Finite Group Databasebeta

← C11×#24335 #14601528

Subgroups — C11×#24335 #14601528

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic, complemented
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2057C211yesmaximal, characteristic, complemented
7C11×#2025C211yesmaximal, characteristic, complemented
8C11×#2023C211yesmaximal, characteristic, complemented
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1984C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic
12C11×#1879C211yesmaximal, characteristic
13C11×#1864C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C11×#554—24no—
18C11×#554—24no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4—21no—
31C11×#478—24no—
32C4×C11×D8—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#399—21no—
45C11×#393—21no—
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#385—21no—
51C11×#385—21no—
52C11×#382C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8Q814yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8—22no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125—22no—
83C11×#125D414yes—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—28no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11D414yes—
97C2×C11×C4⋊C4—28no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
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×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C11×#107—22no—
126C11×#107—22no—
127C11×#106—22no—
128C11×C4⋊C8—22no—
129C11×#102—22no—
130C11×#102—22no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C4×C8×C11—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24335C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—41no—
147C2×Q8×C11—81no—
148C2×Q8×C11—81no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C2×D412yes—
158C2×D4×C11C2×Q812yes—
159C2×D4×C11C2×Q812yes—
160C2×D4×C11#4112yes—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C11×D8—28no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×Q812yes—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—81no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4C2×D412yes—
219C11×C4⋊C4C2×D412yes—
220C11×C4⋊C4C2×D412yes—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11C2×D412yes—
234C42×C11C2×D412yes—
235C2×#554C2×C1111yescharacteristic, complemented
236C2×#478C2×C1111yescharacteristic, complemented
237C2×C4×D8C2×C1111yescharacteristic
238#2580C2×C1111yescharacteristic, complemented
239#2059C2×C1111yescharacteristic, complemented
240#2057C2×C1111yescharacteristic, complemented
241#2025C2×C1111yescharacteristic, complemented
242#2023C2×C1111yescharacteristic, complemented
243#1991C2×C1111yescharacteristic, complemented
244#1984C2×C1111yescharacteristic, complemented
245#1879C2×C1111yescharacteristic
246#1879C2×C1111yescharacteristic
247#1864C2×C1111yescharacteristic, complemented
248#1862C2×C1111yescharacteristic, complemented
249#1804C2×C1111yescharacteristic, complemented
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11C22×D411yescharacteristic
265Q8×C11—44no—
266Q8×C11—84no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11C22⋊Q814yes—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—48no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—84no—
310C2×C4×C11—84no—
311C2×C4×C11—84no—
312C2×C4×C11#12012yes—
313C2×C4×C11#12012yes—
314C2×C4×C11#13512yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×Q811yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C112−1+411yescharacteristic
320C2×C4×C112−1+411yescharacteristic
321C8×C11—22no—
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C22×D8C22×C1111yescharacteristic
326#554—24no—
327#554—24no—
328C2×C4⋊Q8C22×C1111yescharacteristic
329C2×#125C22×C1111yescharacteristic
330C2×#125C22×C1111yescharacteristic
331C2×C22⋊Q8—21no—
332C2×C22⋊Q8—21no—
333C2×C22⋊Q8—21no—
334C2×C4×Q8C22×C1111yescharacteristic
335C2×C4×D4C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×C4×D4C22×C1111yescharacteristic
339C22×C4⋊C4—21no—
340#478—24no—
341C4×D8—24no—
342C2×#107C22×C1111yescharacteristic
343C2×#107C22×C1111yescharacteristic
344C2×#106C22×C1111yescharacteristic
345C2×C4⋊C8C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×C4×C8C22×C1111yescharacteristic
353#399—21no—
354#393—21no—
355#390C22×C1111yescharacteristic
356#390C22×C1111yescharacteristic
357#389C22×C1111yescharacteristic
358#389C22×C1111yescharacteristic
359#385—21no—
360#385—21no—
361#382C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370#336C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372C22×C11—24no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11C2×#12011yescharacteristic
