Finite Group Databasebeta

← C11×#24560 #14601753

Subgroups — C11×#24560 #14601753

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic, complemented
3C11×#2847C211yesmaximal, characteristic
4C11×#2280C211yesmaximal, characteristic, complemented
5C11×#2077C211yesmaximal, characteristic, complemented
6C11×#2075C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1895C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1854C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#120—21no—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C11×#482—24no—
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#107C2211yescharacteristic, complemented
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×#106C2211yescharacteristic, complemented
30C2×C11×#102C2211yescharacteristic, complemented
31C2×C11×#102C2211yescharacteristic, complemented
32C2×C11×#102C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C11×#407—24no—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#386—21no—
40C11×#386—21no—
41C11×#386—21no—
42C11×#381—21no—
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#379—21no—
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C11×#340C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C25×C11D411yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D411yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16—41no—
83C2×C11×M16—41no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—41no—
93C11×#121—41no—
94C11×#120—44no—
95C11×#117—22no—
96C11×#117—22no—
97C11×#117—41no—
98C11×#117—41no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C11×#107—22no—
121C11×#107—41no—
122C11×#106—22no—
123C11×#106—41no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—41no—
127C11×#102—41no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8D414yescomplemented
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139#24560C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—21no—
144C24×C11—41no—
145C24×C11—41no—
146C24×C11—41no—
147C24×C11—41no—
148C24×C11C2×D411yescharacteristic
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
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—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—41no—
194C22×C4×C11—41no—
195C22×C4×C11—41no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×C4×C11#4112yes—
207C22×C4×C11C2411yescharacteristic
208C11×M16—44no—
209C11×M16—44no—
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×C11C2×D412yes—
221C2×C8×C11C2×D412yes—
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—21no—
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×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C42×C11—42no—
249C42×C11—42no—
250C2×#482C2×C1111yescharacteristic, complemented
251C2×#407C2×C1111yescharacteristic, complemented
252#2847C2×C1111yescharacteristic
253#2280C2×C1111yescharacteristic, complemented
254#2077C2×C1111yescharacteristic, complemented
255#2075C2×C1111yescharacteristic, complemented
256#2034C2×C1111yescharacteristic, complemented
257#2033C2×C1111yescharacteristic, complemented
258#1895C2×C1111yescharacteristic, complemented
259#1895C2×C1111yescharacteristic, complemented
260#1875C2×C1111yescharacteristic, complemented
261#1854C2×C1111yescharacteristic, complemented
262#1825C2×C1111yescharacteristic, complemented
263#1809C2×C1111yescharacteristic, complemented
264#1809C2×C1111yescharacteristic, complemented
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11#12112yes—
298C23×C11#12312yes—
299C23×C11AGL(1,ℤ/8)12yes—
300C23×C11C22×D411yescharacteristic
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—84no—
306D4×C11—84no—
307D4×C11—84no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—44no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
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—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—41no—
351C2×C4×C11#12112yes—
352C2×C4×C11#12312yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C8×C11—22no—
