Finite Group Databasebeta

← C11×#24221 #14601414

Subgroups — C11×#24221 #14601414

Order 2816.

1364 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic
5C2×C11×#451C211yesmaximal, characteristic, complemented
6C11×#2323C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2042C211yesmaximal, characteristic, complemented
9C11×#2016C211yesmaximal, characteristic, complemented
10C11×#2015C211yesmaximal, characteristic, complemented
11C11×#1983C211yesmaximal, characteristic, complemented
12C11×#1981C211yesmaximal, characteristic, complemented
13C11×#1798C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C11×#536—24no—
23C11×#536—24no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C2×C11×#123—21no—
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8—21no—
31C2×C11×C22⋊Q8—21no—
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#464—24no—
36C11×#462—24no—
37C11×#452—24no—
38C11×#451—24no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C11×#391C2211yescharacteristic
56C11×#389—21no—
57C11×#389C2211yescharacteristic
58C11×#388—21no—
59C11×#388—21no—
60C11×#387—21no—
61C11×#380C2211yescharacteristic
62C4×C11×C4⋊C4C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—21no—
74C22×Q8×C11—22no—
75C22×Q8×C11—22no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C2×C11×Q16—22no—
88C2×C11×Q16—22no—
89C2×C11×Q16—22no—
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—41no—
94C2×C11×Q16—41no—
95C2×C11×Q16—41no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—41no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×C4⋊Q8—22no—
104C11×C4⋊Q8—22no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8D414yes—
107C11×#124—22no—
108C11×#124—22no—
109C11×#124—22no—
110C11×#124D414yes—
111C11×#123—28no—
112C11×#123—28no—
113C11×C22⋊Q8—28no—
114C11×C22⋊Q8—28no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8D414yes—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C11×#117—22no—
120C11×#117—22no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4D411yescharacteristic
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11—21no—
142C2×C42×C11—21no—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C11×C4⋊C8—22no—
146C11×C4⋊C8—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—41no—
154C11×#103—41no—
155C11×#103—41no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×#95—21no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24221C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C11×#41—44no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—24no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—21no—
194C2×Q8×C11—44no—
195C2×Q8×C11—44no—
196C2×Q8×C11—44no—
197C2×Q8×C11—44no—
198C2×Q8×C11—42no—
199C2×Q8×C11—42no—
200C2×Q8×C11C2×D412yes—
201C2×Q8×C11C2×D412yes—
202C2×Q8×C11C2×D412yes—
203C2×Q8×C11C2×D412yes—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11C2×D412yes—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—24no—
218C22×C4×C11—24no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11C2411yescharacteristic
238C11×Q16—44no—
239C11×Q16—44no—
240C11×Q16—44no—
241C11×SD16—44no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—42no—
267C11×C4⋊C4—81no—
268C11×C4⋊C4C2×D412yes—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—81no—
277C42×C11—21no—
278C42×C11—21no—
279C42×C11—42no—
280C42×C11—81no—
281C42×C11C2×D412yes—
282C42×C11C2×D412yes—
283C2×#536C2×C1111yescharacteristic
284C2×#464C2×C1111yescharacteristic, complemented
285C2×#462C2×C1111yescharacteristic, complemented
286C2×#452C2×C1111yescharacteristic
287C2×#451C2×C1111yescharacteristic, complemented
288#2323C2×C1111yescharacteristic, complemented
289#2043C2×C1111yescharacteristic, complemented
290#2042C2×C1111yescharacteristic, complemented
291#2016C2×C1111yescharacteristic, complemented
292#2015C2×C1111yescharacteristic, complemented
293#1983C2×C1111yescharacteristic, complemented
294#1981C2×C1111yescharacteristic, complemented
295#1798C2×C1111yescharacteristic, complemented
