Finite Group Databasebeta

← C11×#24162 #14601355

Subgroups — C11×#24162 #14601355

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#1999C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1982C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1864C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#540—24no—
19C11×#540—24no—
20C2×C11×#127C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#123—21no—
24C2×C11×#121—21no—
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#478—24no—
34C11×#459—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C11×#390—21no—
50C11×#390C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#388—21no—
53C11×#386—21no—
54C11×#385—21no—
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C2×C11×D8—22no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8—41no—
80C2×C11×D8—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×#127—22no—
86C11×#127D414yescomplemented
87C11×#125—22no—
88C11×#125D414yescomplemented
89C11×#123—28no—
90C11×#123—28no—
91C11×#121—28no—
92C11×#121—28no—
93C11×#121—22no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C11×#117—22no—
106C11×#117—22no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C11×C22⋊C4D411yescharacteristic
128C2×C42×C11—21no—
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C11×#107—22no—
132C11×#106—22no—
133C11×C4⋊C8—22no—
134C11×C4⋊C8—22no—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102—41no—
142C11×#102—41no—
143C11×C22⋊C8—41no—
144C11×C22⋊C8—41no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24162C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11—81no—
178C2×D4×C11—81no—
179C2×D4×C11—81no—
180C2×D4×C11—81no—
181C2×D4×C11—81no—
182C2×D4×C11—81no—
183C2×D4×C11C2×D412yes—
184C2×D4×C11C2×D412yes—
185C2×D4×C11#4112yes—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—42no—
200C22×C4×C11—81no—
201C22×C4×C11—81no—
202C22×C4×C11—81no—
203C22×C4×C11—81no—
204C22×C4×C11—81no—
205C22×C4×C11—81no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C11×D8—44no—
213C11×D8—44no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—81no—
238C11×C4⋊C4C2×D412yes—
239C11×C4⋊C4C2×D412yes—
240C11×C4⋊C4#4112yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—42no—
249C11×C22⋊C4—81no—
250C11×C22⋊C4—81no—
251C11×C22⋊C4—81no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—81no—
255C42×C11C2×D412yes—
256C42×C11C2×D412yes—
257C2×#540C2×C1111yescharacteristic, complemented
258C2×#478C2×C1111yescharacteristic, complemented
259C2×#459C2×C1111yescharacteristic, complemented
260#2324C2×C1111yescharacteristic, complemented
261#2034C2×C1111yescharacteristic, complemented
262#2033C2×C1111yescharacteristic, complemented
263#1999C2×C1111yescharacteristic, complemented
264#1999C2×C1111yescharacteristic, complemented
265#1989C2×C1111yescharacteristic, complemented
266#1982C2×C1111yescharacteristic, complemented
267#1879C2×C1111yescharacteristic, complemented
268#1879C2×C1111yescharacteristic, complemented
269#1864C2×C1111yescharacteristic, complemented
270#1862C2×C1111yescharacteristic, complemented
271#1798C2×C1111yescharacteristic, complemented
272C23×C11—21no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11C22×D411yescharacteristic
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—84no—
314D4×C11—84no—
315D4×C11—84no—
316D4×C11—84no—
317D4×C11—84no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—84no—
351C2×C4×C11—84no—
352C2×C4×C11—84no—
353C2×C4×C11#12012yes—
354C2×C4×C11#12012yes—
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C112−1+411yescharacteristic
361C8×C11—41no—
362C8×C11—41no—
363C8×C11—41no—
364C8×C11—41no—
365C22×D8C22×C1111yescharacteristic
366C22×D8C22×C1111yescharacteristic
367#540—24no—
368#540—24no—
369C2×#127C22×C1111yescharacteristic
370C2×#125C22×C1111yescharacteristic
371C2×#123—21no—
372C2×#123—21no—
373C2×#121—21no—
374C2×#121—21no—
375C2×#121C22×C1111yescharacteristic
376C2×#121C22×C1111yescharacteristic
377C2×#121C22×C1111yescharacteristic
378C2×C4×D4C22×C1111yescharacteristic
379C2×C4×D4C22×C1111yescharacteristic
380C2×C4×D4C22×C1111yescharacteristic
381C2×#117C22×C1111yescharacteristic
382#478—24no—
383#459—24no—
384C2×#107C22×C1111yescharacteristic
385C2×#106C22×C1111yescharacteristic
386C2×C4⋊C8C22×C1111yescharacteristic
387C2×C4⋊C8C22×C1111yescharacteristic
388C2×#102C22×C1111yescharacteristic
389C2×#102C22×C1111yescharacteristic
390C2×#102C22×C1111yescharacteristic
391C2×#102C22×C1111yescharacteristic
392C2×#102C22×C1111yescharacteristic
393C2×#102C22×C1111yescharacteristic
394C2×#102C22×C1111yescharacteristic
395C2×#102C22×C1111yescharacteristic
396C2×C22⋊C8C22×C1111yescharacteristic
397C2×C22⋊C8C22×C1111yescharacteristic
398#390—21no—
399#390C22×C1111yescharacteristic
400#389C22×C1111yescharacteristic
401#388—21no—
402#386—21no—
403#385—21no—
404#380C22×C1111yescharacteristic
405C4×C4⋊C4C22×C1111yescharacteristic
406#340C22×C1111yescharacteristic
407#340C22×C1111yescharacteristic
408#340C22×C1111yescharacteristic
409#340C22×C1111yescharacteristic
410#336C22×C1111yescharacteristic
