Finite Group Databasebeta

← C11×#24667 #14601860

Subgroups — C11×#24667 #14601860

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2620C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic, complemented
5C11×#2035C211yesmaximal, characteristic, complemented
6C11×#2034C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1972C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1948C211yesmaximal, characteristic, complemented
13C11×#1935C211yesmaximal, characteristic, complemented
14C11×#1934C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#463—24no—
25C11×#433—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
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×#396—21no—
43C11×#396—21no—
44C11×#394—21no—
45C11×#394—21no—
46C11×#391C2211yescharacteristic
47C11×#390—21no—
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#388—21no—
52C11×#386—21no—
53C11×#385—21no—
54C11×#384C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#124—22no—
79C11×#124—22no—
80C11×C22⋊Q8—41no—
81C11×C22⋊Q8—41no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—41no—
85C11×#121—41no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—22no—
89C11×#117—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
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×#106—41no—
118C11×#106—41no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8D414yescomplemented
121C11×#103—22no—
122C11×#103—22no—
123C11×#103—41no—
124C11×#102—22no—
125C11×#102—22no—
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#24667C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11—24no—
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—42no—
161C2×D4×C11—81no—
162C2×D4×C11—81no—
163C2×D4×C11—81no—
164C2×D4×C11—81no—
165C2×D4×C11#4112yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—42no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C11×SD16—44no—
188C11×D8—44no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11C2×D412yes—
200C2×C8×C11C2×D412yes—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—81no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4—81no—
216C11×C4⋊C4#4112yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—81no—
233C42×C11C2×D412yes—
234C42×C11#4112yes—
235C2×#463C2×C1111yescharacteristic, complemented
236C2×#433C2×C1111yescharacteristic, complemented
237#2620C2×C1111yescharacteristic, complemented
238#2324C2×C1111yescharacteristic, complemented
239#2035C2×C1111yescharacteristic, complemented
240#2034C2×C1111yescharacteristic, complemented
241#2000C2×C1111yescharacteristic, complemented
242#1999C2×C1111yescharacteristic
243#1983C2×C1111yescharacteristic, complemented
244#1972C2×C1111yescharacteristic, complemented
245#1968C2×C1111yescharacteristic, complemented
246#1948C2×C1111yescharacteristic, complemented
247#1935C2×C1111yescharacteristic, complemented
248#1934C2×C1111yescharacteristic, complemented
249#1802C2×C1111yescharacteristic, complemented
250C23×C11—21no—
251C23×C11—22no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C22×D411yescharacteristic
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11—41no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—84no—
285D4×C11—84no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
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—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—84no—
322C2×C4×C11#12112yes—
323C2×C4×C11#12112yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C8×C11—22no—
331C8×C11—22no—
332C8×C11—41no—
333C8×C11—41no—
334C22×SD16C22×C1111yescharacteristic
335C22×D8C22×C1111yescharacteristic
336C2×#124C22×C1111yescharacteristic
337C2×C22⋊Q8C22×C1111yescharacteristic
338C2×#121C22×C1111yescharacteristic
339C2×#121C22×C1111yescharacteristic
340C2×C4×D4C22×C1111yescharacteristic
341C2×#117C22×C1111yescharacteristic
342#463—24no—
343#433—24no—
344C2×#106C22×C1111yescharacteristic
345C2×#106C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×#103C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358C2×#97C22×C1111yescharacteristic
359C2×C4×C8C22×C1111yescharacteristic
360#396—21no—
361#396—21no—
362#394—21no—
363#394—21no—
364#391C22×C1111yescharacteristic
365#390—21no—
366#390C22×C1111yescharacteristic
367#390C22×C1111yescharacteristic
368#389C22×C1111yescharacteristic
369#388—21no—
370#386—21no—
371#385—21no—
372#384C22×C1111yescharacteristic
373#380C22×C1111yescharacteristic
374C4×C4⋊C4C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379C22×C11—41no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—42no—
383C22×C11—41no—
384C22×C11—42no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11C2×#12111yescharacteristic
401C22×C11#52511yescharacteristic
402C22×C11#53511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57711yescharacteristic
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—42no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11#54611yescharacteristic
