Finite Group Databasebeta

← C11×#24192 #14601385

Subgroups — C11×#24192 #14601385

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2580C211yesmaximal, characteristic, complemented
5C11×#2042C211yesmaximal, characteristic, complemented
6C11×#2041C211yesmaximal, characteristic, complemented
7C11×#2012C211yesmaximal, characteristic, complemented
8C11×#2011C211yesmaximal, characteristic
9C11×#1984C211yesmaximal, characteristic, complemented
10C11×#1958C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1863C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C11×#559—24no—
20C11×#559—24no—
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×#123—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C11×#463—24no—
34C4×C11×D8—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C4×C8×C11C2211yescharacteristic
48C11×#399—21no—
49C11×#393—21no—
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#385—21no—
55C11×#385—21no—
56C11×#382C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8—22no—
80C2×C11×D8—22no—
81C2×C11×D8—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#127—22no—
87C11×#127—22no—
88C11×#124—28no—
89C11×#124—22no—
90C11×#124—22no—
91C11×#124—22no—
92C11×#124D414yes—
93C11×#123—28no—
94C11×#123—28no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11—22no—
99C4×D4×C11—28no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11D414yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
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⋊C4—21no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C11×#107—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—41no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×#102—41no—
142C11×#102—41no—
143C4×C8×C11—22no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24192C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—41no—
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—24no—
162C2×D4×C11—24no—
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—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—42no—
179C2×D4×C11—42no—
180C2×D4×C11—81no—
181C2×D4×C11—81no—
182C2×D4×C11C2×D412yes—
183C2×D4×C11C2×D412yes—
184C2×D4×C11#4112yes—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11—81no—
197C22×C4×C11—81no—
198C22×C4×C11—81no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C11×SD16—44no—
207C11×D8—28no—
208C11×D8—44no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
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#4112yes—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—81no—
233C11×C4⋊C4—81no—
234C11×C4⋊C4C2×D412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—81no—
245C11×C22⋊C4—81no—
246C42×C11—24no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11C2×D412yes—
252C42×C11C2×D412yes—
253C2×#559C2×C1111yescharacteristic, complemented
254C2×#463C2×C1111yescharacteristic, complemented
255C2×C4×D8C2×C1111yescharacteristic, complemented
256#2580C2×C1111yescharacteristic, complemented
257#2042C2×C1111yescharacteristic, complemented
258#2041C2×C1111yescharacteristic, complemented
259#2012C2×C1111yescharacteristic, complemented
260#2011C2×C1111yescharacteristic
261#1984C2×C1111yescharacteristic, complemented
262#1958C2×C1111yescharacteristic, complemented
263#1880C2×C1111yescharacteristic, complemented
264#1879C2×C1111yescharacteristic, complemented
265#1863C2×C1111yescharacteristic, complemented
266#1862C2×C1111yescharacteristic, complemented
267#1804C2×C1111yescharacteristic, complemented
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11C22×D411yescharacteristic
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—44no—
293Q8×C11—41no—
294Q8×C11—41no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—48no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—84no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
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—21no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—84no—
340C2×C4×C11—84no—
341C2×C4×C11—84no—
342C2×C4×C11#12012yes—
343C2×C4×C11#12012yes—
344C2×C4×C11#13512yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C2×C4×C112−1+411yescharacteristic
351C8×C11—22no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355C22×SD16C22×C1111yescharacteristic
356C22×D8C22×C1111yescharacteristic
357C22×D8C22×C1111yescharacteristic
358#559—24no—
359#559—24no—
360C2×#127C22×C1111yescharacteristic
361C2×#124—21no—
362C2×#124C22×C1111yescharacteristic
363C2×#124C22×C1111yescharacteristic
364C2×#123—21no—
365C2×#123—21no—
366C2×C4×Q8C22×C1111yescharacteristic
367C2×C4×Q8C22×C1111yescharacteristic
368C2×C4×D4—21no—
369C2×C4×D4C22×C1111yescharacteristic
370C2×C4×D4C22×C1111yescharacteristic
371C2×C4×D4C22×C1111yescharacteristic
372#463—24no—
373C4×D8—24no—
374C2×#107C22×C1111yescharacteristic
375C2×C4⋊C8C22×C1111yescharacteristic
376C2×#103C22×C1111yescharacteristic
377C2×#103C22×C1111yescharacteristic
378C2×#103C22×C1111yescharacteristic
379C2×#102C22×C1111yescharacteristic
380C2×#102C22×C1111yescharacteristic
381C2×#102C22×C1111yescharacteristic
382C2×#102C22×C1111yescharacteristic
383C2×#102C22×C1111yescharacteristic
384C2×#102C22×C1111yescharacteristic
385C2×#102C22×C1111yescharacteristic
386C2×C4×C8C22×C1111yescharacteristic
387#399—21no—
388#393—21no—
389#390C22×C1111yescharacteristic
390#390C22×C1111yescharacteristic
391#389C22×C1111yescharacteristic
392#389C22×C1111yescharacteristic
393#385—21no—
