Finite Group Databasebeta

← C11×#24540 #14601733

Subgroups — C11×#24540 #14601733

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#451C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C11×#2499C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#2074C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2056C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic
10C11×#1878C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic
13C11×#1825C211yesmaximal, characteristic
14C11×#1805C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#451—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×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#397—21no—
38C11×#397—21no—
39C11×#391—21no—
40C11×#391—21no—
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#387—21no—
46C11×#387—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×Q8×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C2×C11×Q16—22no—
74C2×C11×Q16—22no—
75C2×C11×Q16—22no—
76C2×C11×Q16—22no—
77C2×C11×Q16—41no—
78C2×C11×Q16—41no—
79C2×C11×M16—22no—
80C2×C11×M16—41no—
81C2×C11×M16—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—41no—
91C4×Q8×C11—41no—
92C11×#117—22no—
93C11×#117—22no—
94C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×C4⋊C8—41no—
115C11×C4⋊C8—41no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—41no—
123C11×#103—41no—
124C11×C22⋊C8—22no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
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#24540C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—28no—
146C2×Q8×C11—21no—
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—42no—
157C2×Q8×C11—42no—
158C2×Q8×C11—44no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11C2×D412yes—
163C2×Q8×C11#4112yes—
164C2×Q8×C11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—24no—
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—42no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
188C11×Q16—44no—
189C11×Q16—44no—
190C11×M16—44no—
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×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
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—21no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11—42no—
230C2×#451C2×C1111yescharacteristic
231C2×#419C2×C1111yescharacteristic
232#2499C2×C1111yescharacteristic
233Q8×C22⋊C4C2×C1111yescharacteristic
234#2074C2×C1111yescharacteristic, complemented
235#2072C2×C1111yescharacteristic, complemented
236#2056C2×C1111yescharacteristic, complemented
237#2056C2×C1111yescharacteristic, complemented
238#1894C2×C1111yescharacteristic
239#1878C2×C1111yescharacteristic, complemented
240#1878C2×C1111yescharacteristic, complemented
241#1851C2×C1111yescharacteristic
242#1825C2×C1111yescharacteristic
243#1805C2×C1111yescharacteristic, complemented
244#1803C2×C1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11#12112yes—
252C23×C11C22×D411yescharacteristic
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—48no—
259Q8×C11—41no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11#12314yes—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
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—21no—
287C2×C4×C11—48no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
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#12112yes—
309C2×C4×C11#13712yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C8×C11—41no—
320C23×Q8C22×C1111yescharacteristic
321C22×Q16C22×C1111yescharacteristic
322C22×Q16C22×C1111yescharacteristic
323C22×M16C22×C1111yescharacteristic
324C2×C22⋊Q8C22×C1111yescharacteristic
325C2×C4×Q8C22×C1111yescharacteristic
326C2×C4×Q8C22×C1111yescharacteristic
327C2×#117C22×C1111yescharacteristic
328#451—24no—
329C2×C4⋊C8C22×C1111yescharacteristic
330C2×C4⋊C8C22×C1111yescharacteristic
331#419—24no—
332C2×#103C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1111yescharacteristic
341#397—21no—
342#397—21no—
343#391—21no—
344#391—21no—
345#391C22×C1111yescharacteristic
346#391C22×C1111yescharacteristic
347#391C22×C1111yescharacteristic
348#391C22×C1111yescharacteristic
349#387—21no—
350#387—21no—
351#384C22×C1111yescharacteristic
352#382C22×C1111yescharacteristic
353#380—21no—
354#380C22×C1111yescharacteristic
355C4×C22⋊C4—21no—
