Finite Group Databasebeta

← C11×#24879 #14602072

Subgroups — C11×#24879 #14602072

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C11×#2407C211yesmaximal, characteristic
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2094C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1928C211yesmaximal, characteristic, complemented
10C11×#1926C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C11×#1870C211yesmaximal, characteristic, complemented
13C11×#1853C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#483—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C11×#417—24no—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C11×#394—21no—
42C11×#392—21no—
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389—21no—
46C11×#386—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#384C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11D411yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—41no—
86C11×#121—22no—
87C11×#121—41no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—44no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
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×C11C2311yescharacteristic
118C11×#107—41no—
119C11×#106—22no—
120C11×#106—22no—
121C11×#106—41no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—41no—
125C11×#103D414yescomplemented
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—41no—
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#24879C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C11×#41—28no—
144C11×#41—44no—
145C11×#41—44no—
146C11×#41—44no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D412yes—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—81no—
167C2×D4×C11#4112yes—
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—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11#4112yes—
199C22×C4×C11#4112yes—
200C22×C4×C11C2411yescharacteristic
201C11×M16—44no—
202C2×C8×C11—21no—
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×C11C2×D412yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—21no—
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—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—81no—
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—81no—
240C11×C22⋊C4—81no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—42no—
244C2×#483C2×C1111yescharacteristic, complemented
245C2×#417C2×C1111yescharacteristic, complemented
246#2407C2×C1111yescharacteristic
247D4×C4⋊C4C2×C1111yescharacteristic, complemented
248#2094C2×C1111yescharacteristic, complemented
249#2072C2×C1111yescharacteristic, complemented
250#2035C2×C1111yescharacteristic, complemented
251#2033C2×C1111yescharacteristic, complemented
252#1928C2×C1111yescharacteristic, complemented
253#1926C2×C1111yescharacteristic, complemented
254#1874C2×C1111yescharacteristic, complemented
255#1870C2×C1111yescharacteristic, complemented
256#1853C2×C1111yescharacteristic, complemented
257#1809C2×C1111yescharacteristic, complemented
258#1788C2×C1111yescharacteristic, complemented
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
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—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11#12312yes—
279C23×C11AGL(1,ℤ/8)12yes—
280C23×C11C22×D411yescharacteristic
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—41no—
284Q8×C11—41no—
285D4×C11—28no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—48no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—84no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—48no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
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—84no—
333C2×C4×C11—84no—
334C2×C4×C11#12312yes—
335C2×C4×C11#13712yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C8×C11—22no—
343C8×C11—41no—
344C8×C11—41no—
345C8×C11—41no—
346C22×#41C22×C1111yescharacteristic
347C22×M16C22×C1111yescharacteristic
348C2×C22⋊Q8C22×C1111yescharacteristic
349C2×#121C22×C1111yescharacteristic
350C2×C4×D4—21no—
351C2×C4×D4C22×C1111yescharacteristic
352C22×C4⋊C4C22×C1111yescharacteristic
353C22×C4⋊C4C22×C1111yescharacteristic
354#483—24no—
355C2×#107C22×C1111yescharacteristic
356C2×#106C22×C1111yescharacteristic
357C2×#106C22×C1111yescharacteristic
358C2×#106C22×C1111yescharacteristic
359#417—24no—
360C2×#103C22×C1111yescharacteristic
361C2×#103C22×C1111yescharacteristic
362C2×#103C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#102C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371#394—21no—
372#392—21no—
373#391C22×C1111yescharacteristic
374#390C22×C1111yescharacteristic
375#389—21no—
376#386—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#384C22×C1111yescharacteristic
381#380C22×C1111yescharacteristic
382#380C22×C1111yescharacteristic
383#380C22×C1111yescharacteristic
384C4×C4⋊C4C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#340C22×C1111yescharacteristic
388#340C22×C1111yescharacteristic
389#336C22×C1111yescharacteristic
390#336C22×C1111yescharacteristic
