Finite Group Databasebeta

← C11×#23482 #14600675

Subgroups — C11×#23482 #14600675

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C2×C11×#417C211yesmaximal, characteristic, complemented
5C2×C11×#407C211yesmaximal, characteristic, complemented
6C2×C11×#380C211yesmaximal, characteristic, complemented
7C11×#2036C212yesmaximal, complemented
8C11×#2035C212yesmaximal, complemented
9C11×#2034C212yesmaximal, complemented
10C11×#2033C212yesmaximal, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C11×#525—24no—
17C11×#525—24no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—21no—
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11—21no—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4—21no—
30C11×#428—24no—
31C2×C11×#107C2212yescomplemented
32C2×C11×#106C2212yescomplemented
33C11×#417—24no—
34C11×#417—24no—
35C2×C11×#103C2212yescomplemented
36C2×C11×#103C2212yescomplemented
37C2×C11×#102C2212yescomplemented
38C2×C11×#102C2212yescomplemented
39C11×#407—24no—
40C2×C11×C22⋊C8C2212yes—
41C2×C11×C22⋊C8C2212yes—
42C11×#380—21no—
43C11×#380—21no—
44C11×#380C2212yes—
45C11×#380C2212yes—
46C2×C11×#95—21no—
47C11×#340C2212yescomplemented
48C11×#340C2212yescomplemented
49C25×C11D411yescharacteristic
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41D414yes—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11D411yescharacteristic
71C23×C4×C11D411yescharacteristic
72C23×C4×C11D411yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16D414yescomplemented
82C22×C8×C11C2312yes—
83C22×C8×C11C2312yes—
84C11×#123—28no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#120—28no—
94C4×D4×C11—28no—
95C4×D4×C11—28no—
96C11×#117—22no—
97C11×#117D414yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—44no—
118C2×C42×C11—21no—
119C11×#107—24no—
120C11×#106—24no—
121C11×#103—24no—
122C11×#103—24no—
123C11×#102—24no—
124C11×#102—24no—
125C11×C22⋊C8—24no—
126C11×C22⋊C8—24no—
127C11×#95—22no—
128C11×#95—22no—
129#23482C1111yesmaximal, characteristic, direct product factor, Sylow
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—21no—
136C24×C11—41no—
137C24×C11—41no—
138C24×C11C2×D411yescharacteristic
139C24×C11C2×D411yescharacteristic
140C24×C11C2×D411yescharacteristic
141C11×#41—28no—
142C11×#41—28no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D412yes—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11C2×D412yes—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—24no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—42no—
196C22×C4×C11—44no—
197C22×C4×C11—42no—
198C22×C4×C11—44no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11#4112yes—
212C22×C4×C11#4112yes—
213C22×C4×C11#4112yes—
214C22×C4×C11C2411yescharacteristic
215C11×M16—28no—
216C11×M16—44no—
217C2×C8×C11—22no—
218C2×C8×C11—22no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—22no—
222C2×C8×C11C2×D414yes—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—42no—
232C11×C4⋊C4—42no—
233C11×C4⋊C4C2×D412yes—
234C11×C4⋊C4C2×D412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—44no—
241C11×C22⋊C4—44no—
242C42×C11—24no—
243C2×#525C2×C1111yescharacteristic
244C2×#428C2×C1111yescharacteristic, complemented
245C2×#417C2×C1111yescharacteristic, complemented
246C2×#417C2×C1111yescharacteristic, complemented
247C2×#407C2×C1111yescharacteristic, complemented
248C2×#380C2×C1111yescharacteristic, complemented
249#2036C2×C1112yescomplemented
250#2035C2×C1112yescomplemented
251#2034C2×C1112yescomplemented
252#2033C2×C1112yescomplemented
253#1736C2×C1111yescharacteristic, complemented
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—28no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—44no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11#12012yes—
