Finite Group Databasebeta

← C11×#24886 #14602079

Subgroups — C11×#24886 #14602079

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic, complemented
3C11×#2408C211yesmaximal, characteristic
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2094C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1925C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1870C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic, complemented
24C11×#482—24no—
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#106C2211yescharacteristic, complemented
29C11×#418—24no—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic, complemented
40C2×C11×C22⋊C8C2211yescharacteristic, complemented
41C11×#394—21no—
42C11×#392—21no—
43C11×#390—21no—
44C11×#390C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#384C2211yescharacteristic, complemented
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic, complemented
52C11×#379—21no—
53C4×C11×C4⋊C4—21no—
54C4×C11×C4⋊C4C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11D411yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—41no—
86C11×#121—41no—
87C11×#120—44no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—41no—
93C11×#117—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C11×#107—22no—
121C11×#107—41no—
122C11×#106—22no—
123C11×#106—41no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—41no—
130C11×#102—41no—
131C11×#102D414yescomplemented
132C11×C22⋊C8—22no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—41no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139#24886C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—81no—
148C24×C11—81no—
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×D4×C11—28no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—44no—
165C2×D4×C11—44no—
166C2×D4×C11—41no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11C2×D412yes—
178C2×D4×C11#4112yes—
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×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11#4112yes—
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C11×M16—44no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11C2×D412yes—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—81no—
229C11×C4⋊C4C2×D412yes—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—81no—
240C11×C22⋊C4—81no—
241C11×C22⋊C4—81no—
242C11×C22⋊C4—81no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11—42no—
246C42×C11—42no—
247C42×C11—42no—
248C2×#482C2×C1111yescharacteristic, complemented
249C2×#418C2×C1111yescharacteristic, complemented
250#2408C2×C1111yescharacteristic
251#2354C2×C1111yescharacteristic, complemented
252#2094C2×C1111yescharacteristic, complemented
253#2071C2×C1111yescharacteristic, complemented
254#2034C2×C1111yescharacteristic, complemented
255#2033C2×C1111yescharacteristic, complemented
256#1925C2×C1111yescharacteristic, complemented
257#1925C2×C1111yescharacteristic, complemented
258#1875C2×C1111yescharacteristic, complemented
259#1870C2×C1111yescharacteristic, complemented
260#1854C2×C1111yescharacteristic, complemented
261#1809C2×C1111yescharacteristic, complemented
262#1786C2×C1111yescharacteristic, complemented
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—48no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—84no—
292C23×C11—84no—
293C23×C11—84no—
294C23×C11—84no—
295C23×C11—84no—
296C23×C11—84no—
297C23×C11#12312yes—
298C23×C11C22×D411yescharacteristic
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—44no—
304D4×C11—48no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—84no—
310D4×C11—84no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
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#12312yes—
348C2×C4×C11AGL(1,ℤ/8)12yes—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C8×C11—22no—
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C23×D4C22×C1111yescharacteristic
360C22×M16C22×C1111yescharacteristic
361C2×#121C22×C1111yescharacteristic
362C2×#121C22×C1111yescharacteristic
363C2×#120—21no—
364C2×C4×D4C22×C1111yescharacteristic
365C2×#117C22×C1111yescharacteristic
366C2×#117C22×C1111yescharacteristic, complemented
367#482—24no—
368C2×#107C22×C1111yescharacteristic, complemented
369C2×#107C22×C1111yescharacteristic, complemented
370C2×#106C22×C1111yescharacteristic, complemented
371C2×#106C22×C1111yescharacteristic, complemented
372#418—24no—
373C2×#102C22×C1111yescharacteristic
374C2×#102C22×C1111yescharacteristic
375C2×#102C22×C1111yescharacteristic
376C2×#102C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×#102C22×C1111yescharacteristic
380C2×#102C22×C1111yescharacteristic
381C2×C22⋊C8C22×C1111yescharacteristic
382C2×C22⋊C8C22×C1111yescharacteristic, complemented
383C2×C22⋊C8C22×C1111yescharacteristic, complemented
384#394—21no—
385#392—21no—
386#390—21no—
387#390C22×C1111yescharacteristic
388#390C22×C1111yescharacteristic
389#388—21no—
390#388—21no—
391#384C22×C1111yescharacteristic, complemented
392#380C22×C1111yescharacteristic
393#380C22×C1111yescharacteristic
394#380C22×C1111yescharacteristic, complemented
395#379—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4C22×C1111yescharacteristic, complemented
398#340C22×C1111yescharacteristic, complemented
399#340C22×C1111yescharacteristic, complemented
400#340C22×C1111yescharacteristic, complemented
401#340C22×C1111yescharacteristic, complemented
402#336C22×C1111yescharacteristic, complemented
403#336C22×C1111yescharacteristic, complemented
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—41no—
417C22×C11—42no—
418C22×C11—41no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—42no—
422C22×C11—41no—
423C22×C11—42no—
424C22×C11—816no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11C2×#12311yescharacteristic
434C22×C11D4211yescharacteristic
435C22×C11#54611yescharacteristic