419C4×C11#55011yescharacteristic
420C4×C11#55311yescharacteristic
421C4×C11#55511yescharacteristic
422C22×Q8C23×C1111yescharacteristic
423C22×D4—21no—
424C22×D4—21no—
425C22×D4C23×C1111yescharacteristic
426C22×D4C23×C1111yescharacteristic
427C23×C4—21no—
428C23×C4C23×C1111yescharacteristic
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—41no—
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—41no—
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439#124—22no—
440#124—22no—
441C22⋊Q8—41no—
442C22⋊Q8—41no—
443#121—22no—
444#121—22no—
445#121—41no—
446#121—41no—
447C4×D4—22no—
448C4×D4—22no—
449#117—22no—
450#117—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C4⋊C4D4×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4D4×C1111yescharacteristic
474C2×C22⋊C4D4×C1111yescharacteristic
475C2×C42—21no—
476C2×C42C23×C1111yescharacteristic
477C2×C42C23×C1111yescharacteristic
478#106—41no—
479#106—41no—
480C4⋊C8—22no—
481C4⋊C8D4×C1114yescomplemented
482#103—22no—
483#103—22no—
484#103—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488#102—41no—
489#102—41no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#97—22no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C2×C11—81no—
500C2×C11—82no—
501C2×C11—161no—
502C2×C11#241411yescharacteristic
503C2×C11#306011yescharacteristic
504C2×C11#306211yescharacteristic
505C2×C11#311811yescharacteristic
506C2×C11#312511yescharacteristic
507C2×C11#322111yescharacteristic
508C2×C11#322411yescharacteristic
509C24—21no—
510C24—21no—
511C24C2×D4×C1111yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4C11×#4112yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C2×D4×C1111yescharacteristic
553C22×C4C2×D4×C1111yescharacteristic
554C22×C4C2×D4×C1111yescharacteristic
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C24×C1111yescharacteristic
557SD16—44no—
558D8—44no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8C2×D4×C1112yes—
570C2×C8C2×D4×C1112yes—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—81no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4C11×#4112yes—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C42—21no—
601C42—21no—
602C42—81no—
603C42C2×D4×C1112yes—
604C42C11×#4112yes—
605C11#2466711yescharacteristic, direct product factor, Sylow
606C23—21no—
607C23—22no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23C22×D4×C1111yescharacteristic
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632D4—22no—
633D4—22no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—84no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4C11×#12112yes—
679C2×C4C11×#12112yes—
680C2×C4C22×D4×C1111yescharacteristic
681C2×C4C2×C11×#4111yescharacteristic
682C2×C4C2×C11×#4111yescharacteristic
683C2×C4C2×C11×#4111yescharacteristic
684C2×C4C11×H(5,𝔽2)11yescharacteristic
685C2×C4C11×H(5,𝔽2)11yescharacteristic
686C8—22no—
687C8—22no—
688C8—41no—
689C8—41no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—42no—
698C22—41no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C11×#12111yescharacteristic
712C22C11×#52511yescharacteristic
713C22C11×#53511yescharacteristic
714C22C11×#57611yescharacteristic
715C22C11×#57711yescharacteristic
716C22C11×#57711yescharacteristic
717C22C11×#57711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C11×#54611yescharacteristic
730C4C11×#55011yescharacteristic
731C4C11×#55311yescharacteristic
732C4C11×#55511yescharacteristic
733C2—81no—
734C2—82no—
735C2—161no—
736C2C11×#241411yescharacteristic
737C2C11×#306011yescharacteristic
738C2C11×#306211yescharacteristic
739C2C11×#311811yescharacteristic
740C2C11×#312511yescharacteristic
741C2C11×#322111yescharacteristic
742C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#1999C2
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×#463C2semidirect
2. C2×C11×#433C2semidirect
3. C11×#2620C2semidirect
4. C11×#2324C2semidirect
5. C11×#2035C2semidirect
6. C11×#2034C2semidirect
7. C11×#2000C2semidirect
9. C11×#1983C2semidirect
10. C11×#1972C2semidirect
11. C11×#1968C2semidirect
12. C11×#1948C2semidirect
13. C11×#1935C2semidirect
14. C11×#1934C2semidirect
15. C11×#1802C2semidirect
120. C11×C4⋊C8D4semidirect
138. #24667C11direct (N × H)
235. C2×#463C2×C11semidirect
236. C2×#433C2×C11semidirect
237. #2620C2×C11semidirect
238. #2324C2×C11semidirect
239. #2035C2×C11semidirect
240. #2034C2×C11semidirect
241. #2000C2×C11semidirect
243. #1983C2×C11semidirect
244. #1972C2×C11semidirect
245. #1968C2×C11semidirect
246. #1948C2×C11semidirect
247. #1935C2×C11semidirect
248. #1934C2×C11semidirect
249. #1802C2×C11semidirect
481. C4⋊C8D4×C11semidirect
605. C11#24667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4332
C11×#26202
C11×#23242
C11×#20352
C11×#20342
C11×#20002
C11×#19992
C11×#19832
C11×#19722
C11×#19682
C11×#19482
C11×#19352
C11×#19342
C11×#18022
#2466711