Finite Group Databasebeta

← C11×#24873 #14602066

Subgroups — C11×#24873 #14602066

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic, complemented
3C11×#2408C211yesmaximal, characteristic
4C11×#2352C211yesmaximal, characteristic, complemented
5C11×#2092C211yesmaximal, characteristic, complemented
6C11×#2073C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1925C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic, complemented
13C11×#1852C211yesmaximal, characteristic, complemented
14C11×#1807C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#482—24no—
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×#102—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×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#388—21no—
46C11×#387—21no—
47C11×#386—21no—
48C11×#382C2211yescharacteristic, complemented
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic, complemented
52C11×#379—21no—
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C4×C11×C22⋊C4—21no—
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×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—41no—
87C11×#121—41no—
88C11×#120—44no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C11×#117—22no—
92C11×#117—41no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
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⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11—21no—
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#107—41no—
120C11×#106—22no—
121C11×#106—41no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—41no—
128C11×#102—41no—
129C11×#102D414yescomplemented
130C11×C22⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—41no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139#24873C1111yesmaximal, 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—22no—
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—21no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
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×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—81no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11#4112yes—
203C22×C4×C11#4112yes—
204C22×C4×C11C2411yescharacteristic
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×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—44no—
217C2×C8×C11C2×D412yes—
218C11×C4⋊C4—22no—
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—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4C2×D412yes—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—81no—
242C11×C22⋊C4—81no—
243C11×C22⋊C4—81no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11—42no—
247C42×C11—81no—
248C2×#482C2×C1111yescharacteristic, complemented
249C22×#102C2×C1111yescharacteristic, complemented
250#2408C2×C1111yescharacteristic
251#2352C2×C1111yescharacteristic, complemented
252#2092C2×C1111yescharacteristic, complemented
253#2073C2×C1111yescharacteristic, complemented
254#2034C2×C1111yescharacteristic, complemented
255#2033C2×C1111yescharacteristic, complemented
256#1926C2×C1111yescharacteristic, complemented
257#1925C2×C1111yescharacteristic, complemented
258#1875C2×C1111yescharacteristic, complemented
259#1869C2×C1111yescharacteristic, complemented
260#1852C2×C1111yescharacteristic, complemented
261#1807C2×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—22no—
270C23×C11—22no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—48no—
277C23×C11—41no—
278C23×C11—41no—
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—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11—84no—
293C23×C11—84no—
294C23×C11—84no—
295C23×C11#12312yes—
296C23×C11#13512yes—
297C23×C11AGL(1,ℤ/8)12yes—
298C23×C11C22×D411yescharacteristic
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—48no—
304D4×C11—44no—
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—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
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—21no—
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—84no—
349C2×C4×C11#12312yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C8×C11—22no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C23×D4C22×C1111yescharacteristic
361C23×C8C22×C1111yescharacteristic
362C2×#121C22×C1111yescharacteristic
363C2×#121C22×C1111yescharacteristic
364C2×#120—21no—
365C2×C4×D4C22×C1111yescharacteristic
366C2×#117C22×C1111yescharacteristic, complemented
367C22×C4⋊C4C22×C1111yescharacteristic
368#482—24no—
369C2×#107C22×C1111yescharacteristic, complemented
370C2×#107C22×C1111yescharacteristic, complemented
371C2×#106C22×C1111yescharacteristic, complemented
372C2×#106C22×C1111yescharacteristic, complemented
373C2×#102—24no—
374C2×#102C22×C1111yescharacteristic
375C2×#102C22×C1111yescharacteristic
376C2×#102C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×#102C22×C1111yescharacteristic
380C2×#102C22×C1111yescharacteristic
381C2×#102C22×C1111yescharacteristic
382C2×C22⋊C8C22×C1111yescharacteristic
383C2×C22⋊C8C22×C1111yescharacteristic, complemented
384C2×C22⋊C8C22×C1111yescharacteristic, complemented
385#394—21no—
386#392—21no—
387#390C22×C1111yescharacteristic
388#390C22×C1111yescharacteristic
389#388—21no—
390#387—21no—
391#386—21no—
392#382C22×C1111yescharacteristic, complemented
393#380C22×C1111yescharacteristic
394#380C22×C1111yescharacteristic
395#380C22×C1111yescharacteristic, complemented
396#379—21no—
397C4×C4⋊C4C22×C1111yescharacteristic, complemented
398C4×C22⋊C4—21no—
399#340C22×C1111yescharacteristic, complemented
400#340C22×C1111yescharacteristic, complemented
401#340C22×C1111yescharacteristic, complemented
402#340C22×C1111yescharacteristic, complemented
403#336C22×C1111yescharacteristic, complemented
404#336C22×C1111yescharacteristic, complemented
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
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×C11#48214yescomplemented
434C22×C11C2×#12311yescharacteristic
435C22×C11D4211yescharacteristic
