Finite Group Databasebeta

← C11×#23965 #14601158

Subgroups — C11×#23965 #14601158

Order 2816.

1332 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic, complemented
2C2×C11×#449C211yesmaximal, characteristic, complemented
3C2×C11×#416C211yesmaximal, characteristic, complemented
4C11×#2407C211yesmaximal, characteristic, complemented
5C11×#2024C211yesmaximal, characteristic, complemented
6C11×#2023C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1893C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1869C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#555—24no—
21C11×#555—24no—
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#124—21no—
24C2×C11×#124—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C2×C11×#117C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#449—24no—
36C11×#416—24no—
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#394—21no—
49C11×#392—21no—
50C11×#391C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386—21no—
53C11×#385—21no—
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11—21no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11D411yescharacteristic
76C22×D4×C11C2311yescharacteristic
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C2×C11×SD16—22no—
83C2×C11×SD16—22no—
84C2×C11×SD16—41no—
85C2×C11×D8—22no—
86C2×C11×D8—22no—
87C2×C11×D8—41no—
88C22×C8×C11—22no—
89C22×C8×C11—41no—
90C22×C8×C11—41no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×C4⋊Q8—22no—
96C11×C4⋊Q8—22no—
97C11×#124—28no—
98C11×#124—28no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—41no—
101C11×#121—28no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—41no—
107C11×#121D414yescomplemented
108C4×D4×C11—22no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C11×#117—28no—
113C11×#117—22no—
114C11×#117—22no—
115C11×#117—22no—
116C11×#117D414yescomplemented
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4D411yescharacteristic
136C2×C11×C22⋊C4D411yescharacteristic
137C2×C42×C11—21no—
138C2×C42×C11—21no—
139C2×C42×C11C2311yescharacteristic
140C11×#103—22no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#102—22no—
144C11×#102—22no—
145C11×#102—22no—
146C11×#102—41no—
147C11×#102—41no—
148C11×C22⋊C8—22no—
149C11×C22⋊C8—41no—
150C11×C22⋊C8—41no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#23965C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—81no—
170C2×Q8×C11—81no—
171C2×Q8×C11#4112yes—
172C2×D4×C11—22no—
173C2×D4×C11—24no—
174C2×D4×C11—24no—
175C2×D4×C11—22no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—41no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11—42no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—81no—
193C2×D4×C11—81no—
194C2×D4×C11—81no—
195C2×D4×C11—81no—
196C2×D4×C11—81no—
197C2×D4×C11C2×D412yes—
198C2×D4×C11#4112yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C11×SD16—44no—
229C11×D8—44no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—44no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—42no—
253C11×C4⋊C4C2×D412yes—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D412yes—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—42no—
264C11×C22⋊C4—42no—
265C11×C22⋊C4—42no—
266C11×C22⋊C4—81no—
267C11×C22⋊C4—81no—
268C42×C11—24no—
269C42×C11—24no—
270C42×C11—21no—
271C42×C11—21no—
272C2×#555C2×C1111yescharacteristic, complemented
273C2×#449C2×C1111yescharacteristic, complemented
274C2×#416C2×C1111yescharacteristic, complemented
275#2407C2×C1111yescharacteristic, complemented
276#2024C2×C1111yescharacteristic, complemented
277#2023C2×C1111yescharacteristic, complemented
278#2000C2×C1111yescharacteristic, complemented
279#1999C2×C1111yescharacteristic, complemented
280#1893C2×C1111yescharacteristic, complemented
281#1879C2×C1111yescharacteristic, complemented
282#1877C2×C1111yescharacteristic, complemented
283#1875C2×C1111yescharacteristic, complemented
284#1873C2×C1111yescharacteristic, complemented
285#1869C2×C1111yescharacteristic, complemented
286#1825C2×C1111yescharacteristic, complemented
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—21no—
