Finite Group Databasebeta

← C11×#34985 #14612178

Subgroups — C11×#34985 #14612178

Order 2816.

2866 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#543C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic
3C11×#2855C212yesmaximal, complemented
4C11×#2848C212yesmaximal, complemented
5C11×#2627C212yesmaximal, complemented
6C11×#2626C212yesmaximal, complemented
7C11×#2450C218yesmaximal, complemented
8C11×#2449C218yesmaximal, complemented
9C11×#2315C211yesmaximal, characteristic, complemented
10C11×#2308C212yesmaximal
11C2×C11×#385C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C11×#543—28no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2214yescomplemented
19C2×C11×C22⋊Q8C2214yescomplemented
20C2×C11×C22⋊Q8C2214yescomplemented
21C2×C4×D4×C11—28no—
22C2×C4×D4×C11C2218yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2214yescomplemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2212yes—
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C11×#400C2214yescomplemented
31C11×#399C2214yescomplemented
32C11×#398C2218yescomplemented
33C11×#396C2218yescomplemented
34C11×#395C2214yescomplemented
35C11×#393C2214yescomplemented
36C11×#391C2214yescomplemented
37C11×#389C2214yescomplemented
38C11×#387C2218yescomplemented
39C11×#386C2214yes—
40C11×#386C2218yes—
41C11×#386C2214yes—
42C11×#385C2214yes—
43C11×#385C2214yes—
44C11×#385C2218yescomplemented
45C11×#385C2218yescomplemented
46C11×#385C2218yescomplemented
47C11×#381C2214yes—
48C11×#380C2212yes—
49C11×#380C2212yes—
50C11×#380C2214yescomplemented
51C11×#379C2214yes—
52C2×C11×#95C2214yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2312yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11Q818yescomplemented
60C22×D4×C11C2314yes—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11—44no—
64C23×C4×C11—44no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2314yes—
67C23×C4×C11C2314yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×C4×C11C2314yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8—216no—
78C11×C22⋊Q8—216no—
79C11×C22⋊Q8—48no—
80C4×D4×C11—232no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—48no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2318yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C22⋊C4—28no—
93C2×C11×C22⋊C4—28no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4D418yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2318yes—
102C2×C11×C22⋊C4C2318yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11—24no—
105C2×C42×C11C2314yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C11×#95C2314yes—
109C11×#95C2314yes—
110C11×#95C2318yes—
111C11×#95C2318yes—
112#34985C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11C2×D414yes—
120C24×C11C2×Q814yes—
121C24×C11C2×Q814yes—
122C24×C11#4114yes—
123C24×C11C2412yes—
124C24×C11C2411yescharacteristic
125C24×C11C2412yes—
126C2×Q8×C11—24no—
127C2×Q8×C11—24no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×D4×C11—232no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11C2×Q8116yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—28no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—28no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—44no—
147C22×C4×C11—42no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—416no—
156C22×C4×C11—416no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×Q814yes—
160C22×C4×C11C2418yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—216no—
174C11×C4⋊C4—48no—
175C11×C4⋊C4—44no—
176C11×C4⋊C4—44no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—48no—
183C11×C22⋊C4—48no—
184C11×C22⋊C4C2×D4116yes—
185C42×C11—28no—
186C2×#543C2×C1111yescharacteristic, complemented
187C22×C4×D4C2×C1111yescharacteristic
188#2855C2×C1112yescomplemented
189#2848C2×C1112yescomplemented
190#2627C2×C1112yescomplemented
191#2626C2×C1112yescomplemented
192#2450C2×C1118yescomplemented
193#2449C2×C1118yescomplemented
194#2315C2×C1111yescharacteristic, complemented
195#2308C2×C1112yes—
196C2×#385C2×C1112yescomplemented
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—28no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11—48no—
213C23×C11—44no—
214C23×C11C22⋊Q8116yescomplemented
