Finite Group Databasebeta

← C11×#14561 #14591754

Subgroups — C11×#14561 #14591754

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic
2C2×C11×#391C211yesmaximal, characteristic
3C2×C11×#387C211yesmaximal, characteristic
4C11×#1446C211yesmaximal, characteristic
5C11×#1445C211yesmaximal, characteristic
6C11×#1443C211yesmaximal, characteristic
7C11×#1443C211yesmaximal, characteristic
8C11×#1442C211yesmaximal, characteristic
9C11×#1436C211yesmaximal, characteristic
10C11×#1436C211yesmaximal, characteristic
11C11×#1436C211yesmaximal, characteristic
12C11×#1436C211yesmaximal, characteristic
13C11×#1436C211yesmaximal, characteristic
14C11×C4⋊#95C211yesmaximal, characteristic
15C11×#1434C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#395C418yescomplemented
26C11×#391—24no—
27C11×#387—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
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
54C22×Q8×C11—22no—
55C22×Q8×C11—22no—
56C22×Q8×C11—41no—
57C22×Q8×C11—41no—
58C22×Q8×C11—41no—
59C22×Q8×C11—41no—
60C22×Q8×C11C2×C414yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4C2×C414yes—
88C2×C11×C4⋊C4C2×C414yes—
89C2×C11×C4⋊C4C2×C414yes—
90C2×C11×C4⋊C4D414yes—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—41no—
96C2×C42×C11—41no—
97C2×C42×C11—41no—
98C2×C42×C11—41no—
99C2×C42×C11—41no—
100C11×#95—22no—
101C11×#95—22no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95—22no—
110C11×#95—22no—
111C11×#95—22no—
112C11×#95—22no—
113C11×#95—22no—
114C11×#95—41no—
115C11×#95—41no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95—41no—
119C11×#95—41no—
120C11×#95—41no—
121C11×#95—41no—
122C11×#95C2×C414yes—
123C11×#95C2×C414yes—
124C11×#95C2×C414yes—
125C11×#95Q814yescomplemented
126#14561C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2411yescharacteristic
128C2×Q8×C11—28no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11—44no—
132C2×Q8×C11—44no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
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×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×Q812yes—
234C22×C4×C11C2×Q812yes—
235C22×C4×C11C2×Q812yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
240C11×C4⋊C4—28no—
241C11×C4⋊C4—44no—
242C11×C4⋊C4—44no—
243C11×C4⋊C4—44no—
244C11×C4⋊C4—44no—
245C42×C11—44no—
246C42×C11—44no—
247C42×C11—44no—
248C2×#395C2×C1111yescharacteristic
249C2×#391C2×C1111yescharacteristic
250C2×#387C2×C1111yescharacteristic
251#1446C2×C1111yescharacteristic
252#1445C2×C1111yescharacteristic
253#1443C2×C1111yescharacteristic
254#1443C2×C1111yescharacteristic
255#1442C2×C1111yescharacteristic
256#1436C2×C1111yescharacteristic
257#1436C2×C1111yescharacteristic
258#1436C2×C1111yescharacteristic
259#1436C2×C1111yescharacteristic
260#1436C2×C1111yescharacteristic
261C4⋊#95C2×C1111yescharacteristic
262#1434C2×C1111yescharacteristic
263C23×C11C23×C411yescharacteristic
264C23×C11C22×D411yescharacteristic
265C23×C11C22×Q811yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11H(5,𝔽2)11yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C11H(5,𝔽2)11yescharacteristic
274C23×C112−1+411yescharacteristic
275C23×C112−1+411yescharacteristic
276C23×C112−1+411yescharacteristic
277C23×C112−1+411yescharacteristic
278Q8×C11—416no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
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—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×C11C4×D414yes—
383C2×C4×C11C4×Q814yes—
384C23×Q8C22×C1111yescharacteristic
385C22×C4⋊C4C22×C1111yescharacteristic
386C22×C4⋊C4C22×C1111yescharacteristic
387C22×C4⋊C4C22×C1111yescharacteristic
388C22×C4⋊C4C22×C1111yescharacteristic
389C22×C4⋊C4C22×C1111yescharacteristic
390C22×C42C22×C1111yescharacteristic
391C22×C42C22×C1111yescharacteristic
392C22×C42C22×C1111yescharacteristic
393#395C4×C1118yescomplemented
394#391—24no—
395#387—24no—
