Finite Group Databasebeta

← C11×#24126 #14601319

Subgroups — C11×#24126 #14601319

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic, complemented
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1954C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1853C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C11×#553—24no—
18C11×#553—24no—
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#479—24no—
34C4×C11×SD16—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C4×C8×C11C2211yescharacteristic
50C11×#398—21no—
51C11×#394—21no—
52C11×#388—21no—
53C11×#388—21no—
54C11×#382C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#126—28no—
80C11×#125—22no—
81C11×#125D414yes—
82C11×#123—28no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—41no—
86C11×C22⋊Q8—41no—
87C11×#121—28no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×D4×C11—28no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11D414yes—
99C11×#117—22no—
100C11×#117—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C42×C11—21no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#106—22no—
131C11×#106—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#102—22no—
137C11×#102—41no—
138C11×#102—41no—
139C11×C22⋊C8—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C4×C8×C11—22no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24126C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D411yescharacteristic
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11#4112yes—
158C2×D4×C11—24no—
159C2×D4×C11—22no—
160C2×D4×C11—24no—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—41no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11C2×D412yes—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11—81no—
197C22×C4×C11—81no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C11×SD16—28no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
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#4112yes—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—42no—
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D412yes—
234C11×C4⋊C4C2×D412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C42×C11—24no—
246C42×C11—42no—
247C42×C11C2×D412yes—
248C42×C11C2×D412yes—
249C2×#553C2×C1111yescharacteristic
250C2×#479C2×C1111yescharacteristic, complemented
251C2×C4×SD16C2×C1111yescharacteristic, complemented
252#2536C2×C1111yescharacteristic, complemented
253#2034C2×C1111yescharacteristic, complemented
254#2033C2×C1111yescharacteristic, complemented
255#2000C2×C1111yescharacteristic, complemented
256#2000C2×C1111yescharacteristic, complemented
257#1991C2×C1111yescharacteristic, complemented
258#1954C2×C1111yescharacteristic, complemented
259#1873C2×C1111yescharacteristic, complemented
260#1872C2×C1111yescharacteristic, complemented
261#1854C2×C1111yescharacteristic, complemented
262#1853C2×C1111yescharacteristic, complemented
263#1804C2×C1111yescharacteristic, complemented
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11#13512yes—
285C23×C11C22×D411yescharacteristic
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—41no—
289Q8×C11—41no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—44no—
293D4×C11—48no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—84no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
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—84no—
337C2×C4×C11—84no—
338C2×C4×C11#12012yes—
339C2×C4×C11#12012yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C112−1+411yescharacteristic
346C8×C11—22no—
347C8×C11—41no—
348C8×C11—41no—
349C8×C11—41no—
350C22×SD16C22×C1111yescharacteristic
351#553—24no—
352#553—24no—
353C2×#126—21no—
354C2×#125C22×C1111yescharacteristic
355C2×#123—21no—
356C2×C22⋊Q8C22×C1111yescharacteristic
357C2×C22⋊Q8C22×C1111yescharacteristic
358C2×#121—21no—
359C2×#121C22×C1111yescharacteristic
360C2×#121C22×C1111yescharacteristic
361C2×C4×Q8C22×C1111yescharacteristic
362C2×C4×D4—21no—
363C2×C4×D4C22×C1111yescharacteristic
364C2×C4×D4C22×C1111yescharacteristic
365C2×#117C22×C1111yescharacteristic
366C22×C4⋊C4C22×C1111yescharacteristic
367#479—24no—
368C4×SD16—24no—
369C2×#107C22×C1111yescharacteristic
370C2×#106C22×C1111yescharacteristic
371C2×#106C22×C1111yescharacteristic
372C2×C4⋊C8C22×C1111yescharacteristic
373C2×#103C22×C1111yescharacteristic
374C2×#103C22×C1111yescharacteristic
375C2×#103C22×C1111yescharacteristic
376C2×#102C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×C22⋊C8C22×C1111yescharacteristic
380C2×C22⋊C8C22×C1111yescharacteristic
381C2×C22⋊C8C22×C1111yescharacteristic
382C2×C22⋊C8C22×C1111yescharacteristic
383C2×C4×C8C22×C1111yescharacteristic
384#398—21no—
385#394—21no—
386#388—21no—
387#388—21no—
388#382C22×C1111yescharacteristic
389#380C22×C1111yescharacteristic
390#380C22×C1111yescharacteristic
391#340C22×C1111yescharacteristic
392#340C22×C1111yescharacteristic
393#340C22×C1111yescharacteristic
394#340C22×C1111yescharacteristic
395#340C22×C1111yescharacteristic
396#340C22×C1111yescharacteristic
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—42no—
408C22×C11—41no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11C2×#12011yescharacteristic
