Finite Group Databasebeta

← C11×#11123 #14588316

Subgroups — C11×#11123 #14588316

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#107C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic
3C22×C11×#102C211yesmaximal, characteristic
4C2×C11×#390C211yesmaximal, characteristic
5C2×C11×#340C211yesmaximal, characteristic, complemented
6C2×C11×#336C211yesmaximal, characteristic, complemented
7C11×C4⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4—22no—
15C22×C42×C11C2211yescharacteristic
16C2×C11×#107—22no—
17C2×C11×#107—22no—
18C2×C11×#107—22no—
19C2×C11×#102—22no—
20C2×C11×#102—22no—
21C2×C11×#102—22no—
22C2×C11×#102—22no—
23C2×C11×#102—22no—
24C2×C11×#102C414yescomplemented
25C11×#390—22no—
26C11×#390—22no—
27C2×C11×#95—22no—
28C11×#340—22no—
29C11×#336—22no—
30C25×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11D412yes—
44C22×D4×C11Q812yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11C2×C412yes—
61C22×C8×C11D412yes—
62C22×C8×C11D412yes—
63C22×C8×C11D412yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—44no—
84C2×C11×C22⋊C4—44no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C11×#107—28no—
92C11×#102—28no—
93C11×#102—28no—
94C11×#95—44no—
95#11123C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—41no—
102C24×C11—41no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11C2×D411yescharacteristic
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11C4⋊C414yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11D814yes—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×Q811yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11#4111yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11C22⋊C414yescomplemented
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C22⋊C4—416no—
199C42×C11—41no—
200C42×C11—41no—
201C42×C11—41no—
202C42×C11—41no—
203C22×#107C2×C1111yescharacteristic, complemented
204C22×#102C2×C1111yescharacteristic
205C22×#102C2×C1111yescharacteristic
206C2×#390C2×C1111yescharacteristic
207C2×#340C2×C1111yescharacteristic, complemented
208C2×#336C2×C1111yescharacteristic, complemented
209C4⋊#95C2×C1111yescharacteristic, complemented
210C23×C11—24no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—82no—
224C23×C11—82no—
225C23×C11—82no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—81no—
230C23×C11—81no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11C4×D411yescharacteristic
234C23×C11#12011yescharacteristic
235C23×C11#12111yescharacteristic
236C23×C11#12111yescharacteristic
237C23×C11C22⋊Q811yescharacteristic
238C23×C11#12311yescharacteristic
239C23×C11#12711yescharacteristic
240C23×C11C2×D812yes—
241C23×C11#13512yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11#13712yes—
244D4×C11—24no—
245D4×C11—24no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—82no—
266C2×C4×C11—82no—
267C2×C4×C11—82no—
268C2×C4×C11—81no—
269C2×C4×C11—81no—
270C2×C4×C11—81no—
271C2×C4×C11—81no—
272C2×C4×C11—81no—
273C2×C4×C11—81no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C4⋊C411yescharacteristic
276C2×C4×C11#11711yescharacteristic
277C2×C4×C11C4×D411yescharacteristic
278C2×C4×C11C4×D411yescharacteristic
279C2×C4×C11C4×D411yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12111yescharacteristic
283C2×C4×C11#12111yescharacteristic
284C2×C4×C11#12111yescharacteristic
285C2×C4×C11#12111yescharacteristic
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11#12111yescharacteristic
288C2×C4×C11C22⋊Q811yescharacteristic
289C2×C4×C11C22⋊Q811yescharacteristic
290C2×C4×C11C22⋊Q811yescharacteristic
291C2×C4×C11C22⋊Q811yescharacteristic
292C2×C4×C11C22⋊Q811yescharacteristic
293C2×C4×C11#12311yescharacteristic
294C2×C4×C11#12311yescharacteristic
