Finite Group Databasebeta

← C11×#22048 #14599241

Subgroups — C11×#22048 #14599241

Order 2816.

1000 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#452C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#2297C211yesmaximal, characteristic
4C11×#1973C211yesmaximal, characteristic, complemented
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1936C211yesmaximal, characteristic, complemented
7C11×#1935C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic
15C11×#1749C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#452C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#387—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#385—21no—
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4—21no—
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C4×C11×C22⋊C4—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yes—
66C22×Q8×C11C2311yescharacteristic
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11D411yescharacteristic
72C23×C4×C11D411yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C2×C11×Q16—41no—
75C2×C11×Q16—41no—
76C2×C11×Q16C2×C414yescomplemented
77C2×C11×SD16—41no—
78C2×C11×SD16—41no—
79C2×C11×SD16C2×C414yescomplemented
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8C2×C414yes—
86C4×Q8×C11—41no—
87C4×Q8×C11—41no—
88C11×#117—41no—
89C11×#117—41no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11—41no—
109C2×C42×C11—41no—
110C2×C42×C11D411yescharacteristic
111C2×C42×C11D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107—41no—
115C11×#106—41no—
116C11×#103—41no—
117C11×#103—41no—
118C11×#103—41no—
119C11×#103—41no—
120C11×#103C2×C414yescomplemented
121C11×#102—41no—
122C11×#102—41no—
123C11×#102C2×C414yescomplemented
124C11×C22⋊C8—22no—
125C11×C22⋊C8C2×C414yes—
126C11×#97—41no—
127C11×#97—41no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137#22048C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22×C412yes—
155C2×Q8×C11C22×C412yes—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11C22×C412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4112yes—
192C22×C4×C11C2411yescharacteristic
193C11×Q16—44no—
194C11×SD16—44no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
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×C11C22×C412yes—
206C2×C8×C11C22×C412yes—
207C11×C4⋊C4—24no—
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—21no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4C22×C412yes—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—41no—
232C42×C11—41no—
233C42×C11—42no—
234C42×C11—42no—
235C42×C11—42no—
236C2×#452C2×C1111yescharacteristic
237C4×C22⋊Q8C2×C1111yescharacteristic, complemented
238#2297C2×C1111yescharacteristic
239#1973C2×C1111yescharacteristic, complemented
240#1971C2×C1111yescharacteristic, complemented
241#1936C2×C1111yescharacteristic, complemented
242#1935C2×C1111yescharacteristic, complemented
243#1928C2×C1111yescharacteristic, complemented
244#1926C2×C1111yescharacteristic, complemented
245#1880C2×C1111yescharacteristic, complemented
246#1878C2×C1111yescharacteristic, complemented
247#1873C2×C1111yescharacteristic, complemented
248#1854C2×C1111yescharacteristic, complemented
249#1788C2×C1111yescharacteristic
250#1749C2×C1111yescharacteristic, complemented
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—22no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11C4×D412yes—
265C23×C11C22×D411yescharacteristic
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—48no—
277D4×C11—41no—
278D4×C11—41no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—44no—
300C2×C4×C11—48no—
301C2×C4×C11—44no—
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—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×C11C4×D412yes—
321C2×C4×C11#13712yes—
322C2×C4×C11C23×C411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C8×C11—22no—
329C8×C11—22no—
330C8×C11—41no—
331C8×C11—41no—
332C22×#41C22×C1111yescharacteristic
333C22×Q16C22×C1111yescharacteristic
334C22×SD16C22×C1111yescharacteristic
335C2×C22⋊Q8C22×C1111yescharacteristic
336C2×C4×Q8C22×C1111yescharacteristic
337C2×#117C22×C1111yescharacteristic
338C22×C42C22×C1111yescharacteristic
339#452C4×C1118yescomplemented
340C2×#107C22×C1111yescharacteristic
341C2×#106C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352C2×#97C22×C1111yescharacteristic
353C2×#97C22×C1111yescharacteristic
354#391C22×C1111yescharacteristic
355#391C22×C1111yescharacteristic
356#391C22×C1111yescharacteristic
357#390C22×C1111yescharacteristic
358#390C22×C1111yescharacteristic
359#389C22×C1111yescharacteristic
360#387—21no—
361#386—21no—
362#386—21no—
363#385—21no—
364#380C22×C1111yescharacteristic
365C4×C4⋊C4—21no—
366C4×C4⋊C4C22×C1111yescharacteristic
367C4×C22⋊C4—21no—
368C4×C22⋊C4—21no—
369C4×C22⋊C4—21no—
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11C2×C4×D411yescharacteristic
391C22×C11#53411yescharacteristic
392C22×C11#53511yescharacteristic
393C22×C11C2×#13711yescharacteristic
394C22×C11#57511yescharacteristic
