Finite Group Databasebeta

← C11×#33358 #14610551

Subgroups — C11×#33358 #14610551

Order 2816.

1252 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3449C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal, complemented
3C11×#2129C212yesmaximal, complemented
4C11×#2128C212yesmaximal, complemented
5C11×#2127C214yesmaximal, complemented
6C11×#2126C214yesmaximal, complemented
7C22×C11×#41C411yescharacteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C11×#537—22no—
10C11×#536C412yescomplemented
11C11×#536C411yescharacteristic, complemented
12C11×#536C2211yescharacteristic
13C11×#535C411yescharacteristic, complemented
14C11×#535C2212yes—
15C11×#535C2211yescharacteristic
16C11×#534—22no—
17C11×#532C412yescomplemented
18C11×#532C2212yes—
19C11×#525—22no—
20C11×#525—22no—
21C2×C11×#117—22no—
22C2×C11×#117C411yescharacteristic, complemented
23C11×#410—22no—
24C11×#410—22no—
25C11×#410C2214yes—
26C11×#410C2214yescomplemented
27C2×C11×#99—22no—
28C2×C11×#99C2214yescomplemented
29C11×#354C2218yescomplemented
30C11×#353C2218yescomplemented
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×C411yescharacteristic
39C2×C11×#41C2×C411yescharacteristic
40C2×C11×#41C2×C412yescomplemented
41C2×C11×#41D412yes—
42C2×C11×#41D412yes—
43C2×C11×#41C2311yescharacteristic
44C2×C11×#41C2311yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C22×Q8×C11C2×C411yescharacteristic, complemented
47C22×D4×C11—21no—
48C22×D4×C11C2×C411yescharacteristic, complemented
49C22×D4×C11D412yes—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11D412yes—
54C11×C4⋊Q8C2×C412yescomplemented
55C11×C4⋊Q8C2×C412yescomplemented
56C11×#127C2×C412yes—
57C11×#127C2312yes—
58C11×#124C2×C412yes—
59C11×#124C2×C412yescomplemented
60C11×#124C2×C412yescomplemented
61C11×#124C2312yes—
62C11×#123—22no—
63C11×#123—22no—
64C11×#123—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×#121—24no—
69C11×#121—24no—
70C11×#121—24no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#120—24no—
74C11×#120—22no—
75C11×#120—22no—
76C4×D4×C11—24no—
77C4×D4×C11—24no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—24no—
81C11×#117—24no—
82C11×#117—42no—
83C11×#117—42no—
84C11×#117C2×C412yes—
85C11×#117C2×C411yescharacteristic, complemented
86C11×#117C2×C411yescharacteristic, complemented
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—42no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—24no—
91C2×C42×C11—42no—
92C2×C42×C11C2×C412yescomplemented
93C11×#99—24no—
94C11×#99—24no—
95C11×#99—24no—
96C11×#99C2318yes—
97#33358C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C22⋊C411yescharacteristic
100C24×C11C2×D412yes—
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×C412yes—
122C2×Q8×C11C22×C411yescharacteristic
123C2×Q8×C11C22×C411yescharacteristic
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×C411yescharacteristic
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D412yes—
140C2×D4×C11C2×D412yes—
141C2×D4×C11C2411yescharacteristic
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×C11—44no—
155C22×C4×C11C22⋊C411yescharacteristic
156C22×C4×C11C22⋊C411yescharacteristic
157C22×C4×C11C22⋊C412yes—
158C22×C4×C11C22⋊C412yes—
159C22×C4×C11C22⋊C412yes—
160C22×C4×C11C22⋊C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—44no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—44no—
182C42×C11—22no—
183C42×C11—44no—
184C42×C11—44no—
185C42×C11C22×C412yes—
186C42×C11C22×C412yes—
187#3449C2×C1111yescharacteristic
188C2×#410C2×C1112yescomplemented
189#2129C2×C1112yescomplemented
190#2128C2×C1112yescomplemented
191#2127C2×C1114yescomplemented
192#2126C2×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⋊C411yescharacteristic
