Finite Group Databasebeta

← C11×#24662 #14601855

Subgroups — C11×#24662 #14601855

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2619C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#1999C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1982C211yesmaximal, characteristic, complemented
10C11×#1972C211yesmaximal, characteristic, complemented
11C11×#1970C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1936C211yesmaximal, characteristic, complemented
14C11×#1934C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#459—24no—
25C11×#433—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#394—21no—
43C11×#394—21no—
44C11×#392—21no—
45C11×#392—21no—
46C11×#390—21no—
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#388—21no—
52C11×#386—21no—
53C11×#385—21no—
54C11×#382C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8—41no—
76C2×C11×D8—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#127—22no—
82C11×#127—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—41no—
86C11×#121—41no—
87C11×#121—41no—
88C11×#121—41no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C11×#117—22no—
92C11×#117—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—41no—
118C11×#106—41no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8D414yescomplemented
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102—41no—
127C11×#102—41no—
128C11×#102—41no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×#97—22no—
132C4×C8×C11—22no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24662C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11—81no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11#4112yes—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
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—42no—
188C22×C4×C11—81no—
189C22×C4×C11—81no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C11×D8—44no—
197C11×D8—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11C2×D412yes—
209C2×C8×C11C2×D412yes—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4#4112yes—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—81no—
239C42×C11C2×D412yes—
240C42×C11#4112yes—
241C2×#459C2×C1111yescharacteristic, complemented
242C2×#433C2×C1111yescharacteristic, complemented
243#2619C2×C1111yescharacteristic, complemented
244#2324C2×C1111yescharacteristic, complemented
245#2034C2×C1111yescharacteristic, complemented
246#2033C2×C1111yescharacteristic, complemented
247#1999C2×C1111yescharacteristic, complemented
248#1999C2×C1111yescharacteristic, complemented
249#1982C2×C1111yescharacteristic, complemented
250#1972C2×C1111yescharacteristic, complemented
251#1970C2×C1111yescharacteristic, complemented
252#1949C2×C1111yescharacteristic, complemented
253#1936C2×C1111yescharacteristic, complemented
254#1934C2×C1111yescharacteristic, complemented
255#1804C2×C1111yescharacteristic, complemented
256C23×C11—21no—
257C23×C11—22no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11C22×D411yescharacteristic
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—84no—
298D4×C11—84no—
299D4×C11—84no—
300D4×C11—84no—
301D4×C11—84no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—41no—
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—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—84no—
335C2×C4×C11#12112yes—
336C2×C4×C11#12112yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C8×C11—22no—
344C8×C11—22no—
345C8×C11—41no—
346C8×C11—41no—
347C22×D8C22×C1111yescharacteristic
348C22×D8C22×C1111yescharacteristic
349C2×#127C22×C1111yescharacteristic
350C2×#121C22×C1111yescharacteristic
351C2×#121C22×C1111yescharacteristic
352C2×#121C22×C1111yescharacteristic
353C2×C4×D4C22×C1111yescharacteristic
354C2×#117C22×C1111yescharacteristic
355#459—24no—
356#433—24no—
357C2×#107C22×C1111yescharacteristic
358C2×#106C22×C1111yescharacteristic
359C2×C4⋊C8C22×C1111yescharacteristic
360C2×C4⋊C8C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×#102C22×C1111yescharacteristic
364C2×#102C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371C2×#97C22×C1111yescharacteristic
372C2×C4×C8C22×C1111yescharacteristic
373#394—21no—
374#394—21no—
375#392—21no—
376#392—21no—
377#390—21no—
378#390C22×C1111yescharacteristic
379#390C22×C1111yescharacteristic
380#390C22×C1111yescharacteristic
381#389C22×C1111yescharacteristic
382#388—21no—
383#386—21no—
384#385—21no—
385#382C22×C1111yescharacteristic
386#380C22×C1111yescharacteristic
387C4×C4⋊C4C22×C1111yescharacteristic
388#340C22×C1111yescharacteristic
389#340C22×C1111yescharacteristic
390#340C22×C1111yescharacteristic
391#340C22×C1111yescharacteristic
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11C2×#12111yescharacteristic
421C22×C11#52511yescharacteristic
422C22×C11#53511yescharacteristic
