Finite Group Databasebeta

← C11×#22471 #14599664

Subgroups — C11×#22471 #14599664

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×#41C211yesmaximal, characteristic
2C2×C11×#435C212yesmaximal, complemented
3C11×#1985C212yesmaximal, complemented
4C11×#1870C212yesmaximal, complemented
5C11×#1869C212yesmaximal, complemented
6C11×#1817C211yesmaximal, characteristic, complemented
7C11×#1817C211yesmaximal, characteristic, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C11×#1728C211yesmaximal, characteristic, complemented
11C2×C11×#336C211yesmaximal, characteristic, complemented
12C22×C11×#41C411yescharacteristic
13C22×C11×M16C2212yes—
14C23×C8×C11C2212yes—
15C4×C11×#41—28no—
16C2×C4×Q8×C11C411yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C411yescharacteristic
19C2×C4×D4×C11C411yescharacteristic
20C2×C4×D4×C11C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C411yescharacteristic
25C2×C11×#117C411yescharacteristic
26C2×C11×#117C411yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C11×#435—28no—
31C2×C11×C4⋊C8C2212yes—
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2212yes—
37C11×#336C2212yes—
38C11×#336C2212yes—
39C11×#336C2212yes—
40C11×#336C2212yes—
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C22×Q8×C11C2×C411yescharacteristic
49C22×D4×C11C2×C411yescharacteristic
50C22×D4×C11C2×C411yescharacteristic
51C22×D4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11C2×C411yescharacteristic
54C23×C4×C11C2×C411yescharacteristic
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—24no—
62C2×C11×M16—24no—
63C2×C11×M16—42no—
64C22×C8×C11—24no—
65C22×C8×C11—24no—
66C22×C8×C11—42no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C4×Q8×C11—24no—
72C4×Q8×C11—24no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C4×D4×C11—24no—
78C4×D4×C11D418yes—
79C11×#117—24no—
80C11×#117—24no—
81C11×#117—24no—
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C4⋊C4C2×C411yescharacteristic
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C4⋊C4C2×C411yescharacteristic
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C42×C11—24no—
95C2×C42×C11—24no—
96C2×C42×C11—24no—
97C2×C42×C11C2×C411yescharacteristic
98C2×C42×C11C2×C411yescharacteristic
99C2×C42×C11C2×C411yescharacteristic
100C2×C42×C11C2×C411yescharacteristic
101C2×C42×C11C2×C411yescharacteristic
102C2×C42×C11C2×C411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×C4⋊C8—24no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—24no—
110C11×C22⋊C8—24no—
111C11×C22⋊C8—42no—
112C11×#97—24no—
113#22471C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11C22×C411yescharacteristic
115C24×C11C22×C411yescharacteristic
116C24×C11C22×C411yescharacteristic
117C11×#41—232no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11C22⋊C414yes—
129C2×D4×C11M1614yescomplemented
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11M1614yescomplemented
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2411yescharacteristic
172C11×M16—48no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—48no—
185C2×C8×C11#4114yescomplemented
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4C22⋊C414yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4C22⋊C414yes—
197C11×C22⋊C4C22⋊C414yes—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11C2×D414yes—
208C2×C4×#41C2×C1111yescharacteristic
209C2×#435C2×C1112yescomplemented
210#1985C2×C1112yescomplemented
211#1870C2×C1112yescomplemented
212#1869C2×C1112yescomplemented
213#1817C2×C1111yescharacteristic, complemented
214#1817C2×C1111yescharacteristic, complemented
215#1797C2×C1111yescharacteristic, complemented
216#1749C2×C1111yescharacteristic, complemented
217#1728C2×C1111yescharacteristic, complemented
218C2×#336C2×C1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C2×C22⋊C412yes—
236C23×C11C2×C22⋊C412yes—
237C23×C11C2×M1612yes—
238C23×C11C2×M1612yes—
239C23×C11C2×M1612yes—
240C23×C11C23×C411yescharacteristic
241Q8×C11—28no—
242D4×C11—28no—
243D4×C11—28no—
244D4×C11—28no—
245C2×C4×C11—28no—
