Finite Group Databasebeta

← C11×#24148 #14601341

Subgroups — C11×#24148 #14601341

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2544C211yesmaximal, characteristic, complemented
5C11×#2038C211yesmaximal, characteristic, complemented
6C11×#2037C211yesmaximal, characteristic, complemented
7C11×#2003C211yesmaximal, characteristic, complemented
8C11×#2002C211yesmaximal, characteristic
9C11×#1986C211yesmaximal, characteristic, complemented
10C11×#1967C211yesmaximal, characteristic, complemented
11C11×#1888C211yesmaximal, characteristic, complemented
12C11×#1887C211yesmaximal, characteristic, complemented
13C11×#1857C211yesmaximal, characteristic, complemented
14C11×#1856C211yesmaximal, characteristic, complemented
15C11×#1806C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C11×#559—21no—
18C11×#559—21no—
19C11×#556—21no—
20C11×#556—21no—
21C11×#551—22no—
22C11×#551—22no—
23C11×#542—21no—
24C11×#542—21no—
25C11×#536C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C11×#529—21no—
30C11×#529—21no—
31C2×C11×#124C2211yescharacteristic
32C2×C11×#124C2211yescharacteristic
33C11×#519C2211yescharacteristic
34C11×#518C2211yescharacteristic
35C4×C11×#41C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C11×#478—21no—
38C11×#478—21no—
39C11×#476—21no—
40C11×#474—21no—
41C11×#442—21no—
42C11×#440—21no—
43C4×C11×SD16—21no—
44C4×C11×D8—21no—
45C11×#428C2211yescharacteristic
46C11×#428C2211yescharacteristic
47C11×#428C2211yescharacteristic
48C11×#423C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C11×#418C2211yescharacteristic
52C11×#418C2211yescharacteristic
53C11×#418C2211yescharacteristic
54C11×#417C2211yescharacteristic
55C2×C11×#101C2211yescharacteristic
56C2×C11×#101C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C2×C11×#100C2211yescharacteristic
59C4×C11×M16C2211yescharacteristic
60C11×#394—22no—
61C11×#391C2211yescharacteristic
62C11×#390C2211yescharacteristic
63C11×#386—22no—
64C4×C11×C4⋊C4C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11C2311yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11—21no—
77C11×AGL(1,ℤ/8)—22no—
78C11×AGL(1,ℤ/8)—22no—
79C2×C11×SD16—21no—
80C2×C11×D8—21no—
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8D411yescharacteristic, complemented
87C11×C4⋊Q8D411yescharacteristic, complemented
88C11×#127—21no—
89C11×#127—22no—
90C11×#127—41no—
91C11×#126—22no—
92C11×#126—22no—
93C11×#126—22no—
94C11×#126—22no—
95C11×#125D411yescharacteristic, complemented
96C11×#125D411yescharacteristic, complemented
97C11×#124—22no—
98C11×#124—22no—
99C11×#124—21no—
100C11×#124—21no—
101C11×#124—22no—
102C11×#124—21no—
103C11×#124—21no—
104C11×#124—21no—
105C11×#124—21no—
106C11×#124—41no—
107C11×#123—22no—
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#120—22no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11D411yescharacteristic, complemented
128C4×Q8×C11D411yescharacteristic, complemented
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11D411yescharacteristic, complemented
142C4×D4×C11D411yescharacteristic, complemented
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—21no—
147C11×#117C2311yescharacteristic
148C11×#117C2311yescharacteristic
149C11×#117C2311yescharacteristic
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4—22no—
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—22no—
155C2×C11×C22⋊C4—22no—
156C2×C11×C22⋊C4D412yes—
157C2×C11×C22⋊C4D412yes—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C11×#107—21no—
163C11×#107—21no—
164C11×#107—21no—
165C11×#106—21no—
166C11×#106—21no—
167C11×#106—21no—
168C11×C4⋊C8—21no—
169C11×C4⋊C8—21no—
170C11×#104—41no—
171C11×#104—41no—
172C11×#103—21no—
173C11×#102—21no—
174C11×#102—21no—
175C11×#102—21no—
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#102—21no—
180C11×#101—22no—
181C11×#101—41no—
