Finite Group Databasebeta

← C11×#61319 #14638512

Subgroups — C11×#61319 #14638512

Order 2816.

1836 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×#3480C211yesmaximal, characteristic
2C2×Q82×C11C211yesmaximal, characteristic, complemented
3C11×#3375C216yesmaximal, complemented
4C11×#3369C216yesmaximal, complemented
5C11×#3363C212yesmaximal, complemented
6C11×#3362C212yesmaximal, complemented
7C11×#3141C213yesmaximal, complemented
8C11×#3079C213yesmaximal, complemented
9C11×#3037C213yesmaximal, complemented
10Q8×C11×M16C211yesmaximal, characteristic, complemented
11C4×C11×#137C213yesmaximal, complemented
12C2×C11×#137C2213yes—
13C11×#559C2213yes—
14Q82×C11—21no—
15Q82×C11—23no—
16Q82×C11C2212yes—
17Q82×C11C2216yes—
18C11×#557C2211yescharacteristic
19C11×#556C2213yes—
20C11×#553—23no—
21C11×#550C2211yescharacteristic
22C11×#548—21no—
23C11×#532C2213yes—
24C2×C11×C4⋊Q8—23no—
25C2×C11×C4⋊Q8C2213yes—
26C11×#529—23no—
27C4×C11×#41—21no—
28C4×C11×#41C2213yes—
29C2×C4×Q8×C11—21no—
30C2×C4×Q8×C11C2213yes—
31C2×C4×Q8×C11C2211yescharacteristic
32C11×#489C22112yes—
33C11×#487C2216yes—
34C11×#486C2216yes—
35C11×#477C2216yes—
36C11×#476C2216yes—
37C11×#475C2216yes—
38C11×#474C2216yes—
39C11×#464C22112yes—
40C11×#462C2216yes—
41C11×#460C2216yes—
42C11×#446C2216yes—
43C8×Q8×C11C2212yes—
44C11×#441C2216yes—
45C11×#440C2216yes—
46C4×C11×Q16C2216yes—
47C4×C11×SD16C2216yes—
48C11×#428C2213yes—
49C11×#423C2213yes—
50C11×#419C2211yescharacteristic
51C11×#417C2213yes—
52C11×#417C2216yes—
53C4×C11×M16C2213yes—
54C2×C11×#41—21no—
55C2×C11×#41C2313yes—
56C22×Q8×C11—23no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C11×#137—212no—
60C2×C11×Q16C2316yes—
61C2×C11×SD16C2316yes—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2313yes—
64C11×C4⋊Q8—26no—
65C11×C4⋊Q8—26no—
66C11×C4⋊Q8—212no—
67C11×C4⋊Q8—23no—
68C11×C4⋊Q8—23no—
69C11×C4⋊Q8C2313yes—
70C11×C4⋊Q8C2316yes—
71C11×C4⋊Q8C2316yes—
72C11×#127C2313yes—
73C11×#126—26no—
74C11×#125—23no—
75C11×#124—23no—
76C11×#124C2316yes—
77C11×#123—26no—
78C11×C22⋊Q8—23no—
79C11×#121—23no—
80C11×#121—23no—
81C11×#121—23no—
82C4×Q8×C11—26no—
83C4×Q8×C11—22no—
84C4×Q8×C11—21no—
85C4×Q8×C11—23no—
86C4×Q8×C11—23no—
87C4×Q8×C11D411yescharacteristic
88C4×Q8×C11D413yes—
89C4×Q8×C11C2316yes—
90C4×Q8×C11C2316yes—
91C4×Q8×C11C2313yes—
92C4×Q8×C11C2313yes—
93C4×Q8×C11C2311yescharacteristic
94C4×Q8×C11C2313yes—
95C4×D4×C11—23no—
96C4×D4×C11—23no—
97C4×D4×C11—23no—
98C4×D4×C11—23no—
99C4×D4×C11—23no—
100C4×D4×C11C2313yes—
101C4×D4×C11C2313yes—
102C11×#117—23no—
103C11×#117—23no—
104C11×#117C2311yescharacteristic
105C2×C11×C4⋊C4—23no—
106C2×C11×C4⋊C4—23no—
107C2×C11×C4⋊C4D413yes—
108C2×C11×C4⋊C4C2313yes—
109C2×C42×C11—23no—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2316yes—
113C11×#106C2316yes—
114C11×C4⋊C8C2316yes—
115C11×C4⋊C8C2316yes—
116C11×#103C2316yes—
117C11×#103C23112yes—
118C11×#103C2312yes—
119C11×#103C2312yes—
120C11×#102C2316yes—
