Finite Group Databasebeta

← C11×#22054 #14599247

Subgroups — C11×#22054 #14599247

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#451C211yesmaximal, characteristic
2C11×#2323C211yesmaximal, characteristic
3C11×#2310C211yesmaximal, characteristic
4C11×#1971C211yesmaximal, characteristic, complemented
5C11×#1969C211yesmaximal, characteristic, complemented
6C11×#1935C211yesmaximal, characteristic, complemented
7C11×#1933C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1927C211yesmaximal, characteristic, complemented
10C11×#1878C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic
13C11×#1854C211yesmaximal, characteristic
14C11×#1787C211yesmaximal, characteristic
15C11×#1750C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#451C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#391—21no—
39C11×#391—21no—
40C11×#391C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#389—21no—
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#388—21no—
49C11×#387—21no—
50C11×#381—21no—
51C11×#381—21no—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×Q8×C11—22no—
62C22×Q8×C11—41no—
63C22×Q8×C11—41no—
64C22×Q8×C11—41no—
65C22×Q8×C11—41no—
66C22×Q8×C11C2×C414yes—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C2×C11×Q16—41no—
73C2×C11×Q16—41no—
74C2×C11×Q16—41no—
75C2×C11×Q16—41no—
76C2×C11×Q16C2×C414yes—
77C2×C11×Q16C2×C414yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8C2×C414yes—
84C4×Q8×C11—41no—
85C4×Q8×C11—41no—
86C11×#117—41no—
87C11×#117—41no—
88C11×#117—41no—
89C11×#117—41no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×#107—41no—
111C11×#106—41no—
112C11×#103—41no—
113C11×#103—41no—
114C11×#103—41no—
115C11×#103—41no—
116C11×#103—41no—
117C11×#103—41no—
118C11×#103C2×C414yes—
119C11×#103C2×C414yes—
120C11×C22⋊C8—22no—
121C11×C22⋊C8C2×C414yes—
122C11×#97—41no—
123C4×C8×C11—41no—
124C11×#95—21no—
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×#95—21no—
137#22054C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11C2×D411yescharacteristic
139C2×Q8×C11—24no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
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×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—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11C22×C412yes—
162C2×Q8×C11C22×C412yes—
163C2×Q8×C11C22×C412yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
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—42no—
178C22×C4×C11—42no—
179C22×C4×C11C22×C412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C11×Q16—44no—
188C11×Q16—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×C11C22×C412yes—
200C2×C8×C11C22×C412yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—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—41no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4C22×C412yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—81no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C42×C11—42no—
227C42×C11—81no—
228C2×#451C2×C1111yescharacteristic
229#2323C2×C1111yescharacteristic
230#2310C2×C1111yescharacteristic
231#1971C2×C1111yescharacteristic, complemented
232#1969C2×C1111yescharacteristic, complemented
233#1935C2×C1111yescharacteristic, complemented
234#1933C2×C1111yescharacteristic, complemented
235#1928C2×C1111yescharacteristic, complemented
236#1927C2×C1111yescharacteristic, complemented
237#1878C2×C1111yescharacteristic, complemented
238#1878C2×C1111yescharacteristic, complemented
239#1873C2×C1111yescharacteristic
240#1854C2×C1111yescharacteristic
241#1787C2×C1111yescharacteristic
242#1750C2×C1111yescharacteristic
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C4×D412yes—
250C23×C11C22×D411yescharacteristic
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—48no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
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—48no—
287C2×C4×C11—41no—
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×C11C4×D412yes—
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C8×C11—22no—
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C23×Q8C22×C1111yescharacteristic
319C22×Q16C22×C1111yescharacteristic
320C22×Q16C22×C1111yescharacteristic
321C2×C22⋊Q8C22×C1111yescharacteristic
322C2×C4×Q8C22×C1111yescharacteristic
323C2×#117C22×C1111yescharacteristic
324C2×#117C22×C1111yescharacteristic
325#451C4×C1118yescomplemented
326C2×#107C22×C1111yescharacteristic
327C2×#106C22×C1111yescharacteristic
328C2×#103C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#103C22×C1111yescharacteristic
331C2×#103C22×C1111yescharacteristic
332C2×#103C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×C22⋊C8C22×C1111yescharacteristic
337C2×C22⋊C8C22×C1111yescharacteristic
338C2×#97C22×C1111yescharacteristic
339C2×C4×C8C22×C1111yescharacteristic
340#391—21no—
341#391—21no—