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11C2×#12311yescharacteristic
413C22×C11D4211yescharacteristic
414C22×C11#54611yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11C2×#13711yescharacteristic
417C22×C11#57711yescharacteristic
418C22×C11#57711yescharacteristic
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11#52511yescharacteristic
431C4×C11#53811yescharacteristic
432C4×C11#54611yescharacteristic
433C4×C11#55111yescharacteristic
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41—41no—
439C2×#41—41no—
440C22×Q8C23×C1111yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4D4×C1111yescharacteristic
444C22×D4C23×C1111yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4C23×C1111yescharacteristic
449C23×C4C23×C1111yescharacteristic
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459#121—22no—
460#121—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—44no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4D4×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4D4×C1111yescharacteristic
488C2×C22⋊C4D4×C1111yescharacteristic
489C2×C42—21no—
490C2×C42C23×C1111yescharacteristic
491#107—41no—
492#106—22no—
493#106—22no—
494#106—41no—
495#103—22no—
496#103—22no—
497#103—41no—
498#103D4×C1114yescomplemented
499#102—22no—
500#102—22no—
501#102—22no—
502#102—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—41no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512C2×C11—42no—
513C2×C11—42no—
514C2×C11—82no—
515C2×C11#241811yescharacteristic
516C2×C11#309211yescharacteristic
517C2×C11#309911yescharacteristic
518C2×C11#326511yescharacteristic
519C2×C11#327811yescharacteristic
520C2×C11#330611yescharacteristic
521C2×C11#333111yescharacteristic
522C24—21no—
523C24C2×D4×C1111yescharacteristic
524C24C2×D4×C1111yescharacteristic
525#41—28no—
526#41—44no—
527#41—44no—
528#41—44no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8C2×D4×C1112yes—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—81no—
549C2×D4C11×#4112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4C2×D4×C1111yescharacteristic
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C11×#4112yes—
581C22×C4C11×#4112yes—
582C22×C4C24×C1111yescharacteristic
583M16—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C2×D4×C1112yes—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—81no—
613C4⋊C4C2×D4×C1112yes—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—42no—
626C11#2487911yescharacteristic, direct product factor, Sylow
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C11×#12312yes—
647C23C11×AGL(1,ℤ/8)12yes—
648C23C22×D4×C1111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653D4—28no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—84no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—48no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4C11×#12312yes—
703C2×C4C11×#13712yes—
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C2×C11×#4111yescharacteristic
706C2×C4C2×C11×#4111yescharacteristic
707C2×C4C2×C11×#4111yescharacteristic
708C2×C4C11×H(5,𝔽2)11yescharacteristic
709C2×C4C11×H(5,𝔽2)11yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C2×C11×#12311yescharacteristic
736C22D42×C1111yescharacteristic
737C22C11×#54611yescharacteristic
738C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
739C22C2×C11×#13711yescharacteristic
740C22C11×#57711yescharacteristic
741C22C11×#57711yescharacteristic
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4C11×#52511yescharacteristic
754C4C11×#53811yescharacteristic
755C4C11×#54611yescharacteristic
756C4C11×#55111yescharacteristic
757C2—42no—
758C2—42no—
759C2—82no—
760C2C11×#241811yescharacteristic
761C2C11×#309211yescharacteristic
762C2C11×#309911yescharacteristic
763C2C11×#326511yescharacteristic
764C2C11×#327811yescharacteristic
765C2C11×#330611yescharacteristic
766C2C11×#333111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2407C2
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×#483C2semidirect
2. C2×C11×#417C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2094C2semidirect
6. C11×#2072C2semidirect
7. C11×#2035C2semidirect
8. C11×#2033C2semidirect
9. C11×#1928C2semidirect
10. C11×#1926C2semidirect
11. C11×#1874C2semidirect
12. C11×#1870C2semidirect
13. C11×#1853C2semidirect
14. C11×#1809C2semidirect
15. C11×#1788C2semidirect
125. C11×#103D4semidirect
139. #24879C11direct (N × H)
244. C2×#483C2×C11semidirect
245. C2×#417C2×C11semidirect
247. D4×C4⋊C4C2×C11semidirect
248. #2094C2×C11semidirect
249. #2072C2×C11semidirect
250. #2035C2×C11semidirect
251. #2033C2×C11semidirect
252. #1928C2×C11semidirect
253. #1926C2×C11semidirect
254. #1874C2×C11semidirect
255. #1870C2×C11semidirect
256. #1853C2×C11semidirect
257. #1809C2×C11semidirect
258. #1788C2×C11semidirect
498. #103D4×C11semidirect
626. C11#24879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C2×C11×#4172
C11×#24072
D4×C11×C4⋊C42
C11×#20942
C11×#20722
C11×#20352
C11×#20332
C11×#19282
C11×#19262
C11×#18742
C11×#18702
C11×#18532
C11×#18092
C11×#17882
#2487911