Finite Group Databasebeta

← C11×#24008 #14601201

Subgroups — C11×#24008 #14601201

Order 2816.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic, complemented
3C2×C11×#482C211yesmaximal, characteristic, complemented
4C11×#2280C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1875C211yesmaximal, characteristic, complemented
10C11×#1873C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic, complemented
12C11×#1854C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1779C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C11×#525—24no—
19C11×#525—24no—
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11—21no—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C11×#485—24no—
32C11×#482—24no—
33C2×C11×#107C2211yescharacteristic, complemented
34C2×C11×#107C2211yescharacteristic, complemented
35C2×C11×#106C2211yescharacteristic, complemented
36C2×C11×#106C2211yescharacteristic, complemented
37C2×C11×#103C2211yescharacteristic, complemented
38C2×C11×#103C2211yescharacteristic, complemented
39C2×C11×#103C2211yescharacteristic, complemented
40C2×C11×#103C2211yescharacteristic, complemented
41C2×C11×#102C2211yescharacteristic, complemented
42C2×C11×#102C2211yescharacteristic, complemented
43C2×C11×#102C2211yescharacteristic, complemented
44C2×C11×#102C2211yescharacteristic, complemented
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C11×#381—21no—
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C11×#380C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C11×#379—21no—
57C4×C11×C22⋊C4—21no—
58C4×C11×C22⋊C4—21no—
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C25×C11D411yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—21no—
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—22no—
77C23×C4×C11—22no—
78C23×C4×C11—22no—
79C23×C4×C11—22no—
80C23×C4×C11—41no—
81C23×C4×C11—41no—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#123—28no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8D414yes—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121D414yes—
101C11×#120—28no—
102C4×D4×C11—28no—
103C4×D4×C11—28no—
104C11×#117—22no—
105C11×#117—22no—
106C11×#117—22no—
107C11×#117—22no—
108C11×#117—41no—
109C11×#117—41no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11—21no—
132C11×#107—22no—
133C11×#107—22no—
134C11×#106—22no—
135C11×#106—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—41no—
139C11×#103—41no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#102—41no—
144C11×C22⋊C8—22no—
145C11×C22⋊C8—22no—
146C11×C22⋊C8—22no—
147C11×C22⋊C8—22no—
148C11×C22⋊C8—41no—
149C11×C22⋊C8—41no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#24008C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—21no—
159C24×C11—41no—
160C24×C11—41no—
161C24×C11—41no—
162C24×C11—41no—
163C24×C11C2×D411yescharacteristic
164C24×C11C2×D411yescharacteristic
165C24×C11C2×D411yescharacteristic
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C2×D412yes—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11—42no—
190C2×D4×C11C2×D412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—24no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
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—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—41no—
220C22×C4×C11—41no—
221C22×C4×C11—41no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11#4112yes—
234C22×C4×C11#4112yes—
235C22×C4×C11C2411yescharacteristic
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—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4C2×D412yes—
261C11×C4⋊C4C2×D412yes—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—42no—
269C11×C22⋊C4—42no—
270C11×C22⋊C4—42no—
271C11×C22⋊C4—42no—
272C11×C22⋊C4—42no—
273C42×C11—24no—
274C42×C11—42no—
275C42×C11—42no—
276C2×#525C2×C1111yescharacteristic
277C2×#485C2×C1111yescharacteristic, complemented
278C2×#482C2×C1111yescharacteristic, complemented
279#2280C2×C1111yescharacteristic, complemented
280#2036C2×C1111yescharacteristic, complemented
281#2035C2×C1111yescharacteristic, complemented
282#2034C2×C1111yescharacteristic, complemented
283#2033C2×C1111yescharacteristic, complemented
284#1875C2×C1111yescharacteristic, complemented
285#1873C2×C1111yescharacteristic, complemented
286#1854C2×C1111yescharacteristic, complemented
287#1854C2×C1111yescharacteristic, complemented
288#1788C2×C1111yescharacteristic, complemented
289#1788C2×C1111yescharacteristic, complemented