215C23×C11C22×D412yes—
216C23×C11C22×D414yes—
217C23×C11C22×Q814yes—
218C23×C11C22×Q812yes—
219C23×C11C22×Q814yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4114yes—
222C23×C11C2511yescharacteristic
223Q8×C11—84no—
224Q8×C11—84no—
225D4×C11—232no—
226C2×C4×C11—28no—
227C2×C4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—28no—
238C2×C4×C11—28no—
239C2×C4×C11—28no—
240C2×C4×C11—24no—
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—416no—
246C2×C4×C11—416no—
247C2×C4×C11—416no—
248C2×C4×C11—44no—
249C2×C4×C11—84no—
250C2×C4×C11—84no—
251C2×C4×C11C22×D414yes—
252C2×C4×C11C22×D414yes—
253C2×C4×C11C22×Q814yes—
254C2×C4×C11H(5,𝔽2)14yes—
255C23×D4C22×C1111yescharacteristic
256C24×C4C22×C1111yescharacteristic
257C24×C4C22×C1111yescharacteristic
258#543—28no—
259C2×C22⋊Q8C22×C1112yes—
260C2×C22⋊Q8C22×C1112yes—
261C2×C22⋊Q8C22×C1114yescomplemented
262C2×C22⋊Q8C22×C1114yescomplemented
263C2×C22⋊Q8C22×C1114yescomplemented
264C2×C4×D4—28no—
265C2×C4×D4C22×C1118yes—
266C22×C4⋊C4C22×C1111yescharacteristic
267C22×C4⋊C4C22×C1114yescomplemented
268C22×C22⋊C4C22×C1112yes—
269C22×C22⋊C4C22×C1112yes—
270C22×C22⋊C4C22×C1111yescharacteristic
271C22×C22⋊C4C22×C1111yescharacteristic
272C22×C42C22×C1111yescharacteristic
273#400C22×C1114yescomplemented
274#399C22×C1114yescomplemented
275#398C22×C1118yescomplemented
276#396C22×C1118yescomplemented
277#395C22×C1114yescomplemented
278#393C22×C1114yescomplemented
279#391C22×C1114yescomplemented
280#389C22×C1114yescomplemented
281#387C22×C1118yescomplemented
282#386C22×C1114yes—
283#386C22×C1118yes—
284#386C22×C1114yes—
285#385C22×C1114yes—
286#385C22×C1114yes—
287#385C22×C1118yescomplemented
288#385C22×C1118yescomplemented
289#385C22×C1118yescomplemented
290#381C22×C1114yes—
291#380C22×C1112yes—
292#380C22×C1112yes—
293#380C22×C1114yescomplemented
294#379C22×C1114yes—
295C2×#95C22×C1114yescomplemented
296C22×C11—28no—
297C22×C11—24no—
298C22×C11—22no—
299C22×C11—24no—
300C22×C11—22no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—24no—
305C22×C11—28no—
306C22×C11—416no—
307C22×C11—416no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11C2×C22⋊Q814yes—
312C22×C11C2×C22⋊Q818yes—
313C22×C11C23×D411yescharacteristic
314C22×C11C23×Q811yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11#58512yes—
318C4×C11—24no—
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—48no—
323C4×C11—42no—
324C4×C11—44no—
325C4×C11—44no—
326C25C23×C1111yescharacteristic
327C25C23×C1111yescharacteristic
328C22×Q8C23×C1112yes—
329C22×Q8C23×C1112yes—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4Q8×C1118yescomplemented
333C22×D4C23×C1114yes—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4C23×C1111yescharacteristic
339C23×C4C23×C1114yes—
340C23×C4C23×C1114yes—
341C23×C4C23×C1111yescharacteristic
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1112yes—
344C23×C4C23×C1114yes—
345C23×C4C23×C1112yes—
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C22⋊Q8—28no—
349C22⋊Q8—28no—
350C22⋊Q8—216no—
351C22⋊Q8—216no—
352C22⋊Q8—48no—
353C4×D4—232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—48no—
356C2×C4⋊C4C23×C1114yes—
357C2×C4⋊C4C23×C1118yes—
358C2×C4⋊C4C23×C1112yes—
359C2×C4⋊C4C23×C1114yes—
360C2×C4⋊C4C23×C1114yes—
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1118yes—
363C2×C4⋊C4C23×C1114yes—
364C2×C4⋊C4C23×C1114yes—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4D4×C1118yes—
369C2×C22⋊C4C23×C1114yes—
370C2×C22⋊C4C23×C1114yes—
371C2×C22⋊C4C23×C1114yes—
372C2×C22⋊C4C23×C1114yes—
373C2×C22⋊C4C23×C1114yes—
374C2×C22⋊C4C23×C1118yes—
375C2×C22⋊C4C23×C1118yes—
376C2×C22⋊C4C23×C1114yes—
377C2×C42—24no—
378C2×C42C23×C1114yes—
379#95C23×C1118yes—
380#95C23×C1118yes—
381#95C23×C1114yes—
382#95C23×C1114yes—
383#95C23×C1118yes—
384#95C23×C1118yes—
385C2×C11—24no—
386C2×C11—28no—
387C2×C11—44no—
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11#345912yes—
390C2×C11#348411yescharacteristic
391C2×C11#348511yescharacteristic
392C2×C11#350112yes—
393C24—22no—
394C24—22no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24C2×D4×C1114yes—
400C24C2×Q8×C1114yes—
401C24C2×Q8×C1114yes—
402C24C11×#4114yes—
403C24C24×C1112yes—
404C24C24×C1111yescharacteristic
