Finite Group Databasebeta

← C11×#24168 #14601361

Subgroups — C11×#24168 #14601361

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#464C211yesmaximal, characteristic, complemented
4C11×#2323C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic
9C11×#1988C211yesmaximal, characteristic, complemented
10C11×#1983C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic, complemented
13C11×#1863C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C11×#542—24no—
19C11×#542—24no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126—21no—
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#477—24no—
34C11×#464—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#107C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#389—21no—
51C11×#389C2211yescharacteristic
52C11×#388—21no—
53C11×#388—21no—
54C11×#387—21no—
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C2×C11×Q16—41no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8D414yes—
82C11×#126—28no—
83C11×#124—28no—
84C11×#124—22no—
85C11×#124D414yes—
86C11×#123—28no—
87C11×C22⋊Q8—28no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×#121—22no—
93C11×#121—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C11×#117—22no—
101C11×#117—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C42×C11—21no—
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#107—22no—
131C11×C4⋊C8—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24168C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—24no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—81no—
163C2×Q8×C11—81no—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11#4112yes—
166C2×D4×C11—24no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11C2×D412yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—24no—
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—81no—
190C22×C4×C11—81no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C11×Q16—44no—
198C11×SD16—44no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
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—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
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—42no—
225C11×C4⋊C4—81no—
226C11×C4⋊C4C2×D412yes—
227C11×C4⋊C4C2×D412yes—
228C11×C4⋊C4#4112yes—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—81no—
238C42×C11—24no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—42no—
242C42×C11—81no—
243C42×C11C2×D412yes—
244C42×C11C2×D412yes—
245C2×#542C2×C1111yescharacteristic
246C2×#477C2×C1111yescharacteristic, complemented
247C2×#464C2×C1111yescharacteristic, complemented
248#2323C2×C1111yescharacteristic, complemented
249#2036C2×C1111yescharacteristic, complemented
250#2033C2×C1111yescharacteristic
251#2001C2×C1111yescharacteristic, complemented
252#2000C2×C1111yescharacteristic
253#1988C2×C1111yescharacteristic, complemented
254#1983C2×C1111yescharacteristic, complemented
255#1878C2×C1111yescharacteristic, complemented
256#1877C2×C1111yescharacteristic, complemented
257#1863C2×C1111yescharacteristic, complemented
258#1862C2×C1111yescharacteristic, complemented
259#1798C2×C1111yescharacteristic, complemented
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C22×D411yescharacteristic
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11—41no—
282Q8×C11—41no—
283Q8×C11—84no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—84no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
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—84no—
328C2×C4×C11#12012yes—
329C2×C4×C11#12012yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C112−1+411yescharacteristic
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C22×Q16C22×C1111yescharacteristic
341C22×SD16C22×C1111yescharacteristic
342#542—24no—
343#542—24no—
344C2×C4⋊Q8C22×C1111yescharacteristic
345C2×#126—21no—
346C2×#124—21no—
347C2×#124C22×C1111yescharacteristic
348C2×#123—21no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8C22×C1111yescharacteristic
351C2×C22⋊Q8C22×C1111yescharacteristic
352C2×#121C22×C1111yescharacteristic
353C2×C4×Q8C22×C1111yescharacteristic
354C2×C4×Q8C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C2×#117C22×C1111yescharacteristic
357#477—24no—
358#464—24no—
359C2×#107C22×C1111yescharacteristic
360C2×#107C22×C1111yescharacteristic
361C2×C4⋊C8C22×C1111yescharacteristic
362C2×C4⋊C8C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#103C22×C1111yescharacteristic
365C2×#103C22×C1111yescharacteristic
366C2×#103C22×C1111yescharacteristic
367C2×#103C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371C2×C22⋊C8C22×C1111yescharacteristic
372C2×C22⋊C8C22×C1111yescharacteristic
373#391C22×C1111yescharacteristic
374#389—21no—
375#389C22×C1111yescharacteristic
376#388—21no—
377#388—21no—
378#387—21no—
379#380C22×C1111yescharacteristic
380C4×C4⋊C4C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—42no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—41no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11C2×#12011yescharacteristic
