Finite Group Databasebeta

← C11×#24541 #14601734

Subgroups — C11×#24541 #14601734

Order 2816.

982 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×#448C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic, complemented
3C11×#2500C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2074C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1805C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#448—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#419—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#394—21no—
38C11×#394—21no—
39C11×#391—21no—
40C11×#391—21no—
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380—21no—
50C11×#380C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—41no—
66C22×Q8×C11—41no—
67C22×Q8×C11D414yes—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—41no—
79C2×C11×SD16—41no—
80C2×C11×M16—22no—
81C2×C11×M16—41no—
82C2×C11×M16—41no—
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×#121—22no—
88C11×#121—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—41no—
92C4×Q8×C11—41no—
93C11×#117—22no—
94C11×#117—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×C4⋊C8—41no—
119C11×C4⋊C8—41no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—22no—
126C11×#102—41no—
127C11×#102—41no—
128C11×C22⋊C8—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24541C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C2×Q8×C11—24no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—28no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—42no—
152C2×Q8×C11—42no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11C2×D412yes—
158C2×Q8×C11#4112yes—
159C2×Q8×C11#4112yes—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—42no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—24no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4112yes—
190C22×C4×C11C2411yescharacteristic
191C11×SD16—44no—
192C11×SD16—44no—
193C11×M16—44no—
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—21no—
204C2×C8×C11—21no—
205C2×C8×C11—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—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4—81no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—42no—
234C42×C11—42no—
235C42×C11—42no—
236C2×#448C2×C1111yescharacteristic
237C2×#419C2×C1111yescharacteristic, complemented
238#2500C2×C1111yescharacteristic
239Q8×C22⋊C4C2×C1111yescharacteristic, complemented
240#2074C2×C1111yescharacteristic, complemented
241#2072C2×C1111yescharacteristic, complemented
242#2055C2×C1111yescharacteristic, complemented
243#2055C2×C1111yescharacteristic, complemented
244#1895C2×C1111yescharacteristic
245#1880C2×C1111yescharacteristic, complemented
246#1880C2×C1111yescharacteristic, complemented
247#1851C2×C1111yescharacteristic, complemented
248#1825C2×C1111yescharacteristic, complemented
249#1805C2×C1111yescharacteristic, complemented
250#1803C2×C1111yescharacteristic, complemented
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11#12112yes—
265C23×C11C22×D411yescharacteristic
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—48no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11#12314yes—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—84no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—48no—
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#12112yes—
320C2×C4×C11#13712yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C23×Q8C22×C1111yescharacteristic
332C22×SD16C22×C1111yescharacteristic
333C22×SD16C22×C1111yescharacteristic
334C22×M16C22×C1111yescharacteristic
335C2×#121C22×C1111yescharacteristic
336C2×C4×Q8C22×C1111yescharacteristic
337C2×C4×Q8C22×C1111yescharacteristic
338C2×#117C22×C1111yescharacteristic
339#448—24no—
340C2×C4⋊C8C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342#419—24no—
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352#394—21no—
353#394—21no—
354#391—21no—
355#391—21no—
356#391C22×C1111yescharacteristic
357#391C22×C1111yescharacteristic
358#390C22×C1111yescharacteristic
359#390C22×C1111yescharacteristic
360#388—21no—
361#388—21no—
362#384C22×C1111yescharacteristic
363#382C22×C1111yescharacteristic
364#380—21no—
365#380C22×C1111yescharacteristic
366C4×C22⋊C4—21no—
367C4×C22⋊C4C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11C2×#12111yescharacteristic
391C22×C11#54611yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11C2×#13711yescharacteristic
394C22×C11#57511yescharacteristic
395C22×C11#57711yescharacteristic
396C22×C11#57711yescharacteristic
397C4×C11—22no—
398C4×C11—24no—