423C22×C11#57611yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57611yescharacteristic
426C22×C11#57711yescharacteristic
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—42no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—81no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11—81no—
437C4×C11#54611yescharacteristic
438C4×C11#55011yescharacteristic
439C4×C11#55311yescharacteristic
440C4×C11#55511yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C23×C1111yescharacteristic
447C22×D4C23×C1111yescharacteristic
448C22×D4C23×C1111yescharacteristic
449C23×C4—21no—
450C23×C4C23×C1111yescharacteristic
451C2×D8—22no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—22no—
455C2×D8—41no—
456C2×D8—41no—
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461#127—22no—
462#127—22no—
463#121—22no—
464#121—22no—
465#121—41no—
466#121—41no—
467#121—41no—
468#121—41no—
469C4×D4—22no—
470C4×D4—22no—
471#117—22no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4D4×C1111yescharacteristic
475C2×C4⋊C4D4×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C1111yescharacteristic
493C2×C22⋊C4D4×C1111yescharacteristic
494C2×C42—21no—
495C2×C42C23×C1111yescharacteristic
496C2×C42C23×C1111yescharacteristic
497#107—41no—
498#106—41no—
499C4⋊C8—22no—
500C4⋊C8D4×C1114yescomplemented
501#102—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507#102—41no—
508#102—41no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511#97—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518C2×C11—81no—
519C2×C11—82no—
520C2×C11—161no—
521C2×C11—161no—
522C2×C11#241411yescharacteristic
523C2×C11#305811yescharacteristic
524C2×C11#306211yescharacteristic
525C2×C11#311911yescharacteristic
526C2×C11#312211yescharacteristic
527C2×C11#322011yescharacteristic
528C2×C11#322411yescharacteristic
529C24—21no—
530C24—21no—
531C24—21no—
532C24C2×D4×C1111yescharacteristic
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4C11×#4112yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C2×D4×C1111yescharacteristic
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C2×D4×C1111yescharacteristic
584C22×C4C2×D4×C1111yescharacteristic
585C22×C4C24×C1111yescharacteristic
586D8—44no—
587D8—44no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8C2×D4×C1112yes—
599C2×C8C2×D4×C1112yes—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—81no—
612C4⋊C4C11×#4112yes—
613C22⋊C4—24no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C42—21no—
627C42—21no—
628C42—81no—
629C42C2×D4×C1112yes—
630C42C11×#4112yes—
631C11#2466211yescharacteristic, direct product factor, Sylow
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C1111yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
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—84no—
711C2×C4C11×#12112yes—
712C2×C4C11×#12112yes—
713C2×C4C22×D4×C1111yescharacteristic
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C2×C11×#4111yescharacteristic
716C2×C4C2×C11×#4111yescharacteristic
717C2×C4C11×H(5,𝔽2)11yescharacteristic
718C2×C4C11×H(5,𝔽2)11yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×C11×#12111yescharacteristic
752C22C11×#52511yescharacteristic
753C22C11×#53511yescharacteristic
754C22C11×#57611yescharacteristic
755C22C11×#57611yescharacteristic
756C22C11×#57611yescharacteristic
757C22C11×#57711yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C11×#54611yescharacteristic
769C4C11×#55011yescharacteristic
770C4C11×#55311yescharacteristic
771C4C11×#55511yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C11×#241411yescharacteristic
777C2C11×#305811yescharacteristic
778C2C11×#306211yescharacteristic
779C2C11×#311911yescharacteristic
780C2C11×#312211yescharacteristic
781C2C11×#322011yescharacteristic
782C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#459C2semidirect
2. C2×C11×#433C2semidirect
3. C11×#2619C2semidirect
4. C11×#2324C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1999C2semidirect
9. C11×#1982C2semidirect
10. C11×#1972C2semidirect
11. C11×#1970C2semidirect
12. C11×#1949C2semidirect
13. C11×#1936C2semidirect
14. C11×#1934C2semidirect
15. C11×#1804C2semidirect
120. C11×C4⋊C8D4semidirect
138. #24662C11direct (N × H)
241. C2×#459C2×C11semidirect
242. C2×#433C2×C11semidirect
243. #2619C2×C11semidirect
244. #2324C2×C11semidirect
245. #2034C2×C11semidirect
246. #2033C2×C11semidirect
247. #1999C2×C11semidirect
248. #1999C2×C11semidirect
249. #1982C2×C11semidirect
250. #1972C2×C11semidirect
251. #1970C2×C11semidirect
252. #1949C2×C11semidirect
253. #1936C2×C11semidirect
254. #1934C2×C11semidirect
255. #1804C2×C11semidirect
500. C4⋊C8D4×C11semidirect
631. C11#24662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4332
C11×#26192
C11×#23242
C11×#20342
C11×#20332
C11×#19992
C11×#19822
C11×#19722
C11×#19702
C11×#19492
C11×#19362
C11×#19342
C11×#18042
#2466211