Finite Group Databasebeta

← C11×#24766 #14601959

Subgroups — C11×#24766 #14601959

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic
2C2×C11×#465C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C2×C11×#424C211yesmaximal, characteristic, complemented
5C11×#2621C211yesmaximal, characteristic, complemented
6C11×#2324C211yesmaximal, characteristic
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#2055C211yesmaximal, characteristic, complemented
10C11×#2055C211yesmaximal, characteristic, complemented
11C11×#1981C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1894C211yesmaximal, characteristic, complemented
14C11×#1892C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#468—24no—
27C11×#465—24no—
28C11×#461—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C11×#424—24no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C11×#398—21no—
45C11×#398—21no—
46C11×#397—21no—
47C11×#397—21no—
48C11×#391C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#390—21no—
51C11×#390C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#388—21no—
54C11×#386—21no—
55C11×#385—21no—
56C11×#382C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—41no—
74C2×C11×SD16—41no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—41no—
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×#121—22no—
92C11×#121D414yes—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—22no—
96C11×#117—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
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—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×#107—22no—
122C11×#106—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8—22no—
125C11×C4⋊C8—22no—
126C11×C4⋊C8D414yescomplemented
127C11×#103—22no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#103—41no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24766C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×D4×C11—24no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11C2×D412yes—
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—21no—
179C22×C4×C11—42no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C11×SD16—44no—
191C11×SD16—44no—
192C11×M16—44no—
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×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—44no—
204C2×C8×C11C2×D412yes—
205C2×C8×C11C2×D412yes—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4C2×D412yes—
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—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—81no—
235C42×C11C2×D412yes—
236C42×C11#4112yes—
237C2×#468C2×C1111yescharacteristic
238C2×#465C2×C1111yescharacteristic
239C2×#461C2×C1111yescharacteristic, complemented
240C2×#424C2×C1111yescharacteristic, complemented
241#2621C2×C1111yescharacteristic, complemented
242#2324C2×C1111yescharacteristic
243#2068C2×C1111yescharacteristic, complemented
244#2066C2×C1111yescharacteristic, complemented
245#2055C2×C1111yescharacteristic, complemented
246#2055C2×C1111yescharacteristic, complemented
247#1981C2×C1111yescharacteristic, complemented
248#1949C2×C1111yescharacteristic, complemented
249#1894C2×C1111yescharacteristic, complemented
250#1892C2×C1111yescharacteristic, complemented
251#1804C2×C1111yescharacteristic, complemented
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11#12112yes—
266C23×C11C22×D411yescharacteristic
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275D4×C11—22no—
276D4×C11—22no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—84no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
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—84no—
318C2×C4×C11#12112yes—
319C2×C4×C11#12112yes—
320C2×C4×C11#12112yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—22no—
329C8×C11—41no—
330C8×C11—41no—
331C22×SD16C22×C1111yescharacteristic
332C22×SD16C22×C1111yescharacteristic
333C22×M16C22×C1111yescharacteristic
334C23×C8C22×C1111yescharacteristic
335C2×C4⋊Q8C22×C1111yescharacteristic
336C2×C22⋊Q8C22×C1111yescharacteristic
337C2×C22⋊Q8C22×C1111yescharacteristic
338C2×#121C22×C1111yescharacteristic
339C2×C4×D4C22×C1111yescharacteristic
340C2×#117C22×C1111yescharacteristic
341#468—24no—
342#465—24no—
343#461—24no—
344C2×#107C22×C1111yescharacteristic
345C2×#106C22×C1111yescharacteristic
346#424—24no—
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×C4⋊C8C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359#398—21no—
360#398—21no—
361#397—21no—
362#397—21no—
363#391C22×C1111yescharacteristic
364#391C22×C1111yescharacteristic
365#390—21no—
366#390C22×C1111yescharacteristic
367#389C22×C1111yescharacteristic
368#388—21no—
369#386—21no—
370#385—21no—
371#382C22×C1111yescharacteristic
