Finite Group Databasebeta

← C11×#22464 #14599657

Subgroups — C11×#22464 #14599657

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic
2C2×C11×#444C211yesmaximal, characteristic, complemented
3C11×#2951C211yesmaximal, characteristic, complemented
4C11×#2898C211yesmaximal, characteristic, complemented
5C11×#2897C211yesmaximal, characteristic, complemented
6C11×#1977C211yesmaximal, characteristic, complemented
7C11×#1973C211yesmaximal, characteristic, complemented
8C11×#1908C211yesmaximal, characteristic, complemented
9C11×#1907C211yesmaximal, characteristic, complemented
10C11×#1883C211yesmaximal, characteristic, complemented
11C11×#1882C211yesmaximal, characteristic, complemented
12C11×#1816C211yesmaximal, characteristic, complemented
13C11×#1793C211yesmaximal, characteristic, complemented
14C11×#1792C211yesmaximal, characteristic, complemented
15C11×#1765C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#577—24no—
19C11×#577C418yescomplemented
20C2×C11×#137—21no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×AGL(1,ℤ/8)—21no—
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C11×#135—21no—
25C2×C11×#135C2211yescharacteristic
26C22×C11×SD16—21no—
27C22×C11×SD16C2211yescharacteristic
28C2×C11×#131C2211yescharacteristic
29C2×C11×#131C2211yescharacteristic
30C2×C11×#131C2211yescharacteristic, complemented
31C11×#520C2211yescharacteristic
32C11×#520C2211yescharacteristic, complemented
33C11×#444—24no—
34C11×#440—21no—
35C11×#440—21no—
36C4×C11×Q16—21no—
37C4×C11×D8—21no—
38C2×C11×#108C2211yescharacteristic, complemented
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×#104C2211yescharacteristic
41C2×C11×#104C2211yescharacteristic
42C2×C11×#104C2211yescharacteristic, complemented
43C11×#419—21no—
44C11×#419C2211yescharacteristic, complemented
45C11×#418—21no—
46C11×#418C2211yescharacteristic
47C11×#417—21no—
48C11×#417—21no—
49C11×#417C2211yescharacteristic
50C11×#417C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic, complemented
53C11×#416—21no—
54C11×#416—21no—
55C11×#416C2211yescharacteristic
56C2×C11×#103—21no—
57C2×C11×#103C2211yescharacteristic, complemented
58C2×C11×#102—21no—
59C2×C11×#102C2211yescharacteristic
60C2×C11×#101C2211yescharacteristic, complemented
61C2×C11×#100C2211yescharacteristic
62C11×#405C2211yescharacteristic, complemented
63C2×C11×#97C2211yescharacteristic, complemented
64C11×#391C2211yescharacteristic, complemented
65C11×#390C2211yescharacteristic
66C11×#343C2211yescharacteristic, complemented
67C11×#343C2211yescharacteristic, complemented
68C11×#341C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×2−1+4—22no—
71C11×2−1+4—22no—
72C11×2−1+4—41no—
73C11×2−1+4C2×C414yescomplemented
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—41no—
77C11×H(5,𝔽2)C2×C414yescomplemented
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—41no—
83C2×C11×#41C2311yescharacteristic
84C2×C11×#41C2311yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C22×Q8×C11—21no—
87C22×Q8×C11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—41no—
92C22×D4×C11C2311yescharacteristic
93C11×#137—22no—
94C11×#137—28no—
95C11×#137C2×C414yescomplemented
96C11×AGL(1,ℤ/8)—22no—
97C11×AGL(1,ℤ/8)—28no—
98C11×AGL(1,ℤ/8)C2×C414yescomplemented
99C11×#135—28no—
100C11×#135C2×C414yes—
101C11×#135D414yes—
102C2×C11×Q16—21no—
103C2×C11×Q16D411yescharacteristic
104C2×C11×SD16—21no—
105C2×C11×SD16—21no—
106C2×C11×SD16—28no—
107C2×C11×SD16—21no—
108C2×C11×SD16—21no—
109C2×C11×SD16—22no—
110C2×C11×SD16C2×C414yescomplemented
111C2×C11×SD16D411yescharacteristic
112C2×C11×SD16D411yescharacteristic
113C2×C11×D8—21no—
114C2×C11×D8D411yescharacteristic
115C11×#131—22no—
116C11×#131—22no—
117C11×#131—22no—
118C11×#131—41no—
119C11×#131—41no—
120C11×#131C2×C414yescomplemented
121C2×C11×M16—21no—
122C2×C11×M16—21no—
123C2×C11×M16—21no—
124C2×C11×M16C2311yescharacteristic
125C2×C11×M16C2311yescharacteristic
126C2×C11×M16C2311yescharacteristic
127C2×C11×M16C2311yescharacteristic
128C22×C8×C11—21no—
129C22×C8×C11—21no—
130C22×C8×C11—21no—
131C22×C8×C11C2311yescharacteristic
132C22×C8×C11C2311yescharacteristic
133C4×Q8×C11—21no—
134C4×Q8×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—41no—
138C4×D4×C11—41no—
139C11×#117—21no—
140C11×#117—21no—
141C11×#117C2311yescharacteristic
142C2×C11×C4⋊C4—21no—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4—41no—
147C2×C42×C11C2311yescharacteristic
148C11×#108—22no—
149C11×#107—21no—
150C11×#107—21no—
151C11×#104—22no—
152C11×#104—22no—
153C11×#104—22no—
154C11×#103—21no—
155C11×#103—21no—
156C11×#103—21no—
157C11×#103—21no—
158C11×#103—21no—
159C11×#103—21no—