402C22×C11#52511yescharacteristic
403C22×C11#53711yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57811yescharacteristic
407C22×C11#57811yescharacteristic
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—42no—
411C4×C11—41no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11#54611yescharacteristic
421C4×C11#54711yescharacteristic
422C4×C11#54811yescharacteristic
423C4×C11#55011yescharacteristic
424C22×Q8—21no—
425C22×Q8C23×C1111yescharacteristic
426C22×Q8C23×C1111yescharacteristic
427C22×D4—21no—
428C22×D4C23×C1111yescharacteristic
429C23×C4—21no—
430C23×C4C23×C1111yescharacteristic
431C2×Q16—22no—
432C2×Q16—22no—
433C2×Q16—41no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—41no—
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441C4⋊Q8—22no—
442C4⋊Q8D4×C1114yes—
443#126—28no—
444#124—28no—
445#124—22no—
446#124D4×C1114yes—
447#123—28no—
448C22⋊Q8—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453#121—22no—
454#121—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×D4—22no—
460C4×D4—22no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4D4×C1111yescharacteristic
470C2×C4⋊C4D4×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C1111yescharacteristic
484C2×C22⋊C4D4×C1111yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42C23×C1111yescharacteristic
489C2×C42C23×C1111yescharacteristic
490#107—22no—
491#107—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494#103—22no—
495#103—22no—
496#103—22no—
497#103—22no—
498#103—41no—
499#102—22no—
500#102—22no—
501#102—41no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C2×C11—81no—
510C2×C11—82no—
511C2×C11#240711yescharacteristic
512C2×C11#301111yescharacteristic
513C2×C11#301211yescharacteristic
514C2×C11#312111yescharacteristic
515C2×C11#312411yescharacteristic
516C2×C11#325811yescharacteristic
517C2×C11#326211yescharacteristic
518C24—21no—
519C24C2×D4×C1111yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—81no—
532C2×Q8—81no—
533C2×Q8C2×D4×C1112yes—
534C2×Q8C11×#4112yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—81no—
542C2×D4—81no—
543C2×D4C2×D4×C1112yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
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—81no—
559C22×C4—81no—
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C2×D4×C1111yescharacteristic
562C22×C4C2×D4×C1111yescharacteristic
563C22×C4C2×D4×C1111yescharacteristic
564C22×C4C2×D4×C1111yescharacteristic
565C22×C4C24×C1111yescharacteristic
566Q16—44no—
567SD16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4C2×D4×C1112yes—
596C4⋊C4C2×D4×C1112yes—
597C4⋊C4C11×#4112yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—81no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42—42no—
611C42—81no—
612C42C2×D4×C1112yes—
613C42C2×D4×C1112yes—
614C11#2416811yescharacteristic, direct product factor, Sylow
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C22×D4×C1111yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—84no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4C11×#12012yes—
684C2×C4C11×#12012yes—
685C2×C4C22×D4×C1111yescharacteristic
686C2×C4C22×D4×C1111yescharacteristic
687C2×C4C2×C11×#4111yescharacteristic
688C2×C4C2×C11×#4111yescharacteristic
689C2×C4C11×H(5,𝔽2)11yescharacteristic
690C2×C4C11×2−1+411yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×C11×#12011yescharacteristic
710C22C11×#52511yescharacteristic
711C22C11×#53711yescharacteristic
712C22C11×#57611yescharacteristic
713C22C11×#57711yescharacteristic
714C22C11×#57811yescharacteristic
715C22C11×#57811yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4C11×#54611yescharacteristic
729C4C11×#54711yescharacteristic
730C4C11×#54811yescharacteristic
731C4C11×#55011yescharacteristic
732C2—81no—
733C2—82no—
734C2C11×#240711yescharacteristic
735C2C11×#301111yescharacteristic
736C2C11×#301211yescharacteristic
737C2C11×#312111yescharacteristic
738C2C11×#312411yescharacteristic
739C2C11×#325811yescharacteristic
740C2C11×#326211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#477C2semidirect
3. C2×C11×#464C2semidirect
4. C11×#2323C2semidirect
5. C11×#2036C2semidirect
7. C11×#2001C2semidirect
9. C11×#1988C2semidirect
10. C11×#1983C2semidirect
11. C11×#1878C2semidirect
12. C11×#1877C2semidirect
13. C11×#1863C2semidirect
14. C11×#1862C2semidirect
15. C11×#1798C2semidirect
148. #24168C11direct (N × H)
246. C2×#477C2×C11semidirect
247. C2×#464C2×C11semidirect
248. #2323C2×C11semidirect
249. #2036C2×C11semidirect
251. #2001C2×C11semidirect
253. #1988C2×C11semidirect
254. #1983C2×C11semidirect
255. #1878C2×C11semidirect
256. #1877C2×C11semidirect
257. #1863C2×C11semidirect
258. #1862C2×C11semidirect
259. #1798C2×C11semidirect
614. C11#24168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C2×C11×#4772
C2×C11×#4642
C11×#23232
C11×#20362
C11×#20332
C11×#20012
C11×#20002
C11×#19882
C11×#19832
C11×#18782
C11×#18772
C11×#18632
C11×#18622
C11×#17982
#2416811