Finite Group Databasebeta

← C11×#14074 #14591267

Subgroups — C11×#14074 #14591267

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#388C211yesmaximal, characteristic
2C2×C11×#388C211yesmaximal, characteristic
3C2×C11×#376C211yesmaximal, characteristic, complemented
4C11×#1442C211yesmaximal, characteristic, complemented
5C11×#1441C211yesmaximal, characteristic, complemented
6C11×#1440C211yesmaximal, characteristic
7C11×#1439C211yesmaximal, characteristic
8C11×#1437C211yesmaximal, characteristic
9C11×#1437C211yesmaximal, characteristic
10C11×#1437C211yesmaximal, characteristic
11C11×#1436C211yesmaximal, characteristic, complemented
12C11×C4⋊#95C211yesmaximal, characteristic, complemented
13C11×#1434C211yesmaximal, characteristic, complemented
14C11×#1434C211yesmaximal, characteristic, complemented
15C4×C11×#95C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C11×#388—24no—
32C11×#388C418yescomplemented
33C11×#376—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2×C414yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C11×C22⋊C4C2×C414yes—
98C2×C11×C22⋊C4C2×C414yes—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11—22no—
108C2×C42×C11—22no—
109C2×C42×C11—22no—
110C2×C42×C11—41no—
111C2×C42×C11—41no—
112C2×C42×C11C2×C414yes—
113C2×C42×C11D414yes—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—41no—
128C11×#95—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95C2×C414yes—
133C11×#95C2×C414yes—
134#14074C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11C22×C412yes—
150C24×C11C2411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
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—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
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—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
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—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C22×C412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11#4112yes—
241C22×C4×C11#4112yes—
242C22×C4×C11#4112yes—
243C22×C4×C11#4112yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
246C22×C4×C11#4112yes—
247C22×C4×C11#4112yes—
248C22×C4×C11#4112yes—
249C11×C4⋊C4—44no—
250C11×C4⋊C4—44no—
251C11×C4⋊C4—44no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—44no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C11×C22⋊C4—44no—
258C11×C22⋊C4—44no—
259C42×C11—28no—
260C42×C11—28no—
261C42×C11—28no—
262C42×C11—44no—
263C42×C11—44no—
264C2×#388C2×C1111yescharacteristic
265C2×#388C2×C1111yescharacteristic
266C2×#376C2×C1111yescharacteristic, complemented
267#1442C2×C1111yescharacteristic, complemented
268#1441C2×C1111yescharacteristic, complemented
269#1440C2×C1111yescharacteristic
270#1439C2×C1111yescharacteristic
271#1437C2×C1111yescharacteristic
272#1437C2×C1111yescharacteristic
273#1437C2×C1111yescharacteristic
274#1436C2×C1111yescharacteristic, complemented
275C4⋊#95C2×C1111yescharacteristic, complemented
276#1434C2×C1111yescharacteristic, complemented
277#1434C2×C1111yescharacteristic, complemented
278C4×#95C2×C1111yescharacteristic, complemented
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
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×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C112−1+411yescharacteristic
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
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—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—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
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—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11#11714yes—
425C2×C4×C11C4×D414yes—
426C2×C4×C11#12314yes—
427C22×C4⋊C4C22×C1111yescharacteristic
428C22×C4⋊C4C22×C1111yescharacteristic
429C22×C4⋊C4C22×C1111yescharacteristic
430C22×C22⋊C4C22×C1111yescharacteristic
431C22×C22⋊C4C22×C1111yescharacteristic
432C22×C22⋊C4C22×C1111yescharacteristic
433C22×C22⋊C4C22×C1111yescharacteristic
434C22×C22⋊C4C22×C1111yescharacteristic
