Finite Group Databasebeta

← C11×#23013 #14600206

Subgroups — C11×#23013 #14600206

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2367C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#1959C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic
9C11×#1933C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1865C211yesmaximal, characteristic, complemented
13C11×#1864C211yesmaximal, characteristic
14C11×#1771C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#464C418yescomplemented
25C11×#441—24no—
26C4×C11×SD16—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
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×#391C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#389—21no—
44C11×#389—21no—
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#388—21no—
49C11×#385—21no—
50C11×#384—21no—
51C11×#384C2211yescharacteristic
52C4×C11×C4⋊C4—21no—
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16C2×C414yescomplemented
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#124—22no—
77C11×#124C2×C414yes—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—41no—
83C4×Q8×C11—41no—
84C4×Q8×C11—41no—
85C4×Q8×C11C2×C414yescomplemented
86C4×D4×C11—22no—
87C4×D4×C11—41no—
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⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
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×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#106—22no—
117C11×#106—22no—
118C11×C4⋊C8C2×C414yescomplemented
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—41no—
122C11×#103C2×C414yescomplemented
123C11×#103D414yes—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102C2×C414yes—
127C11×#97—22no—
128C11×#97—22no—
129C4×C8×C11—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#23013C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C22×C412yes—
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—42no—
165C22×C4×C11—42no—
166C22×C4×C11—81no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×Q16—28no—
175C11×SD16—28no—
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—21no—
184C2×C8×C11—21no—
185C2×C8×C11C22×C412yes—
186C2×C8×C11C22×C412yes—
187C2×C8×C11C2×D412yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
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—21no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—81no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C2×D412yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C42×C11—24no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C42×C11—42no—
220C42×C11—42no—
221C42×C11—81no—
222C42×C11C22×C412yes—
223C42×C11#4112yes—
224C2×#464C2×C1111yescharacteristic
225C2×#441C2×C1111yescharacteristic, complemented
226C2×C4×SD16C2×C1111yescharacteristic
227#2367C2×C1111yescharacteristic
228Q8×C4⋊C4C2×C1111yescharacteristic, complemented
229#1959C2×C1111yescharacteristic
230#1948C2×C1111yescharacteristic, complemented
231#1936C2×C1111yescharacteristic
232#1933C2×C1111yescharacteristic, complemented
233#1880C2×C1111yescharacteristic
234#1878C2×C1111yescharacteristic, complemented
235#1865C2×C1111yescharacteristic, complemented
236#1864C2×C1111yescharacteristic
237#1771C2×C1111yescharacteristic, complemented
238#1763C2×C1111yescharacteristic, complemented
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11C4×D414yes—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—41no—
258D4×C11—41no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
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—84no—
296C2×C4×C11C4×D412yes—
297C2×C4×C11C4×D412yes—
298C2×C4×C11#13712yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—22no—
308C8×C11—41no—
309C22×Q16C22×C1111yescharacteristic
310C22×SD16C22×C1111yescharacteristic
311C2×#124C22×C1111yescharacteristic
312C2×C4×Q8C22×C1111yescharacteristic
313C2×C4×Q8C22×C1111yescharacteristic
314C2×C4×Q8C22×C1111yescharacteristic
315C2×C4×Q8C22×C1111yescharacteristic
316C2×C4×D4C22×C1111yescharacteristic
317#464C4×C1118yescomplemented
318#441—24no—
319C4×SD16—24no—
320C2×#106C22×C1111yescharacteristic
321C2×#106C22×C1111yescharacteristic
322C2×C4⋊C8C22×C1111yescharacteristic
323C2×#103C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#103C22×C1111yescharacteristic
326C2×#103C22×C1111yescharacteristic
327C2×#103C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#97C22×C1111yescharacteristic
332C2×#97C22×C1111yescharacteristic
333C2×C4×C8C22×C1111yescharacteristic
334#391C22×C1111yescharacteristic
335#390C22×C1111yescharacteristic
336#389—21no—
337#389—21no—
338#389C22×C1111yescharacteristic
339#389C22×C1111yescharacteristic
340#388—21no—
341#388—21no—
342#385—21no—
343#384—21no—
344#384C22×C1111yescharacteristic
345C4×C4⋊C4—21no—
346C4×C4⋊C4C22×C1111yescharacteristic
347C4×C4⋊C4C22×C1111yescharacteristic
348C4×C22⋊C4—21no—
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#336C22×C1111yescharacteristic
354#336C22×C1111yescharacteristic
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54811yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57711yescharacteristic
