Finite Group Databasebeta

← C11×#33369 #14610562

Subgroups — C11×#33369 #14610562

Order 2816.

1220 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3449C211yesmaximal, characteristic
2C2×C11×#413C212yesmaximal, complemented
3C11×#2135C212yesmaximal, complemented
4C11×#2134C212yesmaximal, complemented
5C11×#2133C214yesmaximal, complemented
6C11×#2132C214yesmaximal, complemented
7C22×C11×#41C411yescharacteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16—22no—
10C11×#537—22no—
11C11×#536C411yescharacteristic
12C11×#536C2211yescharacteristic
13C11×#536C2212yes—
14C11×#535C412yes—
15C11×#535C411yescharacteristic
16C11×#535C2211yescharacteristic
17C11×#534—22no—
18C11×#532C412yes—
19C11×#532C2212yes—
20C11×#525—22no—
21C11×#525—22no—
22C2×C11×#117C411yescharacteristic
23C11×#413—22no—
24C11×#413—22no—
25C11×#413C2214yes—
26C11×#413C2214yescomplemented
27C2×C11×#101C2214yescomplemented
28C2×C11×#100—22no—
29C11×#356C2218yescomplemented
30C11×#355C2218yescomplemented
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—42no—
34C2×C11×#41—42no—
35C2×C11×#41—42no—
36C2×C11×#41—42no—
37C2×C11×#41C2×C412yes—
38C2×C11×#41C2×C412yes—
39C2×C11×#41C2×C411yescharacteristic
40C2×C11×#41C2×C411yescharacteristic
41C2×C11×#41D412yes—
42C2×C11×#41D412yes—
43C2×C11×#41C2311yescharacteristic
44C2×C11×#41C2311yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2×C411yescharacteristic
49C22×D4×C11C2×C411yescharacteristic
50C22×D4×C11D412yes—
51C23×C4×C11—21no—
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11D412yes—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16—24no—
57C2×C11×M16—42no—
58C2×C11×M16—42no—
59C2×C11×M16—42no—
60C22×C8×C11—42no—
61C11×C4⋊Q8C2×C412yes—
62C11×C4⋊Q8C2312yes—
63C11×#127C2×C412yes—
64C11×#127C2×C412yes—
65C11×#124C2×C412yes—
66C11×#124C2×C412yes—
67C11×#124C2×C412yes—
68C11×#124C2312yes—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#120—24no—
81C11×#120—22no—
82C11×#120—22no—
83C4×D4×C11—24no—
84C4×D4×C11—24no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117C2×C411yescharacteristic
88C11×#117C2×C412yes—
89C11×#117C2×C411yescharacteristic
90C2×C11×C4⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11C2×C412yes—
93C11×#101—24no—
94C11×#101C2318yes—
95C11×#100—24no—
96C11×#100—24no—
97#33369C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C22⋊C411yescharacteristic
100C24×C11C22⋊C412yes—
101C11×#41—42no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—42no—
108C11×#41—42no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—44no—
112C11×#41—44no—
113C11×#41—42no—
114C11×#41—42no—
115C11×#41—42no—
116C11×#41—42no—
117C2×Q8×C11—21no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11C22×C412yes—
121C2×Q8×C11C22×C411yescharacteristic
122C2×Q8×C11C2×D412yes—
123C2×Q8×C11C2411yescharacteristic
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—21no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—44no—
134C2×D4×C11C22⋊C412yes—
135C2×D4×C11C22⋊C412yes—
136C2×D4×C11C22⋊C412yes—
137C2×D4×C11C22×C412yes—
138C2×D4×C11C22×C411yescharacteristic
139C2×D4×C11C22×C411yescharacteristic
140C2×D4×C11C2×D412yes—
141C2×D4×C11C2×D412yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11C22⋊C411yescharacteristic
155C22×C4×C11C22⋊C411yescharacteristic
156C22×C4×C11C22⋊C412yes—
157C22×C4×C11C22⋊C412yes—
158C22×C4×C11C22⋊C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C11×M16—28no—
166C11×M16—44no—
167C11×M16—44no—
168C11×M16—44no—
169C2×C8×C11—44no—