296C23×C11—22no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11#12012yes—
315C23×C11C22×D411yescharacteristic
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—84no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—44no—
326D4×C11—48no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—41no—
330D4×C11—41no—
331D4×C11—84no—
332D4×C11—84no—
333D4×C11—84no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—21no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—48no—
353C2×C4×C11—48no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11#12012yes—
373C2×C4×C11#13512yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11C2×#4111yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C2×C4×C11H(5,𝔽2)11yescharacteristic
380C8×C11—41no—
381C8×C11—41no—
382C8×C11—41no—
383C8×C11—41no—
384C22×#41C22×C1111yescharacteristic
385C22×SD16C22×C1111yescharacteristic
386C22×D8C22×C1111yescharacteristic
387C23×C8C22×C1111yescharacteristic
388#555—24no—
389#555—24no—
390C2×C4⋊Q8C22×C1111yescharacteristic
391C2×#124—21no—
392C2×#124—21no—
393C2×C22⋊Q8C22×C1111yescharacteristic
394C2×#121—21no—
395C2×#121C22×C1111yescharacteristic
396C2×#121C22×C1111yescharacteristic
397C2×#121C22×C1111yescharacteristic
398C2×C4×D4C22×C1111yescharacteristic
399C2×C4×D4C22×C1111yescharacteristic
400C2×#117—21no—
401C2×#117C22×C1111yescharacteristic
402C2×#117C22×C1111yescharacteristic
403#449—24no—
404#416—24no—
405C2×#103C22×C1111yescharacteristic
406C2×#103C22×C1111yescharacteristic
407C2×#103C22×C1111yescharacteristic
408C2×#102C22×C1111yescharacteristic
409C2×#102C22×C1111yescharacteristic
410C2×#102C22×C1111yescharacteristic
411C2×#102C22×C1111yescharacteristic
412C2×#102C22×C1111yescharacteristic
413C2×C22⋊C8C22×C1111yescharacteristic
414C2×C22⋊C8C22×C1111yescharacteristic
415C2×C22⋊C8C22×C1111yescharacteristic
416#394—21no—
417#392—21no—
418#391C22×C1111yescharacteristic
419#390C22×C1111yescharacteristic
420#386—21no—
421#385—21no—
422#380C22×C1111yescharacteristic
423#340C22×C1111yescharacteristic
424#340C22×C1111yescharacteristic
425#340C22×C1111yescharacteristic
426#340C22×C1111yescharacteristic
427#340C22×C1111yescharacteristic
428#340C22×C1111yescharacteristic
429#336C22×C1111yescharacteristic
430#336C22×C1111yescharacteristic
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—41no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11—41no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11C2×#12011yescharacteristic
460C22×C11#54611yescharacteristic
461C22×C11#54611yescharacteristic
462C22×C11C2×#13511yescharacteristic
463C22×C11#57511yescharacteristic
464C22×C11#57611yescharacteristic
465C22×C11#57711yescharacteristic
466C4×C11—22no—
467C4×C11—22no—
468C4×C11—41no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—41no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—81no—
475C4×C11—81no—
476C4×C11#52511yescharacteristic
477C4×C11#53511yescharacteristic
478C4×C11#54611yescharacteristic
479C4×C11#54611yescharacteristic
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—41no—
485C2×#41—41no—
486C22×Q8—21no—
487C22×Q8C23×C1111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C1111yescharacteristic
493C22×D4C23×C1111yescharacteristic
494C22×D4C23×C1111yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C23×C1111yescharacteristic
498C23×C4C23×C1111yescharacteristic
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—41no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510C22×C8C23×C1111yescharacteristic
511C22×C8C23×C1111yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514#124—28no—
515#124—28no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—41no—
524#121D4×C1114yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529#117—28no—
530#117—22no—
531#117—22no—
532#117—22no—
533#117D4×C1114yescomplemented
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4D4×C1111yescharacteristic
537C2×C4⋊C4C23×C1111yescharacteristic
538C2×C4⋊C4C23×C1111yescharacteristic
539C2×C4⋊C4C23×C1111yescharacteristic
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C4⋊C4C23×C1111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4D4×C1111yescharacteristic
