Finite Group Databasebeta

← C11×#11087 #14588280

Subgroups — C11×#11087 #14588280

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#99C211yesmaximal, characteristic
2C11×#2308C211yesmaximal, characteristic
3C2×C11×#386C211yesmaximal, characteristic
4C2×C11×#385C211yesmaximal, characteristic, complemented
5C2×C11×#342C211yesmaximal, characteristic, complemented
6C2×C11×#342C211yesmaximal, characteristic, complemented
7C11×C22⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×C4⋊C4—21no—
11C22×C11×C22⋊C4—21no—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×C11×#99—22no—
18C2×C11×#99—22no—
19C2×C11×#99C414yescomplemented
20C11×#386—22no—
21C11×#386—21no—
22C11×#386—22no—
23C11×#386—21no—
24C11×#386—22no—
25C11×#385—22no—
26C11×#385—22no—
27C11×#381—21no—
28C11×#379—21no—
29C2×C11×#95—21no—
30C2×C11×#95—21no—
31C2×C11×#95—22no—
32C11×#342—22no—
33C11×#342—22no—
34C25×C11D411yescharacteristic
35C25×C11C2311yescharacteristic
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×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2×C412yes—
49C22×D4×C11Q812yes—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11—44no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D412yes—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D412yes—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—44no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—44no—
96C2×C11×C22⋊C4C2×C412yes—
97C2×C11×C22⋊C4C2×C412yes—
98C2×C11×C22⋊C4D412yes—
99C2×C11×C22⋊C4D412yes—
100C2×C11×C22⋊C4D412yes—
101C11×#99—28no—
102C11×#95—24no—
103C11×#95—24no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—44no—
107#11087C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—42no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11C4⋊C412yescomplemented
119C24×C11C22×C411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D411yescharacteristic
123C24×C11C2×D411yescharacteristic
124C24×C11C2×D411yescharacteristic
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D411yescharacteristic
127C24×C11C2×Q811yescharacteristic
128C24×C11#4111yescharacteristic
129C24×C11#4111yescharacteristic
130C24×C11#4111yescharacteristic
131C24×C11#4111yescharacteristic
132C24×C11#4111yescharacteristic
133C24×C11#4111yescharacteristic
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—41no—
198C22×C4×C11—41no—
199C22×C4×C11—41no—
200C22×C4×C11—41no—
201C22×C4×C11—42no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—41no—
210C22×C4×C11—41no—
211C22×C4×C11—41no—
212C22×C4×C11—41no—
213C22×C4×C11C4⋊C412yescomplemented
214C11×C4⋊C4—48no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—48no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—41no—
228C11×C22⋊C4—41no—
229C11×C22⋊C4—41no—
230C11×C22⋊C4—41no—
231C11×C22⋊C4—41no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C11×C22⋊C4—41no—
235C11×C22⋊C4—82no—
236C11×C22⋊C4—82no—
237C11×C22⋊C4C22⋊C414yescomplemented
238C22×#99C2×C1111yescharacteristic
239#2308C2×C1111yescharacteristic
240C2×#386C2×C1111yescharacteristic
241C2×#385C2×C1111yescharacteristic, complemented
242C2×#342C2×C1111yescharacteristic, complemented
243C2×#342C2×C1111yescharacteristic, complemented
244C22⋊#95C2×C1111yescharacteristic, complemented
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—42no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—41no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—44no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—44no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—82no—
281C23×C11—81no—
282C23×C11—81no—
283C23×C11—82no—
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11C2×C4⋊C411yescharacteristic
286C23×C11#11711yescharacteristic
287C23×C11C4×D411yescharacteristic
288C23×C11C4×D411yescharacteristic
289C23×C11C4×D411yescharacteristic
290C23×C11C4×D411yescharacteristic
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11#12011yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12111yescharacteristic