360C8×C11—22no—
361C8×C11—41no—
362C8×C11—41no—
363C24×C4C22×C1111yescharacteristic
364C22×M16C22×C1111yescharacteristic
365C22×M16C22×C1111yescharacteristic
366C2×#121C22×C1111yescharacteristic
367C2×#121C22×C1111yescharacteristic
368C2×#121C22×C1111yescharacteristic
369C2×#120—21no—
370C2×#117C22×C1111yescharacteristic
371C2×#117C22×C1111yescharacteristic
372#482—24no—
373C2×#107C22×C1111yescharacteristic, complemented
374C2×#107C22×C1111yescharacteristic, complemented
375C2×#106C22×C1111yescharacteristic, complemented
376C2×#106C22×C1111yescharacteristic, complemented
377C2×#102C22×C1111yescharacteristic, complemented
378C2×#102C22×C1111yescharacteristic, complemented
379C2×#102C22×C1111yescharacteristic, complemented
380C2×#102C22×C1111yescharacteristic, complemented
381#407—24no—
382C2×C22⋊C8C22×C1111yescharacteristic
383C2×C22⋊C8C22×C1111yescharacteristic
384C2×C22⋊C8C22×C1111yescharacteristic
385C2×C22⋊C8C22×C1111yescharacteristic
386#386—21no—
387#386—21no—
388#386—21no—
389#381—21no—
390#380C22×C1111yescharacteristic
391#380C22×C1111yescharacteristic
392#380C22×C1111yescharacteristic
393#380C22×C1111yescharacteristic
394#380C22×C1111yescharacteristic
395#380C22×C1111yescharacteristic
396#380C22×C1111yescharacteristic
397#379—21no—
398C4×C22⋊C4—21no—
399C4×C22⋊C4—21no—
400#340C22×C1111yescharacteristic, complemented
401#340C22×C1111yescharacteristic, complemented
402#340C22×C1111yescharacteristic, complemented
403#340C22×C1111yescharacteristic, complemented
404#340C22×C1111yescharacteristic, complemented
405#340C22×C1111yescharacteristic, complemented
406#340C22×C1111yescharacteristic, complemented
407#340C22×C1111yescharacteristic, complemented
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—416no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11C2×#12111yescharacteristic
438C22×C11C2×#12311yescharacteristic
439C22×C11#53411yescharacteristic
440C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
441C22×C11#57511yescharacteristic
442C22×C11#57511yescharacteristic
443C22×C11#57511yescharacteristic
444C4×C11—22no—
445C4×C11—22no—
446C4×C11—41no—
447C4×C11—81no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11—81no—
451C4×C11—81no—
452C4×C11—81no—
453C4×C11—81no—
454C4×C11#54611yescharacteristic
455C4×C11#54611yescharacteristic
456C4×C11#55111yescharacteristic
457C4×C11#55111yescharacteristic
458C25D4×C1111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C1111yescharacteristic
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—41no—
468C23×C4—41no—
469C23×C4D4×C1111yescharacteristic
470C23×C4D4×C1111yescharacteristic
471C23×C4D4×C1111yescharacteristic
472C23×C4C23×C1111yescharacteristic
473C23×C4C23×C1111yescharacteristic
474C23×C4C23×C1111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—41no—
480C2×M16—41no—
481C22×C8C23×C1111yescharacteristic
482C22×C8C23×C1111yescharacteristic
483C22×C8C23×C1111yescharacteristic
484C22×C8C23×C1111yescharacteristic
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#120—44no—
492#117—22no—
493#117—22no—
494#117—41no—
495#117—41no—
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C4⋊C4C23×C1111yescharacteristic
499C2×C4⋊C4C23×C1111yescharacteristic
500C2×C4⋊C4C23×C1111yescharacteristic
501C2×C4⋊C4C23×C1111yescharacteristic
502C2×C4⋊C4C23×C1111yescharacteristic
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×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C42—21no—
516C2×C42—21no—
517#107—22no—
518#107—41no—
519#106—22no—
520#106—41no—
521#102—22no—
522#102—22no—
523#102—41no—
524#102—41no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8D4×C1114yescomplemented
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536C2×C11—42no—
537C2×C11—42no—
538C2×C11—42no—
539C2×C11—161no—
540C2×C11#241211yescharacteristic
541C2×C11#305411yescharacteristic
542C2×C11#305511yescharacteristic
543C2×C11#309311yescharacteristic
