Finite Group Databasebeta

← C11×#61374 #14638567

Subgroups — C11×#61374 #14638567

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C212yesmaximal, complemented
2C11×#3387C214yesmaximal, complemented
3C11×#3384C214yesmaximal, complemented
4C11×#3381C214yesmaximal, complemented
5Q8×C11×SD16C214yesmaximal, complemented
6C11×#3163C212yesmaximal, complemented
7C2×C11×#498C211yesmaximal, characteristic, complemented
8C11×#3084C214yesmaximal, complemented
9C11×#3079C212yesmaximal, complemented
10C11×#2960C211yesmaximal, characteristic, complemented
11C11×#2952C212yesmaximal
12C4×C11×#135C211yesmaximal, characteristic
13C2×C11×#135C2211yescharacteristic
14Q82×C11C2214yes—
15C11×#557C2214yes—
16C11×#554—24no—
17C11×#554C2214yes—
18D4×Q8×C11—24no—
19D4×Q8×C11C2214yes—
20C11×#544—24no—
21C11×#544C2214yes—
22C11×#533—22no—
23C11×#533C2211yescharacteristic
24C2×C11×C4⋊Q8—22no—
25C2×C11×C4⋊Q8C2212yes—
26C11×#520C2214yes—
27C4×C11×#41C2212yes—
28C11×#501C2218yes—
29C11×#499C2214yes—
30C11×#498C2214yes—
31C11×#498C2214yes—
32C11×#498C2214yes—
33C11×#479C2218yes—
34C11×#478C2218yes—
35C11×#477C2214yes—
36C11×#476C2214yes—
37C11×#476C2218yes—
38C11×#475C2214yes—
39C11×#475C2218yes—
40C11×#474C2214yes—
41C11×#446C2214yes—
42C8×Q8×C11C2214yes—
43C11×#442C2214yes—
44C11×#441C2214yes—
45C4×C11×Q16C2212yes—
46C4×C11×SD16C2212yes—
47C4×C11×SD16C2212yes—
48C4×C11×SD16C2218yes—
49C4×C11×D8C2212yes—
50C11×#428C2214yes—
51C11×#427C2211yescharacteristic
52C2×C11×#106C2212yes—
53C2×C11×#106C2212yes—
54C11×#424C2212yes—
55C11×#423C2211yescharacteristic
56C11×#417C2214yes—
57C11×#416C2212yes—
58C11×#405C2212yes—
59C2×C4×C8×C11C2211yescharacteristic
60C2×C11×#41C2312yes—
61C22×Q8×C11—24no—
62C22×Q8×C11—22no—
63C11×#135Q818yescomplemented
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16C2312yes—
66C2×C11×D8C2311yescharacteristic
67C2×C11×M16C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—24no—
71C11×C4⋊Q8—24no—
72C11×C4⋊Q8—24no—
73C11×C4⋊Q8—28no—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8D412yes—
77C11×C4⋊Q8C2314yes—
78C11×C4⋊Q8C2314yes—
79C11×C4⋊Q8C2318yes—
80C11×#125—24no—
81C11×#125—28no—
82C11×#125D412yes—
83C11×#125C2318yes—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—24no—
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8—28no—
88C11×C22⋊Q8—28no—
89C11×C22⋊Q8D414yes—
90C4×Q8×C11—24no—
91C4×Q8×C11—24no—
92C4×Q8×C11C2312yes—
93C4×Q8×C11C2312yes—
94C4×Q8×C11C2318yes—
95C4×Q8×C11C2314yes—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—28no—
99C4×D4×C11C2312yes—
100C4×D4×C11C2312yes—
101C4×D4×C11C2318yes—
102C11×#117—24no—
103C11×#117—22no—
104C11×#117C2312yes—
105C11×#117C2312yes—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—24no—
108C2×C11×C4⋊C4—24no—
109C2×C11×C4⋊C4C2314yes—
110C2×C42×C11—22no—
111C2×C42×C11C2311yescharacteristic
112C11×#107C2318yes—
113C11×#107C2312yes—
114C11×#106C2311yescharacteristic
115C11×#106C2314yes—