553C2×C22⋊C4D4×C1111yescharacteristic
554C2×C42—21no—
555C2×C42—21no—
556C2×C42C23×C1111yescharacteristic
557#103—22no—
558#103—22no—
559#103—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8—41no—
567C22⋊C8—41no—
568#95—21no—
569#95—21no—
570#95—21no—
571C2×C11—42no—
572C2×C11—81no—
573C2×C11—82no—
574C2×C11—82no—
575C2×C11#240411yescharacteristic
576C2×C11#300211yescharacteristic
577C2×C11#301211yescharacteristic
578C2×C11#330311yescharacteristic
579C2×C11#330511yescharacteristic
580C2×C11#331911yescharacteristic
581C2×C11#332111yescharacteristic
582C24—21no—
583C24—21no—
584C24C2×D4×C1111yescharacteristic
585C24C2×D4×C1111yescharacteristic
586#41—28no—
587#41—44no—
588#41—44no—
589#41—44no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—81no—
597C2×Q8—81no—
598C2×Q8C11×#4112yes—
599C2×D4—22no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C1112yes—
625C2×D4C11×#4112yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1111yescharacteristic
651C22×C4C2×D4×C1112yes—
652C22×C4C2×D4×C1112yes—
653C22×C4C2×D4×C1111yescharacteristic
654C22×C4C24×C1111yescharacteristic
655SD16—44no—
656D8—44no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—44no—
670C4⋊C4—24no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—42no—
680C4⋊C4C2×D4×C1112yes—
681C4⋊C4C2×D4×C1112yes—
682C4⋊C4C2×D4×C1112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—24no—
696C42—24no—
697C42—21no—
698C42—21no—
699C11#2396511yescharacteristic, direct product factor, Sylow
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23C11×#12012yes—
728C23C22×D4×C1111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733Q8—84no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—44no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746D4—84no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4C11×#12012yes—
786C2×C4C11×#13512yes—
787C2×C4C22×D4×C1111yescharacteristic
788C2×C4C22×D4×C1111yescharacteristic
789C2×C4C2×C11×#4111yescharacteristic
790C2×C4C2×C11×#4111yescharacteristic
791C2×C4C11×H(5,𝔽2)11yescharacteristic
792C2×C4C11×H(5,𝔽2)11yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×C11×#12011yescharacteristic
826C22C11×#54611yescharacteristic
827C22C11×#54611yescharacteristic
828C22C2×C11×#13511yescharacteristic
829C22C11×#57511yescharacteristic
830C22C11×#57611yescharacteristic
831C22C11×#57711yescharacteristic
832C4—22no—
833C4—22no—
834C4—41no—
835C4—42no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C11×#52511yescharacteristic
843C4C11×#53511yescharacteristic
844C4C11×#54611yescharacteristic
845C4C11×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C11×#240411yescharacteristic
851C2C11×#300211yescharacteristic
852C2C11×#301211yescharacteristic
853C2C11×#330311yescharacteristic
854C2C11×#330511yescharacteristic
855C2C11×#331911yescharacteristic
856C2C11×#332111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#555C2semidirect
2. C2×C11×#449C2semidirect
3. C2×C11×#416C2semidirect
4. C11×#2407C2semidirect
5. C11×#2024C2semidirect
6. C11×#2023C2semidirect
7. C11×#2000C2semidirect
8. C11×#1999C2semidirect
9. C11×#1893C2semidirect
10. C11×#1879C2semidirect
11. C11×#1877C2semidirect
12. C11×#1875C2semidirect
13. C11×#1873C2semidirect
14. C11×#1869C2semidirect
15. C11×#1825C2semidirect
107. C11×#121D4semidirect
116. C11×#117D4semidirect
154. #23965C11direct (N × H)
272. C2×#555C2×C11semidirect
273. C2×#449C2×C11semidirect
274. C2×#416C2×C11semidirect
275. #2407C2×C11semidirect
276. #2024C2×C11semidirect
277. #2023C2×C11semidirect
278. #2000C2×C11semidirect
279. #1999C2×C11semidirect
280. #1893C2×C11semidirect
281. #1879C2×C11semidirect
282. #1877C2×C11semidirect
283. #1875C2×C11semidirect
284. #1873C2×C11semidirect
285. #1869C2×C11semidirect
286. #1825C2×C11semidirect
524. #121D4×C11semidirect
533. #117D4×C11semidirect
699. C11#23965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4492
C2×C11×#4162
C11×#24072
C11×#20242
C11×#20232
C11×#20002
C11×#19992
C11×#18932
C11×#18792
C11×#18772
C11×#18752
C11×#18732
C11×#18692
C11×#18252
#2396511