Finite Group Databasebeta

← C11×#24392 #14601585

Subgroups — C11×#24392 #14601585

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#467C211yesmaximal, characteristic, complemented
4C2×C11×#451C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic
6C11×#2616C211yesmaximal, characteristic
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2001C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C11×#1892C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C11×#536—24no—
23C11×#536—24no—
24C2×C11×C4⋊Q8—21no—
25C2×C11×#124—21no—
26C2×C11×#123—21no—
27C2×C11×#123—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C11×#470—24no—
37C11×#467—24no—
38C11×#451—24no—
39C2×C11×#107C2211yescharacteristic
40C2×C11×#106C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C11×#408—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#395—21no—
55C11×#394—21no—
56C11×#394—21no—
57C11×#394—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
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×C11D411yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11D411yescharacteristic
83C22×D4×C11D411yescharacteristic
84C22×D4×C11D411yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
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×M16—22no—
96C2×C11×M16—22no—
97C2×C11×M16—41no—
98C22×C8×C11—22no—
99C22×C8×C11—22no—
100C22×C8×C11—41no—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C4⋊Q8—28no—
106C11×#124—28no—
107C11×#123—28no—
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—41no—
120C11×C22⋊Q8—41no—
121C11×C22⋊Q8D414yes—
122C11×C22⋊Q8D414yes—
123C11×#117—22no—
124C11×#117—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C42×C11—21no—
149C11×#107—22no—
150C11×#106—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—22no—
156C11×#103—22no—
157C11×#103—41no—
158C11×#103—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8D414yes—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24392C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11C2×D411yescharacteristic
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C2×Q8×C11—24no—
175C2×Q8×C11—22no—
176C2×Q8×C11—22no—
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—41no—
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×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—41no—
209C2×D4×C11—41no—
210C2×D4×C11—41no—
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—24no—
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—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D412yes—
242C22×C4×C11#4112yes—
243C22×C4×C11C2411yescharacteristic
244C11×Q16—44no—
245C11×Q16—44no—
246C11×M16—44no—
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—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—44no—
258C2×C8×C11C2×D412yes—
259C2×C8×C11C2×D412yes—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—24no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—42no—
273C11×C4⋊C4—42no—
274C11×C4⋊C4—42no—
275C11×C4⋊C4C2×D412yes—
276C11×C4⋊C4C2×D412yes—
277C11×C22⋊C4—24no—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—81no—
286C11×C22⋊C4—81no—
287C11×C22⋊C4—81no—
288C42×C11—24no—
289C2×#536C2×C1111yescharacteristic
290C2×#470C2×C1111yescharacteristic, complemented
291C2×#467C2×C1111yescharacteristic, complemented
292C2×#451C2×C1111yescharacteristic, complemented
293C2×#408C2×C1111yescharacteristic
294#2616C2×C1111yescharacteristic
295#2036C2×C1111yescharacteristic, complemented
296#2035C2×C1111yescharacteristic, complemented
297#2001C2×C1111yescharacteristic, complemented
298#2001C2×C1111yescharacteristic, complemented
299#1894C2×C1111yescharacteristic, complemented
300#1892C2×C1111yescharacteristic, complemented
301#1873C2×C1111yescharacteristic, complemented
302#1854C2×C1111yescharacteristic, complemented
303#1787C2×C1111yescharacteristic, complemented
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11#12012yes—
324C23×C11#12112yes—
325C23×C11C22×D411yescharacteristic
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—44no—
331Q8×C11—48no—
