Finite Group Databasebeta

← C11×#20995 #14598188

Subgroups — C11×#20995 #14598188

Order 2816.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic
2C2×C11×#568C211yesmaximal, characteristic, complemented
3C2×C11×#421C211yesmaximal, characteristic, complemented
4C11×#2896C211yesmaximal, characteristic, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C11×#1903C214yesmaximal, complemented
7C11×#1902C214yesmaximal, complemented
8C2×C11×#344C211yesmaximal, characteristic, complemented
9C2×C11×#338C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C11×#575—22no—
13C11×#575—22no—
14C11×#575—22no—
15C11×#575—22no—
16C2×C11×#137C412yescomplemented
17C2×C11×#137C2212yes—
18C2×C11×AGL(1,ℤ/8)C412yescomplemented
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C2×C11×#135C414yescomplemented
21C11×#568—22no—
22C11×#568—22no—
23C11×#568—22no—
24C11×#568C2214yes—
25C2×C11×#131—22no—
26C2×C11×#131—22no—
27C22×C11×M16—22no—
28C22×C11×M16C2211yescharacteristic
29C22×C11×M16C2211yescharacteristic
30C22×C11×M16C2211yescharacteristic
31C22×C11×M16C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#421—22no—
34C11×#421C2214yes—
35C2×C11×#104—22no—
36C11×#419C2212yescomplemented
37C11×#418C2212yescomplemented
38C11×#417—22no—
39C11×#416—22no—
40C11×#413—22no—
41C11×#413—22no—
42C2×C11×#101C2212yescomplemented
43C2×C11×#100C2212yescomplemented
44C11×#344C2214yescomplemented
45C11×#338C2214yescomplemented
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41C2×C412yes—
63C2×C11×#41C2×C412yes—
64C2×C11×#41C2×C412yes—
65C2×C11×#41D412yes—
66C2×C11×#41D412yes—
67C2×C11×#41D412yes—
68C2×C11×#41D412yes—
69C2×C11×#41C2312yes—
70C22×Q8×C11C2×C411yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11—21no—
74C22×D4×C11C2×C411yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11—21no—
77C23×C4×C11—21no—
78C23×C4×C11C2311yescharacteristic
79C11×#137—24no—
80C11×#137—24no—
81C11×#137—24no—
82C11×#137—24no—
83C11×AGL(1,ℤ/8)—24no—
84C11×AGL(1,ℤ/8)—24no—
85C11×AGL(1,ℤ/8)—24no—
86C11×AGL(1,ℤ/8)—24no—
87C11×#135—28no—
88C11×#135—28no—
89C2×C11×Q16C2×C414yescomplemented
90C2×C11×SD16C2×C414yescomplemented
91C2×C11×SD16C2×C414yescomplemented
92C2×C11×D8C2×C414yescomplemented
93C11×#131—28no—
94C11×#131—28no—
95C11×#131—28no—
96C11×#131—28no—
97C2×C11×M16—24no—
98C2×C11×M16—28no—
99C2×C11×M16—21no—
100C2×C11×M16—21no—
101C2×C11×M16—21no—
102C2×C11×M16—21no—
103C2×C11×M16—21no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16—21no—
107C2×C11×M16—21no—
108C2×C11×M16—21no—
109C2×C11×M16—21no—
110C2×C11×M16—28no—
111C2×C11×M16—21no—
112C2×C11×M16—21no—
113C2×C11×M16—21no—
114C2×C11×M16—21no—
115C2×C11×M16—21no—
116C2×C11×M16C2×C412yes—
117C2×C11×M16D412yes—
118C2×C11×M16D412yes—
119C2×C11×M16D412yes—
120C2×C11×M16C2312yes—
121C2×C11×M16C2312yes—
122C2×C11×M16C2312yes—
123C2×C11×M16C2312yes—
124C22×C8×C11—24no—
125C22×C8×C11—21no—
126C22×C8×C11—21no—
127C22×C8×C11C2×C412yes—
128C22×C8×C11D412yes—
129C11×#117—21no—
130C11×#117—21no—
131C11×#117—21no—
132C11×#117C2312yes—
133C2×C11×C4⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C42×C11—21no—
136C11×#104—28no—
137C11×#103—24no—
138C11×#102—24no—
139C11×#101—24no—
140C11×#100—24no—