297C23×C11#12111yescharacteristic
298C23×C11#12111yescharacteristic
299C23×C11#12111yescharacteristic
300C23×C11#12111yescharacteristic
301C23×C11#12111yescharacteristic
302C23×C11C22⋊Q811yescharacteristic
303C23×C11C22⋊Q811yescharacteristic
304C23×C11C22⋊Q811yescharacteristic
305C23×C11C22⋊Q811yescharacteristic
306C23×C11C22⋊Q811yescharacteristic
307C23×C11C22⋊Q811yescharacteristic
308C23×C11#12311yescharacteristic
309C23×C11#12311yescharacteristic
310C23×C11#12311yescharacteristic
311C23×C11#12311yescharacteristic
312C23×C11#12311yescharacteristic
313C23×C11#12411yescharacteristic
314C23×C11#12411yescharacteristic
315C23×C11#12411yescharacteristic
316C23×C11#12611yescharacteristic
317C23×C11#12611yescharacteristic
318C23×C11#12711yescharacteristic
319D4×C11—42no—
320D4×C11—42no—
321D4×C11—42no—
322D4×C11—42no—
323D4×C11—42no—
324D4×C11—42no—
325D4×C11—42no—
326D4×C11—42no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—24no—
334C2×C4×C11—42no—
335C2×C4×C11—44no—
336C2×C4×C11—42no—
337C2×C4×C11—44no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—42no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—44no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11—44no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—44no—
356C2×C4×C11—42no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—82no—
366C2×C4×C11—81no—
367C2×C4×C11—81no—
368C2×C4×C11—82no—
369C2×C4×C11—82no—
370C2×C4×C11—81no—
371C2×C4×C11—81no—
372C2×C4×C11—82no—
373C23×D4C22×C1111yescharacteristic
374C24×C4C22×C1111yescharacteristic
375C22×C4⋊C4—21no—
376C22×C22⋊C4—21no—
377C22×C22⋊C4C22×C1111yescharacteristic
378C22×C22⋊C4C22×C1111yescharacteristic
379C22×C22⋊C4C22×C1111yescharacteristic
380C22×C22⋊C4C22×C1111yescharacteristic
381C22×C22⋊C4C22×C1111yescharacteristic
382C2×#99—22no—
383C2×#99—22no—
384C2×#99C4×C1114yescomplemented
385#386—21no—
386#386—21no—
387#386—22no—
388#386—22no—
389#386—22no—
390#385—22no—
391#385—22no—
392#381—21no—
393#379—21no—
394C2×#95—21no—
395C2×#95—21no—
396C2×#95—22no—
397#342—22no—
398#342—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—21no—
414C22×C11—21no—
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—44no—
440C22×C11—44no—
441C22×C11—42no—
442C22×C11—82no—
443C22×C11—82no—
444C22×C11—82no—
445C22×C11—81no—
446C22×C11—81no—
447C22×C11—82no—
448C22×C11#38011yescharacteristic
449C22×C11#38511yescharacteristic
450C22×C11#38511yescharacteristic
451C22×C11#38611yescharacteristic
452C22×C11#38811yescharacteristic
453C22×C11#38811yescharacteristic
454C22×C11#39011yescharacteristic
455C22×C11#39211yescharacteristic
456C22×C11#39311yescharacteristic
457C22×C11#39411yescharacteristic
458C22×C11#39411yescharacteristic
459C22×C11#39611yescharacteristic
460C22×C11#39611yescharacteristic
461C22×C11#39711yescharacteristic
462C22×C11#39911yescharacteristic
463C22×C11B(4,𝔽2)12yes—
464C22×C11#45812yes—
465C4×C11—44no—
466C4×C11—42no—
467C4×C11—44no—
468C4×C11—82no—
469C4×C11—82no—
470C4×C11—81no—
471C4×C11—81no—
472C4×C11—82no—
473C25D4×C1111yescharacteristic
474C25C23×C1111yescharacteristic
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C2×C4×C1112yes—
488C22×D4Q8×C1112yes—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—44no—
499C23×C4D4×C1111yescharacteristic
500C23×C4D4×C1111yescharacteristic
501C23×C4D4×C1111yescharacteristic
502C23×C4D4×C1112yes—
503C23×C4D4×C1112yes—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—44no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—44no—
535C2×C22⋊C4C2×C4×C1112yes—
536C2×C22⋊C4C2×C4×C1112yes—
537C2×C22⋊C4D4×C1112yes—
538C2×C22⋊C4D4×C1112yes—
539C2×C22⋊C4D4×C1112yes—
540#99—28no—
541#95—24no—
542#95—24no—
543#95—22no—
544#95—22no—
545#95—44no—
546C2×C11—21no—
547C2×C11—21no—
548C2×C11—21no—
549C2×C11—21no—
550C2×C11—21no—
551C2×C11—21no—
552C2×C11—21no—
553C2×C11—21no—
554C2×C11—21no—
555C2×C11—21no—
556C2×C11—21no—
557C2×C11—21no—
558C2×C11—82no—
