Finite Group Databasebeta

← C11×#24536 #14601729

Subgroups — C11×#24536 #14601729

Order 2816.

1006 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×#452C211yesmaximal, characteristic
2C2×C11×#416C211yesmaximal, characteristic
3C11×#2499C211yesmaximal, characteristic, complemented
4C11×#2339C211yesmaximal, characteristic
5C11×#2074C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2056C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1877C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#452—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#397—21no—
38C11×#397—21no—
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#387—21no—
44C11×#387—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#381—21no—
50C11×#380C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C2×C11×#95—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41D414yes—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C2×C11×Q16—22no—
76C2×C11×Q16—41no—
77C2×C11×Q16—41no—
78C2×C11×SD16—22no—
79C2×C11×SD16—22no—
80C2×C11×SD16—22no—
81C22×C8×C11—22no—
82C22×C8×C11—41no—
83C22×C8×C11—41no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—41no—
93C4×D4×C11—41no—
94C11×#117—22no—
95C11×#117—22no—
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⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
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—41no—
120C11×#103—41no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
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#24536C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—28no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
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—21no—
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11C2×D412yes—
164C2×D4×C11#4112yes—
165C2×D4×C11#4112yes—
166C22×C4×C11—21no—
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—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×Q16—44no—
195C11×SD16—44no—
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—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
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—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—81no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—42no—
234C2×#452C2×C1111yescharacteristic
235C2×#416C2×C1111yescharacteristic
236#2499C2×C1111yescharacteristic, complemented
237#2339C2×C1111yescharacteristic
238#2074C2×C1111yescharacteristic, complemented
239#2072C2×C1111yescharacteristic, complemented
240#2056C2×C1111yescharacteristic, complemented
241#2056C2×C1111yescharacteristic, complemented
242#1892C2×C1111yescharacteristic, complemented
243#1877C2×C1111yescharacteristic, complemented
244#1877C2×C1111yescharacteristic, complemented
245#1850C2×C1111yescharacteristic, complemented
246#1825C2×C1111yescharacteristic, complemented
247#1804C2×C1111yescharacteristic, complemented
248#1802C2×C1111yescharacteristic, complemented
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11#12112yes—
263C23×C11C22×D411yescharacteristic
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—41no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—48no—
276D4×C11#12314yes—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—48no—
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—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—84no—
317C2×C4×C11—84no—
318C2×C4×C11#12112yes—
319C2×C4×C11#13512yes—
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×Q16C22×C1111yescharacteristic
332C22×SD16C22×C1111yescharacteristic
333C23×C8C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×C4×D4C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×#117C22×C1111yescharacteristic
338#452—24no—
339C2×C4⋊C8C22×C1111yescharacteristic
340C2×C4⋊C8C22×C1111yescharacteristic
341#416—24no—
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351#397—21no—
352#397—21no—
353#391C22×C1111yescharacteristic
354#391C22×C1111yescharacteristic
355#391C22×C1111yescharacteristic
356#391C22×C1111yescharacteristic
357#387—21no—
358#387—21no—
359#386—21no—
360#386—21no—
361#384C22×C1111yescharacteristic
362#382C22×C1111yescharacteristic
363#381—21no—
364#380C22×C1111yescharacteristic
365C4×C22⋊C4C22×C1111yescharacteristic
366C2×#95—21no—
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375C22×C11—22no—
376C22×C11—24no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—42no—
383C22×C11—41no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—42no—
389C22×C11C2×#12111yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11#54611yescharacteristic
