Finite Group Databasebeta

← C11×#23022 #14600215

Subgroups — C11×#23022 #14600215

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C11×#2361C211yesmaximal, characteristic
5C11×#2360C211yesmaximal, characteristic, complemented
6C11×#1968C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1874C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic, complemented
12C11×#1865C211yesmaximal, characteristic, complemented
13C11×#1864C211yesmaximal, characteristic, complemented
14C4×C11×#106C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#465C418yescomplemented
26C4×C11×SD16—24no—
27C2×C11×#106—24no—
28C2×C11×#106C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389—21no—
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#387—21no—
49C11×#386—21no—
50C11×#385—21no—
51C11×#385—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4—21no—
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yescomplemented
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11C2×C414yescomplemented
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8C2×C414yescomplemented
81C11×#121—22no—
82C11×#121C2×C414yes—
83C4×Q8×C11—22no—
84C4×Q8×C11—41no—
85C4×D4×C11—22no—
86C4×D4×C11—41no—
87C4×D4×C11—44no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#106—22no—
117C11×#106—22no—
118C11×#106—22no—
119C11×#106C2×C414yescomplemented
120C11×#106D414yescomplemented
121C11×#103—22no—
122C11×#103—41no—
123C11×#103C2×C414yescomplemented
124C11×#102—22no—
125C11×#102—41no—
126C11×#102C2×C414yescomplemented
127C11×C22⋊C8—22no—
128C4×C8×C11—22no—
129C4×C8×C11—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#23022C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C412yes—
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
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×C11C22×C412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C11×SD16—28no—
185C2×C8×C11—28no—
186C2×C8×C11—21no—
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×C11C22×C412yes—
195C2×C8×C11C22×C412yes—
196C2×C8×C11C2×D412yes—
197C2×C8×C11#4112yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4C22×C412yes—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4C2×D412yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4SD1614yescomplemented
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11—81no—
230C2×#465C2×C1111yescharacteristic
231C2×C4×SD16C2×C1111yescharacteristic, complemented
232C22×#106C2×C1111yescharacteristic, complemented
233#2361C2×C1111yescharacteristic
234#2360C2×C1111yescharacteristic, complemented
235#1968C2×C1111yescharacteristic, complemented
236#1941C2×C1111yescharacteristic, complemented
237#1927C2×C1111yescharacteristic, complemented
238#1926C2×C1111yescharacteristic, complemented
239#1874C2×C1111yescharacteristic
240#1872C2×C1111yescharacteristic, complemented
241#1865C2×C1111yescharacteristic, complemented
242#1864C2×C1111yescharacteristic, complemented
243C4×#106C2×C1111yescharacteristic, complemented
244C8×C22⋊C4C2×C1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—22no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11C4×D412yes—
257C23×C11C2×SD1612yes—
258C23×C11#13512yes—
259C23×C11C22×D411yescharacteristic
260Q8×C11—22no—
261Q8×C11—22no—
262Q8×C11—41no—
263Q8×C11—41no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—48no—
267D4×C11—41no—
268D4×C11—41no—
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—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
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—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—84no—
307C2×C4×C11—84no—
308C2×C4×C11—84no—