394#385—21no—
395#382C22×C1111yescharacteristic
396#340C22×C1111yescharacteristic
397#340C22×C1111yescharacteristic
398#336C22×C1111yescharacteristic
399#336C22×C1111yescharacteristic
400#336C22×C1111yescharacteristic
401#336C22×C1111yescharacteristic
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11C2×#12011yescharacteristic
424C22×C11#54811yescharacteristic
425C22×C11#55011yescharacteristic
426C22×C11C2×#13511yescharacteristic
427C22×C11#57511yescharacteristic
428C22×C11#57611yescharacteristic
429C22×C11#57611yescharacteristic
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—42no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—41no—
437C4×C11—42no—
438C4×C11—81no—
439C4×C11—81no—
440C4×C11—81no—
441C4×C11#52511yescharacteristic
442C4×C11#53711yescharacteristic
443C4×C11#54611yescharacteristic
444C4×C11#54711yescharacteristic
445C22×Q8D4×C1111yescharacteristic
446C22×Q8C23×C1111yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C1111yescharacteristic
450C22×D4C23×C1111yescharacteristic
451C22×D4C23×C1111yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—41no—
458C2×D8—22no—
459C2×D8—22no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—22no—
463C2×D8—41no—
464C22×C8C23×C1111yescharacteristic
465C22×C8C23×C1111yescharacteristic
466C22×C8C23×C1111yescharacteristic
467C22×C8C23×C1111yescharacteristic
468#127—22no—
469#127—22no—
470#124—28no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124D4×C1114yes—
475#123—28no—
476#123—28no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×D4—28no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4D4×C1114yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4D4×C1111yescharacteristic
492C2×C4⋊C4D4×C1111yescharacteristic
493C2×C4⋊C4D4×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C1111yescharacteristic
511C2×C42C23×C1111yescharacteristic
512C2×C42C23×C1111yescharacteristic
513#107—22no—
514C4⋊C8—22no—
515#103—22no—
516#103—22no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—41no—
523#102—41no—
524#102—41no—
525C4×C8—22no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C2×C11—82no—
531C2×C11—82no—
532C2×C11—82no—
533C2×C11#240711yescharacteristic
534C2×C11#300211yescharacteristic
535C2×C11#300811yescharacteristic
536C2×C11#336111yescharacteristic
537C2×C11#337011yescharacteristic
538C2×C11#339611yescharacteristic
539C2×C11#340311yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—41no—
551C2×Q8C2×D4×C1112yes—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C1112yes—
574C2×D4C2×D4×C1112yes—
575C2×D4C11×#4112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C2×D4×C1111yescharacteristic
593C22×C4C2×D4×C1111yescharacteristic
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C24×C1111yescharacteristic
597SD16—44no—
598D8—28no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8C11×#4112yes—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—81no—
624C4⋊C4—81no—
625C4⋊C4C2×D4×C1112yes—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C42—24no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×D4×C1112yes—
643C42C2×D4×C1112yes—
644C11#2419211yescharacteristic, direct product factor, Sylow
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C22×D4×C1111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—44no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C11×#12012yes—
720C2×C4C11×#12012yes—
721C2×C4C11×#13512yes—
722C2×C4C22×D4×C1111yescharacteristic
723C2×C4C22×D4×C1111yescharacteristic
724C2×C4C2×C11×#4111yescharacteristic
725C2×C4C2×C11×#4111yescharacteristic
726C2×C4C11×H(5,𝔽2)11yescharacteristic
727C2×C4C11×2−1+411yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22C2×C11×#12011yescharacteristic
754C22C11×#54811yescharacteristic
755C22C11×#55011yescharacteristic
756C22C2×C11×#13511yescharacteristic
757C22C11×#57511yescharacteristic
758C22C11×#57611yescharacteristic
759C22C11×#57611yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4C11×#52511yescharacteristic
772C4C11×#53711yescharacteristic
773C4C11×#54611yescharacteristic
774C4C11×#54711yescharacteristic
775C2—82no—
776C2—82no—
777C2—82no—
778C2C11×#240711yescharacteristic
779C2C11×#300211yescharacteristic
780C2C11×#300811yescharacteristic
781C2C11×#336111yescharacteristic
782C2C11×#337011yescharacteristic
783C2C11×#339611yescharacteristic
784C2C11×#340311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#559C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C4×C11×D8C2semidirect
4. C11×#2580C2semidirect
5. C11×#2042C2semidirect
6. C11×#2041C2semidirect
7. C11×#2012C2semidirect
9. C11×#1984C2semidirect
10. C11×#1958C2semidirect
11. C11×#1880C2semidirect
12. C11×#1879C2semidirect
13. C11×#1863C2semidirect
14. C11×#1862C2semidirect
15. C11×#1804C2semidirect
148. #24192C11direct (N × H)
253. C2×#559C2×C11semidirect
254. C2×#463C2×C11semidirect
255. C2×C4×D8C2×C11semidirect
256. #2580C2×C11semidirect
257. #2042C2×C11semidirect
258. #2041C2×C11semidirect
259. #2012C2×C11semidirect
261. #1984C2×C11semidirect
262. #1958C2×C11semidirect
263. #1880C2×C11semidirect
264. #1879C2×C11semidirect
265. #1863C2×C11semidirect
266. #1862C2×C11semidirect
267. #1804C2×C11semidirect
644. C11#24192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C2×C11×#4632
C2×C4×C11×D82
C11×#25802
C11×#20422
C11×#20412
C11×#20122
C11×#20112
C11×#19842
C11×#19582
C11×#18802
C11×#18792
C11×#18632
C11×#18622
C11×#18042
#2419211