295C2×C4×C11#12311yescharacteristic
296C2×C4×C11#12311yescharacteristic
297C2×C4×C11#12411yescharacteristic
298C2×C4×C11#12411yescharacteristic
299C2×C4×C11#12411yescharacteristic
300C2×C4×C11#12611yescharacteristic
301C2×C4×C11#12611yescharacteristic
302C8×C11—24no—
303C8×C11—42no—
304C23×D4C22×C1111yescharacteristic
305C23×C8C22×C1111yescharacteristic
306C23×C8C22×C1111yescharacteristic
307C22×C4⋊C4C22×C1111yescharacteristic
308C22×C4⋊C4C22×C1111yescharacteristic
309C22×C4⋊C4C22×C1111yescharacteristic
310C22×C22⋊C4—22no—
311C22×C42C22×C1111yescharacteristic
312C2×#107—22no—
313C2×#107—22no—
314C2×#107—22no—
315C2×#102—22no—
316C2×#102—22no—
317C2×#102—22no—
318C2×#102—22no—
319C2×#102—22no—
320C2×#102C4×C1114yescomplemented
321#390—22no—
322#390—22no—
323C2×#95—22no—
324#340—22no—
325#336—22no—
326C22×C11—48no—
327C22×C11—44no—
328C22×C11—84no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11—84no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11—84no—
337C22×C11#38511yescharacteristic
338C22×C11#38811yescharacteristic
339C22×C11#39011yescharacteristic
340C22×C11#39211yescharacteristic
341C22×C11#39411yescharacteristic
342C22×C11#39611yescharacteristic
343C22×C11#39911yescharacteristic
344C22×C11C4×D812yes—
345C22×C11#44012yes—
346C22×C11#44712yes—
347C22×C11#45212yes—
348C22×C11#45912yes—
349C22×C11#46412yes—
350C22×C11#46612yes—
351C22×C11#46812yes—
352C22×C11#47412yes—
353C22×C11#47812yes—
354C22×C11#48012yes—
355C22×C11#48212yes—
356C22×C11#49311yescharacteristic
357C22×C11#49511yescharacteristic
358C22×C11#49611yescharacteristic
359C22×C11#49711yescharacteristic
360C4×C11—44no—
361C4×C11—82no—
362C4×C11—82no—
363C4×C11—82no—
364C4×C11#38011yescharacteristic
365C4×C11#38511yescharacteristic
366C4×C11#38611yescharacteristic
367C4×C11#38811yescharacteristic
368C4×C11#39311yescharacteristic
369C4×C11#39411yescharacteristic
370C4×C11#39611yescharacteristic
371C4×C11#39711yescharacteristic
372C25—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C2×C4×C1112yes—
385C22×D4D4×C1112yes—
386C22×D4Q8×C1112yes—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4D4×C1112yes—
391C23×C4C23×C1111yescharacteristic
392C22×C8—21no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8C2×C4×C1112yes—
403C22×C8D4×C1112yes—
404C22×C8D4×C1112yes—
405C22×C8D4×C1112yes—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4C2×C4×C1112yes—
422C2×C4⋊C4D4×C1112yes—
423C2×C4⋊C4D4×C1112yes—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433#107—28no—
434#102—28no—
435#102—28no—
436#95—44no—
437C2×C11—84no—
438C2×C11#143911yescharacteristic
439C2×C11#186212yes—
440C2×C11#192512yes—
441C2×C11#197011yescharacteristic
442C2×C11#197311yescharacteristic
443C2×C11#201111yescharacteristic
444C2×C11#201511yescharacteristic
445C2×C11#203312yes—
446C2×C11#206712yes—
447C2×C11#209211yescharacteristic
448C2×C11#209311yescharacteristic
449C24—22no—
450C24—22no—
451C24—22no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24C2×D4×C1111yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4C11×C4⋊C414yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C11×D814yes—
511C22×C4C22×C4×C1111yescharacteristic
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×Q8×C1111yescharacteristic
519C22×C4C11×#4111yescharacteristic
520C22×C4C11×#4111yescharacteristic
521C22×C4C11×#4111yescharacteristic
522C22×C4C11×#4111yescharacteristic
523C22×C4C11×#4111yescharacteristic
524C22×C4C11×#4111yescharacteristic
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8C11×C22⋊C414yescomplemented
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C22⋊C4—416no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C11#1112311yescharacteristic, direct product factor, Sylow