141#20995C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C24×C11#4111yescharacteristic
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—22no—
155C11×#41—22no—
156C11×#41—22no—
157C11×#41—22no—
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—41no—
166C11×#41—41no—
167C11×#41—41no—
168C11×#41—41no—
169C11×#41—41no—
170C11×#41—41no—
171C11×#41—41no—
172C11×#41—41no—
173C11×#41C22⋊C414yes—
174C11×#41C22⋊C414yes—
175C11×#41C2×D414yes—
176C11×#41C2×D414yes—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11C22⋊C412yes—
186C2×Q8×C11C22⋊C412yes—
187C2×Q8×C11C22×C412yes—
188C2×Q8×C11C22×C412yes—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—41no—
206C2×D4×C11—41no—
207C2×D4×C11—41no—
208C2×D4×C11—41no—
209C2×D4×C11C22⋊C412yes—
210C2×D4×C11C22⋊C412yes—
211C2×D4×C11C22×C412yes—
212C2×D4×C11C22×C412yes—
213C22×C4×C11—21no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—41no—
224C22×C4×C11—41no—
225C22×C4×C11—41no—
226C22×C4×C11—41no—
227C22×C4×C11—41no—
228C22×C4×C11C22×C411yescharacteristic
229C22×C4×C11C22×C411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11#4111yescharacteristic
239C22×C4×C11#4111yescharacteristic
240C22×C4×C11#4111yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C11×Q16—28no—
243C11×SD16—28no—
244C11×SD16—28no—
245C11×D8—28no—
246C11×M16—216no—
247C11×M16—22no—
248C11×M16—22no—
249C11×M16—22no—
250C11×M16—22no—
251C11×M16—22no—
252C11×M16—22no—
253C11×M16—22no—
254C11×M16—22no—
255C11×M16—22no—
256C11×M16—22no—
257C11×M16—22no—
258C11×M16—22no—
259C11×M16—22no—
260C11×M16—41no—
261C11×M16—41no—
262C11×M16C2×D414yes—
263C2×C8×C11—216no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11—22no—
272C2×C8×C11—41no—
273C2×C8×C11—41no—
274C2×C8×C11C22×C414yes—
275C2×C8×C11C2×D414yes—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—41no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—41no—
280C42×C11—22no—
281C42×C11—41no—
282C2×#575C2×C1111yescharacteristic
283C2×#568C2×C1111yescharacteristic, complemented
284C2×#421C2×C1111yescharacteristic, complemented
285#2896C2×C1111yescharacteristic, complemented
286C2×#413C2×C1111yescharacteristic, complemented
287#1903C2×C1114yescomplemented
288#1902C2×C1114yescomplemented
289C2×#344C2×C1111yescharacteristic, complemented
290C2×#338C2×C1111yescharacteristic, complemented
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—81no—
298C23×C11—82no—
299C23×C11—82no—
300C23×C11C4×D411yescharacteristic
301C23×C11C4×D411yescharacteristic
302C23×C11#12111yescharacteristic
303C23×C11#12111yescharacteristic
304C23×C11#12311yescharacteristic
305C23×C11#12311yescharacteristic
306C23×C11C2×#4111yescharacteristic
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—41no—
313Q8×C11—41no—
314Q8×C11C2×C22⋊C414yes—
315D4×C11—24no—
316D4×C11—24no—
317D4×C11—24no—
318D4×C11—24no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—42no—
325D4×C11—42no—
326D4×C11—42no—
327D4×C11—42no—
328D4×C11—41no—
329D4×C11—41no—
330D4×C11C2×C22⋊C414yes—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—82no—
347C2×C4×C11C2×C22⋊C411yescharacteristic
348C2×C4×C11C2×C22⋊C411yescharacteristic
349C2×C4×C11C2×C22⋊C411yescharacteristic
350C2×C4×C11C2×C22⋊C411yescharacteristic
