Finite Group Databasebeta

← C11×#24796 #14601989

Subgroups — C11×#24796 #14601989

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#471C211yesmaximal, characteristic, complemented
2C11×#3057C211yesmaximal, characteristic, complemented
3C11×#3046C211yesmaximal, characteristic, complemented
4C11×#3045C211yesmaximal, characteristic
5C2×C11×#443C211yesmaximal, characteristic, complemented
6C11×#2912C211yesmaximal, characteristic, complemented
7C11×#2064C211yesmaximal, characteristic, complemented
8C11×#2063C211yesmaximal, characteristic, complemented
9C11×#2038C211yesmaximal, characteristic, complemented
10C11×#2037C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1945C211yesmaximal, characteristic, complemented
13C11×#1883C211yesmaximal, characteristic, complemented
14C11×#1882C211yesmaximal, characteristic, complemented
15C11×#1815C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C11×#135C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22C11×#536C2211yescharacteristic
23C11×#535C2211yescharacteristic
24C11×#520C2211yescharacteristic
25C11×#520C2211yescharacteristic
26C11×#471—24no—
27C11×#468—21no—
28C11×#468—21no—
29C11×#465—21no—
30C11×#465—21no—
31C11×#464—21no—
32C11×#464—21no—
33C11×#463—21no—
34C11×#463—21no—
35C11×#462—21no—
36C11×#461—21no—
37C11×#460—21no—
38C11×#459—21no—
39C11×#443—24no—
40C2×C11×#108C2211yescharacteristic
41C2×C11×#108C2211yescharacteristic
42C11×#428—21no—
43C11×#428—21no—
44C11×#428C2211yescharacteristic
45C11×#428C2211yescharacteristic
46C11×#427—21no—
47C11×#427C2211yescharacteristic
48C2×C11×#106—21no—
49C2×C11×#106C2211yescharacteristic
50C11×#424C2211yescharacteristic
51C11×#424C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C11×#419C2211yescharacteristic
55C11×#418C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C11×#417C2211yescharacteristic
58C2×C11×#103C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×C11×#101C2211yescharacteristic
61C2×C11×#100C2211yescharacteristic
62C2×C4×C8×C11C2211yescharacteristic
63C11×#391C2211yescharacteristic
64C11×#390C2211yescharacteristic
65C11×#343C2211yescharacteristic
66C11×#343C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C2×C11×#41C2311yescharacteristic
70C2×C11×#41C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C11×#137—22no—
74C11×#137—22no—
75C11×AGL(1,ℤ/8)—22no—
76C11×AGL(1,ℤ/8)—22no—
77C11×#135—22no—
78C11×#135—22no—
79C2×C11×Q16—21no—
80C2×C11×Q16D411yescharacteristic
81C2×C11×SD16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—22no—
86C2×C11×SD16—22no—
87C2×C11×SD16D411yescharacteristic
88C2×C11×SD16D411yescharacteristic
89C2×C11×D8—21no—
90C2×C11×D8D411yescharacteristic
91C11×#131—22no—
92C11×#131—22no—
93C11×#131—22no—
94C11×#131D414yescomplemented
95C2×C11×M16—21no—
96C2×C11×M16—21no—
97C2×C11×M16C2311yescharacteristic
98C2×C11×M16C2311yescharacteristic
99C2×C11×M16C2311yescharacteristic
100C2×C11×M16C2311yescharacteristic
101C22×C8×C11—21no—
102C22×C8×C11—21no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C4⋊Q8—21no—
106C11×#127—21no—
107C11×#124—21no—
108C11×#124—21no—
109C11×#123—41no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×#121—21no—
113C11×#121—21no—
114C11×#120—41no—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—41no—
120C4×D4×C11—41no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117C2311yescharacteristic
124C11×#117C2311yescharacteristic
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C22⋊C4—41no—
130C2×C42×C11C2311yescharacteristic
131C11×#108—22no—
132C11×#108—22no—
133C11×#107—21no—
134C11×#107—21no—
135C11×#107D411yescharacteristic
136C11×#107D411yescharacteristic
137C11×#106—21no—
138C11×#106—21no—
139C11×#106—21no—
140C11×#106—21no—
141C11×#106D411yescharacteristic
142C11×#106D411yescharacteristic
143C11×C4⋊C8—21no—