369C4×C11—24no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11C2×C4×D411yescharacteristic
383C4×C11#52011yescharacteristic
384C4×C11#54711yescharacteristic
385C4×C11#55311yescharacteristic
386C22×Q8C23×C1111yescharacteristic
387C22×Q8C23×C1111yescharacteristic
388C22×D4C23×C1111yescharacteristic
389C23×C4—21no—
390C2×Q16—22no—
391C2×Q16—22no—
392C2×Q16C2×C4×C1114yescomplemented
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16C2×C4×C1114yes—
396C22×C8C23×C1111yescharacteristic
397C22×C8C23×C1111yescharacteristic
398C22×C8C23×C1111yescharacteristic
399C22×C8C23×C1111yescharacteristic
400#124—22no—
401#124C2×C4×C1114yes—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—41no—
407C4×Q8—41no—
408C4×Q8—41no—
409C4×Q8C2×C4×C1114yescomplemented
410C4×D4—22no—
411C4×D4—41no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C1111yescharacteristic
421C2×C4⋊C4D4×C1111yescharacteristic
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C4⋊C4C23×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42C23×C1111yescharacteristic
438C2×C42C23×C1111yescharacteristic
439C2×C42C23×C1111yescharacteristic
440#106—22no—
441#106—22no—
442C4⋊C8C2×C4×C1114yescomplemented
443#103—22no—
444#103—22no—
445#103—41no—
446#103C2×C4×C1114yescomplemented
447#103D4×C1114yes—
448#102—22no—
449#102—41no—
450#102C2×C4×C1114yes—
451#97—22no—
452#97—22no—
453C4×C8—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95D4×C1111yescharacteristic
460#95D4×C1111yescharacteristic
461C2×C11—82no—
462C2×C11#236111yescharacteristic
463C2×C11C4×#13711yescharacteristic
464C2×C11#295211yescharacteristic
465C2×C11#326611yescharacteristic
466C2×C11#327111yescharacteristic
467C2×C11#336911yescharacteristic
468C2×C11#337111yescharacteristic
469C24—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8C22×C4×C1112yes—
479C2×Q8C22×C4×C1112yes—
480C2×Q8C2×D4×C1112yes—
481C2×Q8C11×#4112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
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—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1111yescharacteristic
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C24×C1111yescharacteristic
505Q16—28no—
506SD16—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8C22×C4×C1112yes—
517C2×C8C22×C4×C1112yes—
518C2×C8C2×D4×C1112yes—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4C22×C4×C1112yes—
538C4⋊C4C2×D4×C1112yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C42—24no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—42no—
551C42—42no—
552C42—81no—
553C42C22×C4×C1112yes—
554C42C11×#4112yes—
555C11#2301311yescharacteristic, direct product factor, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C22×D4×C1111yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8C4×D4×C1114yes—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4C4×D4×C1112yes—
614C2×C4C4×D4×C1112yes—
615C2×C4C11×#13712yes—
616C2×C4C23×C4×C1111yescharacteristic
617C2×C4C22×D4×C1111yescharacteristic
618C2×C4C2×C11×#4111yescharacteristic
619C2×C4C2×C11×#4111yescharacteristic
620C2×C4C11×H(5,𝔽2)11yescharacteristic
621C2×C4C11×2−1+411yescharacteristic
622C8—22no—
623C8—22no—
624C8—22no—
625C8—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×C4×D4×C1111yescharacteristic
634C22D42×C1111yescharacteristic
635C22C11×#54811yescharacteristic
636C22C2×C11×#13711yescharacteristic
637C22C11×#57511yescharacteristic
638C22C11×#57711yescharacteristic
639C22C11×#57711yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—24no—
644C4—42no—
645C4—41no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4C2×C4×D4×C1111yescharacteristic
654C4C11×#52011yescharacteristic
655C4C11×#54711yescharacteristic
656C4C11×#55311yescharacteristic
657C2—82no—
658C2C11×#236111yescharacteristic
659C2C4×C11×#13711yescharacteristic
660C2C11×#295211yescharacteristic
661C2C11×#326611yescharacteristic
662C2C11×#327111yescharacteristic
663C2C11×#336911yescharacteristic
664C2C11×#337111yescharacteristic
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
2. C2×C11×#441C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
7. C11×#1948C2semidirect
9. C11×#1933C2semidirect
11. C11×#1878C2semidirect
12. C11×#1865C2semidirect
14. C11×#1771C2semidirect
15. C11×#1763C2semidirect
24. C11×#464C4semidirect
68. C2×C11×Q16C2×C4semidirect
85. C4×Q8×C11C2×C4semidirect
118. C11×C4⋊C8C2×C4semidirect
122. C11×#103C2×C4semidirect
137. #23013C11direct (N × H)
225. C2×#441C2×C11semidirect
228. Q8×C4⋊C4C2×C11semidirect
230. #1948C2×C11semidirect
232. #1933C2×C11semidirect
234. #1878C2×C11semidirect
235. #1865C2×C11semidirect
237. #1771C2×C11semidirect
238. #1763C2×C11semidirect
317. #464C4×C11semidirect
392. C2×Q16C2×C4×C11semidirect
409. C4×Q8C2×C4×C11semidirect
442. C4⋊C8C2×C4×C11semidirect
446. #103C2×C4×C11semidirect
555. C11#23013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C11×#4412
C2×C4×C11×SD162
C11×#23672
Q8×C11×C4⋊C42
C11×#19592
C11×#19482
C11×#19362
C11×#19332
C11×#18802
C11×#18782
C11×#18652
C11×#18642
C11×#17712
C11×#17632
#2301311