332Q8×C11—41no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11—41no—
336Q8×C11—41no—
337Q8×C11—41no—
338Q8×C11—41no—
339Q8×C11—41no—
340D4×C11—44no—
341D4×C11—44no—
342D4×C11—44no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
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—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—48no—
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—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11#12012yes—
388C2×C4×C11#12112yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C2×#4111yescharacteristic
393C2×C4×C11H(5,𝔽2)11yescharacteristic
394C2×C4×C11H(5,𝔽2)11yescharacteristic
395C8×C11—22no—
396C8×C11—22no—
397C8×C11—41no—
398C8×C11—41no—
399C22×#41C22×C1111yescharacteristic
400C23×Q8C22×C1111yescharacteristic
401C22×Q16C22×C1111yescharacteristic
402C22×Q16C22×C1111yescharacteristic
403C22×M16C22×C1111yescharacteristic
404C23×C8C22×C1111yescharacteristic
405#536—24no—
406#536—24no—
407C2×C4⋊Q8—21no—
408C2×#124—21no—
409C2×#123—21no—
410C2×#123—21no—
411C2×C22⋊Q8C22×C1111yescharacteristic
412C2×C22⋊Q8C22×C1111yescharacteristic
413C2×C22⋊Q8C22×C1111yescharacteristic
414C2×C22⋊Q8C22×C1111yescharacteristic
415C2×C22⋊Q8C22×C1111yescharacteristic
416C2×C22⋊Q8C22×C1111yescharacteristic
417C2×C22⋊Q8C22×C1111yescharacteristic
418C2×#117C22×C1111yescharacteristic
419#470—24no—
420#467—24no—
421#451—24no—
422C2×#107C22×C1111yescharacteristic
423C2×#106C22×C1111yescharacteristic
424C2×#103C22×C1111yescharacteristic
425C2×#103C22×C1111yescharacteristic
426C2×#103C22×C1111yescharacteristic
427C2×#103C22×C1111yescharacteristic
428C2×#103C22×C1111yescharacteristic
429C2×#103C22×C1111yescharacteristic
430C2×#103C22×C1111yescharacteristic
431C2×#103C22×C1111yescharacteristic
432#408—24no—
433C2×C22⋊C8C22×C1111yescharacteristic
434C2×C22⋊C8C22×C1111yescharacteristic
435C2×C22⋊C8C22×C1111yescharacteristic
436C2×C22⋊C8C22×C1111yescharacteristic
437#395—21no—
438#394—21no—
439#394—21no—
440#394—21no—
441#380C22×C1111yescharacteristic
442#380C22×C1111yescharacteristic
443#380C22×C1111yescharacteristic
444#340C22×C1111yescharacteristic
445#340C22×C1111yescharacteristic
446#340C22×C1111yescharacteristic
447#340C22×C1111yescharacteristic
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
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—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11C2×#12011yescharacteristic
470C22×C11C2×#12111yescharacteristic
471C22×C11#53411yescharacteristic
472C22×C11#57711yescharacteristic
473C22×C11#57811yescharacteristic
474C22×C11#57811yescharacteristic
475C22×C11#57811yescharacteristic
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—41no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11D4211yescharacteristic
488C4×C11D4211yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—21no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8D4×C1111yescharacteristic
505C22×Q8C23×C1111yescharacteristic
506C22×Q8C23×C1111yescharacteristic
507C22×Q8C23×C1111yescharacteristic
508C22×D4D4×C1111yescharacteristic
509C22×D4D4×C1111yescharacteristic
510C22×D4D4×C1111yescharacteristic
511C23×C4—21no—
512C23×C4C23×C1111yescharacteristic
513C23×C4C23×C1111yescharacteristic
514C23×C4C23×C1111yescharacteristic
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8C23×C1111yescharacteristic
528C22×C8C23×C1111yescharacteristic
529C22×C8C23×C1111yescharacteristic
530C22×C8C23×C1111yescharacteristic
531C4⋊Q8—28no—
532#124—28no—
533#123—28no—
534#123—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—41no—
546C22⋊Q8—41no—
547C22⋊Q8D4×C1114yes—
548C22⋊Q8D4×C1114yes—
549#117—22no—
550#117—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4C23×C1111yescharacteristic
559C2×C4⋊C4C23×C1111yescharacteristic
560C2×C4⋊C4C23×C1111yescharacteristic
561C2×C4⋊C4C23×C1111yescharacteristic
562C2×C4⋊C4C23×C1111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C42—21no—
575#107—22no—
576#106—22no—
577#103—22no—
578#103—22no—
579#103—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583#103—41no—
