Finite Group Databasebeta

← C11×#22676 #14599869

Subgroups — C11×#22676 #14599869

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#442C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2349C211yesmaximal, characteristic, complemented
5D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#1944C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1864C211yesmaximal, characteristic, complemented
9C11×#1864C211yesmaximal, characteristic, complemented
10C11×#1862C211yesmaximal, characteristic, complemented
11C11×#1862C211yesmaximal, characteristic, complemented
12C11×#1847C211yesmaximal, characteristic, complemented
13C11×#1804C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C11×#442—24no—
25C11×#442C418yescomplemented
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#385—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#384C2211yescharacteristic
51C11×#382C2211yescharacteristic
52C11×#380—21no—
53C11×#380—21no—
54C4×C11×C4⋊C4C2211yescharacteristic
55C2×C11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C2×C11×D8C2×C414yes—
71C2×C11×D8D414yes—
72C2×C11×D8Q814yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C4×D4×C11C2×C414yescomplemented
88C4×D4×C11C2×C414yescomplemented
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—44no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#107—22no—
114C11×#107—41no—
115C11×#106—22no—
116C11×#106—41no—
117C11×#106C2×C414yescomplemented
118C11×C4⋊C8—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102C2×C414yescomplemented
124C11×#102C2×C414yescomplemented
125C11×#97—22no—
126C11×#97C2×C414yescomplemented
127C4×C8×C11—22no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#22676C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11—21no—
138C24×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C22×C412yes—
146C2×D4×C11C22×C412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C2×D4×C11C2×Q812yes—
150C2×D4×C11C2×Q812yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—81no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×D8C4⋊C4116yescomplemented
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11C22×C412yes—
192C2×C8×C11C22×C412yes—
193C2×C8×C11C2×D412yes—
194C2×C8×C11C2×Q812yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
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—21no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—81no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4—81no—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C22×C412yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11C22×C412yes—
226C42×C11#4112yes—
227C2×#442C2×C1111yescharacteristic
228C2×#442C2×C1111yescharacteristic
229C2×C4×D8C2×C1111yescharacteristic
230#2349C2×C1111yescharacteristic, complemented
231D4×C4⋊C4C2×C1111yescharacteristic, complemented
232#1944C2×C1111yescharacteristic, complemented
233#1941C2×C1111yescharacteristic, complemented
234#1864C2×C1111yescharacteristic, complemented
235#1864C2×C1111yescharacteristic, complemented
236#1862C2×C1111yescharacteristic, complemented
237#1862C2×C1111yescharacteristic, complemented
238#1847C2×C1111yescharacteristic, complemented
239#1804C2×C1111yescharacteristic, complemented
240#1802C2×C1111yescharacteristic, complemented
241#1771C2×C1111yescharacteristic, complemented
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11C22×D411yescharacteristic
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11C2×C4⋊C414yes—
264D4×C11C2×C4⋊C414yescomplemented
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
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—21no—
282C2×C4×C11—48no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
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—41no—
299C2×C4×C11—84no—
300C2×C4×C11—84no—
301C2×C4×C11—84no—
302C2×C4×C11—84no—
303C2×C4×C11—84no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11C4×D412yes—
306C2×C4×C11AGL(1,ℤ/8)12yes—
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×Q811yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C112−1+411yescharacteristic
313C8×C11—22no—
314C8×C11—41no—
315C8×C11—41no—
316C8×C11C2×C4⋊C414yescomplemented
317C22×D8C22×C1111yescharacteristic
318C2×C4×D4C22×C1111yescharacteristic
319C2×C4×D4C22×C1111yescharacteristic
320C2×C4×D4C22×C1111yescharacteristic
321C2×C4×D4C22×C1111yescharacteristic
322C2×C4×D4C22×C1111yescharacteristic
323C2×C4×D4C22×C1111yescharacteristic
324C22×C4⋊C4—21no—
325#442—24no—
326#442C4×C1118yescomplemented
327C4×D8—24no—
328C2×#107C22×C1111yescharacteristic
329C2×#107C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#97C22×C1111yescharacteristic
341C2×#97C22×C1111yescharacteristic
342C2×C4×C8C22×C1111yescharacteristic
343#389C22×C1111yescharacteristic
344#389C22×C1111yescharacteristic
345#389C22×C1111yescharacteristic
346#389C22×C1111yescharacteristic
347#385—21no—
348#385—21no—
349#385—21no—
350#385—21no—
351#384C22×C1111yescharacteristic
352#382C22×C1111yescharacteristic
353#380—21no—
354#380—21no—
355C4×C4⋊C4C22×C1111yescharacteristic
356C2×#95—21no—
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362#336C22×C1111yescharacteristic
363C22×C11—24no—
364C22×C11—24no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11C2×C4×D411yescharacteristic
378C22×C11D4211yescharacteristic
379C22×C11D4×Q811yescharacteristic
380C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C11#57511yescharacteristic