121C11×#102C23112yes—
122C11×#97C2316yes—
123C4×C8×C11C2316yes—
124#61319C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41—26no—
126C11×#41—26no—
127C11×#41—44no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—26no—
131C2×Q8×C11—26no—
132C2×Q8×C11—22no—
133C2×Q8×C11—86no—
134C2×Q8×C11C2×D413yes—
135C2×Q8×C11C2×D411yescharacteristic
136C2×Q8×C11#4114yescomplemented
137C2×Q8×C11C2413yes—
138C2×Q8×C11C2412yes—
139C2×D4×C11—23no—
140C2×D4×C11—23no—
141C2×D4×C11—23no—
142C2×D4×C11C2413yes—
143C22×C4×C11—21no—
144C22×C4×C11—23no—
145C22×C4×C11—23no—
146C22×C4×C11—23no—
147C22×C4×C11—23no—
148C22×C4×C11C2×D413yes—
149C22×C4×C11C2×D413yes—
150C22×C4×C11C2411yescharacteristic
151C11×Q16—212no—
152C11×SD16—212no—
153C11×M16—26no—
154C11×M16—22no—
155C2×C8×C11C2412yes—
156C2×C8×C11C2416yes—
157C11×C4⋊C4—26no—
158C11×C4⋊C4—26no—
159C11×C4⋊C4—26no—
160C11×C4⋊C4—26no—
161C11×C4⋊C4—23no—
162C11×C4⋊C4—23no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—23no—
165C11×C4⋊C4—23no—
166C11×C4⋊C4C2×D413yes—
167C11×C4⋊C4C2×D413yes—
168C11×C4⋊C4C2×D416yes—
169C11×C4⋊C4C2416yes—
170C11×C4⋊C4C2411yescharacteristic
171C11×C4⋊C4C2411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—26no—
174C11×C22⋊C4—23no—
175C11×C22⋊C4—23no—
176C11×C22⋊C4—26no—
177C42×C11—21no—
178C42×C11—23no—
179C42×C11—23no—
180C42×C11—26no—
181C42×C11—26no—
182C42×C11C2×D413yes—
183C42×C11C2×D413yes—
184C42×C11C2413yes—
185C42×C11C2413yes—
186#3480C2×C1111yescharacteristic
187C2×Q82C2×C1111yescharacteristic, complemented
188#3375C2×C1116yescomplemented
189#3369C2×C1116yescomplemented
190#3363C2×C1112yescomplemented
191#3362C2×C1112yescomplemented
192#3141C2×C1113yescomplemented
193#3079C2×C1113yescomplemented
194#3037C2×C1113yescomplemented
195Q8×M16C2×C1111yescharacteristic, complemented
196C4×#137C2×C1113yescomplemented
197C23×C11—23no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—24no—
200Q8×C11—26no—
201Q8×C11—22no—
202Q8×C11—23no—
203Q8×C11—23no—
204Q8×C11—86no—
205Q8×C11—86no—
206Q8×C11#13714yescomplemented
207Q8×C11C2×#4114yes—
208D4×C11—23no—
209D4×C11—23no—
210D4×C11—46no—
211D4×C11—46no—
212D4×C11—83no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—26no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—23no—
219C2×C4×C11—26no—
220C2×C4×C11—43no—
221C2×C4×C11—46no—
222C2×C4×C11—46no—
223C2×C4×C11—46no—
224C2×C4×C11—83no—
225C2×C4×C11C22×D413yes—
226C2×C4×C11C22×D413yes—
227C2×C4×C11C22×D413yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D413yes—
230C2×C4×C11C2×#4112yes—
231C2×C4×C112−1+412yes—
232C2×C4×C11C2511yescharacteristic
233C8×C11—26no—
234C8×C11—22no—
235C2×#137C22×C1113yes—
236#559C22×C1113yes—
237Q82—21no—
238Q82—23no—
239Q82C22×C1112yes—
240Q82C22×C1116yes—
241#557C22×C1111yescharacteristic
242#556C22×C1113yes—
243#553—23no—
244#550C22×C1111yescharacteristic
245#548—21no—
246#532C22×C1113yes—
247C2×C4⋊Q8—23no—
248C2×C4⋊Q8C22×C1113yes—
249#529—23no—