351C2×C4×C11C4×D411yescharacteristic
352C2×C4×C11C4×D411yescharacteristic
353C2×C4×C11C4×D411yescharacteristic
354C2×C4×C11C4×D411yescharacteristic
355C2×C4×C11C4×D411yescharacteristic
356C2×C4×C11C4×D411yescharacteristic
357C2×C4×C11#12011yescharacteristic
358C2×C4×C11#12011yescharacteristic
359C2×C4×C11#12011yescharacteristic
360C2×C4×C11#12011yescharacteristic
361C2×C4×C11#12111yescharacteristic
362C2×C4×C11#12111yescharacteristic
363C2×C4×C11#12111yescharacteristic
364C2×C4×C11#12111yescharacteristic
365C2×C4×C11#12111yescharacteristic
366C2×C4×C11#12111yescharacteristic
367C2×C4×C11#12311yescharacteristic
368C2×C4×C11#12311yescharacteristic
369C2×C4×C11C23×C411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C2×#4111yescharacteristic
375C8×C11—24no—
376C8×C11—24no—
377C8×C11—24no—
378C8×C11—42no—
379C22×#41C22×C1111yescharacteristic
380C22×#41C22×C1111yescharacteristic
381#575—22no—
382#575—22no—
383#575—22no—
384#575—22no—
385C2×#137C4×C1112yescomplemented
386C2×#137C22×C1112yes—
387C2×AGL(1,ℤ/8)C4×C1112yescomplemented
388C2×AGL(1,ℤ/8)C22×C1112yes—
389C2×#135C4×C1114yescomplemented
390#568—22no—
391#568—22no—
392#568—22no—
393#568C22×C1114yes—
394C2×#131—22no—
395C2×#131—22no—
396C22×M16—22no—
397C22×M16C22×C1111yescharacteristic
398C22×M16C22×C1111yescharacteristic
399C22×M16C22×C1111yescharacteristic
400C22×M16C22×C1111yescharacteristic
401C2×#117C22×C1111yescharacteristic
402#421—22no—
403#421C22×C1114yes—
404C2×#104—22no—
405#419C22×C1112yescomplemented
406#418C22×C1112yescomplemented
407#417—22no—
408#416—22no—
409#413—22no—
410#413—22no—
411C2×#101C22×C1112yescomplemented
412C2×#100C22×C1112yescomplemented
413#344C22×C1114yescomplemented
414#338C22×C1114yescomplemented
415C22×C11—24no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—44no—
424C22×C11—42no—
425C22×C11—82no—
426C22×C11—82no—
427C22×C11—82no—
428C22×C11—82no—
429C22×C11—82no—
430C22×C11#38611yescharacteristic
431C22×C11#38611yescharacteristic
432C22×C11#38611yescharacteristic
433C22×C11#38611yescharacteristic
434C22×C11C2×C4×D411yescharacteristic
435C22×C11C2×#12111yescharacteristic
436C22×C11C2×#12311yescharacteristic
437C4×C11—24no—
438C4×C11—42no—
439C4×C11—82no—
440C4×C11#38611yescharacteristic
441C4×C11#38611yescharacteristic
442C4×C11#38611yescharacteristic
443C4×C11#38611yescharacteristic
444C4×C11C22×C22⋊C411yescharacteristic
445C4×C11C2×C4×D411yescharacteristic
446C4×C11C2×#12011yescharacteristic
447C4×C11C2×#12111yescharacteristic
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41C2×C4×C1112yes—
465C2×#41C2×C4×C1112yes—
466C2×#41C2×C4×C1112yes—
467C2×#41D4×C1112yes—
468C2×#41D4×C1112yes—
469C2×#41D4×C1112yes—
470C2×#41D4×C1112yes—
471C2×#41C23×C1112yes—
472C22×Q8C2×C4×C1111yescharacteristic
473C22×Q8C23×C1111yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C2×C4×C1111yescharacteristic
477C22×D4C23×C1111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C1111yescharacteristic
481#137—24no—
482#137—24no—
483#137—24no—
484#137—24no—
485AGL(1,ℤ/8)—24no—
486AGL(1,ℤ/8)—24no—
487AGL(1,ℤ/8)—24no—
488AGL(1,ℤ/8)—24no—
489#135—28no—
490#135—28no—
491C2×Q16C2×C4×C1114yescomplemented
492C2×SD16C2×C4×C1114yescomplemented
493C2×SD16C2×C4×C1114yescomplemented