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C22×D412yes—
206Q8×C11—42no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—41no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—41no—
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—48no—
249C2×C4×C11—82no—
250C2×C4×C11—88no—
251C2×C4×C11#9912yes—
252C2×C4×C11#9912yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C22×#41C4×C1111yescharacteristic, complemented
260C22×#41C22×C1111yescharacteristic
261#537—22no—
262#536C4×C1112yescomplemented
263#536C4×C1111yescharacteristic, complemented
264#536C22×C1111yescharacteristic
265#535C4×C1111yescharacteristic, complemented
266#535C22×C1112yes—
267#535C22×C1111yescharacteristic
268#534—22no—
269#532C4×C1112yescomplemented
270#532C22×C1112yes—
271#525—22no—
272#525—22no—
273C2×#117—22no—
274C2×#117C4×C1111yescharacteristic, complemented
275#410—22no—
276#410—22no—
277#410C22×C1114yes—
278#410C22×C1114yescomplemented
279C2×#99—22no—
280C2×#99C22×C1114yescomplemented
281#354C22×C1118yescomplemented
282#353C22×C1118yescomplemented
283C22×C11—22no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—84no—
298C22×C11C2×#9912yes—
299C22×C11C22×C22⋊C411yescharacteristic
300C4×C11—21no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—88no—
308C4×C11C2×#9911yescharacteristic
309C4×C11C2×#9912yes—
310C4×C11C2×#9911yescharacteristic
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—42no—
314C2×#41—42no—
315C2×#41—42no—
316C2×#41—42no—
317C2×#41C2×C4×C1112yes—
318C2×#41C2×C4×C1111yescharacteristic
319C2×#41C2×C4×C1111yescharacteristic
320C2×#41C2×C4×C1112yescomplemented
321C2×#41D4×C1112yes—
322C2×#41D4×C1112yes—
323C2×#41C23×C1111yescharacteristic
324C2×#41C23×C1111yescharacteristic
325C22×Q8C2×C4×C1111yescharacteristic
326C22×Q8C2×C4×C1111yescharacteristic, complemented
327C22×D4—21no—
328C22×D4C2×C4×C1111yescharacteristic, complemented
329C22×D4D4×C1112yes—
330C22×D4C23×C1111yescharacteristic
331C23×C4—21no—
332C23×C4C2×C4×C1111yescharacteristic
333C23×C4D4×C1112yes—
334C4⋊Q8C2×C4×C1112yescomplemented
335C4⋊Q8C2×C4×C1112yescomplemented
336#127C2×C4×C1112yes—
337#127C23×C1112yes—
338#124C2×C4×C1112yes—
339#124C2×C4×C1112yescomplemented
340#124C2×C4×C1112yescomplemented
341#124C23×C1112yes—
342#123—22no—
343#123—22no—
344#123—24no—
345C22⋊Q8—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348#121—24no—
349#121—24no—
350#121—24no—
351#121—22no—
352#121—22no—
353#120—24no—
354#120—22no—
355#120—22no—
356C4×D4—24no—
357C4×D4—24no—
358#117—21no—
359#117—21no—
360#117—24no—
361#117—24no—
362#117—42no—
363#117—42no—
364#117C2×C4×C1112yes—
365#117C2×C4×C1111yescharacteristic, complemented
366#117C2×C4×C1111yescharacteristic, complemented
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—24no—
371C2×C42—42no—
372C2×C42C2×C4×C1112yescomplemented
373#99—24no—
374#99—24no—
375#99—24no—
376#99C23×C1118yes—
377C2×C11—21no—
378C2×C11—22no—
379C2×C11—42no—
380C2×C11—42no—
381C2×C11—41no—
382C2×C11—41no—
383C2×C11—82no—
384C2×C11C22×#9911yescharacteristic
385C24—21no—
386C24C11×C22⋊C411yescharacteristic
387C24C2×D4×C1112yes—
388#41—42no—
389#41—41no—
390#41—41no—
391#41—42no—
392#41—42no—
393#41—42no—
394#41—42no—
395#41—41no—
396#41—42no—
397#41—41no—
398#41—44no—
399#41—44no—
400#41—42no—
401#41—42no—
402#41—42no—
403#41—42no—
404C2×Q8—21no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8C11×C22⋊C412yes—
408C2×Q8C22×C4×C1112yes—
409C2×Q8C22×C4×C1111yescharacteristic
410C2×Q8C22×C4×C1111yescharacteristic
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4C11×C22⋊C412yes—
422C2×D4C11×C22⋊C412yes—
423C2×D4C22×C4×C1112yes—
424C2×D4C22×C4×C1111yescharacteristic
425C2×D4C2×D4×C1112yes—
426C2×D4C2×D4×C1112yes—