435C22×C22⋊C4C22×C1111yescharacteristic
436C22×C22⋊C4C22×C1111yescharacteristic
437C22×C42C22×C1111yescharacteristic
438C22×C42C22×C1111yescharacteristic
439C22×C42C22×C1111yescharacteristic
440C22×C42C22×C1111yescharacteristic
441C22×C42C22×C1111yescharacteristic
442#388—24no—
443#388C4×C1118yescomplemented
444#376—24no—
445C2×#95C22×C1111yescharacteristic
446C2×#95C22×C1111yescharacteristic
447C2×#95C22×C1111yescharacteristic
448C2×#95C22×C1111yescharacteristic
449C2×#95C22×C1111yescharacteristic
450C2×#95C22×C1111yescharacteristic
451C2×#95C22×C1111yescharacteristic
452C2×#95C22×C1111yescharacteristic
453C2×#95C22×C1111yescharacteristic
454C2×#95C22×C1111yescharacteristic
455C2×#95C22×C1111yescharacteristic
456C2×#95C22×C1111yescharacteristic
457C2×#95C22×C1111yescharacteristic
458C2×#95C22×C1111yescharacteristic
459C2×#95C22×C1111yescharacteristic
460C2×#95C22×C1111yescharacteristic
461C2×#95C22×C1111yescharacteristic
462C2×#95C22×C1111yescharacteristic
463C2×#95C22×C1111yescharacteristic
464C2×#95C22×C1111yescharacteristic
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11C2×#11711yescharacteristic
481C22×C11C2×C4×D411yescharacteristic
482C22×C11C4×#4111yescharacteristic
483C22×C11C4×#4111yescharacteristic
484C22×C11C4×#4111yescharacteristic
485C22×C11#51811yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11C2×#12311yescharacteristic
488C22×C11#52511yescharacteristic
489C22×C11#52911yescharacteristic
490C22×C11#52911yescharacteristic
491C22×C11#52911yescharacteristic
492C22×C11#52911yescharacteristic
493C22×C11#53211yescharacteristic
494C22×C11#53211yescharacteristic
495C22×C11#53511yescharacteristic
496C22×C11#53711yescharacteristic
497C22×C11#54011yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#55111yescharacteristic
500C22×C11#55111yescharacteristic
501C22×C11#55111yescharacteristic
502C22×C11#55111yescharacteristic
503C22×C11#55111yescharacteristic
504C22×C11#55211yescharacteristic
505C22×C11#55211yescharacteristic
506C22×C11#55211yescharacteristic
507C22×C11#55311yescharacteristic
508C22×C11#55311yescharacteristic
509C22×C11#55311yescharacteristic
510C22×C11#55511yescharacteristic
511C22×C11#55511yescharacteristic
512C22×C11#55511yescharacteristic
513C22×C11#55511yescharacteristic
514C22×C11#55611yescharacteristic
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11—81no—
528C4×C11—81no—
529C25C23×C1111yescharacteristic
530C23×C4C23×C1111yescharacteristic
531C23×C4C23×C1111yescharacteristic
532C23×C4C23×C1111yescharacteristic
533C23×C4C23×C1111yescharacteristic
534C23×C4C23×C1111yescharacteristic
535C23×C4C23×C1111yescharacteristic
536C23×C4C23×C1111yescharacteristic
537C23×C4C23×C1111yescharacteristic
538C23×C4C23×C1111yescharacteristic
539C23×C4C23×C1111yescharacteristic
540C23×C4C23×C1111yescharacteristic
541C23×C4C23×C1111yescharacteristic
542C23×C4C23×C1111yescharacteristic
543C23×C4C23×C1111yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C2×C4×C1114yes—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4C2×C4×C1114yes—
572C2×C22⋊C4C2×C4×C1114yes—
573C2×C22⋊C4C2×C4×C1114yes—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42C2×C4×C1114yes—
588C2×C42D4×C1114yes—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95C2×C4×C1114yes—
608#95C2×C4×C1114yes—
609C2×C11—82no—
610C2×C11#229311yescharacteristic
611C2×C11C4×#12311yescharacteristic
612C2×C11#232411yescharacteristic
613C2×C11#234611yescharacteristic
614C2×C11#235311yescharacteristic
615C2×C11#237211yescharacteristic
616C2×C11#237311yescharacteristic
617C2×C11#249811yescharacteristic
618C2×C11#250011yescharacteristic
619C2×C11#252611yescharacteristic
620C2×C11#252911yescharacteristic
621C2×C11#253111yescharacteristic
622C2×C11#253211yescharacteristic
623C2×C11#260111yescharacteristic
624C2×C11#261011yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×C4×C1112yes—
640C24C24×C1111yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
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—21no—
