Finite Group Databasebeta

← C11×#22194 #14599387

Subgroups — C11×#22194 #14599387

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C211yesmaximal, characteristic
2C11×#2324C211yesmaximal, characteristic
3C11×#2323C211yesmaximal, characteristic, complemented
4C11×#1928C211yesmaximal, characteristic, complemented
5C11×#1925C211yesmaximal, characteristic, complemented
6C11×#1920C211yesmaximal, characteristic, complemented
7C11×#1919C211yesmaximal, characteristic, complemented
8C11×#1895C211yesmaximal, characteristic
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C11×#1808C211yesmaximal, characteristic, complemented
15C11×#1729C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#465C418yescomplemented
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C11×#391C2211yescharacteristic
35C11×#390—21no—
36C11×#390C2211yescharacteristic
37C11×#389—21no—
38C11×#389C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#388—21no—
41C11×#388—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#385—21no—
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16C2×C414yes—
68C2×C11×M16—22no—
69C2×C11×M16—41no—
70C2×C11×M16—41no—
71C22×C8×C11—41no—
72C22×C8×C11—41no—
73C22×C8×C11C2×C414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2×C414yescomplemented
80C11×#121—22no—
81C11×#121C2×C414yes—
82C4×Q8×C11—41no—
83C4×Q8×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C11×#117—41no—
87C11×#117—41no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107—41no—
115C11×#107—41no—
116C11×#106C2×C414yescomplemented
117C11×#103—41no—
118C11×#103—41no—
119C11×#103C2×C414yescomplemented
120C11×#102—41no—
121C11×#102—41no—
122C11×#102C2×C414yes—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131#22194C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—81no—
147C2×D4×C11—81no—
148C2×D4×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—42no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C11×SD16—44no—
172C11×M16—44no—
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×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—44no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C11×C4⋊C4—24no—
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—41no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—81no—
201C11×C4⋊C4—81no—
202C11×C4⋊C4C22×C412yes—
203C11×C4⋊C4C22×C412yes—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—24no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—42no—
218C42×C11—81no—
219C42×C11—81no—
220C2×#465C2×C1111yescharacteristic
221#2324C2×C1111yescharacteristic
222#2323C2×C1111yescharacteristic, complemented
223#1928C2×C1111yescharacteristic, complemented
224#1925C2×C1111yescharacteristic, complemented
225#1920C2×C1111yescharacteristic, complemented
226#1919C2×C1111yescharacteristic, complemented
227#1895C2×C1111yescharacteristic
228#1894C2×C1111yescharacteristic, complemented
229#1880C2×C1111yescharacteristic, complemented
230#1877C2×C1111yescharacteristic, complemented
231#1863C2×C1111yescharacteristic, complemented
232#1862C2×C1111yescharacteristic, complemented
233#1808C2×C1111yescharacteristic, complemented
234#1729C2×C1111yescharacteristic, complemented
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C4×D412yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
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—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—84no—
299C2×C4×C11C4×D412yes—
300C2×C4×C11C23×C411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C8×C11—22no—
307C8×C11—22no—
308C8×C11—41no—
309C8×C11—41no—
310C22×SD16C22×C1111yescharacteristic
311C22×M16C22×C1111yescharacteristic
312C23×C8C22×C1111yescharacteristic
313C2×C22⋊Q8C22×C1111yescharacteristic
314C2×#121C22×C1111yescharacteristic
315C2×C4×Q8C22×C1111yescharacteristic
316C2×C4×D4C22×C1111yescharacteristic
317C2×#117C22×C1111yescharacteristic
318#465C4×C1118yescomplemented
319C2×#107C22×C1111yescharacteristic
320C2×#107C22×C1111yescharacteristic
321C2×#106C22×C1111yescharacteristic
322C2×#103C22×C1111yescharacteristic
323C2×#103C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#102C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328#391C22×C1111yescharacteristic
329#390—21no—
330#390C22×C1111yescharacteristic
331#389—21no—
332#389C22×C1111yescharacteristic
333#389C22×C1111yescharacteristic
334#388—21no—
335#388—21no—
336#388—21no—
337#387—21no—
338#386—21no—
339#385—21no—
340#380C22×C1111yescharacteristic
341#380C22×C1111yescharacteristic
342C4×C4⋊C4C22×C1111yescharacteristic
343C4×C4⋊C4C22×C1111yescharacteristic
344#340C22×C1111yescharacteristic
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#336C22×C1111yescharacteristic
351#336C22×C1111yescharacteristic
352#336C22×C1111yescharacteristic
353#336C22×C1111yescharacteristic
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11C2×C4×D411yescharacteristic
369C22×C11#53411yescharacteristic