144C11×C4⋊C8—21no—
145C11×C4⋊C8—21no—
146C11×C4⋊C8—21no—
147C11×#104—22no—
148C11×#104—22no—
149C11×#103—21no—
150C11×#103—21no—
151C11×#103—21no—
152C11×#103—21no—
153C11×#103—21no—
154C11×#103—21no—
155C11×#102—21no—
156C11×#102—21no—
157C11×#102—21no—
158C11×#102—21no—
159C11×#102—21no—
160C11×#102—21no—
161C11×#101—22no—
162C11×#100—22no—
163C4×C8×C11—22no—
164C11×#95—41no—
165#24796C1111yesmaximal, characteristic, direct product factor, Sylow
166C24×C11—21no—
167C11×#41—21no—
168C11×#41—21no—
169C11×#41—21no—
170C11×#41—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41C2×D412yes—
174C11×#41#4112yes—
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×Q8×C11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
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—41no—
202C22×C4×C11—41no—
203C22×C4×C11C2411yescharacteristic
204C11×Q16—22no—
205C11×Q16—42no—
206C11×SD16—22no—
207C11×SD16—22no—
208C11×SD16—42no—
209C11×SD16—42no—
210C11×SD16—42no—
211C11×SD16—42no—
212C11×D8—22no—
213C11×D8—42no—
214C11×M16—24no—
215C11×M16—21no—
216C11×M16—21no—
217C11×M16—21no—
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16—42no—
223C11×M16C2×D412yes—
224C2×C8×C11—24no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—42no—
232C2×C8×C11C2×D411yescharacteristic
233C2×C8×C11C2×D411yescharacteristic
234C2×C8×C11C2×D412yes—
235C2×C8×C11C2×D411yescharacteristic
236C2×C8×C11C2×D411yescharacteristic
237C2×C8×C11#4112yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—41no—
243C11×C4⋊C4—41no—
244C11×C4⋊C4—41no—
245C11×C4⋊C4—41no—
246C11×C4⋊C4C2×D411yescharacteristic
247C11×C4⋊C4C2×D411yescharacteristic
248C11×C4⋊C4C2×D411yescharacteristic
249C11×C4⋊C4C2×D411yescharacteristic
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—41no—
253C11×C22⋊C4—41no—
254C11×C22⋊C4—41no—
255C11×C22⋊C4—41no—
256C11×C22⋊C4—41no—
257C11×C22⋊C4—41no—
258C11×C22⋊C4—82no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—41no—
264C42×C11—41no—
265C2×#471C2×C1111yescharacteristic, complemented
266#3057C2×C1111yescharacteristic, complemented
267#3046C2×C1111yescharacteristic, complemented
268#3045C2×C1111yescharacteristic
269C2×#443C2×C1111yescharacteristic, complemented
270#2912C2×C1111yescharacteristic, complemented
271#2064C2×C1111yescharacteristic, complemented
272#2063C2×C1111yescharacteristic, complemented
273#2038C2×C1111yescharacteristic, complemented
274#2037C2×C1111yescharacteristic, complemented
275#1968C2×C1111yescharacteristic, complemented
276#1945C2×C1111yescharacteristic, complemented
277#1883C2×C1111yescharacteristic, complemented
278#1882C2×C1111yescharacteristic, complemented
279#1815C2×C1111yescharacteristic, complemented
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—81no—
286C23×C11—81no—
287C23×C11H(5,𝔽2)11yescharacteristic
288Q8×C11—21no—
289Q8×C11—21no—
290Q8×C11—21no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—41no—
294Q8×C11—41no—
295Q8×C11#12112yes—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—21no—
299D4×C11—21no—
300D4×C11—21no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—161no—
308D4×C11—161no—
309D4×C11#12112yes—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
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—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—81no—
329C2×C4×C11—81no—
330C2×C4×C11—161no—
331C2×C4×C11—161no—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C112−1+411yescharacteristic
338C8×C11—22no—
339C8×C11—21no—
340C8×C11—21no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C8×C11#12112yes—
345C8×C11#12112yes—
346C2×#137C22×C1111yescharacteristic
347C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
348C2×#135C22×C1111yescharacteristic
349C22×SD16C22×C1111yescharacteristic
350C2×#131C22×C1111yescharacteristic
