11×C4⋊C4C2411yescharacteristic
171C11×C4⋊C4C2413yes—
172C11×C22⋊C4—26no—
173C11×C22⋊C4—23no—
174C11×C22⋊C4—26no—
175C11×C22⋊C4—23no—
176C11×C22⋊C4—23no—
177C11×C22⋊C4C2×D416yes—
178C42×C11—21no—
179C42×C11—23no—
180C42×C11—23no—
181C42×C11—26no—
182C42×C11C2×D413yes—
183C42×C11C2×D413yes—
184C42×C11C2413yes—
185C42×C11C2411yescharacteristic
186#3503C2×C1111yescharacteristic, complemented
187#3483C2×C1111yescharacteristic
188#3392C2×C1112yescomplemented
189#3363C2×C1112yescomplemented
190#3329C2×C1116yescomplemented
191#3278C2×C1116yescomplemented
192#3254C2×C1113yescomplemented
193#3206C2×C1113yescomplemented
194#3107C2×C1113yescomplemented
195#3039C2×C1113yescomplemented
196#2991C2×C1111yescharacteristic, complemented
197C23×C11—23no—
198C23×C11C22×D413yes—
199Q8×C11—21no—
200Q8×C11—26no—
201Q8×C11—26no—
202Q8×C11—42no—
203Q8×C11—86no—
204Q8×C11—83no—
205Q8×C11#13714yescomplemented
206Q8×C11H(5,𝔽2)12yes—
207D4×C11—26no—
208D4×C11—23no—
209D4×C11—23no—
210D4×C11—46no—
211D4×C11—46no—
212D4×C11—83no—
213D4×C11—86no—
214C2×C4×C11—21no—
215C2×C4×C11—26no—
216C2×C4×C11—26no—
217C2×C4×C11—23no—
218C2×C4×C11—23no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—23no—
222C2×C4×C11—26no—
223C2×C4×C11—46no—
224C2×C4×C11—46no—
225C2×C4×C11—46no—
226C2×C4×C11—86no—
227C2×C4×C11C22×D413yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D413yes—
230C2×C4×C11C22×D413yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2511yescharacteristic
233C8×C11—26no—
234C8×C11—22no—
235C2×#137C22×C1116yes—
236Q82—21no—
237Q82C22×C1111yescharacteristic
238#557C22×C1112yes—
239#555—23no—
240#555C22×C1113yes—
241#554—23no—
242#550—21no—
243#550C22×C1113yes—
244#550C22×C1111yescharacteristic
245D4×Q8C22×C1116yes—
246#544—23no—
247#533C22×C1113yes—
248#532—23no—
249#532C22×C1113yes—
250C2×C4⋊Q8C22×C1113yes—
251#520—21no—
252C4×#41—21no—
253C4×#41C22×C1113yes—
254C4×#41C22×C1111yescharacteristic
255#492C22×C1116yes—
256#487C22×C1116yes—
257#485C22×C1116yes—
258#477C22×C1116yes—
259#475C22×C1111yescharacteristic
260#474C22×C1113yes—
261#468C22×C11112yes—
262#462C22×C1113yes—
263#462C22×C1116yes—
264#461C22×C1116yes—
265#461C22×C1113yes—
266#461C22×C1116yes—
267#460C22×C1116yes—
268#452C22×C1116yes—
269#448C22×C11112yes—
270C8×Q8C22×C1112yes—
271C4×Q16C22×C1116yes—
272C4×SD16C22×C1116yes—
273#436C22×C1116yes—
274#431C22×C1113yes—
275#423C22×C1113yes—
276#419C22×C1116yes—
277C22×C11—23no—
278C22×C11—23no—
279C22×C11—23no—
280C22×C11—43no—
281C22×C11—43no—
282C22×C11—43no—
283C22×C11C23×D411yescharacteristic
284C4×C11—23no—
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—23no—
288C4×C11—46no—
289C4×C11—41no—
290C4×C11—43no—
291C4×C11—42no—
292C4×C11C2×#13716yes—
293C4×C11#57712yes—
294C4×C11C2×H(5,𝔽2)11yescharacteristic
295C4×C11#58511yescharacteristic
296C2×#41—21no—
297C2×#41—23no—
298C2×#41D4×C1111yescharacteristic
299C2×#41C23×C1113yes—
300C22×Q8C23×C1116yes—
301#137—412no—
302C2×Q16C23×C1116yes—
303C2×SD16C23×C11112yes—
304C2×SD16C23×C1116yes—
305C2×M16C23×C1116yes—
306C4⋊Q8—23no—
307C4⋊Q8—26no—
308C4⋊Q8—23no—
309C4⋊Q8—23no—
310C4⋊Q8C23×C1113yes—
311C4⋊Q8C23×C1116yes—
312C4⋊Q8C23×C1113yes—
313C4⋊Q8C23×C1111yescharacteristic
314#127—23no—
315#127C23×C1113yes—
316#125—26no—
317#125—23no—
318#124—26no—
319#124—23no—
320C22⋊Q8—23no—
321C22⋊Q8—212no—
322C22⋊Q8C23×C1116yes—
323#121—23no—
324#121—23no—
325#121—23no—
326#121—26no—
327#121C23×C1116yes—
328C4×Q8—21no—
329C4×Q8—22no—
330C4×Q8—23no—
331C4×Q8D4×C1111yescharacteristic
332C4×Q8C23×C1111yescharacteristic
333C4×Q8C23×C1113yes—
334C4×Q8C23×C1116yes—
335C4×Q8C23×C1111yescharacteristic
336C4×D4—26no—
337C4×D4—23no—
338C4×D4—23no—
339C4×D4—23no—
340C4×D4—23no—
341C4×D4D4×C1113yes—
342C4×D4C23×C1113yes—