395C22×C11#57511yescharacteristic
396C22×C11#57511yescharacteristic
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—42no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11#51811yescharacteristic
410C4×C11#51811yescharacteristic
411C4×C11#53811yescharacteristic
412C4×C11#53811yescharacteristic
413C2×#41—22no—
414C2×#41—41no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41C2×C4×C1114yes—
419C22×Q8C23×C1111yescharacteristic
420C22×Q8C23×C1111yescharacteristic
421C22×D4—21no—
422C22×D4C23×C1111yescharacteristic
423C23×C4—21no—
424C23×C4D4×C1111yescharacteristic
425C23×C4D4×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C2×Q16—41no—
428C2×Q16—41no—
429C2×Q16C2×C4×C1114yescomplemented
430C2×SD16—41no—
431C2×SD16—41no—
432C2×SD16C2×C4×C1114yescomplemented
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22⋊Q8—22no—
438C22⋊Q8C2×C4×C1114yes—
439C4×Q8—41no—
440C4×Q8—41no—
441#117—41no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—41no—
462C2×C42—41no—
463C2×C42D4×C1111yescharacteristic
464C2×C42D4×C1111yescharacteristic
465C2×C42C23×C1111yescharacteristic
466C2×C42C23×C1111yescharacteristic
467#107—41no—
468#106—41no—
469#103—41no—
470#103—41no—
471#103—41no—
472#103—41no—
473#103C2×C4×C1114yescomplemented
474#102—41no—
475#102—41no—
476#102C2×C4×C1114yescomplemented
477C22⋊C8—22no—
478C22⋊C8C2×C4×C1114yes—
479#97—41no—
480#97—41no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C2×C11—42no—
491C2×C11—82no—
492C2×C11#232111yescharacteristic
493C2×C11#294311yescharacteristic
494C2×C11C4×#13711yescharacteristic
495C2×C11#319611yescharacteristic
496C2×C11#319711yescharacteristic
497C2×C11#321611yescharacteristic
498C2×C11#321911yescharacteristic
499C24—21no—
500C24C2×D4×C1111yescharacteristic
501#41—44no—
502#41—44no—
503#41—44no—
504#41—44no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8C22×C4×C1112yes—
516C2×Q8C22×C4×C1112yes—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C22×C4×C1112yes—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4C22×C4×C1112yes—
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C11×#4112yes—
553C22×C4C24×C1111yescharacteristic
554Q16—44no—
555SD16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8C22×C4×C1112yes—
567C2×C8C22×C4×C1112yes—
568C4⋊C4—24no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4C22×C4×C1112yes—
581C22⋊C4—24no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—41no—
593C42—41no—
594C42—42no—
595C42—42no—
596C42—42no—
597C11#2204811yescharacteristic, direct product factor, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C4×D4×C1112yes—
612C23C22×D4×C1111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—44no—
647C2×C4—48no—
648C2×C4—44no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4C4×D4×C1112yes—
668C2×C4C11×#13712yes—
669C2×C4C23×C4×C1111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×H(5,𝔽2)11yescharacteristic
673C2×C4C11×H(5,𝔽2)11yescharacteristic
674C2×C4C11×H(5,𝔽2)11yescharacteristic
675C8—22no—
676C8—22no—
677C8—41no—
678C8—41no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×C4×D4×C1111yescharacteristic
694C22C11×#53411yescharacteristic
695C22C11×#53511yescharacteristic
696C22C2×C11×#13711yescharacteristic
697C22C11×#57511yescharacteristic
698C22C11×#57511yescharacteristic
699C22C11×#57511yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C11×#51811yescharacteristic
713C4C11×#51811yescharacteristic
714C4C11×#53811yescharacteristic
715C4C11×#53811yescharacteristic
716C2—42no—
717C2—82no—
718C2C11×#232111yescharacteristic
719C2C11×#294311yescharacteristic
720C2C4×C11×#13711yescharacteristic
721C2C11×#319611yescharacteristic
722C2C11×#319711yescharacteristic
723C2C11×#321611yescharacteristic
724C2C11×#321911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C22⋊Q8C2semidirect
4. C11×#1973C2semidirect
5. C11×#1971C2semidirect
6. C11×#1936C2semidirect
7. C11×#1935C2semidirect
8. C11×#1928C2semidirect
9. C11×#1926C2semidirect
10. C11×#1880C2semidirect
11. C11×#1878C2semidirect
12. C11×#1873C2semidirect
13. C11×#1854C2semidirect
15. C11×#1749C2semidirect
23. C11×#452C4semidirect
76. C2×C11×Q16C2×C4semidirect
79. C2×C11×SD16C2×C4semidirect
120. C11×#103C2×C4semidirect
123. C11×#102C2×C4semidirect
137. #22048C11direct (N × H)
237. C4×C22⋊Q8C2×C11semidirect
239. #1973C2×C11semidirect
240. #1971C2×C11semidirect
241. #1936C2×C11semidirect
242. #1935C2×C11semidirect
243. #1928C2×C11semidirect
244. #1926C2×C11semidirect
245. #1880C2×C11semidirect
246. #1878C2×C11semidirect
247. #1873C2×C11semidirect
248. #1854C2×C11semidirect
250. #1749C2×C11semidirect
339. #452C4×C11semidirect
429. C2×Q16C2×C4×C11semidirect
432. C2×SD16C2×C4×C11semidirect
473. #103C2×C4×C11semidirect
476. #102C2×C4×C11semidirect
597. C11#22048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C4×C11×C22⋊Q82
C11×#22972
C11×#19732
C11×#19712
C11×#19362
C11×#19352
C11×#19282
C11×#19262
C11×#18802
C11×#18782
C11×#18732
C11×#18542
C11×#17882
C11×#17492
#2204811