246C2×C4×C11—28no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—28no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
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—44no—
278C2×C4×C11—44no—
279C2×C4×C11—44no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11C2×C22⋊C412yes—
283C2×C4×C11C2×C22⋊C412yes—
284C2×C4×C11C2×C22⋊C412yes—
285C2×C4×C11C2×C22⋊C412yes—
286C2×C4×C11C2×M1612yes—
287C2×C4×C11C2×M1612yes—
288C2×C4×C11C2×M1612yes—
289C2×C4×C11#13112yes—
290C2×C4×C11C22×D412yes—
291C2×C4×C11C2×#4112yes—
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C112−1+411yescharacteristic
294C8×C11—24no—
295C8×C11—42no—
296C8×C11—42no—
297C8×C11—42no—
298C22×#41C4×C1111yescharacteristic
299C22×M16C22×C1112yes—
300C23×C8C22×C1112yes—
301C4×#41—28no—
302C2×C4×Q8C4×C1111yescharacteristic
303C2×C4×Q8C22×C1111yescharacteristic
304C2×C4×D4C4×C1111yescharacteristic
305C2×C4×D4C4×C1111yescharacteristic
306C2×C4×D4C4×C1111yescharacteristic
307C2×C4×D4C22×C1111yescharacteristic
308C2×C4×D4C22×C1111yescharacteristic
309C2×C4×D4C22×C1111yescharacteristic
310C2×#117C4×C1111yescharacteristic
311C2×#117C4×C1111yescharacteristic
312C2×#117C4×C1111yescharacteristic
313C22×C42C22×C1111yescharacteristic
314C22×C42C22×C1111yescharacteristic
315C22×C42C22×C1111yescharacteristic
316#435—28no—
317C2×C4⋊C8C22×C1112yes—
318C2×C22⋊C8C22×C1112yes—
319C2×C22⋊C8C22×C1112yes—
320C2×C22⋊C8C22×C1112yes—
321C2×C22⋊C8C22×C1112yes—
322C2×#97C22×C1112yes—
323#336C22×C1111yescharacteristic
324#336C22×C1111yescharacteristic
325#336C22×C1111yescharacteristic
326#336C22×C1112yes—
327#336C22×C1112yes—
328#336C22×C1112yes—
329#336C22×C1112yes—
330#336C22×C1111yescharacteristic
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11#40714yes—
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11C4×#4111yescharacteristic
354C22×C11#52011yescharacteristic
355C22×C11C22×M1611yescharacteristic
356C22×C11C22×M1611yescharacteristic
357C22×C11C2×#13111yescharacteristic
358C22×C11#56811yescharacteristic
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11#54612yes—
371C4×C11#54712yes—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—24no—
375C22×Q8C2×C4×C1111yescharacteristic
376C22×D4C2×C4×C1111yescharacteristic
377C22×D4C2×C4×C1111yescharacteristic
378C22×D4C2×C4×C1111yescharacteristic
379C23×C4C2×C4×C1111yescharacteristic
380C23×C4C2×C4×C1111yescharacteristic
381C23×C4C2×C4×C1111yescharacteristic
382C23×C4C2×C4×C1111yescharacteristic
383C23×C4C2×C4×C1111yescharacteristic
384C23×C4C2×C4×C1111yescharacteristic
385C23×C4C23×C1111yescharacteristic
386C23×C4C23×C1111yescharacteristic
387C23×C4C23×C1111yescharacteristic
388C2×M16—24no—
389C2×M16—24no—
390C2×M16—42no—
391C22×C8—24no—
392C22×C8—24no—
393C22×C8—42no—
394C22×C8C23×C1112yes—
395C22×C8C23×C1112yes—
396C22×C8C23×C1112yes—
397C22×C8C23×C1112yes—
398C4×Q8—24no—
399C4×Q8—24no—
400C4×D4—24no—
401C4×D4—24no—
402C4×D4—24no—
403C4×D4—24no—
404C4×D4—24no—
405C4×D4D4×C1118yes—
406#117—24no—
407#117—24no—
408#117—24no—
409C2×C4⋊C4C2×C4×C1111yescharacteristic
410C2×C4⋊C4C2×C4×C1111yescharacteristic
411C2×C4⋊C4C2×C4×C1111yescharacteristic
412C2×C4⋊C4C2×C4×C1111yescharacteristic
413C2×C4⋊C4C2×C4×C1111yescharacteristic
414C2×C4⋊C4C2×C4×C1111yescharacteristic
415C2×C22⋊C4C2×C4×C1111yescharacteristic
416C2×C22⋊C4C2×C4×C1111yescharacteristic
417C2×C22⋊C4C2×C4×C1111yescharacteristic
418C2×C22⋊C4C2×C4×C1111yescharacteristic
419C2×C22⋊C4C2×C4×C1111yescharacteristic
420C2×C22⋊C4C2×C4×C1111yescharacteristic
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42C2×C4×C1111yescharacteristic
425C2×C42C2×C4×C1111yescharacteristic
426C2×C42C2×C4×C1111yescharacteristic
427C2×C42C2×C4×C1111yescharacteristic
428C2×C42C2×C4×C1111yescharacteristic
429C2×C42C2×C4×C1111yescharacteristic
430C2×C42C23×C1111yescharacteristic
431C2×C42C23×C1111yescharacteristic
432C2×C42C23×C1111yescharacteristic
433C2×C42C23×C1111yescharacteristic
434C4⋊C8—24no—
435C22⋊C8—24no—
436C22⋊C8—24no—
437C22⋊C8—24no—
438C22⋊C8—42no—
439#97—24no—