116C11×#106C2314yes—
117C11×#106C2318yes—
118C11×#106C2318yes—
119C11×#106C2311yescharacteristic
120C11×C4⋊C8C2314yes—
121C11×C4⋊C8C2318yes—
122C11×#103C2312yes—
123C11×#103C2312yes—
124C11×#103C2318yes—
125C11×#102C2312yes—
126C11×#102C2312yes—
127C11×#102C2318yes—
128C11×#97C2314yes—
129C4×C8×C11C2312yes—
130C4×C8×C11C2312yes—
131C4×C8×C11C2314yes—
132#61374C1111yesmaximal, characteristic, direct product factor, Sylow
133C11×#41—24no—
134C11×#41C2×Q818yescomplemented
135C2×Q8×C11—24no—
136C2×Q8×C11—28no—
137C2×Q8×C11—24no—
138C2×Q8×C11—84no—
139C2×Q8×C11—88no—
140C2×Q8×C11C2×D414yes—
141C2×Q8×C11C2412yes—
142C2×D4×C11—22no—
143C2×D4×C11C2412yes—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2411yescharacteristic
151C11×Q16C2×Q814yescomplemented
152C11×SD16C2×Q818yescomplemented
153C11×D8C2×Q814yescomplemented
154C11×M16—24no—
155C2×C8×C11—22no—
156C2×C8×C11C2×Q814yescomplemented
157C2×C8×C11C2412yes—
158C2×C8×C11C2414yes—
159C2×C8×C11C2411yescharacteristic
160C2×C8×C11C2411yescharacteristic
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2×D414yes—
172C11×C4⋊C4C2×D418yes—
173C11×C4⋊C4C2418yes—
174C11×C4⋊C4C2412yes—
175C11×C4⋊C4C2412yes—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4C2×D414yes—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—28no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2412yes—
188C42×C11C2414yes—
189#3503C2×C1112yescomplemented
190#3387C2×C1114yescomplemented
191#3384C2×C1114yescomplemented
192#3381C2×C1114yescomplemented
193Q8×SD16C2×C1114yescomplemented
194#3163C2×C1112yescomplemented
195C2×#498C2×C1111yescharacteristic, complemented
196#3084C2×C1114yescomplemented
197#3079C2×C1112yescomplemented
198#2960C2×C1111yescharacteristic, complemented
199#2952C2×C1112yes—
200C4×#135C2×C1111yescharacteristic
201C23×C11—22no—
202C23×C11C22×D411yescharacteristic
203Q8×C11—28no—
204Q8×C11—22no—
205Q8×C11—48no—
206Q8×C11—84no—
207Q8×C11—88no—
208Q8×C11C22×Q814yes—
209D4×C11—28no—
210D4×C11—22no—
211D4×C11C22×Q814yes—
212C2×C4×C11—22no—
213C2×C4×C11—28no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—28no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—88no—
221C2×C4×C11—84no—
222C2×C4×C11C22×D418yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×Q812yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C8×C11—22no—
230C8×C11—24no—
231C8×C11C22×Q812yes—
232C8×C11C22×Q812yes—
233C2×#135C22×C1111yescharacteristic
234Q82C22×C1114yes—
235#557C22×C1114yes—
236#554—24no—
237#554C22×C1114yes—
238D4×Q8—24no—
239D4×Q8C22×C1114yes—
240#544—24no—
241#544C22×C1114yes—
242#533—22no—
243#533C22×C1111yescharacteristic
244C2×C4⋊Q8—22no—
245C2×C4⋊Q8C22×C1112yes—
246#520C22×C1114yes—
247C4×#41C22×C1112yes—
248#501C22×C1118yes—
249#499C22×C1114yes—
250#498C22×C1114yes—
251#498C22×C1114yes—
252#498C22×C1114yes—
253#479C22×C1118yes—
254#478C22×C1118yes—
255#477C22×C1114yes—
256#476C22×C1114yes—
257#476C22×C1118yes—
