Finite Group Databasebeta

← C11×#23106 #14600299

Subgroups — C11×#23106 #14600299

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C11×#2366C211yesmaximal, characteristic
3C11×#2356C211yesmaximal, characteristic, complemented
4C11×#1973C211yesmaximal, characteristic, complemented
5C11×#1968C211yesmaximal, characteristic, complemented
6C11×#1961C211yesmaximal, characteristic
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1877C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1771C211yesmaximal, characteristic, complemented
13C11×#1763C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C11×#460C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#390—21no—
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#387—21no—
44C11×#387—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#383—21no—
48C11×#382C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#376—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C2×C11×SD16—41no—
68C2×C11×SD16—41no—
69C2×C11×SD16—41no—
70C2×C11×SD16—41no—
71C2×C11×SD16C2×C414yescomplemented
72C2×C11×SD16C2×C414yescomplemented
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#127—22no—
78C11×#127C2×C414yes—
79C4×Q8×C11—22no—
80C4×Q8×C11C2×C414yescomplemented
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—44no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×#107—41no—
108C11×#106—41no—
109C11×C4⋊C8C2×C414yescomplemented
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×#102—41no—
115C11×#102—41no—
116C11×#102C2×C414yescomplemented
117C11×#102C2×C414yescomplemented
118C11×#97—22no—
119C11×#97—41no—
120C4×C8×C11—41no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#23106C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
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×C11—81no—
156C2×D4×C11—81no—
157C2×D4×C11C22×C412yes—
158C2×D4×C11C22×C412yes—
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—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—81no—
170C22×C4×C11—81no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C11×SD16—44no—
179C11×SD16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C22×C412yes—
190C2×C8×C11C22×C412yes—
191C2×C8×C11#4112yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4C22×C412yes—
204C11×C4⋊C4#4112yes—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C42×C11—24no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—42no—
217C42×C11—42no—
218C42×C11—42no—
219C42×C11C22×C412yes—
220C42×C11#4112yes—
221C2×#460C2×C1111yescharacteristic
222#2366C2×C1111yescharacteristic
223#2356C2×C1111yescharacteristic, complemented
224#1973C2×C1111yescharacteristic, complemented
225#1968C2×C1111yescharacteristic, complemented
226#1961C2×C1111yescharacteristic
227#1949C2×C1111yescharacteristic, complemented
228#1926C2×C1111yescharacteristic, complemented
229#1925C2×C1111yescharacteristic, complemented
230#1877C2×C1111yescharacteristic, complemented
231#1877C2×C1111yescharacteristic, complemented
232#1771C2×C1111yescharacteristic, complemented
233#1763C2×C1111yescharacteristic, complemented
234#1762C2×C1111yescharacteristic, complemented
235C4×#102C2×C1111yescharacteristic, complemented
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C22×D411yescharacteristic
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—48no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—84no—
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—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
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×C11—84no—
300C2×C4×C11C4×D412yes—
301C2×C4×C11C4×D412yes—
302C2×C4×C11AGL(1,ℤ/8)12yes—
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C8×C11—22no—
310C8×C11—22no—
311C8×C11—22no—
312C8×C11—41no—
313C22×SD16C22×C1111yescharacteristic
314C22×SD16C22×C1111yescharacteristic
315C2×#127C22×C1111yescharacteristic
316C2×C4×Q8C22×C1111yescharacteristic
317C2×C4×D4—21no—
318C2×C4×D4C22×C1111yescharacteristic
319C2×C4×D4C22×C1111yescharacteristic
320#460C4×C1118yescomplemented
321C2×#107C22×C1111yescharacteristic
322C2×#106C22×C1111yescharacteristic
323C2×C4⋊C8C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#103C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#97C22×C1111yescharacteristic
333C2×#97C22×C1111yescharacteristic
334C2×C4×C8C22×C1111yescharacteristic
335#391C22×C1111yescharacteristic
336#391C22×C1111yescharacteristic
337#390—21no—
338#390C22×C1111yescharacteristic
339#390C22×C1111yescharacteristic
340#387—21no—
341#387—21no—
342#386—21no—
343#386—21no—
344#383—21no—
345#382C22×C1111yescharacteristic
346C4×C4⋊C4C22×C1111yescharacteristic
347C4×C4⋊C4C22×C1111yescharacteristic
348C4×C4⋊C4C22×C1111yescharacteristic
349C4×C4⋊C4C22×C1111yescharacteristic
350#376—21no—
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11C2×C4×D411yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11#55011yescharacteristic
374C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57711yescharacteristic
377C22×C11#57711yescharacteristic
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C4×#4111yescharacteristic
