Finite Group Databasebeta

← C11×#22149 #14599342

Subgroups — C11×#22149 #14599342

Order 2816.

928 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C4×C11×#124C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic, complemented
4C11×#1983C211yesmaximal, characteristic, complemented
5C11×#1970C211yesmaximal, characteristic
6C11×#1968C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic, complemented
9C11×#1933C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1863C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C11×#463C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#388—21no—
45C11×#388—21no—
46C11×#388—21no—
47C11×#388—21no—
48C11×#382C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4—21no—
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C43×C11C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16C2×C414yescomplemented
68C2×C11×D8—41no—
69C2×C11×D8—41no—
70C2×C11×D8C2×C414yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#124—22no—
76C11×#124C2×C414yes—
77C4×Q8×C11—41no—
78C4×Q8×C11—41no—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C4×D4×C11C2×C414yescomplemented
83C11×#117—44no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
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×C42×C11—21no—
103C2×C42×C11—21no—
104C2×C42×C11D411yescharacteristic
105C2×C42×C11D411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—41no—
112C11×#106—41no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8C2×C414yescomplemented
115C11×#103—41no—
116C11×#103—41no—
117C11×#103C2×C414yescomplemented
118C11×#102—41no—
119C11×#102—41no—
120C11×#102—41no—
121C11×#102—41no—
122C11×#102C2×C414yes—
123C4×C8×C11—41no—
124C4×C8×C11—41no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#22149C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C412yes—
152C2×D4×C11C22×C412yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×SD16—44no—
173C11×D8—44no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4C22×C412yes—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—22no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—41no—
217C42×C11—42no—
218C42×C11—42no—
219C42×C11C22×C412yes—
220C42×C11#4112yes—
221C2×#463C2×C1111yescharacteristic
222C4×#124C2×C1111yescharacteristic, complemented
223#2293C2×C1111yescharacteristic, complemented
224#1983C2×C1111yescharacteristic, complemented
225#1970C2×C1111yescharacteristic
226#1968C2×C1111yescharacteristic, complemented
227#1949C2×C1111yescharacteristic, complemented
228#1934C2×C1111yescharacteristic, complemented
229#1933C2×C1111yescharacteristic, complemented
230#1880C2×C1111yescharacteristic, complemented
231#1879C2×C1111yescharacteristic
232#1864C2×C1111yescharacteristic, complemented
233#1863C2×C1111yescharacteristic, complemented
234#1804C2×C1111yescharacteristic, complemented
235C4×C4⋊C8C2×C1111yescharacteristic, complemented
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C22×D411yescharacteristic
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—48no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
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—84no—
296C2×C4×C11C4×D412yes—
297C2×C4×C11C4×D412yes—
298C2×C4×C11#13512yes—
299C2×C4×C11#13512yes—
300C2×C4×C11AGL(1,ℤ/8)12yes—
301C2×C4×C11C23×C411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C2×C4×C112−1+411yescharacteristic
307C8×C11—22no—
308C8×C11—22no—
309C8×C11—41no—
310C8×C11—41no—
311C22×SD16C22×C1111yescharacteristic
312C22×D8C22×C1111yescharacteristic
313C2×#124C22×C1111yescharacteristic
314C2×C4×Q8C22×C1111yescharacteristic
315C2×C4×D4C22×C1111yescharacteristic
316C2×C4×D4C22×C1111yescharacteristic
317C2×#117—21no—
318#463C4×C1118yescomplemented
319C2×#107C22×C1111yescharacteristic
320C2×#106C22×C1111yescharacteristic
321C2×C4⋊C8C22×C1111yescharacteristic
322C2×C4⋊C8C22×C1111yescharacteristic
323C2×#103C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#103C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×C4×C8C22×C1111yescharacteristic
332C2×C4×C8C22×C1111yescharacteristic
333#391C22×C1111yescharacteristic
334#390C22×C1111yescharacteristic
335#390C22×C1111yescharacteristic
336#390C22×C1111yescharacteristic
337#389C22×C1111yescharacteristic
338#389C22×C1111yescharacteristic
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#382C22×C1111yescharacteristic
344C4×C4⋊C4C22×C1111yescharacteristic
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347C4×C22⋊C4—21no—
348C43C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#336C22×C1111yescharacteristic
354#336C22×C1111yescharacteristic
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#53511yescharacteristic
371C22×C11#53711yescharacteristic
372C22×C11C2×#13511yescharacteristic
373C22×C11C2×#13511yescharacteristic
374C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C11#57511yescharacteristic
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11#51811yescharacteristic
389C4×C11#52011yescharacteristic
