Finite Group Databasebeta

← C11×#24802 #14601995

Subgroups — C11×#24802 #14601995

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#471C211yesmaximal, characteristic, complemented
2C11×#3056C211yesmaximal, characteristic, complemented
3C11×#3055C211yesmaximal, characteristic
4C2×C11×#465C211yesmaximal, characteristic, complemented
5C11×#2929C211yesmaximal, characteristic, complemented
6C22×C11×#108C211yesmaximal, characteristic, complemented
7C11×#2064C211yesmaximal, characteristic, complemented
8C11×#2063C211yesmaximal, characteristic, complemented
9C11×#2052C211yesmaximal, characteristic, complemented
10C11×#2051C211yesmaximal, characteristic, complemented
11C11×#1977C211yesmaximal, characteristic, complemented
12C11×#1951C211yesmaximal, characteristic, complemented
13C11×#1901C211yesmaximal, characteristic, complemented
14C11×#1900C211yesmaximal, characteristic, complemented
15C11×#1815C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C11×#525C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C11×#471—24no—
27C11×#470—21no—
28C11×#469—21no—
29C11×#468—21no—
30C11×#468—21no—
31C11×#467—21no—
32C11×#466—21no—
33C11×#465—21no—
34C11×#465—21no—
35C11×#465—21no—
36C11×#465—21no—
37C11×#465—21no—
38C11×#465—21no—
39C11×#435—21no—
40C11×#435—21no—
41C8×D4×C11—21no—
42C8×D4×C11—21no—
43C2×C11×#108—24no—
44C2×C11×#108C2211yescharacteristic
45C2×C11×#108C2211yescharacteristic
46C2×C11×#108C2211yescharacteristic
47C2×C11×#108C2211yescharacteristic
48C11×#428C2211yescharacteristic
49C11×#428C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C11×#424C2211yescharacteristic
52C11×#419C2211yescharacteristic
53C11×#418C2211yescharacteristic
54C11×#417C2211yescharacteristic
55C11×#417C2211yescharacteristic
56C2×C11×#103C2211yescharacteristic
57C2×C11×#102C2211yescharacteristic
58C2×C11×#101C2211yescharacteristic
59C2×C11×#101C2211yescharacteristic
60C2×C11×#100C2211yescharacteristic
61C2×C11×#100C2211yescharacteristic
62C11×#408C2211yescharacteristic
63C11×#407C2211yescharacteristic
64C11×#405C2211yescharacteristic
65C11×#343C2211yescharacteristic
66C11×#343C2211yescharacteristic
67C11×#343C2211yescharacteristic
68C11×#343C2211yescharacteristic
69C2×C11×#41C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C11×#137—22no—
75C11×#137—41no—
76C11×AGL(1,ℤ/8)—22no—
77C11×AGL(1,ℤ/8)—41no—
78C2×C11×Q16—21no—
79C2×C11×SD16—21no—
80C2×C11×SD16—21no—
81C2×C11×SD16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—22no—
84C2×C11×SD16—22no—
85C2×C11×D8—21no—
86C11×#131—22no—
87C11×#131—22no—
88C2×C11×M16—21no—
89C2×C11×M16—21no—
90C2×C11×M16—21no—
91C2×C11×M16—22no—
92C2×C11×M16—22no—
93C2×C11×M16—41no—
94C2×C11×M16—41no—
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C2×C11×M16C2311yescharacteristic
99C2×C11×M16C2311yescharacteristic
100C2×C11×M16C2311yescharacteristic
101C22×C8×C11—22no—
102C22×C8×C11—22no—
103C22×C8×C11—21no—
104C22×C8×C11—21no—
105C22×C8×C11—21no—
106C22×C8×C11D411yescharacteristic
107C22×C8×C11D411yescharacteristic
108C22×C8×C11D411yescharacteristic
109C22×C8×C11D411yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#123—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8D411yescharacteristic
118C11×C22⋊Q8D411yescharacteristic
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121D411yescharacteristic
124C11×#121D411yescharacteristic
125C11×#120—21no—
126C4×D4×C11—21no—
127C4×D4×C11—21no—
128C11×#117C2311yescharacteristic
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C11×#108—22no—
135C11×#108—22no—
136C11×#108—22no—
137C11×#108D414yescomplemented
138C11×#107—21no—
139C11×#107—21no—
140C11×#106—21no—
141C11×#106—21no—
142C11×#106—21no—
143C11×#106—21no—
144C11×C4⋊C8—21no—
145C11×C4⋊C8—21no—
146C11×#103—21no—
147C11×#103—21no—