250C4×#41—21no—
251C4×#41C22×C1113yes—
252C2×C4×Q8—21no—
253C2×C4×Q8C22×C1113yes—
254C2×C4×Q8C22×C1111yescharacteristic
255#489C22×C11112yes—
256#487C22×C1116yes—
257#486C22×C1116yes—
258#477C22×C1116yes—
259#476C22×C1116yes—
260#475C22×C1116yes—
261#474C22×C1116yes—
262#464C22×C11112yes—
263#462C22×C1116yes—
264#460C22×C1116yes—
265#446C22×C1116yes—
266C8×Q8C22×C1112yes—
267#441C22×C1116yes—
268#440C22×C1116yes—
269C4×Q16C22×C1116yes—
270C4×SD16C22×C1116yes—
271#428C22×C1113yes—
272#423C22×C1113yes—
273#419C22×C1111yescharacteristic
274#417C22×C1116yes—
275#417C22×C1113yes—
276C4×M16C22×C1113yes—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—43no—
280C22×C11—43no—
281C22×C11—43no—
282C22×C11#54812yes—
283C22×C11C23×D411yescharacteristic
284C4×C11—23no—
285C4×C11—23no—
286C4×C11—24no—
287C4×C11—23no—
288C4×C11—46no—
289C4×C11—41no—
290C4×C11—43no—
291C4×C11—41no—
292C4×C11#54812yes—
293C4×C11C2×#13716yes—
294C4×C11C22×#4111yescharacteristic
295C4×C11C2×2−1+411yescharacteristic
296C2×#41—21no—
297C2×#41C23×C1113yes—
298C22×Q8—23no—
299C22×Q8D4×C1111yescharacteristic
300C22×Q8C23×C1111yescharacteristic
301#137—212no—
302C2×Q16C23×C1116yes—
303C2×SD16C23×C1116yes—
304C2×M16C23×C1113yes—
305C2×M16C23×C1111yescharacteristic
306C4⋊Q8—26no—
307C4⋊Q8—26no—
308C4⋊Q8—212no—
309C4⋊Q8—23no—
310C4⋊Q8—23no—
311C4⋊Q8C23×C1113yes—
312C4⋊Q8C23×C1116yes—
313C4⋊Q8C23×C1116yes—
314#127C23×C1113yes—
315#126—26no—
316#125—23no—
317#124—23no—
318#124C23×C1116yes—
319#123—26no—
320C22⋊Q8—23no—
321#121—23no—
322#121—23no—
323#121—23no—
324C4×Q8—26no—
325C4×Q8—22no—
326C4×Q8—21no—
327C4×Q8—23no—
328C4×Q8—23no—
329C4×Q8D4×C1111yescharacteristic
330C4×Q8D4×C1113yes—
331C4×Q8C23×C1116yes—
332C4×Q8C23×C1116yes—
333C4×Q8C23×C1113yes—
334C4×Q8C23×C1113yes—
335C4×Q8C23×C1111yescharacteristic
336C4×Q8C23×C1113yes—
337C4×D4—23no—
338C4×D4—23no—
339C4×D4—23no—
340C4×D4—23no—
341C4×D4—23no—
342C4×D4C23×C1113yes—
343C4×D4C23×C1113yes—
344#117—23no—
345#117—23no—
346#117C23×C1111yescharacteristic
347C2×C4⋊C4—23no—
348C2×C4⋊C4—23no—
349C2×C4⋊C4D4×C1113yes—
350C2×C4⋊C4C23×C1113yes—
351C2×C42—23no—
352C2×C42—23no—
353C2×C42C23×C1113yes—
354#107C23×C1116yes—
355#106C23×C1116yes—
356C4⋊C8C23×C1116yes—
357C4⋊C8C23×C1116yes—
358#103C23×C1116yes—
359#103C23×C11112yes—
360#103C23×C1112yes—
361#103C23×C1112yes—
362#102C23×C1116yes—
363#102C23×C11112yes—
364#97C23×C1116yes—
365C4×C8C23×C1116yes—
366C2×C11—22no—
367C2×C11—83no—
368C2×C11C2×#54811yescharacteristic
369C2×C11C22×#13711yescharacteristic
370C2×C11#358511yescharacteristic
371#41—26no—
372#41—26no—
373#41—44no—
374C2×Q8—24no—
375C2×Q8—21no—
376C2×Q8—26no—
377C2×Q8—26no—
378C2×Q8—22no—
379C2×Q8—86no—
380C2×Q8C2×D4×C1113yes—
381C2×Q8C2×D4×C1111yescharacteristic
382C2×Q8C11×#4114yescomplemented
383C2×Q8C24×C1113yes—
384C2×Q8C24×C1112yes—
385C2×D4—23no—
386C2×D4—23no—
387C2×D4—23no—
388C2×D4C24×C1113yes—
389C22×C4—21no—
390C22×C4—23no—
391C22×C4—23no—