309C2×C4×C11C4×D412yes—
310C2×C4×C11C2×SD1612yes—
311C2×C4×C11C2×SD1612yes—
312C2×C4×C11C23×C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C112−1+411yescharacteristic
318C8×C11—22no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11C4×D414yescomplemented
322C22×SD16C22×C1111yescharacteristic
323C23×C8C22×C1111yescharacteristic
324C2×C22⋊Q8C22×C1111yescharacteristic
325C2×#121C22×C1111yescharacteristic
326C2×C4×Q8C22×C1111yescharacteristic
327C2×C4×D4—21no—
328C2×C4×D4C22×C1111yescharacteristic
329C22×C4⋊C4C22×C1111yescharacteristic
330C22×C4⋊C4C22×C1111yescharacteristic
331#465C4×C1118yescomplemented
332C4×SD16—24no—
333C2×#106—24no—
334C2×#106C22×C1111yescharacteristic
335C2×#106C22×C1111yescharacteristic
336C2×#106C22×C1111yescharacteristic
337C2×#106C22×C1111yescharacteristic
338C2×#106C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×C22⋊C8C22×C1111yescharacteristic
346C2×C4×C8C22×C1111yescharacteristic
347C2×C4×C8C22×C1111yescharacteristic
348#391C22×C1111yescharacteristic
349#390C22×C1111yescharacteristic
350#389—21no—
351#389C22×C1111yescharacteristic
352#389C22×C1111yescharacteristic
353#388—21no—
354#387—21no—
355#386—21no—
356#385—21no—
357#385—21no—
358C4×C4⋊C4C22×C1111yescharacteristic
359C4×C4⋊C4C22×C1111yescharacteristic
360C4×C22⋊C4—21no—
361C4×C22⋊C4C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11C4×SD1614yescomplemented
382C22×C11C2×C4×D411yescharacteristic
383C22×C11D4211yescharacteristic
384C22×C11#54711yescharacteristic
385C22×C11C22×SD1611yescharacteristic
386C22×C11C2×#13511yescharacteristic
387C22×C11#57711yescharacteristic
388C22×C11#57711yescharacteristic
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—41no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—42no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11C2×C4×D411yescharacteristic
402C4×C11#52011yescharacteristic
403C4×C11#54811yescharacteristic
404C4×C11#55311yescharacteristic
405C22×Q8C23×C1111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C1111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4—21no—
411C23×C4C23×C1111yescharacteristic
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16C2×C4×C1114yescomplemented
415C22×C8—22no—
416C22×C8—22no—
417C22×C8C2×C4×C1114yescomplemented
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22⋊Q8—22no—
423C22⋊Q8C2×C4×C1114yescomplemented
424#121—22no—
425#121C2×C4×C1114yes—
426C4×Q8—22no—
427C4×Q8—41no—
428C4×D4—22no—
429C4×D4—41no—
430C4×D4—44no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4D4×C1111yescharacteristic
453C2×C22⋊C4D4×C1111yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42C23×C1111yescharacteristic
458C2×C42C23×C1111yescharacteristic
459#106—22no—
460#106—22no—
461#106—22no—
462#106C2×C4×C1114yescomplemented
463#106D4×C1114yescomplemented
464#103—22no—
465#103—41no—
466#103C2×C4×C1114yescomplemented
467#102—22no—
468#102—41no—
469#102C2×C4×C1114yescomplemented
470C22⋊C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C1111yescharacteristic
480#95D4×C1111yescharacteristic
481C2×C11—24no—
482C2×C11—82no—
483C2×C11#236111yescharacteristic
484C2×C11C2×C4×SD1611yescharacteristic
485C2×C11#295211yescharacteristic
486C2×C11D4×SD1611yescharacteristic
487C2×C11#328211yescharacteristic
488C2×C11#333511yescharacteristic
489C2×C11#333711yescharacteristic
490C24—21no—
491C24C2×D4×C1111yescharacteristic
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C22×C4×C1112yes—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C22×C4×C1112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4C22×C4×C1112yes—
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C11×#4112yes—