148C11×#103—21no—
149C11×#103—21no—
150C11×#103—21no—
151C11×#103—21no—
152C11×#102—21no—
153C11×#102—21no—
154C11×#102—21no—
155C11×#102—21no—
156C11×#102—21no—
157C11×#102—21no—
158C11×#101—22no—
159C11×#101—41no—
160C11×#100—22no—
161C11×#100—41no—
162C11×C22⋊C8—21no—
163C11×C22⋊C8—21no—
164C11×C22⋊C8—21no—
165C11×C22⋊C8—21no—
166C11×#97—21no—
167C4×C8×C11—21no—
168#24802C1111yesmaximal, characteristic, direct product factor, Sylow
169C24×C11—21no—
170C24×C11#4111yescharacteristic
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C2×D411yescharacteristic
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—82no—
194C2×D4×C11C2×D411yescharacteristic
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11#4111yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C11×Q16—42no—
210C11×SD16—42no—
211C11×SD16—42no—
212C11×SD16—42no—
213C11×SD16—42no—
214C11×D8—42no—
215C11×M16—21no—
216C11×M16—21no—
217C11×M16—21no—
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16—21no—
223C11×M16—21no—
224C11×M16—21no—
225C11×M16—42no—
226C11×M16—42no—
227C11×M16—42no—
228C11×M16C2×D412yes—
229C11×M16C2×D412yes—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—42no—
243C2×C8×C11—42no—
244C2×C8×C11—42no—
245C2×C8×C11C2×D411yescharacteristic
246C2×C8×C11C2×D411yescharacteristic
247C2×C8×C11C2×D411yescharacteristic
248C2×C8×C11C2×D411yescharacteristic
249C2×C8×C11C2×D412yes—
250C2×C8×C11#4112yes—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—41no—
258C11×C4⋊C4—41no—
259C11×C4⋊C4C2×D411yescharacteristic
260C11×C4⋊C4C2×D411yescharacteristic
261C11×C22⋊C4—21no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—21no—
266C11×C22⋊C4—41no—
267C11×C22⋊C4—41no—
268C11×C22⋊C4—41no—
269C11×C22⋊C4—41no—
270C42×C11—21no—
271C2×#471C2×C1111yescharacteristic, complemented
272#3056C2×C1111yescharacteristic, complemented
273#3055C2×C1111yescharacteristic
274C2×#465C2×C1111yescharacteristic, complemented
275#2929C2×C1111yescharacteristic, complemented
276C22×#108C2×C1111yescharacteristic, complemented
277#2064C2×C1111yescharacteristic, complemented
278#2063C2×C1111yescharacteristic, complemented
279#2052C2×C1111yescharacteristic, complemented
280#2051C2×C1111yescharacteristic, complemented
281#1977C2×C1111yescharacteristic, complemented
282#1951C2×C1111yescharacteristic, complemented
283#1901C2×C1111yescharacteristic, complemented
284#1900C2×C1111yescharacteristic, complemented
285#1815C2×C1111yescharacteristic, complemented
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—21no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—81no—
295C23×C11—81no—
296C23×C11#12111yescharacteristic
297C23×C11#12111yescharacteristic
298C23×C11C2×#4111yescharacteristic
299Q8×C11—21no—
300Q8×C11—21no—
301Q8×C11—41no—
302Q8×C11—41no—
303Q8×C11—41no—
304Q8×C11—41no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—42no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—42no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—82no—
316D4×C11—82no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—81no—
338C2×C4×C11—81no—
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C2×#4111yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C2×C4×C112−1+411yescharacteristic
347C8×C11—21no—
348C8×C11—21no—
349C8×C11—22no—
350C8×C11—22no—
351C8×C11—41no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11#12112yes—
356C8×C11#12112yes—
357C2×#137C22×C1111yescharacteristic
358C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
359C22×SD16C22×C1111yescharacteristic
360C2×#131C22×C1111yescharacteristic
361C22×M16C22×C1111yescharacteristic
362C22×M16C22×C1111yescharacteristic
363C23×C8C22×C1111yescharacteristic
364#525C22×C1111yescharacteristic
365C2×C22⋊Q8C22×C1111yescharacteristic