290#1779C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—22no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11#12012yes—
324C23×C11#12312yes—
325C23×C11#13512yes—
326C23×C11C22×D411yescharacteristic
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—41no—
330Q8×C11—41no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—48no—
334D4×C11—48no—
335D4×C11—48no—
336D4×C11—41no—
337D4×C11—41no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
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—22no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—48no—
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—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11#12012yes—
383C2×C4×C11#12312yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C2×#4111yescharacteristic
387C2×C4×C11C2×#4111yescharacteristic
388C2×C4×C11H(5,𝔽2)11yescharacteristic
389C2×C4×C11H(5,𝔽2)11yescharacteristic
390C8×C11—41no—
391C8×C11—41no—
392C8×C11—41no—
393C8×C11—41no—
394C22×#41C22×C1111yescharacteristic
395C24×C4C22×C1111yescharacteristic
396#525—24no—
397#525—24no—
398C2×#123—21no—
399C2×C22⋊Q8C22×C1111yescharacteristic
400C2×C22⋊Q8C22×C1111yescharacteristic
401C2×#121C22×C1111yescharacteristic
402C2×#121C22×C1111yescharacteristic
403C2×#120—21no—
404C2×C4×D4—21no—
405C2×C4×D4—21no—
406C2×#117C22×C1111yescharacteristic
407C2×#117C22×C1111yescharacteristic
408C2×#117C22×C1111yescharacteristic
409#485—24no—
410#482—24no—
411C2×#107C22×C1111yescharacteristic, complemented
412C2×#107C22×C1111yescharacteristic, complemented
413C2×#106C22×C1111yescharacteristic, complemented
414C2×#106C22×C1111yescharacteristic, complemented
415C2×#103C22×C1111yescharacteristic, complemented
416C2×#103C22×C1111yescharacteristic, complemented
417C2×#103C22×C1111yescharacteristic, complemented
418C2×#103C22×C1111yescharacteristic, complemented
419C2×#102C22×C1111yescharacteristic, complemented
420C2×#102C22×C1111yescharacteristic, complemented
421C2×#102C22×C1111yescharacteristic, complemented
422C2×#102C22×C1111yescharacteristic, complemented
423C2×C22⋊C8C22×C1111yescharacteristic
424C2×C22⋊C8C22×C1111yescharacteristic
425C2×C22⋊C8C22×C1111yescharacteristic
426C2×C22⋊C8C22×C1111yescharacteristic
427C2×C22⋊C8C22×C1111yescharacteristic
428C2×C22⋊C8C22×C1111yescharacteristic
429#381—21no—
430#380C22×C1111yescharacteristic
431#380C22×C1111yescharacteristic
432#380C22×C1111yescharacteristic
433#380C22×C1111yescharacteristic
434#379—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437#340C22×C1111yescharacteristic, complemented
438#340C22×C1111yescharacteristic, complemented
439#340C22×C1111yescharacteristic, complemented
440#340C22×C1111yescharacteristic, complemented
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—416no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—41no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C2×#12011yescharacteristic
471C22×C11C2×#12311yescharacteristic
472C22×C11#53411yescharacteristic
473C22×C11C2×#13511yescharacteristic
474C22×C11#57511yescharacteristic
475C22×C11#57511yescharacteristic
476C22×C11#57511yescharacteristic
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—41no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491C25D4×C1111yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C1111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C23×C1111yescharacteristic
503C23×C4—21no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4D4×C1111yescharacteristic
511C23×C4D4×C1111yescharacteristic
512C23×C4D4×C1111yescharacteristic
513C23×C4C23×C1111yescharacteristic
514C23×C4C23×C1111yescharacteristic
515C23×C4C23×C1111yescharacteristic
516C22×C8C23×C1111yescharacteristic
517C22×C8C23×C1111yescharacteristic
518C22×C8C23×C1111yescharacteristic
519C22×C8C23×C1111yescharacteristic
520#123—28no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8D4×C1114yes—
525#121—22no—
526#121—22no—
527#121—22no—
528#121D4×C1114yes—
529#120—28no—
530C4×D4—28no—
531C4×D4—28no—
532#117—22no—
533#117—22no—
534#117—22no—
535#117—22no—
536#117—41no—
537#117—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C4⋊C4C23×C1111yescharacteristic
542C2×C4⋊C4C23×C1111yescharacteristic
543C2×C4⋊C4C23×C1111yescharacteristic
544C2×C4⋊C4C23×C1111yescharacteristic
545C2×C4⋊C4C23×C1111yescharacteristic
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⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560#107—22no—
561#107—22no—
562#106—22no—
563#106—22no—
564#103—22no—
565#103—22no—