351C2×#131C22×C1111yescharacteristic
352#536C22×C1111yescharacteristic
353#535C22×C1111yescharacteristic
354#520C22×C1111yescharacteristic
355#520C22×C1111yescharacteristic
356#471—24no—
357#468—21no—
358#468—21no—
359#465—21no—
360#465—21no—
361#464—21no—
362#464—21no—
363#463—21no—
364#463—21no—
365#462—21no—
366#461—21no—
367#460—21no—
368#459—21no—
369#443—24no—
370C2×#108C22×C1111yescharacteristic
371C2×#108C22×C1111yescharacteristic
372#428—21no—
373#428—21no—
374#428C22×C1111yescharacteristic
375#428C22×C1111yescharacteristic
376#427—21no—
377#427C22×C1111yescharacteristic
378C2×#106—21no—
379C2×#106C22×C1111yescharacteristic
380#424C22×C1111yescharacteristic
381#424C22×C1111yescharacteristic
382C2×#104C22×C1111yescharacteristic
383C2×#104C22×C1111yescharacteristic
384#419C22×C1111yescharacteristic
385#418C22×C1111yescharacteristic
386#417C22×C1111yescharacteristic
387#417C22×C1111yescharacteristic
388C2×#103C22×C1111yescharacteristic
389C2×#102C22×C1111yescharacteristic
390C2×#101C22×C1111yescharacteristic
391C2×#100C22×C1111yescharacteristic
392C2×C4×C8C22×C1111yescharacteristic
393#391C22×C1111yescharacteristic
394#390C22×C1111yescharacteristic
395#343C22×C1111yescharacteristic
396#343C22×C1111yescharacteristic
397#339C22×C1111yescharacteristic
398#339C22×C1111yescharacteristic
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—82no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—161no—
412C22×C11#53711yescharacteristic
413C22×C11D4211yescharacteristic
414C22×C11#55311yescharacteristic
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11C2×#12111yescharacteristic
426C4×C11C2×#12111yescharacteristic
427C4×C11#54711yescharacteristic
428C4×C11#54811yescharacteristic
429C2×#41C23×C1111yescharacteristic
430C2×#41C23×C1111yescharacteristic
431C22×Q8C23×C1111yescharacteristic
432C22×D4C23×C1111yescharacteristic
433#137—22no—
434#137—22no—
435AGL(1,ℤ/8)—22no—
436AGL(1,ℤ/8)—22no—
437#135—22no—
438#135—22no—
439C2×Q16—21no—
440C2×Q16D4×C1111yescharacteristic
441C2×SD16—21no—
442C2×SD16—21no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16D4×C1111yescharacteristic
448C2×SD16D4×C1111yescharacteristic
449C2×D8—21no—
450C2×D8D4×C1111yescharacteristic
451#131—22no—
452#131—22no—
453#131—22no—
454#131D4×C1114yescomplemented
455C2×M16—21no—
456C2×M16—21no—
457C2×M16C23×C1111yescharacteristic
458C2×M16C23×C1111yescharacteristic
459C2×M16C23×C1111yescharacteristic
460C2×M16C23×C1111yescharacteristic
461C22×C8—21no—
462C22×C8—21no—
463C22×C8C23×C1111yescharacteristic
464C22×C8C23×C1111yescharacteristic
465C4⋊Q8—21no—
466#127—21no—
467#124—21no—
468#124—21no—
469#123—41no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472#121—21no—
473#121—21no—
474#120—41no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—41no—
480C4×D4—41no—
481#117—21no—
482#117—21no—
483#117C23×C1111yescharacteristic
484#117C23×C1111yescharacteristic
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C1111yescharacteristic
488C2×C4⋊C4C23×C1111yescharacteristic
489C2×C22⋊C4—41no—
490C2×C42C23×C1111yescharacteristic
491#108—22no—
492#108—22no—
493#107—21no—
494#107—21no—
495#107D4×C1111yescharacteristic
496#107D4×C1111yescharacteristic
497#106—21no—
498#106—21no—
499#106—21no—
500#106—21no—
501#106D4×C1111yescharacteristic
502#106D4×C1111yescharacteristic
503C4⋊C8—21no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507#104—22no—
508#104—22no—
509#103—21no—
510#103—21no—
511#103—21no—
512#103—21no—
513#103—21no—
514#103—21no—
515#102—21no—
516#102—21no—
517#102—21no—
518#102—21no—
519#102—21no—
520#102—21no—
521#101—22no—
522#100—22no—
523C4×C8—22no—
524#95—41no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—42no—
528C2×C11—81no—
529C2×C11—161no—
530C2×C11#241611yescharacteristic
531C2×C11#329011yescharacteristic