366C2×#121C22×C1111yescharacteristic
367#471—24no—
368#470—21no—
369#469—21no—
370#468—21no—
371#468—21no—
372#467—21no—
373#466—21no—
374#465—21no—
375#465—21no—
376#465—21no—
377#465—21no—
378#465—21no—
379#465—21no—
380#435—21no—
381#435—21no—
382C8×D4—21no—
383C8×D4—21no—
384C2×#108—24no—
385C2×#108C22×C1111yescharacteristic
386C2×#108C22×C1111yescharacteristic
387C2×#108C22×C1111yescharacteristic
388C2×#108C22×C1111yescharacteristic
389#428C22×C1111yescharacteristic
390#428C22×C1111yescharacteristic
391C2×#106C22×C1111yescharacteristic
392#424C22×C1111yescharacteristic
393#419C22×C1111yescharacteristic
394#418C22×C1111yescharacteristic
395#417C22×C1111yescharacteristic
396#417C22×C1111yescharacteristic
397C2×#103C22×C1111yescharacteristic
398C2×#102C22×C1111yescharacteristic
399C2×#101C22×C1111yescharacteristic
400C2×#101C22×C1111yescharacteristic
401C2×#100C22×C1111yescharacteristic
402C2×#100C22×C1111yescharacteristic
403#408C22×C1111yescharacteristic
404#407C22×C1111yescharacteristic
405#405C22×C1111yescharacteristic
406#343C22×C1111yescharacteristic
407#343C22×C1111yescharacteristic
408#343C22×C1111yescharacteristic
409#343C22×C1111yescharacteristic
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—21no—
414C22×C11—21no—
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—161no—
426C22×C11—161no—
427C22×C11#47112yescomplemented
428C22×C11C2×#12111yescharacteristic
429C22×C11#54811yescharacteristic
430C22×C11#55311yescharacteristic
431C4×C11—21no—
432C4×C11—21no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—81no—
437C4×C11—81no—
438C4×C11—81no—
439C4×C11C2×#12111yescharacteristic
440C4×C11#53711yescharacteristic
441C4×C11D4211yescharacteristic
442C4×C11#54711yescharacteristic
443C2×#41C23×C1111yescharacteristic
444C22×Q8C23×C1111yescharacteristic
445C22×D4—21no—
446C22×D4C23×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448#137—22no—
449#137—41no—
450AGL(1,ℤ/8)—22no—
451AGL(1,ℤ/8)—41no—
452C2×Q16—21no—
453C2×SD16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×D8—21no—
460#131—22no—
461#131—22no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—41no—
468C2×M16—41no—
469C2×M16C23×C1111yescharacteristic
470C2×M16C23×C1111yescharacteristic
471C2×M16C23×C1111yescharacteristic
472C2×M16C23×C1111yescharacteristic
473C2×M16C23×C1111yescharacteristic
474C2×M16C23×C1111yescharacteristic
475C22×C8—22no—
476C22×C8—22no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8D4×C1111yescharacteristic
481C22×C8D4×C1111yescharacteristic
482C22×C8D4×C1111yescharacteristic
483C22×C8D4×C1111yescharacteristic
484C22×C8C23×C1111yescharacteristic
485C22×C8C23×C1111yescharacteristic
486#123—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8D4×C1111yescharacteristic
492C22⋊Q8D4×C1111yescharacteristic
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121D4×C1111yescharacteristic
498#121D4×C1111yescharacteristic
499#120—21no—
500C4×D4—21no—
501C4×D4—21no—
502#117C23×C1111yescharacteristic
503C2×C4⋊C4—21no—
504C2×C4⋊C4C23×C1111yescharacteristic
505C2×C4⋊C4C23×C1111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508#108—22no—
509#108—22no—
510#108—22no—
511#108D4×C1114yescomplemented
512#107—21no—
513#107—21no—
514#106—21no—
515#106—21no—
516#106—21no—
517#106—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#103—21no—
524#103—21no—
525#103—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530#102—21no—
531#102—21no—
532#101—22no—
533#101—41no—
534#100—22no—
535#100—41no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540#97—21no—
541C4×C8—21no—
542C2×C11—21no—
543C2×C11—21no—
544C2×C11—22no—
545C2×C11—41no—
546C2×C11—81no—
547C2×C11—161no—
548C2×C11#241611yescharacteristic
549C2×C11C2×#47111yescharacteristic
550C2×C11#306711yescharacteristic