258#475C22×C1114yes—
259#475C22×C1118yes—
260#474C22×C1114yes—
261#446C22×C1114yes—
262C8×Q8C22×C1114yes—
263#442C22×C1114yes—
264#441C22×C1114yes—
265C4×Q16C22×C1112yes—
266C4×SD16C22×C1112yes—
267C4×SD16C22×C1118yes—
268C4×SD16C22×C1112yes—
269C4×D8C22×C1112yes—
270#428C22×C1114yes—
271#427C22×C1111yescharacteristic
272C2×#106C22×C1112yes—
273C2×#106C22×C1112yes—
274#424C22×C1112yes—
275#423C22×C1111yescharacteristic
276#417C22×C1114yes—
277#416C22×C1112yes—
278#405C22×C1112yes—
279C2×C4×C8C22×C1111yescharacteristic
280C22×C11—22no—
281C22×C11—24no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11D4×Q812yes—
285C22×C11C23×D411yescharacteristic
286C4×C11—24no—
287C4×C11—22no—
288C4×C11—28no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—48no—
292C4×C11D4×Q812yes—
293C4×C11#57714yes—
294C4×C11C23×Q811yescharacteristic
295C4×C11C2×2−1+411yescharacteristic
296C2×#41C23×C1112yes—
297C22×Q8—24no—
298C22×Q8—22no—
299#135Q8×C1118yescomplemented
300C2×Q16C23×C1111yescharacteristic
301C2×SD16C23×C1112yes—
302C2×D8C23×C1111yescharacteristic
303C2×M16C23×C1112yes—
304C22×C8C23×C1111yescharacteristic
305C22×C8C23×C1111yescharacteristic
306C4⋊Q8—24no—
307C4⋊Q8—24no—
308C4⋊Q8—24no—
309C4⋊Q8—28no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8D4×C1112yes—
313C4⋊Q8C23×C1114yes—
314C4⋊Q8C23×C1114yes—
315C4⋊Q8C23×C1118yes—
316#125—24no—
317#125—28no—
318#125D4×C1112yes—
319#125C23×C1118yes—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8D4×C1114yes—
326C4×Q8—24no—
327C4×Q8—24no—
328C4×Q8C23×C1112yes—
329C4×Q8C23×C1112yes—
330C4×Q8C23×C1118yes—
331C4×Q8C23×C1114yes—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—28no—
335C4×D4C23×C1112yes—
336C4×D4C23×C1112yes—
337C4×D4C23×C1118yes—
338#117—24no—
339#117—22no—
340#117C23×C1112yes—
341#117C23×C1112yes—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4C23×C1114yes—
346C2×C42—22no—
347C2×C42C23×C1111yescharacteristic
348#107C23×C1112yes—
349#107C23×C1118yes—
350#106C23×C1114yes—
351#106C23×C1114yes—
352#106C23×C1118yes—
353#106C23×C1111yescharacteristic
354#106C23×C1111yescharacteristic
355#106C23×C1118yes—
356C4⋊C8C23×C1114yes—
357C4⋊C8C23×C1118yes—
358#103C23×C1112yes—
359#103C23×C1112yes—
360#103C23×C1118yes—
361#102C23×C1112yes—
362#102C23×C1112yes—
363#102C23×C1118yes—
364#97C23×C1114yes—
365C4×C8C23×C1112yes—
366C4×C8C23×C1112yes—
367C4×C8C23×C1114yes—
368C2×C11—22no—
369C2×C11—44no—
370C2×C11C2×D4×Q811yescharacteristic
371C2×C11C2×#57712yes—
372#41—24no—
373#41C2×Q8×C1118yescomplemented
374C2×Q8—24no—
375C2×Q8—28no—
376C2×Q8—24no—
377C2×Q8—84no—
378C2×Q8—88no—
379C2×Q8C2×D4×C1114yes—
380C2×Q8C24×C1112yes—
381C2×D4—22no—
382C2×D4C24×C1112yes—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—28no—
388C22×C4C2×D4×C1112yes—
389C22×C4C24×C1111yescharacteristic
390Q16C2×Q8×C1114yescomplemented
391SD16C2×Q8×C1118yescomplemented
392D8C2×Q8×C1114yescomplemented
393M16—24no—
394C2×C8—22no—