170C2×C8×C11—44no—
171C2×C8×C11—44no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C42×C11—22no—
185C42×C11C22×C412yes—
186C42×C11C22×C412yes—
187#3449C2×C1111yescharacteristic
188C2×#413C2×C1112yescomplemented
189#2135C2×C1112yescomplemented
190#2134C2×C1112yescomplemented
191#2133C2×C1114yescomplemented
192#2132C2×C1114yescomplemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—82no—
199C23×C11—81no—
200C23×C11—82no—
201C23×C11C2×C22⋊C411yescharacteristic
202C23×C11C2×C22⋊C412yes—
203C23×C11C2×C22⋊C412yes—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C2×C22⋊C411yescharacteristic
206Q8×C11—41no—
207Q8×C11—42no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—84no—
223D4×C11—84no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—82no—
249C2×C4×C11#9912yes—
250C2×C4×C11#9912yes—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D412yes—
257C8×C11—48no—
258C22×#41C4×C1111yescharacteristic
259C22×#41C22×C1111yescharacteristic
260C22×M16—22no—
261#537—22no—
262#536C4×C1111yescharacteristic
263#536C22×C1111yescharacteristic
264#536C22×C1112yes—
265#535C4×C1112yes—
266#535C4×C1111yescharacteristic
267#535C22×C1111yescharacteristic
268#534—22no—
269#532C4×C1112yes—
270#532C22×C1112yes—
271#525—22no—
272#525—22no—
273C2×#117C4×C1111yescharacteristic
274#413—22no—
275#413—22no—
276#413C22×C1114yes—
277#413C22×C1114yescomplemented
278C2×#101C22×C1114yescomplemented
279C2×#100—22no—
280#356C22×C1118yescomplemented
281#355C22×C1118yescomplemented
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—84no—
297C22×C11C2×#9912yes—
298C22×C11C22×C22⋊C411yescharacteristic
299C4×C11—21no—
300C4×C11—22no—
301C4×C11—21no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11C2×#9911yescharacteristic
307C4×C11C2×#9912yes—
308C4×C11C2×#9911yescharacteristic
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—42no—
312C2×#41—42no—
313C2×#41—42no—
314C2×#41—42no—
315C2×#41C2×C4×C1112yes—
316C2×#41C2×C4×C1112yes—
317C2×#41C2×C4×C1111yescharacteristic
318C2×#41C2×C4×C1111yescharacteristic
319C2×#41D4×C1112yes—
320C2×#41D4×C1112yes—
321C2×#41C23×C1111yescharacteristic
322C2×#41C23×C1111yescharacteristic
323C22×Q8C2×C4×C1111yescharacteristic
324C22×Q8C23×C1111yescharacteristic
325C22×D4—21no—
326C22×D4C2×C4×C1111yescharacteristic
327C22×D4C2×C4×C1111yescharacteristic
328C22×D4D4×C1112yes—
329C23×C4—21no—
330C23×C4C2×C4×C1111yescharacteristic
331C23×C4D4×C1112yes—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—42no—
339C4⋊Q8C2×C4×C1112yes—
340C4⋊Q8C23×C1112yes—
341#127C2×C4×C1112yes—
342#127C2×C4×C1112yes—
343#124C2×C4×C1112yes—
344#124C2×C4×C1112yes—
345#124C2×C4×C1112yes—
346#124C23×C1112yes—
347#123—22no—
348#123—22no—
349#123—24no—
350C22⋊Q8—24no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353#121—24no—
354#121—24no—
355#121—24no—
356#121—22no—
357#121—22no—
358#120—24no—
359#120—22no—
360#120—22no—
361C4×D4—24no—
362C4×D4—24no—
363#117—21no—
364#117—21no—
365#117C2×C4×C1111yescharacteristic
366#117C2×C4×C1112yes—
367#117C2×C4×C1111yescharacteristic
368C2×C4⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42C2×C4×C1112yes—
371#101—24no—
372#101C23×C1118yes—
373#100—24no—
374#100—24no—
375C2×C11—21no—
376C2×C11—22no—
377C2×C11—42no—
378C2×C11—42no—
379C2×C11—41no—
380C2×C11—41no—
381C2×C11—82no—
382C2×C11C22×#9911yescharacteristic
383C24—21no—
384C24C11×C22⋊C411yescharacteristic
385C24C11×C22⋊C412yes—
386#41—42no—
387#41—41no—
388#41—41no—
389#41—42no—
390#41—42no—
391#41—42no—