285C23×C11#12112yes—
286C23×C11#12312yes—
287C23×C11AGL(1,ℤ/8)12yes—
288C23×C11#13712yes—
289C23×C11C22×D411yescharacteristic
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—41no—
293Q8×C11—41no—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—48no—
297D4×C11—48no—
298D4×C11—48no—
299D4×C11—41no—
300D4×C11—41no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—44no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—48no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—84no—
335C2×C4×C11—84no—
336C2×C4×C11#12012yes—
337C2×C4×C11#12114yes—
338C2×C4×C11#12114yes—
339C2×C4×C11#12112yes—
340C2×C4×C11#12314yes—
341C2×C4×C11#12312yes—
342C2×C4×C11#12414yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C8×C11—24no—
350C8×C11—42no—
351C22×#41C22×C1111yescharacteristic
352C24×C4C22×C1111yescharacteristic
353C22×M16C22×C1111yescharacteristic
354C22×M16C22×C1111yescharacteristic
355#525—24no—
356#525—24no—
357C2×#123—21no—
358C2×C22⋊Q8C22×C1111yescharacteristic
359C2×C22⋊Q8C22×C1111yescharacteristic
360C2×#121C22×C1111yescharacteristic
361C2×#121C22×C1111yescharacteristic
362C2×#120—21no—
363C2×C4×D4—21no—
364C2×C4×D4—21no—
365C2×#117C22×C1111yescharacteristic
366C22×C4⋊C4C22×C1111yescharacteristic
367C22×C4⋊C4C22×C1111yescharacteristic
368C22×C22⋊C4—21no—
369#428—24no—
370C2×#107C22×C1112yescomplemented
371C2×#106C22×C1112yescomplemented
372#417—24no—
373#417—24no—
374C2×#103C22×C1112yescomplemented
375C2×#103C22×C1112yescomplemented
376C2×#102C22×C1112yescomplemented
377C2×#102C22×C1112yescomplemented
378#407—24no—
379C2×C22⋊C8C22×C1112yes—
380C2×C22⋊C8C22×C1112yes—
381#380—21no—
382#380—21no—
383#380C22×C1112yes—
384#380C22×C1112yes—
385C2×#95—21no—
386#340C22×C1112yescomplemented
387#340C22×C1112yescomplemented
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—416no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11#39414yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×#12111yescharacteristic
419C22×C11C2×#12311yescharacteristic
420C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C11C2×#13711yescharacteristic
422C22×C11#57511yescharacteristic
423C22×C11#57511yescharacteristic
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—82no—
430C4×C11—82no—
431C4×C11#39414yes—
432C4×C11C2×#12111yescharacteristic
433C4×C11C2×#12111yescharacteristic
434C4×C11C2×#12311yescharacteristic
435C4×C11C2×#12411yescharacteristic
436C25D4×C1111yescharacteristic
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41D4×C1114yes—
443C22×Q8C23×C1111yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C23×C1111yescharacteristic
448C23×C4—21no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4D4×C1111yescharacteristic
458C23×C4D4×C1111yescharacteristic
459C23×C4D4×C1111yescharacteristic
460C23×C4C23×C1111yescharacteristic
461C23×C4C23×C1111yescharacteristic
462C23×C4C23×C1111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16D4×C1114yescomplemented
469C22×C8C23×C1112yes—
470C22×C8C23×C1112yes—
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#120—28no—
481C4×D4—28no—
482C4×D4—28no—
483#117—22no—
484#117D4×C1114yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4C23×C1112yes—
494C2×C4⋊C4C23×C1112yes—
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—44no—
505C2×C42—21no—
506#107—24no—
507#106—24no—
508#103—24no—
509#103—24no—
510#102—24no—
511#102—24no—
512C22⋊C8—24no—
513C22⋊C8—24no—
514#95—22no—
515#95—22no—
516C2×C11—24no—
517C2×C11—42no—
518C2×C11—42no—
519C2×C11—82no—
520C2×C11C2×#39411yescharacteristic
521C2×C11#300611yescharacteristic
522C2×C11#300711yescharacteristic
523C2×C11#305511yescharacteristic
524C2×C11#305611yescharacteristic
525C2×C11#309211yescharacteristic