396C2×#95C22×C1111yescharacteristic
397C2×#95C22×C1111yescharacteristic
398C2×#95C22×C1111yescharacteristic
399C2×#95C22×C1111yescharacteristic
400C2×#95C22×C1111yescharacteristic
401C2×#95C22×C1111yescharacteristic
402C2×#95C22×C1111yescharacteristic
403C2×#95C22×C1111yescharacteristic
404C2×#95C22×C1111yescharacteristic
405C2×#95C22×C1111yescharacteristic
406C2×#95C22×C1111yescharacteristic
407C2×#95C22×C1111yescharacteristic
408C2×#95C22×C1111yescharacteristic
409C2×#95C22×C1111yescharacteristic
410C2×#95C22×C1111yescharacteristic
411C2×#95C22×C1111yescharacteristic
412C2×#95C22×C1111yescharacteristic
413C2×#95C22×C1111yescharacteristic
414C2×#95C22×C1111yescharacteristic
415C2×#95C22×C1111yescharacteristic
416C2×#95C22×C1111yescharacteristic
417C2×#95C22×C1111yescharacteristic
418C2×#95C22×C1111yescharacteristic
419C2×#95C22×C1111yescharacteristic
420C2×#95C22×C1111yescharacteristic
421C2×#95C22×C1111yescharacteristic
422C22×C11C2×C4×D411yescharacteristic
423C22×C11C2×C4×Q811yescharacteristic
424C22×C11C4×#4111yescharacteristic
425C22×C11#51811yescharacteristic
426C22×C11#51811yescharacteristic
427C22×C11#51911yescharacteristic
428C22×C11#51911yescharacteristic
429C22×C11#53411yescharacteristic
430C22×C11#53511yescharacteristic
431C22×C11#53811yescharacteristic
432C22×C11#53811yescharacteristic
433C22×C11#53911yescharacteristic
434C22×C11#53911yescharacteristic
435C22×C11#54211yescharacteristic
436C22×C11#54211yescharacteristic
437C22×C11#54211yescharacteristic
438C22×C11#54211yescharacteristic
439C22×C11#54411yescharacteristic
440C22×C11#54411yescharacteristic
441C22×C11#54711yescharacteristic
442C22×C11#54711yescharacteristic
443C22×C11#54811yescharacteristic
444C22×C11D4×Q811yescharacteristic
445C22×C11#55111yescharacteristic
446C22×C11#55111yescharacteristic
447C22×C11#55211yescharacteristic
448C22×C11#55411yescharacteristic
449C22×C11#55411yescharacteristic
450C22×C11#55611yescharacteristic
451C22×C11#55611yescharacteristic
452C22×C11#55711yescharacteristic
453C22×C11#56311yescharacteristic
454C22×C11#56311yescharacteristic
455C22×C11#56311yescharacteristic
456C22×C11#56311yescharacteristic
457C4×C11—24no—
458C4×C11—24no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—81no—
471C4×C11—81no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8—41no—
477C22×Q8—41no—
478C22×Q8C2×C4×C1114yes—
479C23×C4C23×C1111yescharacteristic
480C23×C4C23×C1111yescharacteristic
481C23×C4C23×C1111yescharacteristic
482C23×C4C23×C1111yescharacteristic
483C23×C4C23×C1111yescharacteristic
484C23×C4C23×C1111yescharacteristic
485C23×C4C23×C1111yescharacteristic
486C23×C4C23×C1111yescharacteristic
487C23×C4C23×C1111yescharacteristic
488C23×C4C23×C1111yescharacteristic
489C23×C4C23×C1111yescharacteristic
490C23×C4C23×C1111yescharacteristic
491C23×C4C23×C1111yescharacteristic
492C23×C4C23×C1111yescharacteristic
493C23×C4C23×C1111yescharacteristic
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4C2×C4×C1114yes—
506C2×C4⋊C4C2×C4×C1114yes—
507C2×C4⋊C4C2×C4×C1114yes—
508C2×C4⋊C4D4×C1114yes—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—41no—
514C2×C42—41no—
515C2×C42—41no—
516C2×C42—41no—
517C2×C42—41no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—41no—
533#95—41no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95—41no—
538#95—41no—
539#95—41no—
540#95C2×C4×C1114yes—
541#95C2×C4×C1114yes—
542#95C2×C4×C1114yes—
543#95Q8×C1114yescomplemented
544C2×C11#232111yescharacteristic
545C2×C11#233111yescharacteristic
546C2×C11#233211yescharacteristic
547C2×C11#236211yescharacteristic
548C2×C11#236511yescharacteristic
549C2×C11#236811yescharacteristic
550C2×C11#238111yescharacteristic
551C2×C11#271711yescharacteristic
552C2×C11#272011yescharacteristic
553C2×C11#272311yescharacteristic
554C2×C11#272911yescharacteristic
555C2×C11#274511yescharacteristic
556C2×C11#275911yescharacteristic