584#103—41no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8D4×C1114yes—
589#95—21no—
590#95—21no—
591#95—21no—
592C2×C11—42no—
593C2×C11—42no—
594C2×C11—81no—
595C2×C11#241011yescharacteristic
596C2×C11#301111yescharacteristic
597C2×C11#301311yescharacteristic
598C2×C11#305911yescharacteristic
599C2×C11#306311yescharacteristic
600C2×C11#320111yescharacteristic
601C2×C11#320211yescharacteristic
602C24C2×D4×C1111yescharacteristic
603C24C2×D4×C1111yescharacteristic
604C24C2×D4×C1111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—24no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—41no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—42no—
634C2×Q8—42no—
635C2×Q8C2×D4×C1112yes—
636C2×Q8C2×D4×C1112yes—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—41no—
644C2×D4—41no—
645C2×D4—41no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4C2×D4×C1111yescharacteristic
672C22×C4C2×D4×C1111yescharacteristic
673C22×C4C2×D4×C1112yes—
674C22×C4C2×D4×C1112yes—
675C22×C4C2×D4×C1111yescharacteristic
676C22×C4C2×D4×C1112yes—
677C22×C4C11×#4112yes—
678C22×C4C24×C1111yescharacteristic
679Q16—44no—
680Q16—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—44no—
693C2×C8C2×D4×C1112yes—
694C2×C8C2×D4×C1112yes—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4C2×D4×C1112yes—
711C4⋊C4C2×D4×C1112yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4—81no—
723C42—24no—
724C11#2439211yescharacteristic, direct product factor, Sylow
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23C11×#12012yes—
745C23C11×#12112yes—
746C23C22×D4×C1111yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—44no—
752Q8—48no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761D4—44no—
762D4—44no—
763D4—44no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
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—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
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×C4—41no—
807C2×C4—41no—
808C2×C4C11×#12012yes—
809C2×C4C11×#12112yes—
810C2×C4C22×D4×C1111yescharacteristic
811C2×C4C22×D4×C1111yescharacteristic
812C2×C4C22×D4×C1111yescharacteristic
813C2×C4C2×C11×#4111yescharacteristic
814C2×C4C11×H(5,𝔽2)11yescharacteristic
815C2×C4C11×H(5,𝔽2)11yescharacteristic
816C8—22no—
817C8—22no—
818C8—41no—
819C8—41no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
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—41no—
841C22C2×C11×#12011yescharacteristic
842C22C2×C11×#12111yescharacteristic
843C22C11×#53411yescharacteristic
844C22C11×#57711yescharacteristic
845C22C11×#57811yescharacteristic
846C22C11×#57811yescharacteristic
847C22C11×#57811yescharacteristic
848C4—22no—
849C4—22no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4D42×C1111yescharacteristic
860C4D42×C1111yescharacteristic
861C4C11×#54611yescharacteristic
862C4C11×#54611yescharacteristic
863C2—42no—
864C2—42no—
865C2—81no—
866C2C11×#241011yescharacteristic
867C2C11×#301111yescharacteristic
868C2C11×#301311yescharacteristic
869C2C11×#305911yescharacteristic
870C2C11×#306311yescharacteristic
871C2C11×#320111yescharacteristic
872C2C11×#320211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#470C2semidirect
3. C2×C11×#467C2semidirect
4. C2×C11×#451C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#2001C2semidirect
10. C11×#2001C2semidirect
11. C11×#1894C2semidirect
12. C11×#1892C2semidirect
13. C11×#1873C2semidirect
14. C11×#1854C2semidirect
15. C11×#1787C2semidirect
166. #24392C11direct (N × H)
290. C2×#470C2×C11semidirect
291. C2×#467C2×C11semidirect
292. C2×#451C2×C11semidirect
295. #2036C2×C11semidirect
296. #2035C2×C11semidirect
297. #2001C2×C11semidirect
298. #2001C2×C11semidirect
299. #1894C2×C11semidirect
300. #1892C2×C11semidirect
301. #1873C2×C11semidirect
302. #1854C2×C11semidirect
303. #1787C2×C11semidirect
724. C11#24392direct (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×#4702
C2×C11×#4672
C2×C11×#4512
C2×C11×#4082
C11×#26162
C11×#20362
C11×#20352
C11×#20012
C11×#18942
C11×#18922
C11×#18732
C11×#18542
C11×#17872
#2439211