566#103—41no—
567#103—41no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102—41no—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575C22⋊C8—22no—
576C22⋊C8—41no—
577C22⋊C8—41no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95—21no—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—42no—
585C2×C11—82no—
586C2×C11#240511yescharacteristic
587C2×C11#300211yescharacteristic
588C2×C11#300511yescharacteristic
589C2×C11#309111yescharacteristic
590C2×C11#309311yescharacteristic
591C2×C11#319111yescharacteristic
592C2×C11#319711yescharacteristic
593C24—22no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—41no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24C2×D4×C1111yescharacteristic
602C24C2×D4×C1111yescharacteristic
603C24C2×D4×C1111yescharacteristic
604#41—44no—
605#41—44no—
606#41—44no—
607#41—44no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8C2×D4×C1112yes—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4C2×D4×C1112yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4C2×D4×C1111yescharacteristic
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C2×D4×C1112yes—
669C22×C4C2×D4×C1112yes—
670C22×C4C2×D4×C1111yescharacteristic
671C22×C4C11×#4112yes—
672C22×C4C11×#4112yes—
673C22×C4C24×C1111yescharacteristic
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4C2×D4×C1112yes—
699C4⋊C4C2×D4×C1112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C42—24no—
712C42—42no—
713C42—42no—
714C11#2400811yescharacteristic, direct product factor, Sylow
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C11×#12012yes—
748C23C11×#12312yes—
749C23C11×#13512yes—
750C23C22×D4×C1111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4C11×#12012yes—
807C2×C4C11×#12312yes—
808C2×C4C22×D4×C1111yescharacteristic
809C2×C4C22×D4×C1111yescharacteristic
810C2×C4C2×C11×#4111yescharacteristic
811C2×C4C2×C11×#4111yescharacteristic
812C2×C4C11×H(5,𝔽2)11yescharacteristic
813C2×C4C11×H(5,𝔽2)11yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×C11×#12011yescharacteristic
848C22C2×C11×#12311yescharacteristic
849C22C11×#53411yescharacteristic
850C22C2×C11×#13511yescharacteristic
851C22C11×#57511yescharacteristic
852C22C11×#57511yescharacteristic
853C22C11×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4C11×#54611yescharacteristic
865C4C11×#54611yescharacteristic
866C4C11×#54611yescharacteristic
867C4C11×#54611yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C11×#240511yescharacteristic
873C2C11×#300211yescharacteristic
874C2C11×#300511yescharacteristic
875C2C11×#309111yescharacteristic
876C2C11×#309311yescharacteristic
877C2C11×#319111yescharacteristic
878C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#485C2semidirect
3. C2×C11×#482C2semidirect
4. C11×#2280C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1875C2semidirect
10. C11×#1873C2semidirect
11. C11×#1854C2semidirect
12. C11×#1854C2semidirect
13. C11×#1788C2semidirect
14. C11×#1788C2semidirect
15. C11×#1779C2semidirect
33. C2×C11×#107C22semidirect
34. C2×C11×#107C22semidirect
35. C2×C11×#106C22semidirect
36. C2×C11×#106C22semidirect
37. C2×C11×#103C22semidirect
38. C2×C11×#103C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#103C22semidirect
41. C2×C11×#102C22semidirect
42. C2×C11×#102C22semidirect
43. C2×C11×#102C22semidirect
44. C2×C11×#102C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
154. #24008C11direct (N × H)
277. C2×#485C2×C11semidirect
278. C2×#482C2×C11semidirect
279. #2280C2×C11semidirect
280. #2036C2×C11semidirect
281. #2035C2×C11semidirect
282. #2034C2×C11semidirect
283. #2033C2×C11semidirect
284. #1875C2×C11semidirect
285. #1873C2×C11semidirect
286. #1854C2×C11semidirect
287. #1854C2×C11semidirect
288. #1788C2×C11semidirect
289. #1788C2×C11semidirect
290. #1779C2×C11semidirect
411. C2×#107C22×C11semidirect
412. C2×#107C22×C11semidirect
413. C2×#106C22×C11semidirect
414. C2×#106C22×C11semidirect
415. C2×#103C22×C11semidirect
416. C2×#103C22×C11semidirect
417. C2×#103C22×C11semidirect
418. C2×#103C22×C11semidirect
419. C2×#102C22×C11semidirect
420. C2×#102C22×C11semidirect
421. C2×#102C22×C11semidirect
422. C2×#102C22×C11semidirect
437. #340C22×C11semidirect
438. #340C22×C11semidirect
439. #340C22×C11semidirect
440. #340C22×C11semidirect
714. C11#24008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4852
C2×C11×#4822
C11×#22802
C11×#20362
C11×#20352
C11×#20342
C11×#20332
C11×#18752
C11×#18732
C11×#18542
C11×#17882
C11×#17792
#2400811