Finite Group Databasebeta

← C11×#22678 #14599871

Subgroups — C11×#22678 #14599871

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#440C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C11×#1865C211yesmaximal, characteristic, complemented
9C11×#1864C211yesmaximal, characteristic
10C11×#1863C211yesmaximal, characteristic, complemented
11C11×#1862C211yesmaximal, characteristic
12C11×#1847C211yesmaximal, characteristic, complemented
13C11×#1805C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C11×#440—24no—
24C11×#440C418yescomplemented
25C4×C11×SD16—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#389—21no—
42C11×#389—21no—
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#385—21no—
48C11×#385—21no—
49C11×#384—21no—
50C11×#384C2211yescharacteristic
51C11×#382C2211yescharacteristic
52C11×#380—21no—
53C4×C11×C4⋊C4—21no—
54C4×C11×C4⋊C4C2211yescharacteristic
55C2×C11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C2×C11×SD16C2×C414yes—
68C2×C11×SD16D414yes—
69C2×C11×SD16Q814yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—41no—
78C4×Q8×C11—41no—
79C4×Q8×C11C2×C414yescomplemented
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11C2×C414yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
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×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×#107—22no—
113C11×#107—41no—
114C11×#107C2×C414yescomplemented
115C11×#106—22no—
116C11×#106—41no—
117C11×C4⋊C8—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103C2×C414yescomplemented
121C11×#102—22no—
122C11×#102—22no—
123C11×#102C2×C414yes—
124C11×#97—22no—
125C11×#97C2×C414yescomplemented
126C4×C8×C11—22no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135#22678C1111yesmaximal, characteristic, direct product factor, Sylow
136C24×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×Q8×C11C2×D412yes—
142C2×Q8×C11C2×Q812yes—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11C22×C412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×Q812yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11—81no—
164C22×C4×C11—81no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×SD16C4⋊C4116yescomplemented
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C22×C412yes—
182C2×C8×C11C22×C412yes—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×Q812yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—81no—
202C11×C4⋊C4—81no—
203C11×C4⋊C4—81no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C42×C11—24no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—42no—
217C42×C11—42no—
218C42×C11C22×C412yes—
219C42×C11#4112yes—
220C2×#440C2×C1111yescharacteristic
221C2×#440C2×C1111yescharacteristic
222C2×C4×SD16C2×C1111yescharacteristic
223Q8×C4⋊C4C2×C1111yescharacteristic, complemented
224#2349C2×C1111yescharacteristic
225#1943C2×C1111yescharacteristic, complemented
226#1942C2×C1111yescharacteristic, complemented
227#1865C2×C1111yescharacteristic, complemented
228#1864C2×C1111yescharacteristic
229#1863C2×C1111yescharacteristic, complemented
230#1862C2×C1111yescharacteristic
231#1847C2×C1111yescharacteristic, complemented
232#1805C2×C1111yescharacteristic, complemented
233#1802C2×C1111yescharacteristic
234#1771C2×C1111yescharacteristic, complemented
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11C2×C4⋊C414yes—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11C2×C4⋊C414yes—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—84no—
288C2×C4×C11—84no—
289C2×C4×C11—84no—
290C2×C4×C11C4×D412yes—
291C2×C4×C11C4×D412yes—
292C2×C4×C11#13712yes—
293C2×C4×C11C23×C411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×Q811yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C112−1+411yescharacteristic
299C8×C11—22no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11C2×C4⋊C414yes—
303C22×SD16C22×C1111yescharacteristic
304C2×C4×Q8C22×C1111yescharacteristic
305C2×C4×Q8C22×C1111yescharacteristic
306C2×C4×Q8C22×C1111yescharacteristic
307C2×C4×D4C22×C1111yescharacteristic
308C2×C4×D4C22×C1111yescharacteristic
309C2×C4×D4C22×C1111yescharacteristic
310#440—24no—
311#440C4×C1118yescomplemented
312C4×SD16—24no—
313C2×#107C22×C1111yescharacteristic
314C2×#107C22×C1111yescharacteristic
315C2×#107C22×C1111yescharacteristic
316C2×#106C22×C1111yescharacteristic
317C2×#106C22×C1111yescharacteristic
318C2×C4⋊C8C22×C1111yescharacteristic
319C2×#103C22×C1111yescharacteristic
320C2×#103C22×C1111yescharacteristic
321C2×#103C22×C1111yescharacteristic
322C2×#102C22×C1111yescharacteristic
323C2×#102C22×C1111yescharacteristic
324C2×#102C22×C1111yescharacteristic
325C2×#97C22×C1111yescharacteristic
326C2×#97C22×C1111yescharacteristic
327C2×C4×C8C22×C1111yescharacteristic
328#389—21no—
329#389—21no—
330#389C22×C1111yescharacteristic
331#389C22×C1111yescharacteristic
332#389C22×C1111yescharacteristic
333#389C22×C1111yescharacteristic
334#385—21no—
335#385—21no—
336#384—21no—
337#384C22×C1111yescharacteristic
338#382C22×C1111yescharacteristic
339#380—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4C22×C1111yescharacteristic
342C2×#95—21no—
343#340C22×C1111yescharacteristic
344#340C22×C1111yescharacteristic
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#336C22×C1111yescharacteristic