559C2×C11#143911yescharacteristic
560C2×C11#186712yes—
561C2×C11#202111yescharacteristic
562C2×C11#202211yescharacteristic
563C2×C11#204412yes—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—42no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24C11×C4⋊C412yescomplemented
575C24C22×C4×C1111yescharacteristic
576C24C2×D4×C1111yescharacteristic
577C24C2×D4×C1111yescharacteristic
578C24C2×D4×C1111yescharacteristic
579C24C2×D4×C1111yescharacteristic
580C24C2×D4×C1111yescharacteristic
581C24C2×D4×C1111yescharacteristic
582C24C2×D4×C1111yescharacteristic
583C24C2×Q8×C1111yescharacteristic
584C24C11×#4111yescharacteristic
585C24C11×#4111yescharacteristic
586C24C11×#4111yescharacteristic
587C24C11×#4111yescharacteristic
588C24C11×#4111yescharacteristic
589C24C11×#4111yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4C11×C4⋊C412yescomplemented
670C4⋊C4—48no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—48no—
679C22⋊C4—41no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4C11×C22⋊C414yescomplemented
694C11#1108711yescharacteristic, direct product factor, Sylow
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—82no—
731C23—81no—
732C23—81no—
733C23—82no—
734C23C2×C11×C22⋊C411yescharacteristic
735C23C2×C11×C4⋊C411yescharacteristic
736C23C11×#11711yescharacteristic
737C23C4×D4×C1111yescharacteristic
738C23C4×D4×C1111yescharacteristic
739C23C4×D4×C1111yescharacteristic
740C23C4×D4×C1111yescharacteristic
741C23C11×#12011yescharacteristic
742C23C11×#12011yescharacteristic
743C23C11×#12011yescharacteristic
744C23C11×#12111yescharacteristic
745C23C11×#12111yescharacteristic
746C23C11×#12111yescharacteristic
747C23C11×#12111yescharacteristic
748C23C11×#12111yescharacteristic
749C23C11×#12111yescharacteristic
750C23C11×#12111yescharacteristic
751C23C11×#12111yescharacteristic
752C23C11×C22⋊Q811yescharacteristic
753C23C11×C22⋊Q811yescharacteristic
754C23C11×C22⋊Q811yescharacteristic
755C23C11×C22⋊Q811yescharacteristic
756C23C11×C22⋊Q811yescharacteristic
757C23C11×C22⋊Q811yescharacteristic
758C23C11×#12311yescharacteristic
759C23C11×#12311yescharacteristic
760C23C11×#12311yescharacteristic
761C23C11×#12311yescharacteristic
762C23C11×#12311yescharacteristic
763C23C11×#12411yescharacteristic
764C23C11×#12411yescharacteristic
765C23C11×#12411yescharacteristic
766C23C11×#12611yescharacteristic
767C23C11×#12611yescharacteristic
768C23C11×#12711yescharacteristic
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—82no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22C11×#38011yescharacteristic
873C22C11×#38511yescharacteristic
874C22C11×#38511yescharacteristic
875C22C11×#38611yescharacteristic
876C22C11×#38811yescharacteristic
877C22C11×#38811yescharacteristic
878C22C11×#39011yescharacteristic
879C22C11×#39211yescharacteristic
880C22C11×#39311yescharacteristic
881C22C11×#39411yescharacteristic
882C22C11×#39411yescharacteristic
883C22C11×#39611yescharacteristic
884C22C11×#39611yescharacteristic
885C22C11×#39711yescharacteristic
886C22C11×#39911yescharacteristic
887C22C11×B(4,𝔽2)12yes—
888C22C11×#45812yes—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2C11×#143911yescharacteristic
911C2C11×#186712yes—
912C2C11×#202111yescharacteristic
913C2C11×#202211yescharacteristic
914C2C11×#204412yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#385C2semidirect
5. C2×C11×#342C2semidirect
6. C2×C11×#342C2semidirect
7. C11×C22⋊#95C2semidirect
19. C2×C11×#99C4semidirect
107. #11087C11direct (N × H)
118. C24×C11C4⋊C4semidirect
213. C22×C4×C11C4⋊C4semidirect
237. C11×C22⋊C4C22⋊C4semidirect
241. C2×#385C2×C11semidirect
242. C2×#342C2×C11semidirect
243. C2×#342C2×C11semidirect
244. C22⋊#95C2×C11semidirect
384. C2×#99C4×C11semidirect
574. C24C11×C4⋊C4semidirect
669. C22×C4C11×C4⋊C4semidirect
693. C22⋊C4C11×C22⋊C4semidirect
694. C11#11087direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#992
C11×#23082
C2×C11×#3862
C2×C11×#3852
C2×C11×#3422
C11×C22⋊#952
#1108711