494C2×D8C2×C4×C1114yescomplemented
495#131—28no—
496#131—28no—
497#131—28no—
498#131—28no—
499C2×M16—24no—
500C2×M16—28no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—28no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16C2×C4×C1112yes—
519C2×M16D4×C1112yes—
520C2×M16D4×C1112yes—
521C2×M16D4×C1112yes—
522C2×M16C23×C1112yes—
523C2×M16C23×C1112yes—
524C2×M16C23×C1112yes—
525C2×M16C23×C1112yes—
526C22×C8—24no—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8C2×C4×C1112yes—
530C22×C8D4×C1112yes—
531#117—21no—
532#117—21no—
533#117—21no—
534#117C23×C1112yes—
535C2×C4⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C42—21no—
538#104—28no—
539#103—24no—
540#102—24no—
541#101—24no—
542#100—24no—
543C2×C11—21no—
544C2×C11—21no—
545C2×C11—21no—
546C2×C11—21no—
547C2×C11—21no—
548C2×C11—21no—
549C2×C11—21no—
550C2×C11—44no—
551C2×C11—82no—
552C2×C11C2×#38611yescharacteristic
553C24—21no—
554C24—21no—
555C24C11×#4111yescharacteristic
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41C11×C22⋊C414yes—
585#41C11×C22⋊C414yes—
586#41C2×D4×C1114yes—
587#41C2×D4×C1114yes—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8C11×C22⋊C412yes—
597C2×Q8C11×C22⋊C412yes—
598C2×Q8C22×C4×C1112yes—
599C2×Q8C22×C4×C1112yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4C11×C22⋊C412yes—
621C2×D4C11×C22⋊C412yes—
622C2×D4C22×C4×C1112yes—
623C2×D4C22×C4×C1112yes—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4C22×C4×C1111yescharacteristic
640C22×C4C22×C4×C1111yescharacteristic
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1111yescharacteristic
643C22×C4C2×D4×C1111yescharacteristic
644C22×C4C2×D4×C1111yescharacteristic
645C22×C4C2×D4×C1111yescharacteristic
646C22×C4C2×D4×C1111yescharacteristic
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C11×#4111yescharacteristic
650C22×C4C11×#4111yescharacteristic
651C22×C4C11×#4111yescharacteristic
652C22×C4C24×C1111yescharacteristic
653Q16—28no—
654SD16—28no—
655SD16—28no—
656D8—28no—
657M16—216no—
658M16—22no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—22no—
668M16—22no—
669M16—22no—
670M16—22no—
671M16—41no—
672M16—41no—
673M16C2×D4×C1114yes—
674C2×C8—216no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8C22×C4×C1114yes—
686C2×C8C2×D4×C1114yes—
687C4⋊C4—22no—
688C4⋊C4—41no—
689C22⋊C4—22no—
690C22⋊C4—41no—
691C42—22no—
692C42—41no—
693C11#2099511yescharacteristic, direct product factor, Sylow
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—81no—
701C23—82no—
702C23—82no—
703C23C4×D4×C1111yescharacteristic
704C23C4×D4×C1111yescharacteristic
705C23C11×#12111yescharacteristic
706C23C11×#12111yescharacteristic
707C23C11×#12311yescharacteristic
708C23C11×#12311yescharacteristic
709C23C2×C11×#4111yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—41no—
716Q8—41no—
717Q8C2×C11×C22⋊C414yes—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—41no—
732D4—41no—
733D4C2×C11×C22⋊C414yes—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—82no—
750C2×C4C2×C11×C22⋊C411yescharacteristic
751C2×C4C2×C11×C22⋊C411yescharacteristic
752C2×C4C2×C11×C22⋊C411yescharacteristic
753C2×C4C2×C11×C22⋊C411yescharacteristic
754C2×C4C4×D4×C1111yescharacteristic
755C2×C4C4×D4×C1111yescharacteristic