392C22×C11C2×#13511yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57711yescharacteristic
395C22×C11#57811yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—42no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11C2×#12311yescharacteristic
409C4×C11#53411yescharacteristic
410C4×C11#55111yescharacteristic
411C4×C11#55111yescharacteristic
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41D4×C1114yes—
418C22×Q8C23×C1111yescharacteristic
419C22×Q8C23×C1111yescharacteristic
420C22×D4—21no—
421C22×D4C23×C1111yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C1111yescharacteristic
426C2×Q16—22no—
427C2×Q16—41no—
428C2×Q16—41no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C22×C8—22no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—41no—
444C4×D4—41no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C4⋊C4C23×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4D4×C1111yescharacteristic
461C2×C22⋊C4D4×C1111yescharacteristic
462C2×C42—21no—
463C2×C42C23×C1111yescharacteristic
464C2×C42C23×C1111yescharacteristic
465C4⋊C8—41no—
466C4⋊C8—41no—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—41no—
471#103—41no—
472#102—22no—
473#102—22no—
474#102—22no—
475C22⋊C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C1111yescharacteristic
488#95D4×C1111yescharacteristic
489C2×C11—42no—
490C2×C11—44no—
491C2×C11#241211yescharacteristic
492C2×C11#303511yescharacteristic
493C2×C11#304611yescharacteristic
494C2×C11#329611yescharacteristic
495C2×C11#330211yescharacteristic
496C2×C11#331111yescharacteristic
497C2×C11#331511yescharacteristic
498C24—21no—
499C24C2×D4×C1111yescharacteristic
500#41—28no—
501#41—44no—
502#41—44no—
503#41—44no—
504C2×Q8—21no—
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×Q8C2×D4×C1112yes—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4C2×D4×C1112yes—
523C2×D4C11×#4112yes—
524C2×D4C11×#4112yes—
525C22×C4—21no—
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—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1112yes—
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C11×#4112yes—
552C22×C4C24×C1111yescharacteristic
553Q16—44no—
554SD16—44no—
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—
566C2×C8—21no—
567C2×C8—44no—
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—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C22⋊C4—22no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C11#2453611yescharacteristic, direct product factor, Sylow
594C23—22no—
595C23—22no—
596C23—22no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C11×#12112yes—
608C23C22×D4×C1111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4C11×#12314yes—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
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—84no—
662C2×C4—84no—
663C2×C4C11×#12112yes—
664C2×C4C11×#13512yes—
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—24no—
677C22—22no—
678C22—22no—
679C22—42no—
680C22—42no—
681C22—41no—
682C22—42no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22—42no—
689C22C2×C11×#12111yescharacteristic
690C22C11×#54611yescharacteristic
691C22C11×#54611yescharacteristic
692C22C2×C11×#13511yescharacteristic
693C22C11×#57511yescharacteristic
694C22C11×#57711yescharacteristic
695C22C11×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C2×C11×#12311yescharacteristic
709C4C11×#53411yescharacteristic
710C4C11×#55111yescharacteristic
711C4C11×#55111yescharacteristic
712C2—42no—
713C2—44no—
714C2C11×#241211yescharacteristic
715C2C11×#303511yescharacteristic
716C2C11×#304611yescharacteristic
717C2C11×#329611yescharacteristic
718C2C11×#330211yescharacteristic
719C2C11×#331111yescharacteristic
720C2C11×#331511yescharacteristic
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
3. C11×#2499C2semidirect
5. C11×#2074C2semidirect
6. C11×#2072C2semidirect
7. C11×#2056C2semidirect
8. C11×#2056C2semidirect
9. C11×#1892C2semidirect
10. C11×#1877C2semidirect
11. C11×#1877C2semidirect
12. C11×#1850C2semidirect
13. C11×#1825C2semidirect
14. C11×#1804C2semidirect
15. C11×#1802C2semidirect
138. #24536C11direct (N × H)
236. #2499C2×C11semidirect
238. #2074C2×C11semidirect
239. #2072C2×C11semidirect
240. #2056C2×C11semidirect
241. #2056C2×C11semidirect
242. #1892C2×C11semidirect
243. #1877C2×C11semidirect
244. #1877C2×C11semidirect
245. #1850C2×C11semidirect
246. #1825C2×C11semidirect
247. #1804C2×C11semidirect
248. #1802C2×C11semidirect
593. C11#24536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C2×C11×#4162
C11×#24992
C11×#23392
C11×#20742
C11×#20722
C11×#20562
C11×#18922
C11×#18772
C11×#18502
C11×#18252
C11×#18042
C11×#18022
#2453611