526C2×C11#309311yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—41no—
534C24—41no—
535C24C2×D4×C1111yescharacteristic
536C24C2×D4×C1111yescharacteristic
537C24C2×D4×C1111yescharacteristic
538#41—28no—
539#41—28no—
540#41—44no—
541#41—44no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×D4×C1112yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C2×D4×C1112yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C1111yescharacteristic
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1112yes—
606C22×C4C2×D4×C1112yes—
607C22×C4C2×D4×C1112yes—
608C22×C4C11×#4112yes—
609C22×C4C11×#4112yes—
610C22×C4C11×#4112yes—
611C22×C4C24×C1111yescharacteristic
612M16—28no—
613M16—44no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8C2×D4×C1114yes—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4C2×D4×C1112yes—
631C4⋊C4C2×D4×C1112yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C42—24no—
640C11#2348211yescharacteristic, direct product factor, Sylow
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C11×#12012yes—
672C23C11×#12112yes—
673C23C11×#12312yes—
674C23C11×AGL(1,ℤ/8)12yes—
675C23C11×#13712yes—
676C23C22×D4×C1111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—44no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4C11×#12012yes—
724C2×C4C11×#12114yes—
725C2×C4C11×#12114yes—
726C2×C4C11×#12112yes—
727C2×C4C11×#12314yes—
728C2×C4C11×#12312yes—
729C2×C4C11×#12414yes—
730C2×C4C22×D4×C1111yescharacteristic
731C2×C4C22×D4×C1111yescharacteristic
732C2×C4C22×D4×C1111yescharacteristic
733C2×C4C2×C11×#4111yescharacteristic
734C2×C4C2×C11×#4111yescharacteristic
735C2×C4C2×C11×#4111yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22C11×#39414yes—
767C22C2×C11×#12011yescharacteristic
768C22C2×C11×#12111yescharacteristic
769C22C2×C11×#12311yescharacteristic
770C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
771C22C2×C11×#13711yescharacteristic
772C22C11×#57511yescharacteristic
773C22C11×#57511yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4C11×#39414yes—
782C4C2×C11×#12111yescharacteristic
783C4C2×C11×#12111yescharacteristic
784C4C2×C11×#12311yescharacteristic
785C4C2×C11×#12411yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×C11×#39411yescharacteristic
791C2C11×#300611yescharacteristic
792C2C11×#300711yescharacteristic
793C2C11×#305511yescharacteristic
794C2C11×#305611yescharacteristic
795C2C11×#309211yescharacteristic
796C2C11×#309311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#428C2semidirect
3. C2×C11×#417C2semidirect
4. C2×C11×#417C2semidirect
5. C2×C11×#407C2semidirect
6. C2×C11×#380C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#2034C2semidirect
10. C11×#2033C2semidirect
11. C11×#1736C2semidirect
31. C2×C11×#107C22semidirect
32. C2×C11×#106C22semidirect
35. C2×C11×#103C22semidirect
36. C2×C11×#103C22semidirect
37. C2×C11×#102C22semidirect
38. C2×C11×#102C22semidirect
47. C11×#340C22semidirect
48. C11×#340C22semidirect
81. C2×C11×M16D4semidirect
129. #23482C11direct (N × H)
244. C2×#428C2×C11semidirect
245. C2×#417C2×C11semidirect
246. C2×#417C2×C11semidirect
247. C2×#407C2×C11semidirect
248. C2×#380C2×C11semidirect
249. #2036C2×C11semidirect
250. #2035C2×C11semidirect
251. #2034C2×C11semidirect
252. #2033C2×C11semidirect
253. #1736C2×C11semidirect
370. C2×#107C22×C11semidirect
371. C2×#106C22×C11semidirect
374. C2×#103C22×C11semidirect
375. C2×#103C22×C11semidirect
376. C2×#102C22×C11semidirect
377. C2×#102C22×C11semidirect
386. #340C22×C11semidirect
387. #340C22×C11semidirect
468. C2×M16D4×C11semidirect
640. C11#23482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4282
C2×C11×#4172
C2×C11×#4072
C2×C11×#3802
C11×#20362
C11×#20352
C11×#20342
C11×#20332
C11×#17362
#2348211