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—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4C22×C4×C1112yes—
722C22×C4C22×C4×C1112yes—
723C22×C4C22×C4×C1112yes—
724C22×C4C22×C4×C1112yes—
725C22×C4C22×C4×C1112yes—
726C22×C4C22×C4×C1112yes—
727C22×C4C2×D4×C1112yes—
728C22×C4C2×D4×C1112yes—
729C22×C4C2×D4×C1112yes—
730C22×C4C11×#4112yes—
731C22×C4C11×#4112yes—
732C22×C4C11×#4112yes—
733C22×C4C11×#4112yes—
734C22×C4C11×#4112yes—
735C22×C4C11×#4112yes—
736C22×C4C11×#4112yes—
737C22×C4C11×#4112yes—
738C22×C4C11×#4112yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C42—28no—
750C42—28no—
751C42—28no—
752C42—44no—
753C42—44no—
754C11#1407411yescharacteristic, direct product factor, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C23×C4×C1111yescharacteristic
791C23C22×D4×C1111yescharacteristic
792C23C2×C11×#4111yescharacteristic
793C23C2×C11×#4111yescharacteristic
794C23C2×C11×#4111yescharacteristic
795C23C2×C11×#4111yescharacteristic
796C23C2×C11×#4111yescharacteristic
797C23C2×C11×#4111yescharacteristic
798C23C2×C11×#4111yescharacteristic
799C23C2×C11×#4111yescharacteristic
800C23C2×C11×#4111yescharacteristic
801C23C11×H(5,𝔽2)11yescharacteristic
802C23C11×H(5,𝔽2)11yescharacteristic
803C23C11×H(5,𝔽2)11yescharacteristic
804C23C11×2−1+411yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4C11×#11714yes—
901C2×C4C4×D4×C1114yes—
902C2×C4C11×#12314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×C11×#11711yescharacteristic
919C22C2×C4×D4×C1111yescharacteristic
920C22C4×C11×#4111yescharacteristic
921C22C4×C11×#4111yescharacteristic
922C22C4×C11×#4111yescharacteristic
923C22C11×#51811yescharacteristic
924C22C11×#52011yescharacteristic
925C22C2×C11×#12311yescharacteristic
926C22C11×#52511yescharacteristic
927C22C11×#52911yescharacteristic
928C22C11×#52911yescharacteristic
929C22C11×#52911yescharacteristic
930C22C11×#52911yescharacteristic
931C22C11×#53211yescharacteristic
932C22C11×#53211yescharacteristic
933C22C11×#53511yescharacteristic
934C22C11×#53711yescharacteristic
935C22C11×#54011yescharacteristic
936C22C11×#54211yescharacteristic
937C22C11×#55111yescharacteristic
938C22C11×#55111yescharacteristic
939C22C11×#55111yescharacteristic
940C22C11×#55111yescharacteristic
941C22C11×#55111yescharacteristic
942C22C11×#55211yescharacteristic
943C22C11×#55211yescharacteristic
944C22C11×#55211yescharacteristic
945C22C11×#55311yescharacteristic
946C22C11×#55311yescharacteristic
947C22C11×#55311yescharacteristic
948C22C11×#55511yescharacteristic
949C22C11×#55511yescharacteristic
950C22C11×#55511yescharacteristic
951C22C11×#55511yescharacteristic
952C22C11×#55611yescharacteristic
953C4—24no—
954C4—24no—
955C4—24no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—81no—
966C4—81no—
967C2—82no—
968C2C11×#229311yescharacteristic
969C2C4×C11×#12311yescharacteristic
970C2C11×#232411yescharacteristic
971C2C11×#234611yescharacteristic
972C2C11×#235311yescharacteristic
973C2C11×#237211yescharacteristic
974C2C11×#237311yescharacteristic
975C2C11×#249811yescharacteristic
976C2C11×#250011yescharacteristic
977C2C11×#252611yescharacteristic
978C2C11×#252911yescharacteristic
979C2C11×#253111yescharacteristic
980C2C11×#253211yescharacteristic
981C2C11×#260111yescharacteristic
982C2C11×#261011yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#376C2semidirect
4. C11×#1442C2semidirect
5. C11×#1441C2semidirect
11. C11×#1436C2semidirect
12. C11×C4⋊#95C2semidirect
13. C11×#1434C2semidirect
14. C11×#1434C2semidirect
15. C4×C11×#95C2semidirect
32. C11×#388C4semidirect
134. #14074C11direct (N × H)
266. C2×#376C2×C11semidirect
267. #1442C2×C11semidirect
268. #1441C2×C11semidirect
274. #1436C2×C11semidirect
275. C4⋊#95C2×C11semidirect
276. #1434C2×C11semidirect
277. #1434C2×C11semidirect
278. C4×#95C2×C11semidirect
443. #388C4×C11semidirect
754. C11#14074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3882
C2×C11×#3762
C11×#14422
C11×#14412
C11×#14402
C11×#14392
C11×#14372
C11×#14362
C11×C4⋊#952
C11×#14342
C4×C11×#952
#1407411