370C22×C11#53711yescharacteristic
371C22×C11#57611yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C22×C11#57811yescharacteristic
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11#51811yescharacteristic
388C4×C11#52011yescharacteristic
389C4×C11#53811yescharacteristic
390C4×C11#53911yescharacteristic
391C22×Q8C23×C1111yescharacteristic
392C22×D4—21no—
393C22×D4C23×C1111yescharacteristic
394C23×C4—21no—
395C23×C4C23×C1111yescharacteristic
396C2×SD16—41no—
397C2×SD16—41no—
398C2×SD16C2×C4×C1114yes—
399C2×M16—22no—
400C2×M16—41no—
401C2×M16—41no—
402C22×C8—41no—
403C22×C8—41no—
404C22×C8C2×C4×C1114yescomplemented
405C22×C8C23×C1111yescharacteristic
406C22×C8C23×C1111yescharacteristic
407C22×C8C23×C1111yescharacteristic
408C22×C8C23×C1111yescharacteristic
409C22⋊Q8—22no—
410C22⋊Q8C2×C4×C1114yescomplemented
411#121—22no—
412#121C2×C4×C1114yes—
413C4×Q8—41no—
414C4×Q8—41no—
415C4×D4—41no—
416C4×D4—41no—
417#117—41no—
418#117—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C1111yescharacteristic
424C2×C4⋊C4D4×C1111yescharacteristic
425C2×C4⋊C4C23×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C1111yescharacteristic
439C2×C22⋊C4D4×C1111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C1111yescharacteristic
444C2×C42C23×C1111yescharacteristic
445#107—41no—
446#107—41no—
447#106C2×C4×C1114yescomplemented
448#103—41no—
449#103—41no—
450#103C2×C4×C1114yescomplemented
451#102—41no—
452#102—41no—
453#102C2×C4×C1114yes—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462C2×C11—42no—
463C2×C11—82no—
464C2×C11#232511yescharacteristic
465C2×C11#294911yescharacteristic
466C2×C11#295111yescharacteristic
467C2×C11#319811yescharacteristic
468C2×C11#320111yescharacteristic
469C2×C11#325711yescharacteristic
470C2×C11#325811yescharacteristic
471C24—21no—
472C24C2×D4×C1111yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8C22×C4×C1112yes—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4C22×C4×C1112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C22×C4×C1112yes—
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C11×#4112yes—
509C22×C4C24×C1111yescharacteristic
510SD16—44no—
511M16—44no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—44no—
523C2×C8C22×C4×C1112yes—
524C2×C8C22×C4×C1112yes—
525C4⋊C4—24no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4C22×C4×C1112yes—
542C4⋊C4C22×C4×C1112yes—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—42no—
557C42—81no—
558C42—81no—
559C11#2219411yescharacteristic, direct product factor, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C4×D4×C1112yes—
574C23C22×D4×C1111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—84no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—84no—
624C2×C4C4×D4×C1112yes—
625C2×C4C23×C4×C1111yescharacteristic
626C2×C4C2×C11×#4111yescharacteristic
627C2×C4C11×H(5,𝔽2)11yescharacteristic
628C2×C4C11×H(5,𝔽2)11yescharacteristic
629C2×C4C11×H(5,𝔽2)11yescharacteristic
630C2×C4C11×2−1+411yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×C4×D4×C1111yescharacteristic
650C22C11×#53411yescharacteristic
651C22C11×#53711yescharacteristic
652C22C11×#57611yescharacteristic
653C22C11×#57711yescharacteristic
654C22C11×#57711yescharacteristic
655C22C11×#57811yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C11×#51811yescharacteristic
669C4C11×#52011yescharacteristic
670C4C11×#53811yescharacteristic
671C4C11×#53911yescharacteristic
672C2—42no—
673C2—82no—
674C2C11×#232511yescharacteristic
675C2C11×#294911yescharacteristic
676C2C11×#295111yescharacteristic
677C2C11×#319811yescharacteristic
678C2C11×#320111yescharacteristic
679C2C11×#325711yescharacteristic
680C2C11×#325811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2323C2semidirect
4. C11×#1928C2semidirect
5. C11×#1925C2semidirect
6. C11×#1920C2semidirect
7. C11×#1919C2semidirect
9. C11×#1894C2semidirect
10. C11×#1880C2semidirect
11. C11×#1877C2semidirect
12. C11×#1863C2semidirect
13. C11×#1862C2semidirect
14. C11×#1808C2semidirect
15. C11×#1729C2semidirect
24. C11×#465C4semidirect
73. C22×C8×C11C2×C4semidirect
79. C11×C22⋊Q8C2×C4semidirect
116. C11×#106C2×C4semidirect
119. C11×#103C2×C4semidirect
131. #22194C11direct (N × H)
222. #2323C2×C11semidirect
223. #1928C2×C11semidirect
224. #1925C2×C11semidirect
225. #1920C2×C11semidirect
226. #1919C2×C11semidirect
228. #1894C2×C11semidirect
229. #1880C2×C11semidirect
230. #1877C2×C11semidirect
231. #1863C2×C11semidirect
232. #1862C2×C11semidirect
233. #1808C2×C11semidirect
234. #1729C2×C11semidirect
318. #465C4×C11semidirect
404. C22×C8C2×C4×C11semidirect
410. C22⋊Q8C2×C4×C11semidirect
447. #106C2×C4×C11semidirect
450. #103C2×C4×C11semidirect
559. C11#22194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C11×#23242
C11×#23232
C11×#19282
C11×#19252
C11×#19202
C11×#19192
C11×#18952
C11×#18942
C11×#18802
C11×#18772
C11×#18632
C11×#18622
C11×#18082
C11×#17292
#2219411