182C11×#100—22no—
183C11×#100—41no—
184C11×#97—21no—
185C4×C8×C11—21no—
186C11×#95—21no—
187C11×#95—22no—
188#24148C1111yesmaximal, characteristic, direct product factor, Sylow
189C24×C11—21no—
190C24×C11C2×D412yes—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C11×#41—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11C2×D411yescharacteristic
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—82no—
221C2×D4×C11C2×D411yescharacteristic
222C2×D4×C11#4112yes—
223C22×C4×C11—21no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—41no—
232C22×C4×C11—41no—
233C22×C4×C11—82no—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C11×SD16—24no—
239C11×D8—24no—
240C11×M16—21no—
241C11×M16—21no—
242C11×M16—21no—
243C11×M16—21no—
244C11×M16—21no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16#4112yes—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—42no—
267C11×C4⋊C4C2×D411yescharacteristic
268C11×C4⋊C4C2×D411yescharacteristic
269C11×C4⋊C4C2×D411yescharacteristic
270C11×C4⋊C4C2×D411yescharacteristic
271C11×C4⋊C4C2×D411yescharacteristic
272C11×C4⋊C4C2×D411yescharacteristic
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—22no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—44no—
289C11×C22⋊C4—41no—
290C11×C22⋊C4—41no—
291C11×C22⋊C4—82no—
292C42×C11—22no—
293C42×C11—22no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307#3510C2×C1111yescharacteristic, complemented
308#3077C2×C1111yescharacteristic, complemented
309C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
310#2544C2×C1111yescharacteristic, complemented
311#2038C2×C1111yescharacteristic, complemented
312#2037C2×C1111yescharacteristic, complemented
313#2003C2×C1111yescharacteristic, complemented
314#2002C2×C1111yescharacteristic
315#1986C2×C1111yescharacteristic, complemented
316#1967C2×C1111yescharacteristic, complemented
317#1888C2×C1111yescharacteristic, complemented
318#1887C2×C1111yescharacteristic, complemented
319#1857C2×C1111yescharacteristic, complemented
320#1856C2×C1111yescharacteristic, complemented
321#1806C2×C1111yescharacteristic, complemented
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11C22×D411yescharacteristic
334Q8×C11—21no—
335Q8×C11—21no—
336Q8×C11—41no—
337Q8×C11—41no—
338Q8×C11—41no—
339Q8×C11—41no—
340Q8×C11—81no—
341Q8×C11—81no—
342D4×C11—21no—
343D4×C11—22no—
344D4×C11—21no—
345D4×C11—22no—
346D4×C11—41no—
347D4×C11—41no—
348D4×C11—41no—
349D4×C11—41no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11—82no—
355D4×C11—82no—
356D4×C11—88no—
357C2×C4×C11—22no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—81no—
380C2×C4×C11—81no—
381C2×C4×C11—82no—
382C2×C4×C11—82no—
383C2×C4×C11—82no—
384C2×C4×C11—82no—
385C2×C4×C11#12011yescharacteristic
386C2×C4×C11#12011yescharacteristic
387C2×C4×C11#12011yescharacteristic
388C2×C4×C11#12011yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C2×#4111yescharacteristic
392C2×C4×C11C2×#4111yescharacteristic
393C2×C4×C11H(5,𝔽2)11yescharacteristic
394C2×C4×C112−1+411yescharacteristic
395C8×C11—22no—
396C8×C11—41no—
397C8×C11—41no—
398C8×C11—41no—
399C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
400#559—21no—
401#559—21no—
402#556—21no—
403#556—21no—
404#551—22no—
405#551—22no—
406#542—21no—
407#542—21no—
408#536C22×C1111yescharacteristic
409#535C22×C1111yescharacteristic
410#533C22×C1111yescharacteristic
411C2×#127C22×C1111yescharacteristic
412#529—21no—
413#529—21no—
414C2×#124C22×C1111yescharacteristic
415C2×#124C22×C1111yescharacteristic
416#519C22×C1111yescharacteristic
417#518C22×C1111yescharacteristic
418C4×#41C22×C1111yescharacteristic
419C2×C4×D4C22×C1111yescharacteristic
420#478—21no—
421#478—21no—
422#476—21no—
423#474—21no—
424#442—21no—
425#440—21no—
426C4×SD16—21no—
427C4×D8—21no—
428#428C22×C1111yescharacteristic
429#428C22×C1111yescharacteristic