392#41—42no—
393#41—41no—
394#41—42no—
395#41—41no—
396#41—44no—
397#41—44no—
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402C2×Q8—21no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8C22×C4×C1112yes—
406C2×Q8C22×C4×C1111yescharacteristic
407C2×Q8C2×D4×C1112yes—
408C2×Q8C24×C1111yescharacteristic
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4C11×C22⋊C412yes—
420C2×D4C11×C22⋊C412yes—
421C2×D4C11×C22⋊C412yes—
422C2×D4C22×C4×C1112yes—
423C2×D4C22×C4×C1111yescharacteristic
424C2×D4C22×C4×C1111yescharacteristic
425C2×D4C2×D4×C1112yes—
426C2×D4C2×D4×C1112yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4C11×C22⋊C411yescharacteristic
440C22×C4C11×C22⋊C411yescharacteristic
441C22×C4C11×C22⋊C412yes—
442C22×C4C11×C22⋊C412yes—
443C22×C4C11×C22⋊C411yescharacteristic
444C22×C4C22×C4×C1111yescharacteristic
445C22×C4C22×C4×C1111yescharacteristic
446C22×C4C22×C4×C1111yescharacteristic
447C22×C4C2×D4×C1112yes—
448C22×C4C2×D4×C1112yes—
449C22×C4C2×D4×C1112yes—
450M16—28no—
451M16—44no—
452M16—44no—
453M16—44no—
454C2×C8—44no—
455C2×C8—44no—
456C2×C8—44no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—22no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C42—22no—
470C42C22×C4×C1112yes—
471C42C22×C4×C1112yes—
472C11#3336911yescharacteristic, direct product factor, Sylow
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—42no—
478C23—82no—
479C23—81no—
480C23—82no—
481C23C2×C11×C22⋊C411yescharacteristic
482C23C2×C11×C22⋊C412yes—
483C23C2×C11×C22⋊C412yes—
484C23C2×C11×C22⋊C411yescharacteristic
485C23C2×C11×C22⋊C411yescharacteristic
486Q8—41no—
487Q8—42no—
488Q8—41no—
489Q8—42no—
490Q8—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—41no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—44no—
500D4—44no—
501D4—42no—
502D4—84no—
503D4—84no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4C11×#9912yes—
530C2×C4C11×#9912yes—
531C2×C4C2×C11×C22⋊C412yes—
532C2×C4C2×C11×C22⋊C411yescharacteristic
533C2×C4C2×C11×C22⋊C411yescharacteristic
534C2×C4C2×C11×C22⋊C411yescharacteristic
535C2×C4C23×C4×C1111yescharacteristic
536C2×C4C22×D4×C1112yes—
537C8—48no—
538C22—21no—
539C22—21no—
540C22—22no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—44no—
548C22—44no—
549C22—42no—
550C22—82no—
551C22—82no—
552C22—84no—
553C22C2×C11×#9912yes—
554C22C22×C11×C22⋊C411yescharacteristic
555C4—22no—
556C4—21no—
557C4—22no—
558C4—21no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4C2×C11×#9911yescharacteristic
563C4C2×C11×#9911yescharacteristic
564C4C2×C11×#9912yes—
565C2—21no—
566C2—22no—
567C2—42no—
568C2—42no—
569C2—41no—
570C2—41no—
571C2—82no—
572C2C22×C11×#9911yescharacteristic
subgroupG/H
centerC4×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
socleC2×C11C22×#99
prime radicalC11×#3449C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#413C2semidirect
3. C11×#2135C2semidirect
4. C11×#2134C2semidirect
5. C11×#2133C2semidirect
6. C11×#2132C2semidirect
26. C11×#413C22semidirect
27. C2×C11×#101C22semidirect
29. C11×#356C22semidirect
30. C11×#355C22semidirect
97. #33369C11direct (N × H)
188. C2×#413C2×C11semidirect
189. #2135C2×C11semidirect
190. #2134C2×C11semidirect
191. #2133C2×C11semidirect
192. #2132C2×C11semidirect
277. #413C22×C11semidirect
278. C2×#101C22×C11semidirect
280. #356C22×C11semidirect
281. #355C22×C11semidirect
472. C11#33369direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34492
C2×C11×#4132
C11×#21352
C11×#21342
C11×#21332
C11×#21322
#3336911