427C2×D4C2×D4×C1112yes—
428C2×D4C24×C1111yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—44no—
442C22×C4C11×C22⋊C411yescharacteristic
443C22×C4C11×C22⋊C411yescharacteristic
444C22×C4C11×C22⋊C412yes—
445C22×C4C11×C22⋊C412yes—
446C22×C4C11×C22⋊C412yes—
447C22×C4C11×C22⋊C411yescharacteristic
448C22×C4C22×C4×C1111yescharacteristic
449C22×C4C22×C4×C1111yescharacteristic
450C22×C4C22×C4×C1111yescharacteristic
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1112yes—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—44no—
459C4⋊C4—44no—
460C22⋊C4—22no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—28no—
468C22⋊C4—44no—
469C42—22no—
470C42—44no—
471C42—44no—
472C42C22×C4×C1112yes—
473C42C22×C4×C1112yes—
474C11#3335811yescharacteristic, direct product factor, Sylow
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—42no—
480C23—82no—
481C23—81no—
482C23—82no—
483C23C2×C11×C22⋊C411yescharacteristic
484C23C2×C11×C22⋊C412yes—
485C23C2×C11×C22⋊C411yescharacteristic
486C23C2×C11×C22⋊C411yescharacteristic
487C23C22×D4×C1112yes—
488Q8—42no—
489Q8—41no—
490Q8—41no—
491Q8—42no—
492Q8—42no—
493D4—42no—
494D4—42no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—41no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—82no—
532C2×C4—88no—
533C2×C4C11×#9912yes—
534C2×C4C11×#9912yes—
535C2×C4C2×C11×C22⋊C412yes—
536C2×C4C2×C11×C22⋊C412yes—
537C2×C4C2×C11×C22⋊C411yescharacteristic
538C2×C4C2×C11×C22⋊C411yescharacteristic
539C2×C4C2×C11×C22⋊C411yescharacteristic
540C2×C4C23×C4×C1111yescharacteristic
541C22—22no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—82no—
554C22—82no—
555C22—84no—
556C22C2×C11×#9912yes—
557C22C22×C11×C22⋊C411yescharacteristic
558C4—21no—
559C4—22no—
560C4—22no—
561C4—21no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—88no—
566C4C2×C11×#9911yescharacteristic
567C4C2×C11×#9911yescharacteristic
568C4C2×C11×#9912yes—
569C2—21no—
570C2—22no—
571C2—42no—
572C2—42no—
573C2—41no—
574C2—41no—
575C2—82no—
576C2C22×C11×#9911yescharacteristic
subgroupG/H
centerC4×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×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×#410C2semidirect
3. C11×#2129C2semidirect
4. C11×#2128C2semidirect
5. C11×#2127C2semidirect
6. C11×#2126C2semidirect
7. C22×C11×#41C4semidirect
10. C11×#536C4semidirect
11. C11×#536C4semidirect
13. C11×#535C4semidirect
17. C11×#532C4semidirect
22. C2×C11×#117C4semidirect
26. C11×#410C22semidirect
28. C2×C11×#99C22semidirect
29. C11×#354C22semidirect
30. C11×#353C22semidirect
40. C2×C11×#41C2×C4semidirect
46. C22×Q8×C11C2×C4semidirect
48. C22×D4×C11C2×C4semidirect
54. C11×C4⋊Q8C2×C4semidirect
55. C11×C4⋊Q8C2×C4semidirect
59. C11×#124C2×C4semidirect
60. C11×#124C2×C4semidirect
85. C11×#117C2×C4semidirect
86. C11×#117C2×C4semidirect
92. C2×C42×C11C2×C4semidirect
97. #33358C11direct (N × H)
188. C2×#410C2×C11semidirect
189. #2129C2×C11semidirect
190. #2128C2×C11semidirect
191. #2127C2×C11semidirect
192. #2126C2×C11semidirect
259. C22×#41C4×C11semidirect
262. #536C4×C11semidirect
263. #536C4×C11semidirect
265. #535C4×C11semidirect
269. #532C4×C11semidirect
274. C2×#117C4×C11semidirect
278. #410C22×C11semidirect
280. C2×#99C22×C11semidirect
281. #354C22×C11semidirect
282. #353C22×C11semidirect
320. C2×#41C2×C4×C11semidirect
326. C22×Q8C2×C4×C11semidirect
328. C22×D4C2×C4×C11semidirect
334. C4⋊Q8C2×C4×C11semidirect
335. C4⋊Q8C2×C4×C11semidirect
339. #124C2×C4×C11semidirect
340. #124C2×C4×C11semidirect
365. #117C2×C4×C11semidirect
366. #117C2×C4×C11semidirect
372. C2×C42C2×C4×C11semidirect
474. C11#33358direct (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×#4102
C11×#21292
C11×#21282
C11×#21272
C11×#21262
#3335811