532C2×C11#329111yescharacteristic
533C24—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41C2×D4×C1112yes—
541#41C11×#4112yes—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C1111yescharacteristic
549C2×Q8C2×D4×C1111yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4C2×D4×C1111yescharacteristic
561C2×D4C2×D4×C1111yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4C24×C1111yescharacteristic
571Q16—22no—
572Q16—42no—
573SD16—22no—
574SD16—22no—
575SD16—42no—
576SD16—42no—
577SD16—42no—
578SD16—42no—
579D8—22no—
580D8—42no—
581M16—21no—
582M16—24no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—42no—
590M16C2×D4×C1112yes—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—24no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—42no—
599C2×C8C2×D4×C1111yescharacteristic
600C2×C8C2×D4×C1111yescharacteristic
601C2×C8C2×D4×C1112yes—
602C2×C8C2×D4×C1111yescharacteristic
603C2×C8C2×D4×C1111yescharacteristic
604C2×C8C11×#4112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4C2×D4×C1111yescharacteristic
614C4⋊C4C2×D4×C1111yescharacteristic
615C4⋊C4C2×D4×C1111yescharacteristic
616C4⋊C4C2×D4×C1111yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—82no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—41no—
631C42—41no—
632C11#2479611yescharacteristic, direct product factor, Sylow
633C23—21no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—81no—
639C23—81no—
640C23C11×H(5,𝔽2)11yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8C11×#12112yes—
649D4—22no—
650D4—22no—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—161no—
661D4—161no—
662D4C11×#12112yes—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—161no—
684C2×C4—161no—
685C2×C4C22×D4×C1111yescharacteristic
686C2×C4C22×D4×C1111yescharacteristic
687C2×C4C22×D4×C1111yescharacteristic
688C2×C4C2×C11×#4111yescharacteristic
689C2×C4C2×C11×#4111yescharacteristic
690C2×C4C11×2−1+411yescharacteristic
691C8—22no—
692C8—21no—
693C8—21no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8C11×#12112yes—
698C8C11×#12112yes—
699C22—21no—
700C22—21no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—82no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—161no—
712C22C11×#53711yescharacteristic
713C22D42×C1111yescharacteristic
714C22C11×#55311yescharacteristic
715C4—22no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4C2×C11×#12111yescharacteristic
726C4C2×C11×#12111yescharacteristic
727C4C11×#54711yescharacteristic
728C4C11×#54811yescharacteristic
729C2—21no—
730C2—21no—
731C2—42no—
732C2—81no—
733C2—161no—
734C2C11×#241611yescharacteristic
735C2C11×#329011yescharacteristic
736C2C11×#329111yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3045C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#471C2semidirect
2. C11×#3057C2semidirect
3. C11×#3046C2semidirect
5. C2×C11×#443C2semidirect
6. C11×#2912C2semidirect
7. C11×#2064C2semidirect
8. C11×#2063C2semidirect
9. C11×#2038C2semidirect
10. C11×#2037C2semidirect
11. C11×#1968C2semidirect
12. C11×#1945C2semidirect
13. C11×#1883C2semidirect
14. C11×#1882C2semidirect
15. C11×#1815C2semidirect
94. C11×#131D4semidirect
165. #24796C11direct (N × H)
265. C2×#471C2×C11semidirect
266. #3057C2×C11semidirect
267. #3046C2×C11semidirect
269. C2×#443C2×C11semidirect
270. #2912C2×C11semidirect
271. #2064C2×C11semidirect
272. #2063C2×C11semidirect
273. #2038C2×C11semidirect
274. #2037C2×C11semidirect
275. #1968C2×C11semidirect
276. #1945C2×C11semidirect
277. #1883C2×C11semidirect
278. #1882C2×C11semidirect
279. #1815C2×C11semidirect
454. #131D4×C11semidirect
632. C11#24796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4712
C11×#30572
C11×#30462
C11×#30452
C2×C11×#4432
C11×#29122
C11×#20642
C11×#20632
C11×#20382
C11×#20372
C11×#19682
C11×#19452
C11×#18832
C11×#18822
C11×#18152
#2479611