551C24—21no—
552C24C11×#4111yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C2×D4×C1111yescharacteristic
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—82no—
576C2×D4C2×D4×C1111yescharacteristic
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×C4C2×D4×C1111yescharacteristic
586C22×C4C2×D4×C1111yescharacteristic
587C22×C4C2×D4×C1111yescharacteristic
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C11×#4111yescharacteristic
590C22×C4C24×C1111yescharacteristic
591Q16—42no—
592SD16—42no—
593SD16—42no—
594SD16—42no—
595SD16—42no—
596D8—42no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—42no—
608M16—42no—
609M16—42no—
610M16C2×D4×C1112yes—
611M16C2×D4×C1112yes—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—42no—
625C2×C8—42no—
626C2×C8—42no—
627C2×C8C2×D4×C1111yescharacteristic
628C2×C8C2×D4×C1111yescharacteristic
629C2×C8C2×D4×C1111yescharacteristic
630C2×C8C2×D4×C1111yescharacteristic
631C2×C8C2×D4×C1112yes—
632C2×C8C11×#4112yes—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4C2×D4×C1111yescharacteristic
642C4⋊C4C2×D4×C1111yescharacteristic
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C42—21no—
653C11#2480211yescharacteristic, direct product factor, Sylow
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—81no—
663C23—81no—
664C23C11×#12111yescharacteristic
665C23C11×#12111yescharacteristic
666C23C2×C11×#4111yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673D4—21no—
674D4—21no—
675D4—42no—
676D4—41no—
677D4—41no—
678D4—42no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4C11×#12111yescharacteristic
708C2×C4C11×#12111yescharacteristic
709C2×C4C22×D4×C1111yescharacteristic
710C2×C4C22×D4×C1111yescharacteristic
711C2×C4C22×D4×C1111yescharacteristic
712C2×C4C2×C11×#4111yescharacteristic
713C2×C4C11×H(5,𝔽2)11yescharacteristic
714C2×C4C11×2−1+411yescharacteristic
715C8—21no—
716C8—21no—
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8C11×#12112yes—
724C8C11×#12112yes—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—161no—
741C22—161no—
742C22C11×#47112yescomplemented
743C22C2×C11×#12111yescharacteristic
744C22C11×#54811yescharacteristic
745C22C11×#55311yescharacteristic
746C4—21no—
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4C2×C11×#12111yescharacteristic
755C4C11×#53711yescharacteristic
756C4D42×C1111yescharacteristic
757C4C11×#54711yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—161no—
764C2C11×#241611yescharacteristic
765C2C2×C11×#47111yescharacteristic
766C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3055C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#471C2semidirect
2. C11×#3056C2semidirect
4. C2×C11×#465C2semidirect
5. C11×#2929C2semidirect
6. C22×C11×#108C2semidirect
7. C11×#2064C2semidirect
8. C11×#2063C2semidirect
9. C11×#2052C2semidirect
10. C11×#2051C2semidirect
11. C11×#1977C2semidirect
12. C11×#1951C2semidirect
13. C11×#1901C2semidirect
14. C11×#1900C2semidirect
15. C11×#1815C2semidirect
137. C11×#108D4semidirect
168. #24802C11direct (N × H)
271. C2×#471C2×C11semidirect
272. #3056C2×C11semidirect
274. C2×#465C2×C11semidirect
275. #2929C2×C11semidirect
276. C22×#108C2×C11semidirect
277. #2064C2×C11semidirect
278. #2063C2×C11semidirect
279. #2052C2×C11semidirect
280. #2051C2×C11semidirect
281. #1977C2×C11semidirect
282. #1951C2×C11semidirect
283. #1901C2×C11semidirect
284. #1900C2×C11semidirect
285. #1815C2×C11semidirect
427. C22×C11#471semidirect
511. #108D4×C11semidirect
653. C11#24802direct (N × H)
742. C22C11×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4712
C11×#30562
C11×#30552
C2×C11×#4652
C11×#29292
C22×C11×#1082
C11×#20642
C11×#20632
C11×#20522
C11×#20512
C11×#19772
C11×#19512
C11×#19012
C11×#19002
C11×#18152
#2480211