544C2×C11#309411yescharacteristic
545C2×C11#319411yescharacteristic
546C2×C11#319711yescharacteristic
547C24—22no—
548C24—22no—
549C24—22no—
550C24—21no—
551C24—41no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24C2×D4×C1111yescharacteristic
556C24C2×D4×C1111yescharacteristic
557C24C2×D4×C1111yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4C2×D4×C1111yescharacteristic
608C22×C4C2×D4×C1111yescharacteristic
609C22×C4C2×D4×C1112yes—
610C22×C4C2×D4×C1111yescharacteristic
611C22×C4C11×#4112yes—
612C22×C4C11×#4112yes—
613C22×C4C11×#4112yes—
614C22×C4C24×C1111yescharacteristic
615M16—44no—
616M16—44no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C1112yes—
628C2×C8C2×D4×C1112yes—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C42—42no—
656C42—42no—
657C11#2456011yescharacteristic, direct product factor, Sylow
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C11×#12112yes—
691C23C11×#12312yes—
692C23C11×AGL(1,ℤ/8)12yes—
693C23C22×D4×C1111yescharacteristic
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
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×C4C11×#12112yes—
745C2×C4C11×#12312yes—
746C2×C4C22×D4×C1111yescharacteristic
747C2×C4C2×C11×#4111yescharacteristic
748C2×C4C2×C11×#4111yescharacteristic
749C2×C4C2×C11×#4111yescharacteristic
750C2×C4C11×H(5,𝔽2)11yescharacteristic
751C2×C4C11×H(5,𝔽2)11yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—416no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×C11×#12111yescharacteristic
786C22C2×C11×#12311yescharacteristic
787C22C11×#53411yescharacteristic
788C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
789C22C11×#57511yescharacteristic
790C22C11×#57511yescharacteristic
791C22C11×#57511yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C11×#54611yescharacteristic
803C4C11×#54611yescharacteristic
804C4C11×#55111yescharacteristic
805C4C11×#55111yescharacteristic
806C2—42no—
807C2—42no—
808C2—42no—
809C2—161no—
810C2C11×#241211yescharacteristic
811C2C11×#305411yescharacteristic
812C2C11×#305511yescharacteristic
813C2C11×#309311yescharacteristic
814C2C11×#309411yescharacteristic
815C2C11×#319411yescharacteristic
816C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#482C2semidirect
2. C2×C11×#407C2semidirect
4. C11×#2280C2semidirect
5. C11×#2077C2semidirect
6. C11×#2075C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1895C2semidirect
10. C11×#1895C2semidirect
11. C11×#1875C2semidirect
12. C11×#1854C2semidirect
13. C11×#1825C2semidirect
14. C11×#1809C2semidirect
15. C11×#1809C2semidirect
26. C2×C11×#107C22semidirect
27. C2×C11×#107C22semidirect
28. C2×C11×#106C22semidirect
29. C2×C11×#106C22semidirect
30. C2×C11×#102C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
53. C11×#340C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
131. C11×C22⋊C8D4semidirect
139. #24560C11direct (N × H)
250. C2×#482C2×C11semidirect
251. C2×#407C2×C11semidirect
253. #2280C2×C11semidirect
254. #2077C2×C11semidirect
255. #2075C2×C11semidirect
256. #2034C2×C11semidirect
257. #2033C2×C11semidirect
258. #1895C2×C11semidirect
259. #1895C2×C11semidirect
260. #1875C2×C11semidirect
261. #1854C2×C11semidirect
262. #1825C2×C11semidirect
263. #1809C2×C11semidirect
264. #1809C2×C11semidirect
373. C2×#107C22×C11semidirect
374. C2×#107C22×C11semidirect
375. C2×#106C22×C11semidirect
376. C2×#106C22×C11semidirect
377. C2×#102C22×C11semidirect
378. C2×#102C22×C11semidirect
379. C2×#102C22×C11semidirect
380. C2×#102C22×C11semidirect
400. #340C22×C11semidirect
401. #340C22×C11semidirect
402. #340C22×C11semidirect
403. #340C22×C11semidirect
404. #340C22×C11semidirect
405. #340C22×C11semidirect
406. #340C22×C11semidirect
407. #340C22×C11semidirect
528. C22⋊C8D4×C11semidirect
657. C11#24560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C2×C11×#4072
C11×#28472
C11×#22802
C11×#20772
C11×#20752
C11×#20342
C11×#20332
C11×#18952
C11×#18752
C11×#18542
C11×#18252
C11×#18092
#2456011