296#1788C2×C1111yescharacteristic
297#1787C2×C1111yescharacteristic, complemented
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11#12112yes—
312C23×C11C22×D411yescharacteristic
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—48no—
322Q8×C11—41no—
323Q8×C11—41no—
324Q8×C11—41no—
325Q8×C11—41no—
326Q8×C11—41no—
327Q8×C11—41no—
328Q8×C11—41no—
329Q8×C11—41no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—48no—
333D4×C11—41no—
334D4×C11—41no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—48no—
357C2×C4×C11—48no—
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—41no—
373C2×C4×C11—41no—
374C2×C4×C11#12012yes—
375C2×C4×C11#12012yes—
376C2×C4×C11#12112yes—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C2×#4111yescharacteristic
381C2×C4×C11H(5,𝔽2)11yescharacteristic
382C2×C4×C11H(5,𝔽2)11yescharacteristic
383C8×C11—41no—
384C8×C11—41no—
385C8×C11—41no—
386C8×C11—41no—
387C22×#41C22×C1111yescharacteristic
388C23×Q8C22×C1111yescharacteristic
389C22×Q16C22×C1111yescharacteristic
390C22×Q16C22×C1111yescharacteristic
391C22×Q16C22×C1111yescharacteristic
392C22×SD16C22×C1111yescharacteristic
393#536—24no—
394#536—24no—
395C2×C4⋊Q8C22×C1111yescharacteristic
396C2×C4⋊Q8C22×C1111yescharacteristic
397C2×#124C22×C1111yescharacteristic
398C2×#124C22×C1111yescharacteristic
399C2×#123—21no—
400C2×#123—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C22×C1111yescharacteristic
404C2×C4×Q8C22×C1111yescharacteristic
405C2×#117C22×C1111yescharacteristic
406#464—24no—
407#462—24no—
408#452—24no—
409#451—24no—
410C2×C4⋊C8C22×C1111yescharacteristic
411C2×C4⋊C8C22×C1111yescharacteristic
412C2×#103C22×C1111yescharacteristic
413C2×#103C22×C1111yescharacteristic
414C2×#103C22×C1111yescharacteristic
415C2×#103C22×C1111yescharacteristic
416C2×#103C22×C1111yescharacteristic
417C2×#103C22×C1111yescharacteristic
418C2×#103C22×C1111yescharacteristic
419C2×#103C22×C1111yescharacteristic
420C2×#103C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×#102C22×C1111yescharacteristic
423C2×#102C22×C1111yescharacteristic
424C2×C22⋊C8C22×C1111yescharacteristic
425C2×C22⋊C8C22×C1111yescharacteristic
426#391C22×C1111yescharacteristic
427#389—21no—
428#389C22×C1111yescharacteristic
429#388—21no—
430#388—21no—
431#387—21no—
432#380C22×C1111yescharacteristic
433C4×C4⋊C4C22×C1111yescharacteristic
434#336C22×C1111yescharacteristic
435#336C22×C1111yescharacteristic
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—81no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11C2×#12011yescharacteristic
451C22×C11C2×#12111yescharacteristic
452C22×C11#53511yescharacteristic
453C22×C11#57711yescharacteristic
454C22×C11#57811yescharacteristic
455C22×C11#57811yescharacteristic
456C22×C11#57811yescharacteristic
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—41no—
465C4×C11—41no—
466C4×C11—42no—
467C4×C11—81no—
468C4×C11—81no—
469C4×C11D4211yescharacteristic
470C4×C11D4211yescharacteristic
471C4×C11#54611yescharacteristic
472C4×C11#54611yescharacteristic
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—41no—
478C2×#41—41no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8C23×C1111yescharacteristic
487C22×Q8C23×C1111yescharacteristic
488C22×Q8C23×C1111yescharacteristic
489C22×Q8C23×C1111yescharacteristic
490C22×D4—21no—
491C22×D4C23×C1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C1111yescharacteristic
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16—22no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C22×C8C23×C1111yescharacteristic
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510C22×C8C23×C1111yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8D4×C1114yes—
515#124—22no—
516#124—22no—
517#124—22no—
518#124D4×C1114yes—
519#123—28no—
520#123—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—22no—
524C22⋊Q8D4×C1114yes—
525C4×Q8—22no—
526C4×Q8—22no—
527#117—22no—
528#117—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4D4×C1111yescharacteristic
537C2×C4⋊C4D4×C1111yescharacteristic
