Finite Group Databasebeta

← C11×#24489 #14601682

Subgroups — C11×#24489 #14601682

Order 2816.

992 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#484C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic
3C11×#2432C211yesmaximal, characteristic
4C11×#2344C211yesmaximal, characteristic, complemented
5C11×#2068C211yesmaximal, characteristic, complemented
6C11×#2067C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2042C211yesmaximal, characteristic, complemented
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1981C211yesmaximal, characteristic, complemented
11C11×#1928C211yesmaximal, characteristic, complemented
12C11×#1925C211yesmaximal, characteristic, complemented
13C11×#1894C211yesmaximal, characteristic, complemented
14C11×#1851C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#117—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#484—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C11×#417—24no—
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C11×#394—21no—
43C11×#394—21no—
44C11×#391C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#387—21no—
49C11×#387—21no—
50C11×#385—21no—
51C11×#385—21no—
52C11×#381—21no—
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×M16—22no—
75C2×C11×M16—41no—
76C2×C11×M16—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8—41no—
83C11×#124—22no—
84C11×#124—41no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×#117—44no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D414yes—
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⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#107—22no—
114C11×#107—22no—
115C11×C4⋊C8—41no—
116C11×C4⋊C8—41no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—41no—
123C11×#103—41no—
124C11×#103—41no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—41no—
129C11×C22⋊C8—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#24489C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—28no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
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—21no—
157C2×Q8×C11#4112yes—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11#4112yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
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—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
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—21no—
204C2×C8×C11—21no—
205C11×C4⋊C4—24no—
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—42no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4C2×D412yes—
220C11×C4⋊C4C2×D412yes—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—42no—
234C42×C11—42no—
235C2×#484C2×C1111yescharacteristic, complemented
236C2×#417C2×C1111yescharacteristic
237#2432C2×C1111yescharacteristic
238#2344C2×C1111yescharacteristic, complemented
239#2068C2×C1111yescharacteristic, complemented
240#2067C2×C1111yescharacteristic, complemented
241#2043C2×C1111yescharacteristic, complemented
242#2042C2×C1111yescharacteristic, complemented
243#1983C2×C1111yescharacteristic, complemented
244#1981C2×C1111yescharacteristic, complemented
245#1928C2×C1111yescharacteristic, complemented
246#1925C2×C1111yescharacteristic, complemented
247#1894C2×C1111yescharacteristic, complemented
248#1851C2×C1111yescharacteristic, complemented
249#1788C2×C1111yescharacteristic
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11#12112yes—
264C23×C11C22×D411yescharacteristic
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—48no—
276D4×C11—41no—
277D4×C11—41no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
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—48no—
299C2×C4×C11—48no—
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#12112yes—
319C2×C4×C11AGL(1,ℤ/8)12yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C8×C11—41no—
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C22×#41C22×C1111yescharacteristic
331C22×M16C22×C1111yescharacteristic
332C2×C4⋊Q8C22×C1111yescharacteristic
333C2×#124C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×#117—21no—
336C22×C4⋊C4C22×C1111yescharacteristic
337#484—24no—
338C2×#107C22×C1111yescharacteristic
339C2×#107C22×C1111yescharacteristic
340C2×C4⋊C8C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342#417—24no—
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×#103C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356#394—21no—
357#394—21no—
358#391C22×C1111yescharacteristic
359#390C22×C1111yescharacteristic
360#389C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#387—21no—
363#387—21no—
364#385—21no—
365#385—21no—
366#381—21no—
367#380C22×C1111yescharacteristic
368C4×C4⋊C4C22×C1111yescharacteristic