419C22×C11#54611yescharacteristic
420C22×C11#54711yescharacteristic
421C22×C11C2×#13511yescharacteristic
422C22×C11#57511yescharacteristic
423C22×C11#57711yescharacteristic
424C22×C11#57711yescharacteristic
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—81no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11#52511yescharacteristic
437C4×C11#53711yescharacteristic
438C4×C11#54811yescharacteristic
439C4×C11#55011yescharacteristic
440C22×Q8C23×C1111yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4D4×C1111yescharacteristic
444C22×D4C23×C1111yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4C23×C1111yescharacteristic
448C23×C4C23×C1111yescharacteristic
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—22no—
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456#126—28no—
457#125—22no—
458#125D4×C1114yes—
459#123—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463C22⋊Q8—41no—
464#121—28no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×D4—28no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4D4×C1114yes—
476#117—22no—
477#117—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C1111yescharacteristic
487C2×C4⋊C4C23×C1111yescharacteristic
488C2×C4⋊C4C23×C1111yescharacteristic
489C2×C4⋊C4C23×C1111yescharacteristic
490C2×C4⋊C4C23×C1111yescharacteristic
491C2×C4⋊C4C23×C1111yescharacteristic
492C2×C4⋊C4C23×C1111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4D4×C1111yescharacteristic
502C2×C22⋊C4D4×C1111yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42C23×C1111yescharacteristic
506#107—22no—
507#106—22no—
508#106—22no—
509C4⋊C8—22no—
510#103—22no—
511#103—22no—
512#103—22no—
513#102—22no—
514#102—41no—
515#102—41no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525C2×C11—42no—
526C2×C11—81no—
527C2×C11—82no—
528C2×C11#240711yescharacteristic
529C2×C11#300211yescharacteristic
530C2×C11#300911yescharacteristic
531C2×C11#330111yescharacteristic
532C2×C11#332611yescharacteristic
533C2×C11#333711yescharacteristic
534C2×C11#335111yescharacteristic
535C24—21no—
536C24C2×D4×C1111yescharacteristic
537C24C2×D4×C1111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C11×#4112yes—
544C2×D4—24no—
545C2×D4—22no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4C2×D4×C1112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C1111yescharacteristic
585C22×C4C2×D4×C1111yescharacteristic
586C22×C4C2×D4×C1111yescharacteristic
587C22×C4C2×D4×C1111yescharacteristic
588C22×C4C24×C1111yescharacteristic
589SD16—28no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8C11×#4112yes—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4C2×D4×C1112yes—
619C4⋊C4C2×D4×C1112yes—
620C4⋊C4C2×D4×C1112yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C42—24no—
632C42—42no—
633C42C2×D4×C1112yes—
634C42C2×D4×C1112yes—
635C11#2412611yescharacteristic, direct product factor, Sylow
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C11×#13512yes—
657C23C22×D4×C1111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—44no—
665D4—48no—
666D4—41no—
667D4—41no—
668D4—84no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4C11×#12012yes—
711C2×C4C11×#12012yes—
712C2×C4C22×D4×C1111yescharacteristic
713C2×C4C22×D4×C1111yescharacteristic
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C2×C11×#4111yescharacteristic
716C2×C4C11×H(5,𝔽2)11yescharacteristic
717C2×C4C11×2−1+411yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×C11×#12011yescharacteristic
744C22C11×#54611yescharacteristic
745C22C11×#54711yescharacteristic
746C22C2×C11×#13511yescharacteristic
747C22C11×#57511yescharacteristic
748C22C11×#57711yescharacteristic
749C22C11×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C11×#52511yescharacteristic
762C4C11×#53711yescharacteristic
763C4C11×#54811yescharacteristic
764C4C11×#55011yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2C11×#240711yescharacteristic
769C2C11×#300211yescharacteristic
770C2C11×#300911yescharacteristic
771C2C11×#330111yescharacteristic
772C2C11×#332611yescharacteristic
773C2C11×#333711yescharacteristic
774C2C11×#335111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C4×C11×SD16C2semidirect
4. C11×#2536C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#2000C2semidirect
8. C11×#2000C2semidirect
9. C11×#1991C2semidirect
10. C11×#1954C2semidirect
11. C11×#1873C2semidirect
12. C11×#1872C2semidirect
13. C11×#1854C2semidirect
14. C11×#1853C2semidirect
15. C11×#1804C2semidirect
148. #24126C11direct (N × H)
250. C2×#479C2×C11semidirect
251. C2×C4×SD16C2×C11semidirect
252. #2536C2×C11semidirect
253. #2034C2×C11semidirect
254. #2033C2×C11semidirect
255. #2000C2×C11semidirect
256. #2000C2×C11semidirect
257. #1991C2×C11semidirect
258. #1954C2×C11semidirect
259. #1873C2×C11semidirect
260. #1872C2×C11semidirect
261. #1854C2×C11semidirect
262. #1853C2×C11semidirect
263. #1804C2×C11semidirect
635. C11#24126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#4792
C2×C4×C11×SD162
C11×#25362
C11×#20342
C11×#20332
C11×#20002
C11×#19912
C11×#19542
C11×#18732
C11×#18722
C11×#18542
C11×#18532
C11×#18042
#2412611