430#428C22×C1111yescharacteristic
431#423C22×C1111yescharacteristic
432C2×#104C22×C1111yescharacteristic
433C2×#104C22×C1111yescharacteristic
434#418C22×C1111yescharacteristic
435#418C22×C1111yescharacteristic
436#418C22×C1111yescharacteristic
437#417C22×C1111yescharacteristic
438C2×#101C22×C1111yescharacteristic
439C2×#101C22×C1111yescharacteristic
440C2×#100C22×C1111yescharacteristic
441C2×#100C22×C1111yescharacteristic
442C4×M16C22×C1111yescharacteristic
443#394—22no—
444#391C22×C1111yescharacteristic
445#390C22×C1111yescharacteristic
446#386—22no—
447C4×C4⋊C4C22×C1111yescharacteristic
448#339C22×C1111yescharacteristic
449#339C22×C1111yescharacteristic
450#339C22×C1111yescharacteristic
451#339C22×C1111yescharacteristic
452#339C22×C1111yescharacteristic
453#339C22×C1111yescharacteristic
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—44no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—41no—
463C22×C11—42no—
464C22×C11—82no—
465C22×C11—82no—
466C22×C11—82no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11C2×#12011yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11#54711yescharacteristic
472C4×C11—21no—
473C4×C11—21no—
474C4×C11—21no—
475C4×C11—21no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—41no—
479C4×C11—41no—
480C4×C11—41no—
481C4×C11—41no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11#52511yescharacteristic
488C4×C11#53711yescharacteristic
489C4×C11#54811yescharacteristic
490C4×C11#55011yescharacteristic
491C2×#41C23×C1111yescharacteristic
492C22×Q8C23×C1111yescharacteristic
493C22×D4—22no—
494C22×D4C23×C1111yescharacteristic
495C22×D4C23×C1111yescharacteristic
496C23×C4—21no—
497AGL(1,ℤ/8)—22no—
498AGL(1,ℤ/8)—22no—
499C2×SD16—21no—
500C2×D8—21no—
501C2×M16C23×C1111yescharacteristic
502C2×M16C23×C1111yescharacteristic
503C2×M16C23×C1111yescharacteristic
504C2×M16C23×C1111yescharacteristic
505C4⋊Q8—21no—
506C4⋊Q8D4×C1111yescharacteristic, complemented
507C4⋊Q8D4×C1111yescharacteristic, complemented
508#127—21no—
509#127—22no—
510#127—41no—
511#126—22no—
512#126—22no—
513#126—22no—
514#126—22no—
515#125D4×C1111yescharacteristic, complemented
516#125D4×C1111yescharacteristic, complemented
517#124—22no—
518#124—22no—
519#124—21no—
520#124—21no—
521#124—22no—
522#124—21no—
523#124—21no—
524#124—21no—
525#124—21no—
526#124—41no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538#121—21no—
539#121—21no—
540#120—22no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8D4×C1111yescharacteristic, complemented
548C4×Q8D4×C1111yescharacteristic, complemented
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4D4×C1111yescharacteristic, complemented
562C4×D4D4×C1111yescharacteristic, complemented
563#117—22no—
564#117—22no—
565#117—22no—
566#117—21no—
567#117C23×C1111yescharacteristic
568#117C23×C1111yescharacteristic
569#117C23×C1111yescharacteristic
570C2×C4⋊C4—21no—
571C2×C4⋊C4C23×C1111yescharacteristic
572C2×C22⋊C4—22no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4D4×C1112yes—
577C2×C22⋊C4D4×C1112yes—
578C2×C42—21no—
579C2×C42C23×C1111yescharacteristic
580C2×C42C23×C1111yescharacteristic
581C2×C42C23×C1111yescharacteristic
582#107—21no—
583#107—21no—
584#107—21no—
585#106—21no—
586#106—21no—
587#106—21no—
588C4⋊C8—21no—
589C4⋊C8—21no—
590#104—41no—
591#104—41no—
592#103—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#102—21no—
598#102—21no—
599#102—21no—
600#101—22no—
601#101—41no—
602#100—22no—
603#100—41no—
604#97—21no—
605C4×C8—21no—
606#95—21no—
607#95—22no—
608C2×C11—21no—
609C2×C11—21no—
610C2×C11—81no—
611C2×C11—82no—
612C2×C11—82no—
613C2×C11#240711yescharacteristic
614C2×C11#301811yescharacteristic
615C2×C11#302111yescharacteristic
616C24—21no—
617C24C2×D4×C1112yes—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8C2×D4×C1111yescharacteristic