436C22×C11#54611yescharacteristic
437C22×C11C2×#13511yescharacteristic
438C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
439C22×C11#57611yescharacteristic
440C22×C11#57711yescharacteristic
441C4×C11—22no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—42no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11—81no—
451C4×C11#52511yescharacteristic
452C4×C11#53811yescharacteristic
453C4×C11#54611yescharacteristic
454C4×C11#55111yescharacteristic
455C25—21no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4D4×C1111yescharacteristic
466C22×D4C23×C1111yescharacteristic
467C22×D4C23×C1111yescharacteristic
468C23×C4—21no—
469C23×C4C23×C1111yescharacteristic
470C23×C4C23×C1111yescharacteristic
471C22×C8—22no—
472C22×C8—22no—
473C22×C8—41no—
474C22×C8C23×C1111yescharacteristic
475C22×C8C23×C1111yescharacteristic
476C22×C8C23×C1111yescharacteristic
477C22×C8C23×C1111yescharacteristic
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#120—44no—
483C4×D4—22no—
484C4×D4—22no—
485#117—22no—
486#117—41no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4D4×C1111yescharacteristic
491C2×C4⋊C4C23×C1111yescharacteristic
492C2×C4⋊C4C23×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
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×C42C23×C1111yescharacteristic
512#107—22no—
513#107—41no—
514#106—22no—
515#106—41no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—41no—
522#102—41no—
523#102D4×C1114yescomplemented
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533C2×C11—24no—
534C2×C11—81no—
535C2×C11—82no—
536C2×C11—82no—
537C2×C11#241811yescharacteristic
538C2×C11C2×#48211yescharacteristic
539C2×C11#309611yescharacteristic
540C2×C11#326411yescharacteristic
541C2×C11#328211yescharacteristic
542C2×C11#329711yescharacteristic
543C2×C11#331011yescharacteristic
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C1111yescharacteristic
554C24C2×D4×C1111yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
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—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C1112yes—
582C2×D4C11×#4112yes—
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—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4C2×D4×C1111yescharacteristic
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1111yescharacteristic
606C22×C4C11×#4112yes—
607C22×C4C11×#4112yes—
608C22×C4C24×C1111yescharacteristic
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×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—44no—
621C2×C8C2×D4×C1112yes—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—42no—
635C4⋊C4C2×D4×C1112yes—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C42—21no—
649C42—21no—
650C42—42no—
651C42—81no—
652C11#2487311yescharacteristic, direct product factor, Sylow
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23C11×#12312yes—
686C23C11×#13512yes—
687C23C11×AGL(1,ℤ/8)12yes—
688C23C22×D4×C1111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
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×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4C11×#12312yes—
740C2×C4C22×D4×C1111yescharacteristic
741C2×C4C2×C11×#4111yescharacteristic
742C2×C4C2×C11×#4111yescharacteristic
743C2×C4C2×C11×#4111yescharacteristic
744C2×C4C11×H(5,𝔽2)11yescharacteristic
745C2×C4C11×H(5,𝔽2)11yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—816no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22C11×#48214yescomplemented
779C22C2×C11×#12311yescharacteristic
780C22D42×C1111yescharacteristic
781C22C11×#54611yescharacteristic
782C22C2×C11×#13511yescharacteristic
783C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
784C22C11×#57611yescharacteristic
785C22C11×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C11×#52511yescharacteristic
797C4C11×#53811yescharacteristic
798C4C11×#54611yescharacteristic
799C4C11×#55111yescharacteristic
800C2—24no—
801C2—81no—
802C2—82no—
803C2—82no—
804C2C11×#241811yescharacteristic
805C2C2×C11×#48211yescharacteristic
806C2C11×#309611yescharacteristic
807C2C11×#326411yescharacteristic
808C2C11×#328211yescharacteristic
809C2C11×#329711yescharacteristic
810C2C11×#331011yescharacteristic
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. C22×C11×#102C2semidirect
4. C11×#2352C2semidirect
5. C11×#2092C2semidirect
6. C11×#2073C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1926C2semidirect
10. C11×#1925C2semidirect
11. C11×#1875C2semidirect
12. C11×#1869C2semidirect
13. C11×#1852C2semidirect
14. C11×#1807C2semidirect
15. C11×#1786C2semidirect
22. 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×#382C22semidirect
51. C11×#380C22semidirect
53. C4×C11×C4⋊C4C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
129. C11×#102D4semidirect
139. #24873C11direct (N × H)
248. C2×#482C2×C11semidirect
249. C22×#102C2×C11semidirect
251. #2352C2×C11semidirect
252. #2092C2×C11semidirect
253. #2073C2×C11semidirect
254. #2034C2×C11semidirect
255. #2033C2×C11semidirect
256. #1926C2×C11semidirect
257. #1925C2×C11semidirect
258. #1875C2×C11semidirect
259. #1869C2×C11semidirect
260. #1852C2×C11semidirect
261. #1807C2×C11semidirect
262. #1786C2×C11semidirect
366. C2×#117C22×C11semidirect
369. C2×#107C22×C11semidirect
370. C2×#107C22×C11semidirect
371. C2×#106C22×C11semidirect
372. C2×#106C22×C11semidirect
383. C2×C22⋊C8C22×C11semidirect
384. C2×C22⋊C8C22×C11semidirect
392. #382C22×C11semidirect
395. #380C22×C11semidirect
397. C4×C4⋊C4C22×C11semidirect
399. #340C22×C11semidirect
400. #340C22×C11semidirect
401. #340C22×C11semidirect
402. #340C22×C11semidirect
403. #336C22×C11semidirect
404. #336C22×C11semidirect
433. C22×C11#482semidirect
523. #102D4×C11semidirect
652. C11#24873direct (N × H)
778. C22C11×#482semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C22×C11×#1022
C11×#24082
C11×#23522
C11×#20922
C11×#20732
C11×#20342
C11×#20332
C11×#19262
C11×#19252
C11×#18752
C11×#18692
C11×#18522
C11×#18072
C11×#17862
#2487311