Finite Group Databasebeta

← C4×C11×#463 #14598694

Subgroups — C4×C11×#463 #14598694

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C4×C11×#124C211yesmaximal, characteristic, complemented
5C42×D4×C11C211yesmaximal, characteristic, complemented
6C11×#1983C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1804C211yesmaximal, characteristic, complemented
13C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
14C4×C11×#103C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C42×C11—21no—
25C11×#463C418yesdirect product factor
26C4×C11×SD16—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#388—21no—
45C11×#388—21no—
46C11×#382C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4—21no—
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C4×C11×C22⋊C4—21no—
54C4×C11×C22⋊C4—21no—
55C43×C11C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yescomplemented
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#124—22no—
80C11×#124C2×C414yescomplemented
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11C2×C414yescomplemented
90C4×D4×C11D414yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—44no—
110C2×C42×C11D411yescharacteristic
111C2×C42×C11D411yescharacteristic
112C2×C42×C11D411yescharacteristic
113C2×C42×C11D411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#106—22no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8C2×C414yescomplemented
121C11×#103—22no—
122C11×#103—22no—
123C11×#103C2×C414yescomplemented
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102C2×C414yescomplemented
129C4×C8×C11—22no—
130C4×C8×C11—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C4×#463C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C412yes—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C412yes—
156C2×D4×C11C22×C412yes—
157C2×D4×C11C2×D412yes—
158C2×D4×C11#4112yes—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C11×SD16—28no—
185C11×D8—28no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11C22×C412yes—
197C2×C8×C11C22×C412yes—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4#4112yes—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C42×C11—22no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—41no—
223C42×C11—42no—
224C42×C11—42no—
225C42×C11—42no—
226C42×C11—42no—
227C42×C11C22×C412yes—
228C42×C11C2×D412yes—
229C42×C11#4112yes—
230C42×C11#4112yes—
231C2×#463C2×C1111yescharacteristic
232C2×C4×SD16C2×C1111yescharacteristic, complemented
233C2×C4×D8C2×C1111yescharacteristic
234C4×#124C2×C1111yescharacteristic, complemented
235C42×D4C2×C1111yescharacteristic, complemented
236#1983C2×C1111yescharacteristic, complemented
237#1949C2×C1111yescharacteristic, complemented
238#1928C2×C1111yescharacteristic, complemented
239#1926C2×C1111yescharacteristic, complemented
240#1879C2×C1111yescharacteristic
241#1877C2×C1111yescharacteristic, complemented
242#1804C2×C1111yescharacteristic, complemented
243C4×C4⋊C8C2×C1111yescharacteristic, complemented
244C4×#103C2×C1111yescharacteristic, complemented
245C4×#102C2×C1111yescharacteristic, complemented
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11C22×D411yescharacteristic
261Q8×C11—22no—
262Q8×C11—22no—
263Q8×C11—41no—
264Q8×C11—41no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11C4×D414yes—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—48no—
289C2×C4×C11—48no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—48no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11C4×D412yes—
308C2×C4×C11#12112yes—
309C2×C4×C11#12112yes—
310C2×C4×C11#13512yes—
311C2×C4×C11#13512yes—
312C2×C4×C11AGL(1,ℤ/8)12yes—
313C2×C4×C11C23×C411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C8×C11—22no—
320C8×C11—22no—
321C8×C11—41no—
322C8×C11—41no—
323C22×SD16C22×C1111yescharacteristic
324C22×D8C22×C1111yescharacteristic
325C2×#124C22×C1111yescharacteristic
326C2×C4×Q8C22×C1111yescharacteristic
327C2×C4×D4C22×C1111yescharacteristic
328C2×C4×D4C22×C1111yescharacteristic
329C2×C4×D4C22×C1111yescharacteristic
330C2×C4×D4C22×C1111yescharacteristic
331C22×C42—21no—
332#463C4×C1118yesdirect product factor
333C4×SD16—24no—
334C4×D8—24no—
335C2×#107C22×C1111yescharacteristic
336C2×#106C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×C4×C8C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#391C22×C1111yescharacteristic
350#390C22×C1111yescharacteristic
351#388—21no—
352#388—21no—
353#382C22×C1111yescharacteristic
354C4×C4⋊C4C22×C1111yescharacteristic
355C4×C4⋊C4C22×C1111yescharacteristic
356C4×C4⋊C4C22×C1111yescharacteristic
357C4×C22⋊C4—21no—
358C4×C22⋊C4—21no—
359C4×C22⋊C4—21no—
360C4×C22⋊C4—21no—
361C4×C22⋊C4—21no—
362C43C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—24no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×C4×D411yescharacteristic
384C22×C11C2×#12111yescharacteristic
385C22×C11#52511yescharacteristic
386C22×C11C2×#13511yescharacteristic
387C22×C11C2×#13511yescharacteristic
388C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C11#57511yescharacteristic
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—41no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11#46314yesdirect product factor