440C2×C11—24no—
441C2×C11—42no—
442C2×C11—42no—
443C2×C11#233911yescharacteristic
444C2×C11C2×#40711yescharacteristic
445C2×C11#288011yescharacteristic
446C2×C11#296511yescharacteristic
447C2×C11#297011yescharacteristic
448C2×C11#298911yescharacteristic
449C2×C11#299011yescharacteristic
450C24C22×C4×C1111yescharacteristic
451C24C22×C4×C1111yescharacteristic
452C24C22×C4×C1111yescharacteristic
453#41—232no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4C11×C22⋊C414yes—
465C2×D4C11×M1614yescomplemented
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4C11×M1614yescomplemented
494C22×C4C22×C4×C1111yescharacteristic
495C22×C4C22×C4×C1111yescharacteristic
496C22×C4C22×C4×C1111yescharacteristic
497C22×C4C22×C4×C1111yescharacteristic
498C22×C4C22×C4×C1111yescharacteristic
499C22×C4C22×C4×C1111yescharacteristic
500C22×C4C22×C4×C1111yescharacteristic
501C22×C4C22×C4×C1111yescharacteristic
502C22×C4C22×C4×C1111yescharacteristic
503C22×C4C22×C4×C1111yescharacteristic
504C22×C4C22×C4×C1111yescharacteristic
505C22×C4C2×D4×C1114yes—
506C22×C4C2×D4×C1114yes—
507C22×C4C24×C1111yescharacteristic
508M16—48no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—48no—
521C2×C8C11×#4114yescomplemented
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4C11×C22⋊C414yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4C11×C22⋊C414yes—
533C22⋊C4C11×C22⋊C414yes—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42C2×D4×C1114yes—
544C11#2247111yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23C2×C11×C22⋊C412yes—
562C23C2×C11×C22⋊C412yes—
563C23C2×C11×M1612yes—
564C23C2×C11×M1612yes—
565C23C2×C11×M1612yes—
566C23C23×C4×C1111yescharacteristic
567Q8—28no—
568D4—28no—
569D4—28no—
570D4—28no—
571C2×C4—28no—
572C2×C4—28no—
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—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
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—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4C2×C11×C22⋊C412yes—
609C2×C4C2×C11×C22⋊C412yes—
610C2×C4C2×C11×C22⋊C412yes—
611C2×C4C2×C11×C22⋊C412yes—
612C2×C4C2×C11×M1612yes—
613C2×C4C2×C11×M1612yes—
614C2×C4C2×C11×M1612yes—
615C2×C4C11×#13112yes—
616C2×C4C22×D4×C1112yes—
617C2×C4C2×C11×#4112yes—
618C2×C4C11×H(5,𝔽2)11yescharacteristic
619C2×C4C11×2−1+411yescharacteristic
620C8—24no—
621C8—42no—
622C8—42no—
623C8—42no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22C11×#40714yes—
645C22C22×C11×C22⋊C411yescharacteristic
646C22C4×C11×#4111yescharacteristic
647C22C11×#52011yescharacteristic
648C22C22×C11×M1611yescharacteristic
649C22C22×C11×M1611yescharacteristic
650C22C2×C11×#13111yescharacteristic
651C22C11×#56811yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4C11×#54612yes—
664C4C11×#54712yes—
665C2—24no—
666C2—42no—
667C2—42no—
668C2C11×#233911yescharacteristic
669C2C2×C11×#40711yescharacteristic
670C2C11×#288011yescharacteristic
671C2C11×#296511yescharacteristic
672C2C11×#297011yescharacteristic
673C2C11×#298911yescharacteristic
674C2C11×#299011yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×C11×#41C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. C11×#1985C2semidirect
4. C11×#1870C2semidirect
5. C11×#1869C2semidirect
6. C11×#1817C2semidirect
7. C11×#1817C2semidirect
8. C11×#1797C2semidirect
9. C11×#1749C2semidirect
10. C11×#1728C2semidirect
11. C2×C11×#336C2semidirect
113. #22471C11direct (N × H)
129. C2×D4×C11M16semidirect
157. C22×C4×C11M16semidirect
185. C2×C8×C11#41semidirect
209. C2×#435C2×C11semidirect
210. #1985C2×C11semidirect
211. #1870C2×C11semidirect
212. #1869C2×C11semidirect
213. #1817C2×C11semidirect
214. #1817C2×C11semidirect
215. #1797C2×C11semidirect
216. #1749C2×C11semidirect
217. #1728C2×C11semidirect
218. C2×#336C2×C11semidirect
465. C2×D4C11×M16semidirect
493. C22×C4C11×M16semidirect
521. C2×C8C11×#41semidirect
544. C11#22471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×#412
C2×C11×#4352
C11×#19852
C11×#18702
C11×#18692
C11×#18172
C11×#17972
C11×#17492
C11×#17282
C2×C11×#3362
#2247111