557C23—24no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23—81no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—82no—
579C23—82no—
580C23C4×D4×C1111yescharacteristic
581C23C11×#12011yescharacteristic
582C23C11×#12111yescharacteristic
583C23C11×#12111yescharacteristic
584C23C11×C22⋊Q811yescharacteristic
585C23C11×#12311yescharacteristic
586C23C11×#12711yescharacteristic
587C23C2×C11×D812yes—
588C23C11×#13512yes—
589C23C11×AGL(1,ℤ/8)12yes—
590C23C11×#13712yes—
591D4—24no—
592D4—24no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—42no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4C2×C11×C22⋊C411yescharacteristic
622C2×C4C2×C11×C4⋊C411yescharacteristic
623C2×C4C11×#11711yescharacteristic
624C2×C4C4×D4×C1111yescharacteristic
625C2×C4C4×D4×C1111yescharacteristic
626C2×C4C4×D4×C1111yescharacteristic
627C2×C4C11×#12011yescharacteristic
628C2×C4C11×#12011yescharacteristic
629C2×C4C11×#12111yescharacteristic
630C2×C4C11×#12111yescharacteristic
631C2×C4C11×#12111yescharacteristic
632C2×C4C11×#12111yescharacteristic
633C2×C4C11×#12111yescharacteristic
634C2×C4C11×#12111yescharacteristic
635C2×C4C11×C22⋊Q811yescharacteristic
636C2×C4C11×C22⋊Q811yescharacteristic
637C2×C4C11×C22⋊Q811yescharacteristic
638C2×C4C11×C22⋊Q811yescharacteristic
639C2×C4C11×C22⋊Q811yescharacteristic
640C2×C4C11×#12311yescharacteristic
641C2×C4C11×#12311yescharacteristic
642C2×C4C11×#12311yescharacteristic
643C2×C4C11×#12311yescharacteristic
644C2×C4C11×#12411yescharacteristic
645C2×C4C11×#12411yescharacteristic
646C2×C4C11×#12411yescharacteristic
647C2×C4C11×#12611yescharacteristic
648C2×C4C11×#12611yescharacteristic
649C8—24no—
650C8—42no—
651C22—44no—
652C22—48no—
653C22—84no—
654C22—82no—
655C22—82no—
656C22—82no—
657C22—82no—
658C22—84no—
659C22—84no—
660C22—82no—
661C22—82no—
662C22C11×#38511yescharacteristic
663C22C11×#38811yescharacteristic
664C22C11×#39011yescharacteristic
665C22C11×#39211yescharacteristic
666C22C11×#39411yescharacteristic
667C22C11×#39611yescharacteristic
668C22C11×#39911yescharacteristic
669C22C4×C11×D812yes—
670C22C11×#44012yes—
671C22C11×#44712yes—
672C22C11×#45212yes—
673C22C11×#45912yes—
674C22C11×#46412yes—
675C22C11×#46612yes—
676C22C11×#46812yes—
677C22C11×#47412yes—
678C22C11×#47812yes—
679C22C11×#48012yes—
680C22C11×#48212yes—
681C22C11×#49311yescharacteristic
682C22C11×#49511yescharacteristic
683C22C11×#49611yescharacteristic
684C22C11×#49711yescharacteristic
685C4—44no—
686C4—82no—
687C4—82no—
688C4—82no—
689C4C11×#38011yescharacteristic
690C4C11×#38511yescharacteristic
691C4C11×#38611yescharacteristic
692C4C11×#38811yescharacteristic
693C4C11×#39311yescharacteristic
694C4C11×#39411yescharacteristic
695C4C11×#39611yescharacteristic
696C4C11×#39711yescharacteristic
697C2—84no—
698C2C11×#143911yescharacteristic
699C2C11×#186212yes—
700C2C11×#192512yes—
701C2C11×#197011yescharacteristic
702C2C11×#197311yescharacteristic
703C2C11×#201111yescharacteristic
704C2C11×#201511yescharacteristic
705C2C11×#203312yes—
706C2C11×#206712yes—
707C2C11×#209211yescharacteristic
708C2C11×#209311yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#107C2semidirect
5. C2×C11×#340C2semidirect
6. C2×C11×#336C2semidirect
7. C11×C4⋊#95C2semidirect
24. C2×C11×#102C4semidirect
95. #11123C11direct (N × H)
185. C2×C8×C11C22⋊C4semidirect
203. C22×#107C2×C11semidirect
207. C2×#340C2×C11semidirect
208. C2×#336C2×C11semidirect
209. C4⋊#95C2×C11semidirect
320. C2×#102C4×C11semidirect
538. C2×C8C11×C22⋊C4semidirect
556. C11#11123direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C22×C11×#1022
C2×C11×#3902
C2×C11×#3402
C2×C11×#3362
C11×C4⋊#952
#1112311