392C22×C4—23no—
393C22×C4—23no—
394C22×C4C2×D4×C1113yes—
395C22×C4C2×D4×C1113yes—
396C22×C4C24×C1111yescharacteristic
397Q16—212no—
398SD16—212no—
399M16—26no—
400M16—22no—
401C2×C8C24×C1112yes—
402C2×C8C24×C1116yes—
403C4⋊C4—26no—
404C4⋊C4—26no—
405C4⋊C4—26no—
406C4⋊C4—26no—
407C4⋊C4—23no—
408C4⋊C4—23no—
409C4⋊C4—23no—
410C4⋊C4—23no—
411C4⋊C4—23no—
412C4⋊C4C2×D4×C1113yes—
413C4⋊C4C2×D4×C1113yes—
414C4⋊C4C2×D4×C1116yes—
415C4⋊C4C24×C1116yes—
416C4⋊C4C24×C1111yescharacteristic
417C4⋊C4C24×C1111yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—26no—
420C22⋊C4—23no—
421C22⋊C4—23no—
422C22⋊C4—26no—
423C42—21no—
424C42—23no—
425C42—23no—
426C42—26no—
427C42—26no—
428C42C2×D4×C1113yes—
429C42C2×D4×C1113yes—
430C42C24×C1113yes—
431C42C24×C1113yes—
432C11#6131911yescharacteristic, direct product factor, Sylow
433C23—23no—
434C23C22×D4×C1111yescharacteristic
435Q8—24no—
436Q8—26no—
437Q8—22no—
438Q8—23no—
439Q8—23no—
440Q8—86no—
441Q8—86no—
442Q8C11×#13714yescomplemented
443Q8C2×C11×#4114yes—
444D4—23no—
445D4—23no—
446D4—46no—
447D4—46no—
448D4—83no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—26no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—23no—
455C2×C4—26no—
456C2×C4—43no—
457C2×C4—46no—
458C2×C4—46no—
459C2×C4—46no—
460C2×C4—83no—
461C2×C4C22×D4×C1113yes—
462C2×C4C22×D4×C1113yes—
463C2×C4C22×D4×C1113yes—
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1113yes—
466C2×C4C2×C11×#4112yes—
467C2×C4C11×2−1+412yes—
468C2×C4C25×C1111yescharacteristic
469C8—26no—
470C8—22no—
471C22—21no—
472C22—21no—
473C22—43no—
474C22—43no—
475C22—43no—
476C22C11×#54812yes—
477C22C23×D4×C1111yescharacteristic
478C4—24no—
479C4—23no—
480C4—23no—
481C4—23no—
482C4—43no—
483C4—41no—
484C4—46no—
485C4—41no—
486C4C11×#54812yes—
487C4C2×C11×#13716yes—
488C4C22×C11×#4111yescharacteristic
489C4C2×C11×2−1+411yescharacteristic
490C2—22no—
491C2—83no—
492C2C2×C11×#54811yescharacteristic
493C2C22×C11×#13711yescharacteristic
494C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3480C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×Q82×C11C2semidirect
3. C11×#3375C2semidirect
4. C11×#3369C2semidirect
5. C11×#3363C2semidirect
6. C11×#3362C2semidirect
7. C11×#3141C2semidirect
8. C11×#3079C2semidirect
9. C11×#3037C2semidirect
10. Q8×C11×M16C2semidirect
11. C4×C11×#137C2semidirect
124. #61319C11direct (N × H)
136. C2×Q8×C11#41semidirect
187. C2×Q82C2×C11semidirect
188. #3375C2×C11semidirect
189. #3369C2×C11semidirect
190. #3363C2×C11semidirect
191. #3362C2×C11semidirect
192. #3141C2×C11semidirect
193. #3079C2×C11semidirect
194. #3037C2×C11semidirect
195. Q8×M16C2×C11semidirect
196. C4×#137C2×C11semidirect
206. Q8×C11#137semidirect
382. C2×Q8C11×#41semidirect
432. C11#61319direct (N × H)
442. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#34802
C2×Q82×C112
C11×#33752
C11×#33692
C11×#33632
C11×#33622
C11×#31412
C11×#30792
C11×#30372
Q8×C11×M162
C4×C11×#1372
#6131911