387C22×C11#54811yescharacteristic
388C22×C11D4×Q811yescharacteristic
389C22×C11C2×#13511yescharacteristic
390C22×C11#57511yescharacteristic
391C22×C11#57611yescharacteristic
392C22×C11#57611yescharacteristic
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—41no—
397C4×C11—42no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11C2×C22⋊Q811yescharacteristic
406C4×C11#53611yescharacteristic
407C4×C11#54811yescharacteristic
408C4×C11D4×Q811yescharacteristic
409C22×Q8—21no—
410C22×Q8D4×C1111yescharacteristic
411C22×D4C23×C1111yescharacteristic
412C22×D4C23×C1111yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—21no—
417C2×D8—22no—
418C2×D8—22no—
419C2×D8Q8×C1114yescomplemented
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C4⋊Q8—22no—
425C4⋊Q8—22no—
426#125—22no—
427#125—22no—
428#125—22no—
429#125D4×C1114yes—
430C22⋊Q8—28no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4D4×C1114yes—
443C2×C4⋊C4—28no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C1111yescharacteristic
452C2×C4⋊C4D4×C1111yescharacteristic
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42C23×C1111yescharacteristic
469C2×C42C23×C1111yescharacteristic
470C2×C42C23×C1111yescharacteristic
471#107—22no—
472#107—22no—
473#106—22no—
474C4⋊C8—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481C4×C8—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C2×C11—44no—
487C2×C11—82no—
488C2×C11#240911yescharacteristic
489C2×C11#300211yescharacteristic
490C2×C11#300811yescharacteristic
491C2×C11#336111yescharacteristic
492C2×C11#337011yescharacteristic
493C2×C11#338011yescharacteristic
494C2×C11#338911yescharacteristic
495C24—21no—
496C24—21no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—41no—
501C2×Q8—81no—
502C2×Q8—81no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×D4×C1112yes—
512C2×D4C2×Q8×C1112yes—
513C2×D4C2×Q8×C1112yes—
514C2×D4C11×#4112yes—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C24×C1111yescharacteristic
540D8—28no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8C2×Q8×C1112yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—81no—
572C4⋊C4C2×D4×C1112yes—
573C4⋊C4C2×D4×C1112yes—
574C4⋊C4C2×D4×C1112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42C2×D4×C1112yes—
588C42C2×D4×C1112yes—
589C11#2433511yescharacteristic, direct product factor, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C1111yescharacteristic
605Q8—44no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4C11×C22⋊Q814yes—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—48no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4C11×#12012yes—
653C2×C4C11×#12012yes—
654C2×C4C11×#13512yes—
655C2×C4C22×D4×C1111yescharacteristic
656C2×C4C22×D4×C1111yescharacteristic
657C2×C4C22×Q8×C1111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C2×C4C11×2−1+411yescharacteristic
660C2×C4C11×2−1+411yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C11×#12011yescharacteristic
680C22C11×#54811yescharacteristic
681C22D4×Q8×C1111yescharacteristic
682C22C2×C11×#13511yescharacteristic
683C22C11×#57511yescharacteristic
684C22C11×#57611yescharacteristic
685C22C11×#57611yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C2×C11×C22⋊Q811yescharacteristic
699C4C11×#53611yescharacteristic
700C4C11×#54811yescharacteristic
701C4D4×Q8×C1111yescharacteristic
702C2—44no—
703C2—82no—
704C2C11×#240911yescharacteristic
705C2C11×#300211yescharacteristic
706C2C11×#300811yescharacteristic
707C2C11×#336111yescharacteristic
708C2C11×#337011yescharacteristic
709C2C11×#338011yescharacteristic
710C2C11×#338911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#554C2semidirect
2. C2×C11×#478C2semidirect
4. C11×#2580C2semidirect
5. C11×#2059C2semidirect
6. C11×#2057C2semidirect
7. C11×#2025C2semidirect
8. C11×#2023C2semidirect
9. C11×#1991C2semidirect
10. C11×#1984C2semidirect
13. C11×#1864C2semidirect
14. C11×#1862C2semidirect
15. C11×#1804C2semidirect
73. C2×C11×D8Q8semidirect
140. #24335C11direct (N × H)
235. C2×#554C2×C11semidirect
236. C2×#478C2×C11semidirect
238. #2580C2×C11semidirect
239. #2059C2×C11semidirect
240. #2057C2×C11semidirect
241. #2025C2×C11semidirect
242. #2023C2×C11semidirect
243. #1991C2×C11semidirect
244. #1984C2×C11semidirect
247. #1864C2×C11semidirect
248. #1862C2×C11semidirect
249. #1804C2×C11semidirect
419. C2×D8Q8×C11semidirect
589. C11#24335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4782
C2×C4×C11×D82
C11×#25802
C11×#20592
C11×#20572
C11×#20252
C11×#20232
C11×#19912
C11×#19842
C11×#18792
C11×#18642
C11×#18622
C11×#18042
#2433511