390C4×C11#54011yescharacteristic
391C4×C11#54211yescharacteristic
392C22×Q8C23×C1111yescharacteristic
393C22×D4C23×C1111yescharacteristic
394C22×D4C23×C1111yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C2×SD16—41no—
398C2×SD16—41no—
399C2×SD16C2×C4×C1114yescomplemented
400C2×D8—41no—
401C2×D8—41no—
402C2×D8C2×C4×C1114yes—
403C22×C8C23×C1111yescharacteristic
404C22×C8C23×C1111yescharacteristic
405C22×C8C23×C1111yescharacteristic
406C22×C8C23×C1111yescharacteristic
407#124—22no—
408#124C2×C4×C1114yes—
409C4×Q8—41no—
410C4×Q8—41no—
411C4×D4—22no—
412C4×D4—41no—
413C4×D4—41no—
414C4×D4C2×C4×C1114yescomplemented
415#117—44no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42D4×C1111yescharacteristic
437C2×C42D4×C1111yescharacteristic
438C2×C42D4×C1111yescharacteristic
439C2×C42D4×C1111yescharacteristic
440C2×C42C23×C1111yescharacteristic
441C2×C42C23×C1111yescharacteristic
442C2×C42C23×C1111yescharacteristic
443#107—41no—
444#106—41no—
445C4⋊C8—22no—
446C4⋊C8C2×C4×C1114yescomplemented
447#103—41no—
448#103—41no—
449#103C2×C4×C1114yescomplemented
450#102—41no—
451#102—41no—
452#102—41no—
453#102—41no—
454#102C2×C4×C1114yes—
455C4×C8—41no—
456C4×C8—41no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464C2×C11—82no—
465C2×C11—82no—
466C2×C11#232411yescharacteristic
467C2×C11C4×#13511yescharacteristic
468C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
469C2×C11#320711yescharacteristic
470C2×C11#321111yescharacteristic
471C2×C11#324711yescharacteristic
472C2×C11#325011yescharacteristic
473C24—21no—
474C24—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C22×C4×C1112yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—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—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C2×D4×C1111yescharacteristic
509C22×C4C2×D4×C1111yescharacteristic
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C24×C1111yescharacteristic
512SD16—44no—
513D8—44no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C22×C4×C1112yes—
525C2×C8C22×C4×C1112yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4C22×C4×C1112yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—41no—
557C42—42no—
558C42—42no—
559C42C22×C4×C1112yes—
560C42C11×#4112yes—
561C11#2214911yescharacteristic, direct product factor, Sylow
562C23—22no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23C22×D4×C1111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581D4—22no—
582D4—22no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—48no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4C4×D4×C1112yes—
623C2×C4C4×D4×C1112yes—
624C2×C4C11×#13512yes—
625C2×C4C11×#13512yes—
626C2×C4C11×AGL(1,ℤ/8)12yes—
627C2×C4C23×C4×C1111yescharacteristic
628C2×C4C2×C11×#4111yescharacteristic
629C2×C4C11×H(5,𝔽2)11yescharacteristic
630C2×C4C11×H(5,𝔽2)11yescharacteristic
631C2×C4C11×H(5,𝔽2)11yescharacteristic
632C2×C4C11×2−1+411yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22C2×C4×D4×C1111yescharacteristic
652C22C11×#53511yescharacteristic
653C22C11×#53711yescharacteristic
654C22C2×C11×#13511yescharacteristic
655C22C2×C11×#13511yescharacteristic
656C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
657C22C11×#57511yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C11×#51811yescharacteristic
671C4C11×#52011yescharacteristic
672C4C11×#54011yescharacteristic
673C4C11×#54211yescharacteristic
674C2—82no—
675C2—82no—
676C2C11×#232411yescharacteristic
677C2C4×C11×#13511yescharacteristic
678C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
679C2C11×#320711yescharacteristic
680C2C11×#321111yescharacteristic
681C2C11×#324711yescharacteristic
682C2C11×#325011yescharacteristic
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 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#124C2semidirect
3. C11×#2293C2semidirect
4. C11×#1983C2semidirect
6. C11×#1968C2semidirect
7. C11×#1949C2semidirect
8. C11×#1934C2semidirect
9. C11×#1933C2semidirect
10. C11×#1880C2semidirect
12. C11×#1864C2semidirect
13. C11×#1863C2semidirect
14. C11×#1804C2semidirect
15. C4×C11×C4⋊C8C2semidirect
23. C11×#463C4semidirect
67. C2×C11×SD16C2×C4semidirect
82. C4×D4×C11C2×C4semidirect
114. C11×C4⋊C8C2×C4semidirect
117. C11×#103C2×C4semidirect
132. #22149C11direct (N × H)
222. C4×#124C2×C11semidirect
223. #2293C2×C11semidirect
224. #1983C2×C11semidirect
226. #1968C2×C11semidirect
227. #1949C2×C11semidirect
228. #1934C2×C11semidirect
229. #1933C2×C11semidirect
230. #1880C2×C11semidirect
232. #1864C2×C11semidirect
233. #1863C2×C11semidirect
234. #1804C2×C11semidirect
235. C4×C4⋊C8C2×C11semidirect
318. #463C4×C11semidirect
399. C2×SD16C2×C4×C11semidirect
414. C4×D4C2×C4×C11semidirect
446. C4⋊C8C2×C4×C11semidirect
449. #103C2×C4×C11semidirect
561. C11#22149direct (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
C4×C11×#1242
C11×#22932
C11×#19832
C11×#19702
C11×#19682
C11×#19492
C11×#19342
C11×#19332
C11×#18802
C11×#18792
C11×#18642
C11×#18632
C11×#18042
C4×C11×C4⋊C82
#2214911