395C2×C8C2×Q8×C1114yescomplemented
396C2×C8C24×C1112yes—
397C2×C8C24×C1114yes—
398C2×C8C24×C1111yescharacteristic
399C2×C8C24×C1111yescharacteristic
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—28no—
403C4⋊C4—24no—
404C4⋊C4—28no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4C2×D4×C1114yes—
410C4⋊C4C2×D4×C1114yes—
411C4⋊C4C2×D4×C1118yes—
412C4⋊C4C24×C1118yes—
413C4⋊C4C24×C1112yes—
414C4⋊C4C24×C1112yes—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—28no—
419C22⋊C4C2×D4×C1114yes—
420C42—22no—
421C42—22no—
422C42—22no—
423C42—28no—
424C42C2×D4×C1111yescharacteristic
425C42C2×D4×C1111yescharacteristic
426C42C24×C1112yes—
427C42C24×C1114yes—
428C11#6137411yescharacteristic, direct product factor, Sylow
429C23—22no—
430C23C22×D4×C1111yescharacteristic
431Q8—28no—
432Q8—22no—
433Q8—48no—
434Q8—84no—
435Q8—88no—
436Q8C22×Q8×C1114yes—
437D4—28no—
438D4—22no—
439D4C22×Q8×C1114yes—
440C2×C4—22no—
441C2×C4—28no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—28no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—88no—
449C2×C4—84no—
450C2×C4C22×D4×C1118yes—
451C2×C4C22×D4×C1112yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1112yes—
454C2×C4C22×Q8×C1112yes—
455C2×C4C11×2−1+412yes—
456C2×C4C25×C1111yescharacteristic
457C8—22no—
458C8—24no—
459C8C22×Q8×C1112yes—
460C8C22×Q8×C1112yes—
461C22—22no—
462C22—24no—
463C22—42no—
464C22—42no—
465C22D4×Q8×C1112yes—
466C22C23×D4×C1111yescharacteristic
467C4—24no—
468C4—22no—
469C4—28no—
470C4—42no—
471C4—42no—
472C4—48no—
473C4D4×Q8×C1112yes—
474C4C11×#57714yes—
475C4C23×Q8×C1111yescharacteristic
476C4C2×C11×2−1+411yescharacteristic
477C2—22no—
478C2—44no—
479C2C2×D4×Q8×C1111yescharacteristic
480C2C2×C11×#57712yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#135C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3503C2semidirect
2. C11×#3387C2semidirect
3. C11×#3384C2semidirect
4. C11×#3381C2semidirect
5. Q8×C11×SD16C2semidirect
6. C11×#3163C2semidirect
7. C2×C11×#498C2semidirect
8. C11×#3084C2semidirect
9. C11×#3079C2semidirect
10. C11×#2960C2semidirect
63. C11×#135Q8semidirect
132. #61374C11direct (N × H)
134. C11×#41C2×Q8semidirect
151. C11×Q16C2×Q8semidirect
152. C11×SD16C2×Q8semidirect
153. C11×D8C2×Q8semidirect
156. C2×C8×C11C2×Q8semidirect
189. #3503C2×C11semidirect
190. #3387C2×C11semidirect
191. #3384C2×C11semidirect
192. #3381C2×C11semidirect
193. Q8×SD16C2×C11semidirect
194. #3163C2×C11semidirect
195. C2×#498C2×C11semidirect
196. #3084C2×C11semidirect
197. #3079C2×C11semidirect
198. #2960C2×C11semidirect
299. #135Q8×C11semidirect
373. #41C2×Q8×C11semidirect
390. Q16C2×Q8×C11semidirect
391. SD16C2×Q8×C11semidirect
392. D8C2×Q8×C11semidirect
395. C2×C8C2×Q8×C11semidirect
428. C11#61374direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#33872
C11×#33842
C11×#33812
Q8×C11×SD162
C11×#31632
C2×C11×#4982
C11×#30842
C11×#30792
C11×#29602
C11×#29522
C4×C11×#1352
#6137411