534C22×C4C24×C1111yescharacteristic
535SD16—28no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C22×C4×C1112yes—
546C2×C8C22×C4×C1112yes—
547C2×C8C2×D4×C1112yes—
548C2×C8C11×#4112yes—
549C4⋊C4—24no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C4⋊C4C22×C4×C1112yes—
564C4⋊C4C22×C4×C1112yes—
565C4⋊C4C2×D4×C1112yes—
566C4⋊C4C2×D4×C1112yes—
567C22⋊C4—24no—
568C22⋊C4—22no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4C11×SD1614yescomplemented
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C42—42no—
580C42—81no—
581C11#2302211yescharacteristic, direct product factor, Sylow
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×D4×C1112yes—
594C23C2×C11×SD1612yes—
595C23C11×#13512yes—
596C23C22×D4×C1111yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
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—84no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4C4×D4×C1112yes—
647C2×C4C2×C11×SD1612yes—
648C2×C4C2×C11×SD1612yes—
649C2×C4C23×C4×C1111yescharacteristic
650C2×C4C22×D4×C1111yescharacteristic
651C2×C4C2×C11×#4111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C11×H(5,𝔽2)11yescharacteristic
654C2×C4C11×2−1+411yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8C4×D4×C1114yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C4×C11×SD1614yescomplemented
673C22C2×C4×D4×C1111yescharacteristic
674C22D42×C1111yescharacteristic
675C22C11×#54711yescharacteristic
676C22C22×C11×SD1611yescharacteristic
677C22C2×C11×#13511yescharacteristic
678C22C11×#57711yescharacteristic
679C22C11×#57711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C2×C4×D4×C1111yescharacteristic
693C4C11×#52011yescharacteristic
694C4C11×#54811yescharacteristic
695C4C11×#55311yescharacteristic
696C2—24no—
697C2—82no—
698C2C11×#236111yescharacteristic
699C2C2×C4×C11×SD1611yescharacteristic
700C2C11×#295211yescharacteristic
701C2D4×C11×SD1611yescharacteristic
702C2C11×#328211yescharacteristic
703C2C11×#333511yescharacteristic
704C2C11×#333711yescharacteristic
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
3. C22×C11×#106C2semidirect
5. C11×#2360C2semidirect
6. C11×#1968C2semidirect
7. C11×#1941C2semidirect
8. C11×#1927C2semidirect
9. C11×#1926C2semidirect
11. C11×#1872C2semidirect
12. C11×#1865C2semidirect
13. C11×#1864C2semidirect
14. C4×C11×#106C2semidirect
15. C8×C11×C22⋊C4C2semidirect
25. C11×#465C4semidirect
71. C2×C11×SD16C2×C4semidirect
74. C22×C8×C11C2×C4semidirect
80. C11×C22⋊Q8C2×C4semidirect
119. C11×#106C2×C4semidirect
120. C11×#106D4semidirect
123. C11×#103C2×C4semidirect
126. C11×#102C2×C4semidirect
138. #23022C11direct (N × H)
222. C11×C22⋊C4SD16semidirect
231. C2×C4×SD16C2×C11semidirect
232. C22×#106C2×C11semidirect
234. #2360C2×C11semidirect
235. #1968C2×C11semidirect
236. #1941C2×C11semidirect
237. #1927C2×C11semidirect
238. #1926C2×C11semidirect
240. #1872C2×C11semidirect
241. #1865C2×C11semidirect
242. #1864C2×C11semidirect
243. C4×#106C2×C11semidirect
244. C8×C22⋊C4C2×C11semidirect
321. C8×C11C4×D4semidirect
331. #465C4×C11semidirect
381. C22×C11C4×SD16semidirect
414. C2×SD16C2×C4×C11semidirect
417. C22×C8C2×C4×C11semidirect
423. C22⋊Q8C2×C4×C11semidirect
462. #106C2×C4×C11semidirect
463. #106D4×C11semidirect
466. #103C2×C4×C11semidirect
469. #102C2×C4×C11semidirect
573. C22⋊C4C11×SD16semidirect
581. C11#23022direct (N × H)
658. C8C4×D4×C11semidirect
672. C22C4×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C2×C4×C11×SD162
C22×C11×#1062
C11×#23612
C11×#23602
C11×#19682
C11×#19412
C11×#19272
C11×#19262
C11×#18742
C11×#18722
C11×#18652
C11×#18642
C4×C11×#1062
C8×C11×C22⋊C42
#2302211