372#380C22×C1111yescharacteristic
373C4×C4⋊C4C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11C2×#12111yescharacteristic
393C22×C11C2×#12111yescharacteristic
394C22×C11#53711yescharacteristic
395C22×C11#57711yescharacteristic
396C22×C11#57711yescharacteristic
397C22×C11#57711yescharacteristic
398C22×C11#57811yescharacteristic
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—41no—
404C4×C11—41no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11—81no—
411C4×C11D4211yescharacteristic
412C4×C11#54711yescharacteristic
413C4×C11#54811yescharacteristic
414C4×C11#55311yescharacteristic
415C22×Q8C23×C1111yescharacteristic
416C22×Q8C23×C1111yescharacteristic
417C22×D4—21no—
418C22×D4C23×C1111yescharacteristic
419C23×C4—21no—
420C23×C4C23×C1111yescharacteristic
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—41no—
426C2×SD16—41no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—41no—
430C22×C8—22no—
431C22×C8—22no—
432C22×C8—41no—
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#121—22no—
444#121D4×C1114yes—
445C4×D4—22no—
446C4×D4—22no—
447#117—22no—
448#117—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4D4×C1111yescharacteristic
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
469C2×C22⋊C4D4×C1111yescharacteristic
470C2×C42—21no—
471C2×C42C23×C1111yescharacteristic
472C2×C42C23×C1111yescharacteristic
473#107—22no—
474#106—22no—
475C4⋊C8—22no—
476C4⋊C8—22no—
477C4⋊C8—22no—
478C4⋊C8D4×C1114yescomplemented
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#102—22no—
486#102—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C2×C11—42no—
497C2×C11—82no—
498C2×C11#241611yescharacteristic
499C2×C11#304211yescharacteristic
500C2×C11#304611yescharacteristic
501C2×C11#305711yescharacteristic
502C2×C11#306311yescharacteristic
503C2×C11#325811yescharacteristic
504C2×C11#326011yescharacteristic
505C24—21no—
506C24C2×D4×C1111yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4C2×D4×C1112yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1112yes—
548C22×C4C11×#4112yes—
549C22×C4C24×C1111yescharacteristic
550SD16—44no—
551SD16—44no—
552M16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8C2×D4×C1112yes—
565C2×C8C2×D4×C1112yes—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C4⋊C4C2×D4×C1112yes—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C42—21no—
593C42—21no—
594C42—81no—
595C42C2×D4×C1112yes—
596C42C11×#4112yes—
597C11#2476611yescharacteristic, direct product factor, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C11×#12112yes—
612C23C22×D4×C1111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—84no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4C11×#12112yes—
665C2×C4C11×#12112yes—
666C2×C4C11×#12112yes—
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C22×D4×C1111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×2−1+411yescharacteristic
673C8—22no—
674C8—22no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C11×#12111yescharacteristic
692C22C2×C11×#12111yescharacteristic
693C22C11×#53711yescharacteristic
694C22C11×#57711yescharacteristic
695C22C11×#57711yescharacteristic
696C22C11×#57711yescharacteristic
697C22C11×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4D42×C1111yescharacteristic
711C4C11×#54711yescharacteristic
712C4C11×#54811yescharacteristic
713C4C11×#55311yescharacteristic
714C2—42no—
715C2—82no—
716C2C11×#241611yescharacteristic
717C2C11×#304211yescharacteristic
718C2C11×#304611yescharacteristic
719C2C11×#305711yescharacteristic
720C2C11×#306311yescharacteristic
721C2C11×#325811yescharacteristic
722C2C11×#326011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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
3. C2×C11×#461C2semidirect
4. C2×C11×#424C2semidirect
5. C11×#2621C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#2055C2semidirect
10. C11×#2055C2semidirect
11. C11×#1981C2semidirect
12. C11×#1949C2semidirect
13. C11×#1894C2semidirect
14. C11×#1892C2semidirect
15. C11×#1804C2semidirect
126. C11×C4⋊C8D4semidirect
144. #24766C11direct (N × H)
239. C2×#461C2×C11semidirect
240. C2×#424C2×C11semidirect
241. #2621C2×C11semidirect
243. #2068C2×C11semidirect
244. #2066C2×C11semidirect
245. #2055C2×C11semidirect
246. #2055C2×C11semidirect
247. #1981C2×C11semidirect
248. #1949C2×C11semidirect
249. #1894C2×C11semidirect
250. #1892C2×C11semidirect
251. #1804C2×C11semidirect
478. C4⋊C8D4×C11semidirect
597. C11#24766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4682
C2×C11×#4652
C2×C11×#4612
C2×C11×#4242
C11×#26212
C11×#23242
C11×#20682
C11×#20662
C11×#20552
C11×#19812
C11×#19492
C11×#18942
C11×#18922
C11×#18042
#2476611