391C4×C11#51811yescharacteristic
392C4×C11#55311yescharacteristic
393C4×C11#55511yescharacteristic
394C22×Q8C23×C1111yescharacteristic
395C22×D4—21no—
396C22×D4—21no—
397C22×D4C23×C1111yescharacteristic
398C22×D4C23×C1111yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C2×SD16—41no—
402C2×SD16—41no—
403C2×SD16—41no—
404C2×SD16—41no—
405C2×SD16C2×C4×C1114yescomplemented
406C2×SD16C2×C4×C1114yescomplemented
407C22×C8C23×C1111yescharacteristic
408C22×C8C23×C1111yescharacteristic
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411#127—22no—
412#127C2×C4×C1114yes—
413C4×Q8—22no—
414C4×Q8C2×C4×C1114yescomplemented
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—41no—
418C4×D4—41no—
419C4×D4—44no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4D4×C1111yescharacteristic
422C2×C4⋊C4D4×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C4⋊C4C23×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C1111yescharacteristic
439C2×C42C23×C1111yescharacteristic
440C2×C42C23×C1111yescharacteristic
441#107—41no—
442#106—41no—
443C4⋊C8C2×C4×C1114yescomplemented
444#103—22no—
445#103—22no—
446#102—22no—
447#102—22no—
448#102—41no—
449#102—41no—
450#102C2×C4×C1114yescomplemented
451#102C2×C4×C1114yescomplemented
452#97—22no—
453#97—41no—
454C4×C8—41no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95D4×C1111yescharacteristic
465#95D4×C1111yescharacteristic
466C2×C11—82no—
467C2×C11—82no—
468C2×C11#236311yescharacteristic
469C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
470C2×C11#294911yescharacteristic
471C2×C11#331011yescharacteristic
472C2×C11#331711yescharacteristic
473C2×C11#339711yescharacteristic
474C2×C11#340111yescharacteristic
475C24—21no—
476C24—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C22×C4×C1112yes—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C22×C4×C1112yes—
500C2×D4C22×C4×C1112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C24×C1111yescharacteristic
520SD16—44no—
521SD16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C22×C4×C1112yes—
532C2×C8C22×C4×C1112yes—
533C2×C8C11×#4112yes—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—41no—
545C4⋊C4C22×C4×C1112yes—
546C4⋊C4C11×#4112yes—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C42—24no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C42—42no—
561C42C22×C4×C1112yes—
562C42C11×#4112yes—
563C11#2310611yescharacteristic, direct product factor, Sylow
564C23—22no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4—48no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—84no—
627C2×C4—84no—
628C2×C4C4×D4×C1112yes—
629C2×C4C4×D4×C1112yes—
630C2×C4C11×AGL(1,ℤ/8)12yes—
631C2×C4C23×C4×C1111yescharacteristic
632C2×C4C2×C11×#4111yescharacteristic
633C2×C4C2×C11×#4111yescharacteristic
634C2×C4C2×C11×#4111yescharacteristic
635C2×C4C11×H(5,𝔽2)11yescharacteristic
636C2×C4C11×H(5,𝔽2)11yescharacteristic
637C8—22no—
638C8—22no—
639C8—22no—
640C8—41no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×C4×D4×C1111yescharacteristic
656C22C11×#54611yescharacteristic
657C22C11×#55011yescharacteristic
658C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
659C22C11×#57511yescharacteristic
660C22C11×#57711yescharacteristic
661C22C11×#57711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C4×C11×#4111yescharacteristic
675C4C11×#51811yescharacteristic
676C4C11×#55311yescharacteristic
677C4C11×#55511yescharacteristic
678C2—82no—
679C2—82no—
680C2C11×#236311yescharacteristic
681C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
682C2C11×#294911yescharacteristic
683C2C11×#331011yescharacteristic
684C2C11×#331711yescharacteristic
685C2C11×#339711yescharacteristic
686C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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
3. C11×#2356C2semidirect
4. C11×#1973C2semidirect
5. C11×#1968C2semidirect
7. C11×#1949C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1877C2semidirect
11. C11×#1877C2semidirect
12. C11×#1771C2semidirect
13. C11×#1763C2semidirect
14. C11×#1762C2semidirect
15. C4×C11×#102C2semidirect
23. C11×#460C4semidirect
71. C2×C11×SD16C2×C4semidirect
72. C2×C11×SD16C2×C4semidirect
80. C4×Q8×C11C2×C4semidirect
109. C11×C4⋊C8C2×C4semidirect
116. C11×#102C2×C4semidirect
117. C11×#102C2×C4semidirect
132. #23106C11direct (N × H)
223. #2356C2×C11semidirect
224. #1973C2×C11semidirect
225. #1968C2×C11semidirect
227. #1949C2×C11semidirect
228. #1926C2×C11semidirect
229. #1925C2×C11semidirect
230. #1877C2×C11semidirect
231. #1877C2×C11semidirect
232. #1771C2×C11semidirect
233. #1763C2×C11semidirect
234. #1762C2×C11semidirect
235. C4×#102C2×C11semidirect
320. #460C4×C11semidirect
405. C2×SD16C2×C4×C11semidirect
406. C2×SD16C2×C4×C11semidirect
414. C4×Q8C2×C4×C11semidirect
443. C4⋊C8C2×C4×C11semidirect
450. #102C2×C4×C11semidirect
451. #102C2×C4×C11semidirect
563. C11#23106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C11×#23662
C11×#23562
C11×#19732
C11×#19682
C11×#19612
C11×#19492
C11×#19262
C11×#19252
C11×#18772
C11×#17712
C11×#17632
C11×#17622
C4×C11×#1022
#2310611