557C2×C11#277411yescharacteristic
558C2×C11#280511yescharacteristic
559C24C24×C1111yescharacteristic
560C2×Q8—28no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
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—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
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×C4C22×C4×C1112yes—
656C22×C4C22×C4×C1112yes—
657C22×C4C22×C4×C1112yes—
658C22×C4C22×C4×C1112yes—
659C22×C4C22×C4×C1112yes—
660C22×C4C22×C4×C1112yes—
661C22×C4C22×C4×C1112yes—
662C22×C4C2×D4×C1112yes—
663C22×C4C2×D4×C1112yes—
664C22×C4C2×D4×C1112yes—
665C22×C4C2×Q8×C1112yes—
666C22×C4C2×Q8×C1112yes—
667C22×C4C2×Q8×C1112yes—
668C22×C4C11×#4112yes—
669C22×C4C11×#4112yes—
670C22×C4C11×#4112yes—
671C22×C4C11×#4112yes—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C42—44no—
678C42—44no—
679C42—44no—
680C11#1456111yescharacteristic, direct product factor, Sylow
681C23C23×C4×C1111yescharacteristic
682C23C22×D4×C1111yescharacteristic
683C23C22×Q8×C1111yescharacteristic
684C23C2×C11×#4111yescharacteristic
685C23C2×C11×#4111yescharacteristic
686C23C2×C11×#4111yescharacteristic
687C23C2×C11×#4111yescharacteristic
688C23C11×H(5,𝔽2)11yescharacteristic
689C23C11×H(5,𝔽2)11yescharacteristic
690C23C11×H(5,𝔽2)11yescharacteristic
691C23C11×H(5,𝔽2)11yescharacteristic
692C23C11×2−1+411yescharacteristic
693C23C11×2−1+411yescharacteristic
694C23C11×2−1+411yescharacteristic
695C23C11×2−1+411yescharacteristic
696Q8—416no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
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×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×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×C4C4×D4×C1114yes—
801C2×C4C4×Q8×C1114yes—
802C22C2×C4×D4×C1111yescharacteristic
803C22C2×C4×Q8×C1111yescharacteristic
804C22C4×C11×#4111yescharacteristic
805C22C11×#51811yescharacteristic
806C22C11×#51811yescharacteristic
807C22C11×#51911yescharacteristic
808C22C11×#51911yescharacteristic
809C22C11×#53411yescharacteristic
810C22C11×#53511yescharacteristic
811C22C11×#53811yescharacteristic
812C22C11×#53811yescharacteristic
813C22C11×#53911yescharacteristic
814C22C11×#53911yescharacteristic
815C22C11×#54211yescharacteristic
816C22C11×#54211yescharacteristic
817C22C11×#54211yescharacteristic
818C22C11×#54211yescharacteristic
819C22C11×#54411yescharacteristic
820C22C11×#54411yescharacteristic
821C22C11×#54711yescharacteristic
822C22C11×#54711yescharacteristic
823C22C11×#54811yescharacteristic
824C22D4×Q8×C1111yescharacteristic
825C22C11×#55111yescharacteristic
826C22C11×#55111yescharacteristic
827C22C11×#55211yescharacteristic
828C22C11×#55411yescharacteristic
829C22C11×#55411yescharacteristic
830C22C11×#55611yescharacteristic
831C22C11×#55611yescharacteristic
832C22C11×#55711yescharacteristic
833C22C11×#56311yescharacteristic
834C22C11×#56311yescharacteristic
835C22C11×#56311yescharacteristic
836C22C11×#56311yescharacteristic
837C4—24no—
838C4—24no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C2C11×#232111yescharacteristic
853C2C11×#233111yescharacteristic
854C2C11×#233211yescharacteristic
855C2C11×#236211yescharacteristic
856C2C11×#236511yescharacteristic
857C2C11×#236811yescharacteristic
858C2C11×#238111yescharacteristic
859C2C11×#271711yescharacteristic
860C2C11×#272011yescharacteristic
861C2C11×#272311yescharacteristic
862C2C11×#272911yescharacteristic
863C2C11×#274511yescharacteristic
864C2C11×#275911yescharacteristic
865C2C11×#277411yescharacteristic
866C2C11×#280511yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
25. C11×#395C4semidirect
125. C11×#95Q8semidirect
126. #14561C11direct (N × H)
393. #395C4×C11semidirect
543. #95Q8×C11semidirect
680. C11#14561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C2×C11×#3912
C2×C11×#3872
C11×#14462
C11×#14452
C11×#14432
C11×#14422
C11×#14362
C11×C4⋊#952
C11×#14342
#1456111