436C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C11#57511yescharacteristic
438C22×C11#57611yescharacteristic
439C22×C11#57711yescharacteristic
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—42no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11#52511yescharacteristic
451C4×C11#53811yescharacteristic
452C4×C11#54611yescharacteristic
453C4×C11#55111yescharacteristic
454C25—21no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—41no—
463C22×D4—41no—
464C22×D4D4×C1111yescharacteristic
465C22×D4C23×C1111yescharacteristic
466C22×D4C23×C1111yescharacteristic
467C23×C4C23×C1111yescharacteristic
468C23×C4C23×C1111yescharacteristic
469C2×M16—22no—
470C2×M16—22no—
471C2×M16—41no—
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474C22×C8C23×C1111yescharacteristic
475C22×C8C23×C1111yescharacteristic
476#121—22no—
477#121—22no—
478#121—41no—
479#121—41no—
480#120—44no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485#117—41no—
486#117—41no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4D4×C1111yescharacteristic
490C2×C4⋊C4C23×C1111yescharacteristic
491C2×C4⋊C4C23×C1111yescharacteristic
492C2×C4⋊C4C23×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4D4×C1111yescharacteristic
508C2×C22⋊C4D4×C1111yescharacteristic
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C23×C1111yescharacteristic
513#107—22no—
514#107—41no—
515#106—22no—
516#106—41no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—41no—
523#102—41no—
524#102D4×C1114yescomplemented
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—41no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532C2×C11—42no—
533C2×C11—81no—
534C2×C11—82no—
535C2×C11—82no—
536C2×C11#241811yescharacteristic
537C2×C11#309411yescharacteristic
538C2×C11#309611yescharacteristic
539C2×C11#326811yescharacteristic
540C2×C11#327211yescharacteristic
541C2×C11#331111yescharacteristic
542C2×C11#332511yescharacteristic
543C24—21no—
544C24—21no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—81no—
551C24—81no—
552C24C2×D4×C1111yescharacteristic
553C24C2×D4×C1111yescharacteristic
554C2×D4—28no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C1112yes—
581C2×D4C11×#4112yes—
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×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1111yescharacteristic
600C22×C4C2×D4×C1111yescharacteristic
601C22×C4C2×D4×C1111yescharacteristic
602C22×C4C11×#4112yes—
603C22×C4C11×#4112yes—
604C22×C4C24×C1111yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8C2×D4×C1112yes—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—42no—
631C4⋊C4—81no—
632C4⋊C4C2×D4×C1112yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C42—21no—
647C42—21no—
648C42—42no—
649C42—42no—
650C42—42no—
651C11#2488611yescharacteristic, direct product factor, Sylow
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23C11×#12312yes—
687C23C22×D4×C1111yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4C11×#12312yes—
737C2×C4C11×AGL(1,ℤ/8)12yes—
738C2×C4C22×D4×C1111yescharacteristic
739C2×C4C2×C11×#4111yescharacteristic
740C2×C4C2×C11×#4111yescharacteristic
741C2×C4C2×C11×#4111yescharacteristic
742C2×C4C11×H(5,𝔽2)11yescharacteristic
743C2×C4C11×H(5,𝔽2)11yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×C11×#12311yescharacteristic
778C22D42×C1111yescharacteristic
779C22C11×#54611yescharacteristic
780C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
781C22C11×#57511yescharacteristic
782C22C11×#57611yescharacteristic
783C22C11×#57711yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C11×#52511yescharacteristic
795C4C11×#53811yescharacteristic
796C4C11×#54611yescharacteristic
797C4C11×#55111yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C11×#241811yescharacteristic
803C2C11×#309411yescharacteristic
804C2C11×#309611yescharacteristic
805C2C11×#326811yescharacteristic
806C2C11×#327211yescharacteristic
807C2C11×#331111yescharacteristic
808C2C11×#332511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#482C2semidirect
2. C2×C11×#418C2semidirect
4. C11×#2354C2semidirect
5. C11×#2094C2semidirect
6. C11×#2071C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1925C2semidirect
10. C11×#1925C2semidirect
11. C11×#1875C2semidirect
12. C11×#1870C2semidirect
13. C11×#1854C2semidirect
14. C11×#1809C2semidirect
15. C11×#1786C2semidirect
23. C2×C11×#117C22semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#107C22semidirect
27. C2×C11×#106C22semidirect
28. C2×C11×#106C22semidirect
39. C2×C11×C22⋊C8C22semidirect
40. C2×C11×C22⋊C8C22semidirect
48. C11×#384C22semidirect
51. C11×#380C22semidirect
54. C4×C11×C4⋊C4C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
131. C11×#102D4semidirect
139. #24886C11direct (N × H)
248. C2×#482C2×C11semidirect
249. C2×#418C2×C11semidirect
251. #2354C2×C11semidirect
252. #2094C2×C11semidirect
253. #2071C2×C11semidirect
254. #2034C2×C11semidirect
255. #2033C2×C11semidirect
256. #1925C2×C11semidirect
257. #1925C2×C11semidirect
258. #1875C2×C11semidirect
259. #1870C2×C11semidirect
260. #1854C2×C11semidirect
261. #1809C2×C11semidirect
262. #1786C2×C11semidirect
366. C2×#117C22×C11semidirect
368. C2×#107C22×C11semidirect
369. C2×#107C22×C11semidirect
370. C2×#106C22×C11semidirect
371. C2×#106C22×C11semidirect
382. C2×C22⋊C8C22×C11semidirect
383. C2×C22⋊C8C22×C11semidirect
391. #384C22×C11semidirect
394. #380C22×C11semidirect
397. C4×C4⋊C4C22×C11semidirect
398. #340C22×C11semidirect
399. #340C22×C11semidirect
400. #340C22×C11semidirect
401. #340C22×C11semidirect
402. #336C22×C11semidirect
403. #336C22×C11semidirect
524. #102D4×C11semidirect
651. C11#24886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C2×C11×#4182
C11×#24082
C11×#23542
C11×#20942
C11×#20712
C11×#20342
C11×#20332
C11×#19252
C11×#18752
C11×#18702
C11×#18542
C11×#18092
C11×#17862
#2488611