402C4×C11C2×C4×D411yescharacteristic
403C4×C11C4×#4111yescharacteristic
404C4×C11#52911yescharacteristic
405C4×C11#53211yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×D4C23×C1111yescharacteristic
408C22×D4C23×C1111yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16C2×C4×C1114yescomplemented
416C2×D8—22no—
417C2×D8—22no—
418C2×D8C2×C4×C1114yes—
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423#124—22no—
424#124C2×C4×C1114yescomplemented
425C4×Q8—22no—
426C4×Q8—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4C2×C4×C1114yescomplemented
434C4×D4D4×C1114yes—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—44no—
454C2×C42D4×C1111yescharacteristic
455C2×C42D4×C1111yescharacteristic
456C2×C42D4×C1111yescharacteristic
457C2×C42D4×C1111yescharacteristic
458C2×C42C23×C1111yescharacteristic
459C2×C42C23×C1111yescharacteristic
460C2×C42C23×C1111yescharacteristic
461#107—22no—
462#106—22no—
463C4⋊C8—22no—
464C4⋊C8C2×C4×C1114yescomplemented
465#103—22no—
466#103—22no—
467#103C2×C4×C1114yescomplemented
468#102—22no—
469#102—22no—
470#102—22no—
471#102—22no—
472#102C2×C4×C1114yescomplemented
473C4×C8—22no—
474C4×C8—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C2×C11—44no—
483C2×C11—82no—
484C2×C11C4×#12111yescharacteristic
485C2×C11C4×#13511yescharacteristic
486C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
487C2×C11C2×#46311yescharacteristic
488C2×C11#303511yescharacteristic
489C2×C11#310211yescharacteristic
490C2×C11#310511yescharacteristic
491C24—21no—
492C24—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×C4×C1112yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C22×C4×C1112yes—
508C2×D4C22×C4×C1112yes—
509C2×D4C2×D4×C1112yes—
510C2×D4C11×#4112yes—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C24×C1111yescharacteristic
536SD16—28no—
537D8—28no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C22×C4×C1112yes—
549C2×C8C22×C4×C1112yes—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4C22×C4×C1112yes—
559C4⋊C4C2×D4×C1112yes—
560C4⋊C4C11×#4112yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—21no—
573C42—21no—
574C42—41no—
575C42—42no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42C22×C4×C1112yes—
580C42C2×D4×C1112yes—
581C42C11×#4112yes—
582C42C11×#4112yes—
583C11C4×#46311yescharacteristic, direct product factor, Sylow
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C1111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C4×D4×C1114yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—48no—
627C2×C4—48no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4C4×D4×C1112yes—
645C2×C4C4×D4×C1112yes—
646C2×C4C11×#12112yes—
647C2×C4C11×#12112yes—
648C2×C4C11×#13512yes—
649C2×C4C11×#13512yes—
650C2×C4C11×AGL(1,ℤ/8)12yes—
651C2×C4C23×C4×C1111yescharacteristic
652C2×C4C22×D4×C1111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C2×C11×#4111yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×D4×C1111yescharacteristic
676C22C2×C11×#12111yescharacteristic
677C22C11×#52511yescharacteristic
678C22C2×C11×#13511yescharacteristic
679C22C2×C11×#13511yescharacteristic
680C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
681C22C11×#57511yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4C11×#46314yesdirect product factor
694C4C2×C4×D4×C1111yescharacteristic
695C4C4×C11×#4111yescharacteristic
696C4C11×#52911yescharacteristic
697C4C11×#53211yescharacteristic
698C2—44no—
699C2—82no—
700C2C4×C11×#12111yescharacteristic
701C2C4×C11×#13511yescharacteristic
702C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
703C2C2×C11×#46311yescharacteristic
704C2C11×#303511yescharacteristic
705C2C11×#310211yescharacteristic
706C2C11×#310511yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
4. C4×C11×#124C2semidirect
5. C42×D4×C11C2semidirect
6. C11×#1983C2semidirect
7. C11×#1949C2semidirect
8. C11×#1928C2semidirect
9. C11×#1926C2semidirect
11. C11×#1877C2semidirect
12. C11×#1804C2semidirect
13. C4×C11×C4⋊C8C2semidirect
14. C4×C11×#103C2semidirect
15. C4×C11×#102C2semidirect
25. C11×#463C4direct (N × H)
71. C2×C11×SD16C2×C4semidirect
80. C11×#124C2×C4semidirect
89. C4×D4×C11C2×C4semidirect
120. C11×C4⋊C8C2×C4semidirect
123. C11×#103C2×C4semidirect
128. C11×#102C2×C4semidirect
138. C4×#463C11direct (N × H)
232. C2×C4×SD16C2×C11semidirect
234. C4×#124C2×C11semidirect
235. C42×D4C2×C11semidirect
236. #1983C2×C11semidirect
237. #1949C2×C11semidirect
238. #1928C2×C11semidirect
239. #1926C2×C11semidirect
241. #1877C2×C11semidirect
242. #1804C2×C11semidirect
243. C4×C4⋊C8C2×C11semidirect
244. C4×#103C2×C11semidirect
245. C4×#102C2×C11semidirect
332. #463C4×C11direct (N × H)
401. C4×C11#463direct (N × H)
415. C2×SD16C2×C4×C11semidirect
424. #124C2×C4×C11semidirect
433. C4×D4C2×C4×C11semidirect
464. C4⋊C8C2×C4×C11semidirect
467. #103C2×C4×C11semidirect
472. #102C2×C4×C11semidirect
583. C11C4×#463direct (N × H)
693. C4C11×#463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C4×C11×SD162
C2×C4×C11×D82
C4×C11×#1242
C42×D4×C112
C11×#19832
C11×#19492
C11×#19282
C11×#19262
C11×#18792
C11×#18772
C11×#18042
C4×C11×C4⋊C82
C4×C11×#1032
C4×C11×#1022
C4×#46311