356C4×C22⋊C4C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#336C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11C2×#12111yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11C2×#13711yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57811yescharacteristic
378C22×C11#57811yescharacteristic
379C4×C11—22no—
380C4×C11—24no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11C2×#12311yescharacteristic
393C4×C11#53411yescharacteristic
394C4×C11#55111yescharacteristic
395C4×C11#55111yescharacteristic
396C22×Q8—21no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8D4×C1114yes—
403C22×Q8C23×C1111yescharacteristic
404C22×Q8C23×C1111yescharacteristic
405C22×Q8C23×C1111yescharacteristic
406C23×C4—21no—
407C23×C4C23×C1111yescharacteristic
408C2×Q16—22no—
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—22no—
412C2×Q16—41no—
413C2×Q16—41no—
414C2×M16—22no—
415C2×M16—41no—
416C2×M16—41no—
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×Q8—41no—
427#117—22no—
428#117—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4D4×C1111yescharacteristic
443C2×C22⋊C4D4×C1111yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C23×C1111yescharacteristic
448C2×C42C23×C1111yescharacteristic
449C4⋊C8—41no—
450C4⋊C8—41no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#103—41no—
458#103—41no—
459C22⋊C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95D4×C1111yescharacteristic
472#95D4×C1111yescharacteristic
473C2×C11—42no—
474C2×C11#241211yescharacteristic
475C2×C11#303711yescharacteristic
476C2×C11#304411yescharacteristic
477C2×C11#331211yescharacteristic
478C2×C11#331311yescharacteristic
479C2×C11#332711yescharacteristic
480C2×C11#332811yescharacteristic
481C24C2×D4×C1111yescharacteristic
482C2×Q8—24no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—28no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8C2×D4×C1112yes—
504C2×Q8C2×D4×C1112yes—
505C2×Q8C11×#4112yes—
506C2×Q8C11×#4112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1112yes—
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C11×#4112yes—
529C22×C4C24×C1111yescharacteristic
530Q16—44no—
531Q16—44no—
532M16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C22⋊C4—22no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—42no—
571C42—42no—
572C11#2454011yescharacteristic, direct product factor, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23C11×#12112yes—
580C23C22×D4×C1111yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593Q8C11×#12314yes—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4C11×#12112yes—
637C2×C4C11×#13712yes—
638C2×C4C22×D4×C1111yescharacteristic
639C2×C4C2×C11×#4111yescharacteristic
640C2×C4C2×C11×#4111yescharacteristic
641C2×C4C2×C11×#4111yescharacteristic
642C2×C4C11×H(5,𝔽2)11yescharacteristic
643C2×C4C11×H(5,𝔽2)11yescharacteristic
644C8—41no—
645C8—41no—
646C8—41no—
647C8—41no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C2×C11×#12111yescharacteristic
656C22C11×#54611yescharacteristic
657C22C11×#54611yescharacteristic
658C22C2×C11×#13711yescharacteristic
659C22C11×#57511yescharacteristic
660C22C11×#57811yescharacteristic
661C22C11×#57811yescharacteristic
662C4—22no—
663C4—24no—
664C4—22no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4C2×C11×#12311yescharacteristic
676C4C11×#53411yescharacteristic
677C4C11×#55111yescharacteristic
678C4C11×#55111yescharacteristic
679C2—42no—
680C2C11×#241211yescharacteristic
681C2C11×#303711yescharacteristic
682C2C11×#304411yescharacteristic
683C2C11×#331211yescharacteristic
684C2C11×#331311yescharacteristic
685C2C11×#332711yescharacteristic
686C2C11×#332811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
5. C11×#2074C2semidirect
6. C11×#2072C2semidirect
7. C11×#2056C2semidirect
8. C11×#2056C2semidirect
10. C11×#1878C2semidirect
11. C11×#1878C2semidirect
14. C11×#1805C2semidirect
15. C11×#1803C2semidirect
138. #24540C11direct (N × H)
234. #2074C2×C11semidirect
235. #2072C2×C11semidirect
236. #2056C2×C11semidirect
237. #2056C2×C11semidirect
239. #1878C2×C11semidirect
240. #1878C2×C11semidirect
243. #1805C2×C11semidirect
244. #1803C2×C11semidirect
572. C11#24540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4512
C2×C11×#4192
C11×#24992
Q8×C11×C22⋊C42
C11×#20742
C11×#20722
C11×#20562
C11×#18942
C11×#18782
C11×#18512
C11×#18252
C11×#18052
C11×#18032
#2454011