382C22×C11#57611yescharacteristic
383C22×C11#57711yescharacteristic
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—22no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11—81no—
395C4×C11—81no—
396C4×C11C22×C4⋊C411yescharacteristic
397C4×C11#52011yescharacteristic
398C4×C11#54711yescharacteristic
399C4×C11#55411yescharacteristic
400C22×D4C23×C1111yescharacteristic
401C22×D4C23×C1111yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—21no—
408C2×D8C2×C4×C1114yes—
409C2×D8D4×C1114yes—
410C2×D8Q8×C1114yes—
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—41no—
422C4×D4—41no—
423C4×D4—41no—
424C4×D4—41no—
425C4×D4C2×C4×C1114yescomplemented
426C4×D4C2×C4×C1114yescomplemented
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4D4×C1111yescharacteristic
435C2×C4⋊C4D4×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
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×C42C23×C1111yescharacteristic
449C2×C42C23×C1111yescharacteristic
450C2×C42C23×C1111yescharacteristic
451#107—22no—
452#107—41no—
453#106—22no—
454#106—41no—
455#106C2×C4×C1114yescomplemented
456C4⋊C8—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—22no—
461#102C2×C4×C1114yescomplemented
462#102C2×C4×C1114yescomplemented
463#97—22no—
464#97C2×C4×C1114yescomplemented
465C4×C8—22no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C1111yescharacteristic
473#95D4×C1111yescharacteristic
474C2×C11—44no—
475C2×C11—44no—
476C2×C11D4×C4⋊C411yescharacteristic
477C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
478C2×C11#294611yescharacteristic
479C2×C11#326411yescharacteristic
480C2×C11#326711yescharacteristic
481C2×C11#338411yescharacteristic
482C2×C11#338911yescharacteristic
483C24—21no—
484C24—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4C22×C4×C1112yes—
492C2×D4C22×C4×C1112yes—
493C2×D4C2×D4×C1112yes—
494C2×D4C2×D4×C1112yes—
495C2×D4C2×Q8×C1112yes—
496C2×D4C2×Q8×C1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C24×C1111yescharacteristic
528D8C11×C4⋊C4116yescomplemented
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8C22×C4×C1112yes—
538C2×C8C22×C4×C1112yes—
539C2×C8C2×D4×C1112yes—
540C2×C8C2×Q8×C1112yes—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—41no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4C22×C4×C1112yes—
560C4⋊C4C22×C4×C1112yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42C22×C4×C1112yes—
572C42C11×#4112yes—
573C11#2267611yescharacteristic, direct product factor, Sylow
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×D4×C1111yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4C2×C11×C4⋊C414yes—
596D4C2×C11×C4⋊C414yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—48no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4C4×D4×C1112yes—
637C2×C4C4×D4×C1112yes—
638C2×C4C11×AGL(1,ℤ/8)12yes—
639C2×C4C23×C4×C1111yescharacteristic
640C2×C4C22×D4×C1111yescharacteristic
641C2×C4C22×Q8×C1111yescharacteristic
642C2×C4C2×C11×#4111yescharacteristic
643C2×C4C11×H(5,𝔽2)11yescharacteristic
644C2×C4C11×2−1+411yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8C2×C11×C4⋊C414yescomplemented
649C22—24no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×C4×D4×C1111yescharacteristic
664C22D42×C1111yescharacteristic
665C22D4×Q8×C1111yescharacteristic
666C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
667C22C11×#57511yescharacteristic
668C22C11×#57611yescharacteristic
669C22C11×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C22×C11×C4⋊C411yescharacteristic
683C4C11×#52011yescharacteristic
684C4C11×#54711yescharacteristic
685C4C11×#55411yescharacteristic
686C2—44no—
687C2—44no—
688C2D4×C11×C4⋊C411yescharacteristic
689C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
690C2C11×#294611yescharacteristic
691C2C11×#326411yescharacteristic
692C2C11×#326711yescharacteristic
693C2C11×#338411yescharacteristic
694C2C11×#338911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2349C2semidirect
5. D4×C11×C4⋊C4C2semidirect
6. C11×#1944C2semidirect
7. C11×#1941C2semidirect
8. C11×#1864C2semidirect
9. C11×#1864C2semidirect
10. C11×#1862C2semidirect
11. C11×#1862C2semidirect
12. C11×#1847C2semidirect
13. C11×#1804C2semidirect
14. C11×#1802C2semidirect
15. C11×#1771C2semidirect
25. C11×#442C4semidirect
87. C4×D4×C11C2×C4semidirect
88. C4×D4×C11C2×C4semidirect
117. C11×#106C2×C4semidirect
123. C11×#102C2×C4semidirect
124. C11×#102C2×C4semidirect
126. C11×#97C2×C4semidirect
136. #22676C11direct (N × H)
182. C11×D8C4⋊C4semidirect
230. #2349C2×C11semidirect
231. D4×C4⋊C4C2×C11semidirect
232. #1944C2×C11semidirect
233. #1941C2×C11semidirect
234. #1864C2×C11semidirect
235. #1864C2×C11semidirect
236. #1862C2×C11semidirect
237. #1862C2×C11semidirect
238. #1847C2×C11semidirect
239. #1804C2×C11semidirect
240. #1802C2×C11semidirect
241. #1771C2×C11semidirect
264. D4×C11C2×C4⋊C4semidirect
316. C8×C11C2×C4⋊C4semidirect
326. #442C4×C11semidirect
425. C4×D4C2×C4×C11semidirect
426. C4×D4C2×C4×C11semidirect
455. #106C2×C4×C11semidirect
461. #102C2×C4×C11semidirect
462. #102C2×C4×C11semidirect
464. #97C2×C4×C11semidirect
528. D8C11×C4⋊C4semidirect
573. C11#22676direct (N × H)
596. D4C2×C11×C4⋊C4semidirect
648. C8C2×C11×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4422
C2×C4×C11×D82
C11×#23492
D4×C11×C4⋊C42
C11×#19442
C11×#19412
C11×#18642
C11×#18622
C11×#18472
C11×#18042
C11×#18022
C11×#17712
#2267611