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4C2×D4×C1111yescharacteristic
649C2×D4C11×#4112yes—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—82no—
661C22×C4C2×D4×C1112yes—
662C22×C4C2×D4×C1111yescharacteristic
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C24×C1111yescharacteristic
665SD16—24no—
666D8—24no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16C11×#4112yes—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4C2×D4×C1111yescharacteristic
695C4⋊C4C2×D4×C1111yescharacteristic
696C4⋊C4C2×D4×C1111yescharacteristic
697C4⋊C4C2×D4×C1111yescharacteristic
698C4⋊C4C2×D4×C1111yescharacteristic
699C4⋊C4C2×D4×C1111yescharacteristic
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—44no—
716C22⋊C4—41no—
717C22⋊C4—41no—
718C22⋊C4—82no—
719C42—22no—
720C42—22no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42C2×D4×C1111yescharacteristic
731C42C2×D4×C1111yescharacteristic
732C42C2×D4×C1111yescharacteristic
733C42C2×D4×C1111yescharacteristic
734C11#2414811yescharacteristic, direct product factor, Sylow
735C23—22no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—41no—
746C23C22×D4×C1111yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—81no—
754Q8—81no—
755D4—21no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—82no—
768D4—82no—
769D4—88no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4C11×#12011yescharacteristic
799C2×C4C11×#12011yescharacteristic
800C2×C4C11×#12011yescharacteristic
801C2×C4C11×#12011yescharacteristic
802C2×C4C22×D4×C1111yescharacteristic
803C2×C4C22×D4×C1111yescharacteristic
804C2×C4C2×C11×#4111yescharacteristic
805C2×C4C2×C11×#4111yescharacteristic
806C2×C4C11×H(5,𝔽2)11yescharacteristic
807C2×C4C11×2−1+411yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—21no—
813C22—21no—
814C22—44no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—81no—
826C22—81no—
827C22C2×C11×#12011yescharacteristic
828C22C11×#54611yescharacteristic
829C22C11×#54711yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—42no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4C11×#52511yescharacteristic
846C4C11×#53711yescharacteristic
847C4C11×#54811yescharacteristic
848C4C11×#55011yescharacteristic
849C2—21no—
850C2—21no—
851C2—82no—
852C2—82no—
853C2—81no—
854C2C11×#240711yescharacteristic
855C2C11×#301811yescharacteristic
856C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3510C2semidirect
2. C11×#3077C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2544C2semidirect
5. C11×#2038C2semidirect
6. C11×#2037C2semidirect
7. C11×#2003C2semidirect
9. C11×#1986C2semidirect
10. C11×#1967C2semidirect
11. C11×#1888C2semidirect
12. C11×#1887C2semidirect
13. C11×#1857C2semidirect
14. C11×#1856C2semidirect
15. C11×#1806C2semidirect
86. C11×C4⋊Q8D4semidirect
87. C11×C4⋊Q8D4semidirect
95. C11×#125D4semidirect
96. C11×#125D4semidirect
127. C4×Q8×C11D4semidirect
128. C4×Q8×C11D4semidirect
141. C4×D4×C11D4semidirect
142. C4×D4×C11D4semidirect
188. #24148C11direct (N × H)
307. #3510C2×C11semidirect
308. #3077C2×C11semidirect
309. C4×AGL(1,ℤ/8)C2×C11semidirect
310. #2544C2×C11semidirect
311. #2038C2×C11semidirect
312. #2037C2×C11semidirect
313. #2003C2×C11semidirect
315. #1986C2×C11semidirect
316. #1967C2×C11semidirect
317. #1888C2×C11semidirect
318. #1887C2×C11semidirect
319. #1857C2×C11semidirect
320. #1856C2×C11semidirect
321. #1806C2×C11semidirect
506. C4⋊Q8D4×C11semidirect
507. C4⋊Q8D4×C11semidirect
515. #125D4×C11semidirect
516. #125D4×C11semidirect
547. C4×Q8D4×C11semidirect
548. C4×Q8D4×C11semidirect
561. C4×D4D4×C11semidirect
562. C4×D4D4×C11semidirect
734. C11#24148direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#30772
C4×C11×AGL(1,ℤ/8)2
C11×#25442
C11×#20382
C11×#20372
C11×#20032
C11×#20022
C11×#19862
C11×#19672
C11×#18882
C11×#18872
C11×#18572
C11×#18562
C11×#18062
#2414811