342#391C22×C1111yescharacteristic
343#391C22×C1111yescharacteristic
344#391C22×C1111yescharacteristic
345#391C22×C1111yescharacteristic
346#391C22×C1111yescharacteristic
347#389—21no—
348#389C22×C1111yescharacteristic
349#388—21no—
350#388—21no—
351#387—21no—
352#381—21no—
353#381—21no—
354#380C22×C1111yescharacteristic
355C4×C4⋊C4C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#53411yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C22×C11#57811yescharacteristic
375C22×C11#57811yescharacteristic
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11#51811yescharacteristic
390C4×C11#51811yescharacteristic
391C4×C11#53811yescharacteristic
392C4×C11#53811yescharacteristic
393C22×Q8—21no—
394C22×Q8—22no—
395C22×Q8—41no—
396C22×Q8—41no—
397C22×Q8—41no—
398C22×Q8—41no—
399C22×Q8C2×C4×C1114yes—
400C22×Q8C23×C1111yescharacteristic
401C22×Q8C23×C1111yescharacteristic
402C22×Q8C23×C1111yescharacteristic
403C23×C4—21no—
404C23×C4C23×C1111yescharacteristic
405C2×Q16—41no—
406C2×Q16—41no—
407C2×Q16—41no—
408C2×Q16—41no—
409C2×Q16C2×C4×C1114yes—
410C2×Q16C2×C4×C1114yes—
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22⋊Q8—22no—
416C22⋊Q8C2×C4×C1114yes—
417C4×Q8—41no—
418C4×Q8—41no—
419#117—41no—
420#117—41no—
421#117—41no—
422#117—41no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C1111yescharacteristic
427C2×C4⋊C4D4×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4D4×C1111yescharacteristic
437C2×C22⋊C4D4×C1111yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42C23×C1111yescharacteristic
442C2×C42C23×C1111yescharacteristic
443#107—41no—
444#106—41no—
445#103—41no—
446#103—41no—
447#103—41no—
448#103—41no—
449#103—41no—
450#103—41no—
451#103C2×C4×C1114yes—
452#103C2×C4×C1114yes—
453C22⋊C8—22no—
454C22⋊C8C2×C4×C1114yes—
455#97—41no—
456C4×C8—41no—
457#95—21no—
458#95—21no—
459#95—21no—
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—
470C2×C11—42no—
471C2×C11#232111yescharacteristic
472C2×C11#294711yescharacteristic
473C2×C11#295011yescharacteristic
474C2×C11#320111yescharacteristic
475C2×C11#320211yescharacteristic
476C2×C11#322311yescharacteristic
477C2×C11#322511yescharacteristic
478C24C2×D4×C1111yescharacteristic
479C2×Q8—24no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8C22×C4×C1112yes—
502C2×Q8C22×C4×C1112yes—
503C2×Q8C22×C4×C1112yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4C22×C4×C1112yes—
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C11×#4112yes—
526C22×C4C24×C1111yescharacteristic
527Q16—44no—
528Q16—44no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8C22×C4×C1112yes—
540C2×C8C22×C4×C1112yes—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4C22×C4×C1112yes—
556C22⋊C4—24no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—81no—
568C11#2205411yescharacteristic, direct product factor, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C4×D4×C1112yes—
576C23C22×D4×C1111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—48no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
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×C4C4×D4×C1112yes—
634C2×C4C23×C4×C1111yescharacteristic
635C2×C4C2×C11×#4111yescharacteristic
636C2×C4C11×H(5,𝔽2)11yescharacteristic
637C2×C4C11×H(5,𝔽2)11yescharacteristic
638C2×C4C11×H(5,𝔽2)11yescharacteristic
639C2×C4C11×H(5,𝔽2)11yescharacteristic
640C8—22no—
641C8—22no—
642C8—41no—
643C8—41no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×C4×D4×C1111yescharacteristic
652C22C11×#53411yescharacteristic
653C22C11×#53511yescharacteristic
654C22C11×#57711yescharacteristic
655C22C11×#57811yescharacteristic
656C22C11×#57811yescharacteristic
657C22C11×#57811yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C11×#51811yescharacteristic
672C4C11×#51811yescharacteristic
673C4C11×#53811yescharacteristic
674C4C11×#53811yescharacteristic
675C2—42no—
676C2C11×#232111yescharacteristic
677C2C11×#294711yescharacteristic
678C2C11×#295011yescharacteristic
679C2C11×#320111yescharacteristic
680C2C11×#320211yescharacteristic
681C2C11×#322311yescharacteristic
682C2C11×#322511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1971C2semidirect
5. C11×#1969C2semidirect
6. C11×#1935C2semidirect
7. C11×#1933C2semidirect
8. C11×#1928C2semidirect
9. C11×#1927C2semidirect
10. C11×#1878C2semidirect
11. C11×#1878C2semidirect
23. C11×#451C4semidirect
137. #22054C11direct (N × H)
231. #1971C2×C11semidirect
232. #1969C2×C11semidirect
233. #1935C2×C11semidirect
234. #1933C2×C11semidirect
235. #1928C2×C11semidirect
236. #1927C2×C11semidirect
237. #1878C2×C11semidirect
238. #1878C2×C11semidirect
325. #451C4×C11semidirect
568. C11#22054direct (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
C11×#23232
C11×#23102
C11×#19712
C11×#19692
C11×#19352
C11×#19332
C11×#19282
C11×#19272
C11×#18782
C11×#18732
C11×#18542
C11×#17872
C11×#17502
#2205411