411#336C22×C1111yescharacteristic
412C22×C11—41no—
413C22×C11—42no—
414C22×C11—41no—
415C22×C11—42no—
416C22×C11—41no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—41no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11C2×#12011yescharacteristic
441C22×C11#52511yescharacteristic
442C22×C11#53711yescharacteristic
443C22×C11#57611yescharacteristic
444C22×C11#57611yescharacteristic
445C22×C11#57611yescharacteristic
446C22×C11#57711yescharacteristic
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—42no—
450C4×C11—41no—
451C4×C11—41no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11#54611yescharacteristic
458C4×C11#54711yescharacteristic
459C4×C11#54811yescharacteristic
460C4×C11#55011yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C1111yescharacteristic
467C22×D4C23×C1111yescharacteristic
468C22×D4C23×C1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C1111yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1111yescharacteristic
481C22×C8C23×C1111yescharacteristic
482C22×C8C23×C1111yescharacteristic
483#127—22no—
484#127D4×C1114yescomplemented
485#125—22no—
486#125D4×C1114yescomplemented
487#123—28no—
488#123—28no—
489#121—28no—
490#121—28no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C1111yescharacteristic
509C2×C4⋊C4D4×C1111yescharacteristic
510C2×C4⋊C4C23×C1111yescharacteristic
511C2×C4⋊C4C23×C1111yescharacteristic
512C2×C4⋊C4C23×C1111yescharacteristic
513C2×C4⋊C4C23×C1111yescharacteristic
514C2×C4⋊C4C23×C1111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
525C2×C22⋊C4D4×C1111yescharacteristic
526C2×C42—21no—
527C2×C42C23×C1111yescharacteristic
528C2×C42C23×C1111yescharacteristic
529#107—22no—
530#106—22no—
531C4⋊C8—22no—
532C4⋊C8—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—41no—
542C22⋊C8—41no—
543#95—21no—
544#95—21no—
545#95—21no—
546C2×C11—81no—
547C2×C11—82no—
548C2×C11—82no—
549C2×C11—82no—
550C2×C11#240711yescharacteristic
551C2×C11#300811yescharacteristic
552C2×C11#301211yescharacteristic
553C2×C11#311911yescharacteristic
554C2×C11#312211yescharacteristic
555C2×C11#325711yescharacteristic
556C2×C11#325911yescharacteristic
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C1111yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4C2×D4×C1112yes—
592C2×D4C2×D4×C1112yes—
593C2×D4C11×#4112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C2×D4×C1111yescharacteristic
616C22×C4C2×D4×C1111yescharacteristic
617C22×C4C2×D4×C1111yescharacteristic
618C22×C4C2×D4×C1111yescharacteristic
619C22×C4C24×C1111yescharacteristic
620D8—44no—
621D8—44no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4C2×D4×C1112yes—
647C4⋊C4C2×D4×C1112yes—
648C4⋊C4C11×#4112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C42—21no—
661C42—21no—
662C42—81no—
663C42C2×D4×C1112yes—
664C42C2×D4×C1112yes—
665C11#2416211yescharacteristic, direct product factor, Sylow
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4C11×#12012yes—
748C2×C4C11×#12012yes—
749C2×C4C22×D4×C1111yescharacteristic
750C2×C4C22×D4×C1111yescharacteristic
751C2×C4C2×C11×#4111yescharacteristic
752C2×C4C2×C11×#4111yescharacteristic
753C2×C4C11×H(5,𝔽2)11yescharacteristic
754C2×C4C11×2−1+411yescharacteristic
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×C11×#12011yescharacteristic
788C22C11×#52511yescharacteristic
789C22C11×#53711yescharacteristic
790C22C11×#57611yescharacteristic
791C22C11×#57611yescharacteristic
792C22C11×#57611yescharacteristic
793C22C11×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C11×#54611yescharacteristic
805C4C11×#54711yescharacteristic
806C4C11×#54811yescharacteristic
807C4C11×#55011yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C11×#240711yescharacteristic
813C2C11×#300811yescharacteristic
814C2C11×#301211yescharacteristic
815C2C11×#311911yescharacteristic
816C2C11×#312211yescharacteristic
817C2C11×#325711yescharacteristic
818C2C11×#325911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#540C2semidirect
2. C2×C11×#478C2semidirect
3. C2×C11×#459C2semidirect
4. C11×#2324C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1999C2semidirect
9. C11×#1989C2semidirect
10. C11×#1982C2semidirect
11. C11×#1879C2semidirect
12. C11×#1879C2semidirect
13. C11×#1864C2semidirect
14. C11×#1862C2semidirect
15. C11×#1798C2semidirect
86. C11×#127D4semidirect
88. C11×#125D4semidirect
148. #24162C11direct (N × H)
257. C2×#540C2×C11semidirect
258. C2×#478C2×C11semidirect
259. C2×#459C2×C11semidirect
260. #2324C2×C11semidirect
261. #2034C2×C11semidirect
262. #2033C2×C11semidirect
263. #1999C2×C11semidirect
264. #1999C2×C11semidirect
265. #1989C2×C11semidirect
266. #1982C2×C11semidirect
267. #1879C2×C11semidirect
268. #1879C2×C11semidirect
269. #1864C2×C11semidirect
270. #1862C2×C11semidirect
271. #1798C2×C11semidirect
484. #127D4×C11semidirect
486. #125D4×C11semidirect
665. C11#24162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5402
C2×C11×#4782
C2×C11×#4592
C11×#23242
C11×#20342
C11×#20332
C11×#19992
C11×#19892
C11×#19822
C11×#18792
C11×#18642
C11×#18622
C11×#17982
#2416211