343C4×D4C23×C1113yes—
344C4×D4C23×C1113yes—
345#117—23no—
346#117—23no—
347#117—23no—
348#117D4×C1113yes—
349#117C23×C1113yes—
350C2×C4⋊C4—23no—
351C2×C4⋊C4—23no—
352C2×C42—23no—
353C2×C42C23×C1113yes—
354#107C23×C1116yes—
355#106C23×C1112yes—
356C4⋊C8C23×C1113yes—
357C4⋊C8C23×C1116yes—
358C4⋊C8C23×C1111yescharacteristic
359#103C23×C1116yes—
360#103C23×C11112yes—
361#103C23×C1112yes—
362#103C23×C1116yes—
363#102C23×C1116yes—
364C22⋊C8C23×C1116yes—
365C4×C8C23×C1116yes—
366C2×C11—43no—
367C2×C11—83no—
368C2×C11#348811yescharacteristic
369C2×C11C22×#13711yescharacteristic
370C2×C11C2×#57711yescharacteristic
371#41—24no—
372#41—26no—
373#41—43no—
374#41—44no—
375#41—86no—
376C2×Q8—21no—
377C2×Q8—26no—
378C2×Q8—23no—
379C2×Q8—46no—
380C2×Q8—46no—
381C2×Q8C2×D4×C1111yescharacteristic
382C2×Q8C24×C1116yes—
383C2×Q8C24×C1111yescharacteristic
384C2×D4—23no—
385C2×D4—26no—
386C2×D4—23no—
387C2×D4—23no—
388C2×D4C2×D4×C1113yes—
389C2×D4C24×C1113yes—
390C22×C4—26no—
391C22×C4—23no—
392C22×C4—23no—
393C22×C4—23no—
394C22×C4C2×D4×C1113yes—
395C22×C4C2×D4×C1113yes—
396C22×C4C24×C1113yes—
397Q16—212no—
398SD16—412no—
399SD16—46no—
400M16—46no—
401C2×C8C24×C1112yes—
402C2×C8C24×C1116yes—
403C4⋊C4—23no—
404C4⋊C4—23no—
405C4⋊C4—26no—
406C4⋊C4—26no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—23no—
410C4⋊C4—23no—
411C4⋊C4—26no—
412C4⋊C4—26no—
413C4⋊C4C2×D4×C1113yes—
414C4⋊C4C2×D4×C1113yes—
415C4⋊C4C24×C1112yes—
416C4⋊C4C24×C1111yescharacteristic
417C4⋊C4C24×C1113yes—
418C22⋊C4—26no—
419C22⋊C4—23no—
420C22⋊C4—26no—
421C22⋊C4—23no—
422C22⋊C4—23no—
423C22⋊C4C2×D4×C1116yes—
424C42—21no—
425C42—23no—
426C42—23no—
427C42—26no—
428C42C2×D4×C1113yes—
429C42C2×D4×C1113yes—
430C42C24×C1113yes—
431C42C24×C1111yescharacteristic
432C11#6200211yescharacteristic, direct product factor, Sylow
433C23—23no—
434C23C22×D4×C1113yes—
435Q8—21no—
436Q8—26no—
437Q8—26no—
438Q8—42no—
439Q8—86no—
440Q8—83no—
441Q8C11×#13714yescomplemented
442Q8C11×H(5,𝔽2)12yes—
443D4—26no—
444D4—23no—
445D4—23no—
446D4—46no—
447D4—46no—
448D4—83no—
449D4—86no—
450C2×C4—21no—
451C2×C4—26no—
452C2×C4—26no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—23no—
458C2×C4—26no—
459C2×C4—46no—
460C2×C4—46no—
461C2×C4—46no—
462C2×C4—86no—
463C2×C4C22×D4×C1113yes—
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1113yes—
466C2×C4C22×D4×C1113yes—
467C2×C4C22×D4×C1111yescharacteristic
468C2×C4C25×C1111yescharacteristic
469C8—26no—
470C8—22no—
471C22—23no—
472C22—23no—
473C22—23no—
474C22—43no—
475C22—43no—
476C22—43no—
477C22C23×D4×C1111yescharacteristic
478C4—23no—
479C4—22no—
480C4—21no—
481C4—23no—
482C4—46no—
483C4—41no—
484C4—43no—
485C4—42no—
486C4C2×C11×#13716yes—
487C4C11×#57712yes—
488C4C2×C11×H(5,𝔽2)11yescharacteristic
489C4C11×#58511yescharacteristic
490C2—43no—
491C2—83no—
492C2C11×#348811yescharacteristic
493C2C22×C11×#13711yescharacteristic
494C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3483C2
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×#3392C2semidirect
4. C11×#3363C2semidirect
5. C11×#3329C2semidirect
6. C11×#3278C2semidirect
7. C11×#3254C2semidirect
8. C11×#3206C2semidirect
9. C11×#3107C2semidirect
10. C11×#3039C2semidirect
11. C11×#2991C2semidirect
124. #62002C11direct (N × H)
186. #3503C2×C11semidirect
188. #3392C2×C11semidirect
189. #3363C2×C11semidirect
190. #3329C2×C11semidirect
191. #3278C2×C11semidirect
192. #3254C2×C11semidirect
193. #3206C2×C11semidirect
194. #3107C2×C11semidirect
195. #3039C2×C11semidirect
196. #2991C2×C11semidirect
205. Q8×C11#137semidirect
432. C11#62002direct (N × H)
441. 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×#34832
C11×#33922
C11×#33632
C11×#33292
C11×#32782
C11×#32542
C11×#32062
C11×#31072
C11×#30392
C11×#29912
#6200211