399C4×C11—22no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11C2×#12311yescharacteristic
410C4×C11#53411yescharacteristic
411C4×C11#55111yescharacteristic
412C4×C11#55111yescharacteristic
413C22×Q8—21no—
414C22×Q8—22no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—41no—
418C22×Q8—41no—
419C22×Q8D4×C1114yes—
420C22×Q8C23×C1111yescharacteristic
421C22×Q8C23×C1111yescharacteristic
422C22×D4—21no—
423C22×D4C23×C1111yescharacteristic
424C23×C4—21no—
425C23×C4C23×C1111yescharacteristic
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C2×SD16—41no—
432C2×M16—22no—
433C2×M16—41no—
434C2×M16—41no—
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439#121—22no—
440#121—22no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C4⋊C4C23×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C1111yescharacteristic
464C2×C22⋊C4D4×C1111yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C1111yescharacteristic
469C2×C42C23×C1111yescharacteristic
470C4⋊C8—41no—
471C4⋊C8—41no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#102—41no—
479#102—41no—
480C22⋊C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95D4×C1111yescharacteristic
489#95D4×C1111yescharacteristic
490C2×C11—42no—
491C2×C11—161no—
492C2×C11#241211yescharacteristic
493C2×C11#303711yescharacteristic
494C2×C11#304311yescharacteristic
495C2×C11#332011yescharacteristic
496C2×C11#332111yescharacteristic
497C2×C11#332611yescharacteristic
498C2×C11#332911yescharacteristic
499C24—21no—
500C24C2×D4×C1111yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—28no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8C2×D4×C1112yes—
517C2×Q8C2×D4×C1112yes—
518C2×Q8C11×#4112yes—
519C2×Q8C11×#4112yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—81no—
528C2×D4—81no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1112yes—
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C11×#4112yes—
550C22×C4C24×C1111yescharacteristic
551SD16—44no—
552SD16—44no—
553M16—44no—
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—21no—
564C2×C8—21no—
565C2×C8—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
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—42no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C22⋊C4—22no—
581C22⋊C4—41no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—42no—
595C42—42no—
596C11#2454111yescharacteristic, direct product factor, Sylow
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C11×#12112yes—
611C23C22×D4×C1111yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—48no—
618Q8—41no—
619Q8—41no—
620Q8C11×#12314yes—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—84no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—48no—
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—41no—
664C2×C4—41no—
665C2×C4C11×#12112yes—
666C2×C4C11×#13712yes—
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×H(5,𝔽2)11yescharacteristic
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C11×#12111yescharacteristic
692C22C11×#54611yescharacteristic
693C22C11×#54611yescharacteristic
694C22C2×C11×#13711yescharacteristic
695C22C11×#57511yescharacteristic
696C22C11×#57711yescharacteristic
697C22C11×#57711yescharacteristic
698C4—22no—
699C4—24no—
700C4—22no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×C11×#12311yescharacteristic
711C4C11×#53411yescharacteristic
712C4C11×#55111yescharacteristic
713C4C11×#55111yescharacteristic
714C2—42no—
715C2—161no—
716C2C11×#241211yescharacteristic
717C2C11×#303711yescharacteristic
718C2C11×#304311yescharacteristic
719C2C11×#332011yescharacteristic
720C2C11×#332111yescharacteristic
721C2C11×#332611yescharacteristic
722C2C11×#332911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#419C2semidirect
4. Q8×C11×C22⋊C4C2semidirect
5. C11×#2074C2semidirect
6. C11×#2072C2semidirect
7. C11×#2055C2semidirect
8. C11×#2055C2semidirect
10. C11×#1880C2semidirect
11. C11×#1880C2semidirect
12. C11×#1851C2semidirect
13. C11×#1825C2semidirect
14. C11×#1805C2semidirect
15. C11×#1803C2semidirect
138. #24541C11direct (N × H)
237. C2×#419C2×C11semidirect
239. Q8×C22⋊C4C2×C11semidirect
240. #2074C2×C11semidirect
241. #2072C2×C11semidirect
242. #2055C2×C11semidirect
243. #2055C2×C11semidirect
245. #1880C2×C11semidirect
246. #1880C2×C11semidirect
247. #1851C2×C11semidirect
248. #1825C2×C11semidirect
249. #1805C2×C11semidirect
250. #1803C2×C11semidirect
596. C11#24541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C2×C11×#4192
C11×#25002
Q8×C11×C22⋊C42
C11×#20742
C11×#20722
C11×#20552
C11×#18952
C11×#18802
C11×#18512
C11×#18252
C11×#18052
C11×#18032
#2454111