756C2×C4C4×D4×C1111yescharacteristic
757C2×C4C4×D4×C1111yescharacteristic
758C2×C4C4×D4×C1111yescharacteristic
759C2×C4C4×D4×C1111yescharacteristic
760C2×C4C11×#12011yescharacteristic
761C2×C4C11×#12011yescharacteristic
762C2×C4C11×#12011yescharacteristic
763C2×C4C11×#12011yescharacteristic
764C2×C4C11×#12111yescharacteristic
765C2×C4C11×#12111yescharacteristic
766C2×C4C11×#12111yescharacteristic
767C2×C4C11×#12111yescharacteristic
768C2×C4C11×#12111yescharacteristic
769C2×C4C11×#12111yescharacteristic
770C2×C4C11×#12311yescharacteristic
771C2×C4C11×#12311yescharacteristic
772C2×C4C23×C4×C1111yescharacteristic
773C2×C4C22×D4×C1111yescharacteristic
774C2×C4C22×D4×C1111yescharacteristic
775C2×C4C22×D4×C1111yescharacteristic
776C2×C4C22×D4×C1111yescharacteristic
777C2×C4C2×C11×#4111yescharacteristic
778C8—24no—
779C8—24no—
780C8—24no—
781C8—42no—
782C22—24no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—44no—
791C22—42no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22C11×#38611yescharacteristic
798C22C11×#38611yescharacteristic
799C22C11×#38611yescharacteristic
800C22C11×#38611yescharacteristic
801C22C2×C4×D4×C1111yescharacteristic
802C22C2×C11×#12111yescharacteristic
803C22C2×C11×#12311yescharacteristic
804C4—24no—
805C4—42no—
806C4—82no—
807C4C11×#38611yescharacteristic
808C4C11×#38611yescharacteristic
809C4C11×#38611yescharacteristic
810C4C11×#38611yescharacteristic
811C4C22×C11×C22⋊C411yescharacteristic
812C4C2×C4×D4×C1111yescharacteristic
813C4C2×C11×#12011yescharacteristic
814C4C2×C11×#12111yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—44no—
823C2—82no—
824C2C2×C11×#38611yescharacteristic
subgroupG/H
centerC4×C11#386
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#386
prime radicalC2×C11×#575C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#568C2semidirect
3. C2×C11×#421C2semidirect
4. C11×#2896C2semidirect
5. C2×C11×#413C2semidirect
6. C11×#1903C2semidirect
7. C11×#1902C2semidirect
8. C2×C11×#344C2semidirect
9. C2×C11×#338C2semidirect
16. C2×C11×#137C4semidirect
18. C2×C11×AGL(1,ℤ/8)C4semidirect
20. C2×C11×#135C4semidirect
36. C11×#419C22semidirect
37. C11×#418C22semidirect
42. C2×C11×#101C22semidirect
43. C2×C11×#100C22semidirect
44. C11×#344C22semidirect
45. C11×#338C22semidirect
89. C2×C11×Q16C2×C4semidirect
90. C2×C11×SD16C2×C4semidirect
91. C2×C11×SD16C2×C4semidirect
92. C2×C11×D8C2×C4semidirect
141. #20995C11direct (N × H)
283. C2×#568C2×C11semidirect
284. C2×#421C2×C11semidirect
285. #2896C2×C11semidirect
286. C2×#413C2×C11semidirect
287. #1903C2×C11semidirect
288. #1902C2×C11semidirect
289. C2×#344C2×C11semidirect
290. C2×#338C2×C11semidirect
385. C2×#137C4×C11semidirect
387. C2×AGL(1,ℤ/8)C4×C11semidirect
389. C2×#135C4×C11semidirect
405. #419C22×C11semidirect
406. #418C22×C11semidirect
411. C2×#101C22×C11semidirect
412. C2×#100C22×C11semidirect
413. #344C22×C11semidirect
414. #338C22×C11semidirect
491. C2×Q16C2×C4×C11semidirect
492. C2×SD16C2×C4×C11semidirect
493. C2×SD16C2×C4×C11semidirect
494. C2×D8C2×C4×C11semidirect
693. C11#20995direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#5682
C2×C11×#4212
C11×#28962
C2×C11×#4132
C11×#19032
C11×#19022
C2×C11×#3442
C2×C11×#3382
#2099511