369C4×C4⋊C4C22×C1111yescharacteristic
370C4×C22⋊C4C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11C2×#12111yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11#54611yescharacteristic
392C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57811yescharacteristic
395C22×C11#57811yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11#52511yescharacteristic
409C4×C11#53511yescharacteristic
410C4×C11#55111yescharacteristic
411C4×C11#55111yescharacteristic
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—41no—
417C2×#41—41no—
418C22×Q8C23×C1111yescharacteristic
419C22×Q8C23×C1111yescharacteristic
420C22×D4—21no—
421C22×D4C23×C1111yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C23×C1111yescharacteristic
425C2×M16—22no—
426C2×M16—41no—
427C2×M16—41no—
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434#124—22no—
435#124—41no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438#117—44no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C1114yes—
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C1111yescharacteristic
459C2×C22⋊C4D4×C1111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C1111yescharacteristic
463C2×C42C23×C1111yescharacteristic
464#107—22no—
465#107—22no—
466C4⋊C8—41no—
467C4⋊C8—41no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—41no—
474#103—41no—
475#103—41no—
476#102—22no—
477#102—22no—
478#102—22no—
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—82no—
492C2×C11#241111yescharacteristic
493C2×C11#303611yescharacteristic
494C2×C11#304411yescharacteristic
495C2×C11#330811yescharacteristic
496C2×C11#331511yescharacteristic
497C2×C11#332711yescharacteristic
498C2×C11#333011yescharacteristic
499C24—21no—
500C24C2×D4×C1111yescharacteristic
501#41—28no—
502#41—44no—
503#41—44no—
504#41—44no—
505C2×Q8—21no—
506C2×Q8—21no—
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×Q8C11×#4112yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C11×#4112yes—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
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
551M16—44no—
552C2×C8—21no—
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—21no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4C2×D4×C1112yes—
579C4⋊C4C2×D4×C1112yes—
580C22⋊C4—22no—
581C22⋊C4—41no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—42no—
594C11#2448911yescharacteristic, direct product factor, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C11×#12112yes—
609C23C22×D4×C1111yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4—41no—
622D4—41no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—48no—
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×C4C11×#12112yes—
664C2×C4C11×AGL(1,ℤ/8)12yes—
665C2×C4C22×D4×C1111yescharacteristic
666C2×C4C2×C11×#4111yescharacteristic
667C2×C4C2×C11×#4111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C11×H(5,𝔽2)11yescharacteristic
670C2×C4C11×H(5,𝔽2)11yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C11×#12111yescharacteristic
690C22C11×#54611yescharacteristic
691C22C11×#54611yescharacteristic
692C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
693C22C11×#57511yescharacteristic
694C22C11×#57811yescharacteristic
695C22C11×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C11×#52511yescharacteristic
709C4C11×#53511yescharacteristic
710C4C11×#55111yescharacteristic
711C4C11×#55111yescharacteristic
712C2—42no—
713C2—82no—
714C2C11×#241111yescharacteristic
715C2C11×#303611yescharacteristic
716C2C11×#304411yescharacteristic
717C2C11×#330811yescharacteristic
718C2C11×#331511yescharacteristic
719C2C11×#332711yescharacteristic
720C2C11×#333011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
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
1. C2×C11×#484C2semidirect
4. C11×#2344C2semidirect
5. C11×#2068C2semidirect
6. C11×#2067C2semidirect
7. C11×#2043C2semidirect
8. C11×#2042C2semidirect
9. C11×#1983C2semidirect
10. C11×#1981C2semidirect
11. C11×#1928C2semidirect
12. C11×#1925C2semidirect
13. C11×#1894C2semidirect
14. C11×#1851C2semidirect
139. #24489C11direct (N × H)
235. C2×#484C2×C11semidirect
238. #2344C2×C11semidirect
239. #2068C2×C11semidirect
240. #2067C2×C11semidirect
241. #2043C2×C11semidirect
242. #2042C2×C11semidirect
243. #1983C2×C11semidirect
244. #1981C2×C11semidirect
245. #1928C2×C11semidirect
246. #1925C2×C11semidirect
247. #1894C2×C11semidirect
248. #1851C2×C11semidirect
594. C11#24489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4842
C2×C11×#4172
C11×#24322
C11×#23442
C11×#20682
C11×#20672
C11×#20432
C11×#20422
C11×#19832
C11×#19812
C11×#19282
C11×#19252
C11×#18942
C11×#18512
C11×#17882
#2448911