538C2×C4⋊C4C23×C1111yescharacteristic
539C2×C4⋊C4C23×C1111yescharacteristic
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C1111yescharacteristic
548C2×C22⋊C4D4×C1111yescharacteristic
549C2×C42—21no—
550C2×C42—21no—
551C2×C42C23×C1111yescharacteristic
552C2×C42C23×C1111yescharacteristic
553C4⋊C8—22no—
554C4⋊C8—22no—
555#103—22no—
556#103—22no—
557#103—22no—
558#103—22no—
559#103—22no—
560#103—22no—
561#103—41no—
562#103—41no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574C2×C11—42no—
575C2×C11—82no—
576C2×C11#240811yescharacteristic
577C2×C11#301111yescharacteristic
578C2×C11#301311yescharacteristic
579C2×C11#304411yescharacteristic
580C2×C11#304611yescharacteristic
581C2×C11#322311yescharacteristic
582C2×C11#322511yescharacteristic
583C24—21no—
584C24C2×D4×C1111yescharacteristic
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—42no—
615C2×Q8—42no—
616C2×Q8C2×D4×C1112yes—
617C2×Q8C2×D4×C1112yes—
618C2×Q8C2×D4×C1112yes—
619C2×Q8C2×D4×C1112yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4C2×D4×C1112yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4C2×D4×C1111yescharacteristic
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1111yescharacteristic
651C22×C4C2×D4×C1112yes—
652C22×C4C11×#4112yes—
653C22×C4C24×C1111yescharacteristic
654Q16—44no—
655Q16—44no—
656Q16—44no—
657SD16—44no—
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—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—81no—
684C4⋊C4C2×D4×C1112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—81no—
693C42—21no—
694C42—21no—
695C42—42no—
696C42—81no—
697C42C2×D4×C1112yes—
698C42C2×D4×C1112yes—
699C11#2422111yescharacteristic, direct product factor, Sylow
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23C11×#12112yes—
714C23C22×D4×C1111yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—41no—
736D4—41no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
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×C4C11×#12012yes—
777C2×C4C11×#12012yes—
778C2×C4C11×#12112yes—
779C2×C4C22×D4×C1111yescharacteristic
780C2×C4C22×D4×C1111yescharacteristic
781C2×C4C22×D4×C1111yescharacteristic
782C2×C4C2×C11×#4111yescharacteristic
783C2×C4C11×H(5,𝔽2)11yescharacteristic
784C2×C4C11×H(5,𝔽2)11yescharacteristic
785C8—41no—
786C8—41no—
787C8—41no—
788C8—41no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×C11×#12011yescharacteristic
804C22C2×C11×#12111yescharacteristic
805C22C11×#53511yescharacteristic
806C22C11×#57711yescharacteristic
807C22C11×#57811yescharacteristic
808C22C11×#57811yescharacteristic
809C22C11×#57811yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—42no—
820C4—81no—
821C4—81no—
822C4D42×C1111yescharacteristic
823C4D42×C1111yescharacteristic
824C4C11×#54611yescharacteristic
825C4C11×#54611yescharacteristic
826C2—42no—
827C2—82no—
828C2C11×#240811yescharacteristic
829C2C11×#301111yescharacteristic
830C2C11×#301311yescharacteristic
831C2C11×#304411yescharacteristic
832C2C11×#304611yescharacteristic
833C2C11×#322311yescharacteristic
834C2C11×#322511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#464C2semidirect
3. C2×C11×#462C2semidirect
5. C2×C11×#451C2semidirect
6. C11×#2323C2semidirect
7. C11×#2043C2semidirect
8. C11×#2042C2semidirect
9. C11×#2016C2semidirect
10. C11×#2015C2semidirect
11. C11×#1983C2semidirect
12. C11×#1981C2semidirect
13. C11×#1798C2semidirect
15. C11×#1787C2semidirect
166. #24221C11direct (N × H)
284. C2×#464C2×C11semidirect
285. C2×#462C2×C11semidirect
287. C2×#451C2×C11semidirect
288. #2323C2×C11semidirect
289. #2043C2×C11semidirect
290. #2042C2×C11semidirect
291. #2016C2×C11semidirect
292. #2015C2×C11semidirect
293. #1983C2×C11semidirect
294. #1981C2×C11semidirect
295. #1798C2×C11semidirect
297. #1787C2×C11semidirect
699. C11#24221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4642
C2×C11×#4622
C2×C11×#4522
C2×C11×#4512
C11×#23232
C11×#20432
C11×#20422
C11×#20162
C11×#20152
C11×#19832
C11×#19812
C11×#17982
C11×#17882
C11×#17872
#2422111