405C24C24×C1112yes—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—44no—
409C2×Q8—44no—
410C2×D4—232no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4C2×Q8×C11116yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—416no—
436C22×C4—416no—
437C22×C4C2×D4×C1114yes—
438C22×C4C2×D4×C1114yes—
439C22×C4C2×Q8×C1114yes—
440C22×C4C24×C1118yes—
441C22×C4C24×C1114yes—
442C22×C4C24×C1112yes—
443C22×C4C24×C1114yes—
444C22×C4C24×C1112yes—
445C22×C4C24×C1112yes—
446C22×C4C24×C1112yes—
447C22×C4C24×C1112yes—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—28no—
453C4⋊C4—216no—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C4⋊C4—44no—
457C22⋊C4—28no—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—28no—
462C22⋊C4—48no—
463C22⋊C4—48no—
464C22⋊C4C2×D4×C11116yes—
465C42—28no—
466C11#3498511yescharacteristic, direct product factor, Sylow
467C23—24no—
468C23—22no—
469C23—24no—
470C23—22no—
471C23—28no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—24no—
476C23—44no—
477C23—44no—
478C23—48no—
479C23—48no—
480C23—48no—
481C23—44no—
482C23—48no—
483C23—44no—
484C23C11×C22⋊Q8116yescomplemented
485C23C22×D4×C1112yes—
486C23C22×D4×C1114yes—
487C23C22×Q8×C1114yes—
488C23C22×Q8×C1112yes—
489C23C22×Q8×C1114yes—
490C23C2×C11×#4112yes—
491C23C2×C11×#4114yes—
492C23C25×C1111yescharacteristic
493Q8—84no—
494Q8—84no—
495D4—232no—
496C2×C4—28no—
497C2×C4—28no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—28no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—416no—
516C2×C4—416no—
517C2×C4—416no—
518C2×C4—44no—
519C2×C4—84no—
520C2×C4—84no—
521C2×C4C22×D4×C1114yes—
522C2×C4C22×D4×C1114yes—
523C2×C4C22×Q8×C1114yes—
524C2×C4C11×H(5,𝔽2)14yes—
525C22—28no—
526C22—24no—
527C22—22no—
528C22—24no—
529C22—22no—
530C22—24no—
531C22—24no—
532C22—28no—
533C22—24no—
534C22—28no—
535C22—416no—
536C22—416no—
537C22—44no—
538C22—42no—
539C22—42no—
540C22C2×C11×C22⋊Q814yes—
541C22C2×C11×C22⋊Q818yes—
542C22C23×D4×C1111yescharacteristic
543C22C23×Q8×C1111yescharacteristic
544C22C22×C11×#4111yescharacteristic
545C22C2×C11×H(5,𝔽2)12yes—
546C22C11×#58512yes—
547C4—24no—
548C4—24no—
549C4—24no—
550C4—24no—
551C4—48no—
552C4—42no—
553C4—44no—
554C4—44no—
555C2—24no—
556C2—28no—
557C2—44no—
558C2C22×C11×C22⋊Q811yescharacteristic
559C2C11×#345912yes—
560C2C11×#348411yescharacteristic
561C2C11×#348511yescharacteristic
562C2C11×#350112yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#543C2semidirect
3. C11×#2855C2semidirect
4. C11×#2848C2semidirect
5. C11×#2627C2semidirect
6. C11×#2626C2semidirect
7. C11×#2450C2semidirect
8. C11×#2449C2semidirect
9. C11×#2315C2semidirect
11. C2×C11×#385C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
24. C22×C11×C4⋊C4C22semidirect
30. C11×#400C22semidirect
31. C11×#399C22semidirect
32. C11×#398C22semidirect
33. C11×#396C22semidirect
34. C11×#395C22semidirect
35. C11×#393C22semidirect
36. C11×#391C22semidirect
37. C11×#389C22semidirect
38. C11×#387C22semidirect
44. C11×#385C22semidirect
45. C11×#385C22semidirect
46. C11×#385C22semidirect
50. C11×#380C22semidirect
52. C2×C11×#95C22semidirect
59. C22×D4×C11Q8semidirect
112. #34985C11direct (N × H)
186. C2×#543C2×C11semidirect
188. #2855C2×C11semidirect
189. #2848C2×C11semidirect
190. #2627C2×C11semidirect
191. #2626C2×C11semidirect
192. #2450C2×C11semidirect
193. #2449C2×C11semidirect
194. #2315C2×C11semidirect
196. C2×#385C2×C11semidirect
214. C23×C11C22⋊Q8semidirect
261. C2×C22⋊Q8C22×C11semidirect
262. C2×C22⋊Q8C22×C11semidirect
263. C2×C22⋊Q8C22×C11semidirect
267. C22×C4⋊C4C22×C11semidirect
273. #400C22×C11semidirect
274. #399C22×C11semidirect
275. #398C22×C11semidirect
276. #396C22×C11semidirect
277. #395C22×C11semidirect
278. #393C22×C11semidirect
279. #391C22×C11semidirect
280. #389C22×C11semidirect
281. #387C22×C11semidirect
287. #385C22×C11semidirect
288. #385C22×C11semidirect
289. #385C22×C11semidirect
293. #380C22×C11semidirect
295. C2×#95C22×C11semidirect
332. C22×D4Q8×C11semidirect
466. C11#34985direct (N × H)
484. C23C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C22×C4×D4×C112
C11×#28552
C11×#28482
C11×#26272
C11×#26262
C11×#24502
C11×#24492
C11×#23152
C11×#23082
C2×C11×#3852
#3498511