348#336C22×C1111yescharacteristic
349C22×C11—24no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11D4×Q811yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—24no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11C22×C4⋊C411yescharacteristic
377C4×C11#52011yescharacteristic
378C4×C11#54711yescharacteristic
379C4×C11#55411yescharacteristic
380C22×Q8C23×C1111yescharacteristic
381C22×D4C23×C1111yescharacteristic
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—21no—
385C2×SD16C2×C4×C1114yes—
386C2×SD16D4×C1114yes—
387C2×SD16Q8×C1114yes—
388C22×C8C23×C1111yescharacteristic
389C22×C8C23×C1111yescharacteristic
390C22×C8C23×C1111yescharacteristic
391C22×C8C23×C1111yescharacteristic
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×Q8—41no—
397C4×Q8C2×C4×C1114yescomplemented
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—41no—
402C4×D4—41no—
403C4×D4C2×C4×C1114yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4D4×C1111yescharacteristic
414C2×C4⋊C4D4×C1111yescharacteristic
415C2×C4⋊C4C23×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C23×C1111yescharacteristic
428C2×C42C23×C1111yescharacteristic
429C2×C42C23×C1111yescharacteristic
430#107—22no—
431#107—41no—
432#107C2×C4×C1114yescomplemented
433#106—22no—
434#106—41no—
435C4⋊C8—22no—
436#103—22no—
437#103—22no—
438#103C2×C4×C1114yescomplemented
439#102—22no—
440#102—22no—
441#102C2×C4×C1114yes—
442#97—22no—
443#97C2×C4×C1114yescomplemented
444C4×C8—22no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95D4×C1111yescharacteristic
452#95D4×C1111yescharacteristic
453C2×C11—44no—
454C2×C11D4×C4⋊C411yescharacteristic
455C2×C11C4×#13711yescharacteristic
456C2×C11#294611yescharacteristic
457C2×C11#326611yescharacteristic
458C2×C11#326811yescharacteristic
459C2×C11#338511yescharacteristic
460C2×C11#338811yescharacteristic
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C22×C4×C1112yes—
466C2×Q8C2×D4×C1112yes—
467C2×Q8C2×Q8×C1112yes—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C22×C4×C1112yes—
472C2×D4C2×D4×C1112yes—
473C2×D4C2×Q8×C1112yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C24×C1111yescharacteristic
497SD16C11×C4⋊C4116yescomplemented
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C22×C4×C1112yes—
507C2×C8C22×C4×C1112yes—
508C2×C8C2×D4×C1112yes—
509C2×C8C2×Q8×C1112yes—
510C4⋊C4—24no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—81no—
527C4⋊C4—81no—
528C4⋊C4—81no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4C22×C4×C1112yes—
532C4⋊C4C22×C4×C1112yes—
533C22⋊C4—24no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C42—24no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—42no—
543C42C22×C4×C1112yes—
544C42C11×#4112yes—
545C11#2267811yescharacteristic, direct product factor, Sylow
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C22×D4×C1111yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8C2×C11×C4⋊C414yes—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C2×C11×C4⋊C414yes—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4C4×D4×C1112yes—
602C2×C4C4×D4×C1112yes—
603C2×C4C11×#13712yes—
604C2×C4C23×C4×C1111yescharacteristic
605C2×C4C22×D4×C1111yescharacteristic
606C2×C4C22×Q8×C1111yescharacteristic
607C2×C4C2×C11×#4111yescharacteristic
608C2×C4C11×H(5,𝔽2)11yescharacteristic
609C2×C4C11×2−1+411yescharacteristic
610C8—22no—
611C8—41no—
612C8—41no—
613C8C2×C11×C4⋊C414yes—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C2×C4×D4×C1111yescharacteristic
622C22D42×C1111yescharacteristic
623C22D4×Q8×C1111yescharacteristic
624C22C2×C11×#13711yescharacteristic
625C22C11×#57511yescharacteristic
626C22C11×#57611yescharacteristic
627C22C11×#57711yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—24no—
632C4—42no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4C22×C11×C4⋊C411yescharacteristic
642C4C11×#52011yescharacteristic
643C4C11×#54711yescharacteristic
644C4C11×#55411yescharacteristic
645C2—44no—
646C2D4×C11×C4⋊C411yescharacteristic
647C2C4×C11×#13711yescharacteristic
648C2C11×#294611yescharacteristic
649C2C11×#326611yescharacteristic
650C2C11×#326811yescharacteristic
651C2C11×#338511yescharacteristic
652C2C11×#338811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. Q8×C11×C4⋊C4C2semidirect
6. C11×#1943C2semidirect
7. C11×#1942C2semidirect
8. C11×#1865C2semidirect
10. C11×#1863C2semidirect
12. C11×#1847C2semidirect
13. C11×#1805C2semidirect
15. C11×#1771C2semidirect
24. C11×#440C4semidirect
79. C4×Q8×C11C2×C4semidirect
114. C11×#107C2×C4semidirect
120. C11×#103C2×C4semidirect
125. C11×#97C2×C4semidirect
135. #22678C11direct (N × H)
172. C11×SD16C4⋊C4semidirect
223. Q8×C4⋊C4C2×C11semidirect
225. #1943C2×C11semidirect
226. #1942C2×C11semidirect
227. #1865C2×C11semidirect
229. #1863C2×C11semidirect
231. #1847C2×C11semidirect
232. #1805C2×C11semidirect
234. #1771C2×C11semidirect
311. #440C4×C11semidirect
397. C4×Q8C2×C4×C11semidirect
432. #107C2×C4×C11semidirect
438. #103C2×C4×C11semidirect
443. #97C2×C4×C11semidirect
497. SD16C11×C4⋊C4semidirect
545. C11#22678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4402
C2×C4×C11×SD162
Q8×C11×C4⋊C42
C11×#23492
C11×#19432
C11×#19422
C11×#18652
C11×#18642
C11×#18632
C11×#18622
C11×#18472
C11×#18052
C11×#18022
C11×#17712
#2267811