160C11×#103—21no—
161C11×#103—21no—
162C11×#103D411yescharacteristic
163C11×#103D411yescharacteristic
164C11×#102—21no—
165C11×#102—21no—
166C11×#102—21no—
167C11×#102—21no—
168C11×#102—21no—
169C11×#102—21no—
170C11×#102—21no—
171C11×#102—21no—
172C11×#102D411yescharacteristic
173C11×#102D411yescharacteristic
174C11×#101—41no—
175C11×#100—41no—
176C11×#97—22no—
177C11×#97—21no—
178C4×C8×C11—21no—
179C11×#95—41no—
180#22464C1111yesmaximal, characteristic, direct product factor, Sylow
181C24×C11—21no—
182C24×C11—41no—
183C11×#41—21no—
184C11×#41—21no—
185C11×#41—21no—
186C11×#41—21no—
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—24no—
192C11×#41—24no—
193C11×#41—44no—
194C11×#41—42no—
195C11×#41—42no—
196C11×#41—42no—
197C11×#41—42no—
198C11×#41—44no—
199C11×#41C22×C412yes—
200C11×#41C22×C412yes—
201C11×#41C22×C412yes—
202C11×#41C2×D412yes—
203C11×#41C2×D412yes—
204C11×#41#4112yes—
205C2×Q8×C11—21no—
206C2×Q8×C11—24no—
207C2×Q8×C11—24no—
208C2×Q8×C11—21no—
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11—21no—
212C2×Q8×C11—41no—
213C2×Q8×C11—42no—
214C2×Q8×C11—42no—
215C2×Q8×C11C22×C412yes—
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D411yescharacteristic
218C2×Q8×C11C2×D411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—24no—
223C2×D4×C11—24no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—42no—
230C2×D4×C11—42no—
231C2×D4×C11—41no—
232C2×D4×C11—41no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—41no—
236C2×D4×C11C22×C412yes—
237C2×D4×C11C2×D411yescharacteristic
238C2×D4×C11C2×D411yescharacteristic
239C2×D4×C11C2×D411yescharacteristic
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—41no—
248C22×C4×C11—41no—
249C22×C4×C11—41no—
250C22×C4×C11—41no—
251C22×C4×C11—41no—
252C22×C4×C11C2411yescharacteristic
253C11×Q16—24no—
254C11×Q16C22⋊C414yescomplemented
255C11×SD16—24no—
256C11×SD16—24no—
257C11×SD16—24no—
258C11×SD16—24no—
259C11×SD16C22⋊C414yescomplemented
260C11×SD16C22⋊C414yescomplemented
261C11×D8—24no—
262C11×D8C22⋊C414yescomplemented
263C11×M16—24no—
264C11×M16—21no—
265C11×M16—21no—
266C11×M16—21no—
267C11×M16—21no—
268C11×M16—21no—
269C11×M16—21no—
270C11×M16—21no—
271C11×M16—42no—
272C11×M16—42no—
273C11×M16C22×C412yes—
274C2×C8×C11—24no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—42no—
282C2×C8×C11—42no—
283C2×C8×C11C22×C412yes—
284C2×C8×C11C2×D411yescharacteristic
285C2×C8×C11C2×D411yescharacteristic
286C2×C8×C11C2×D411yescharacteristic
287C2×C8×C11C2×D411yescharacteristic
288C2×C8×C11C2×D412yes—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—41no—
294C11×C4⋊C4—41no—
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C22⋊C4—21no—
298C11×C22⋊C4—41no—
299C11×C22⋊C4—41no—
300C11×C22⋊C4—82no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11—41no—
305C42×C11—41no—
306C2×#577C2×C1111yescharacteristic
307C2×#444C2×C1111yescharacteristic, complemented
308#2951C2×C1111yescharacteristic, complemented
309#2898C2×C1111yescharacteristic, complemented
310#2897C2×C1111yescharacteristic, complemented
311#1977C2×C1111yescharacteristic, complemented
312#1973C2×C1111yescharacteristic, complemented
313#1908C2×C1111yescharacteristic, complemented
314#1907C2×C1111yescharacteristic, complemented
315#1883C2×C1111yescharacteristic, complemented
316#1882C2×C1111yescharacteristic, complemented
317#1816C2×C1111yescharacteristic, complemented
318#1793C2×C1111yescharacteristic, complemented
319#1792C2×C1111yescharacteristic, complemented
320#1765C2×C1111yescharacteristic, complemented
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—22no—
325C23×C11—44no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—81no—
329C23×C11—81no—
330C23×C11—161no—
331C23×C11—161no—
332C23×C11H(5,𝔽2)11yescharacteristic
333Q8×C11—21no—
334Q8×C11—21no—
335Q8×C11—21no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—44no—
339Q8×C11—41no—
340Q8×C11—41no—
341Q8×C11C2×C22⋊C412yes—
342Q8×C11C2×C22⋊C412yes—
343Q8×C11C4×D412yes—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—21no—
353D4×C11—21no—
354D4×C11—21no—
355D4×C11—44no—
356D4×C11—44no—
357D4×C11—44no—
358D4×C11—41no—
359D4×C11—41no—
360D4×C11C2×C22⋊C412yes—
361D4×C11C2×C22⋊C412yes—
362D4×C11C4×D412yes—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—81no—
386C2×C4×C11—81no—
387C2×C4×C11—161no—
388C2×C4×C11—161no—
389C2×C4×C11C23×C411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2×#4111yescharacteristic
394C2×C4×C11H(5,𝔽2)11yescharacteristic
395C8×C11—22no—
396C8×C11—21no—
397C8×C11—21no—
398C8×C11—41no—
399C8×C11—41no—
400C8×C11—41no—
401C8×C11C2×C22⋊C412yes—
402C8×C11C2×C22⋊C412yes—
403C2×2−1+4C22×C1111yescharacteristic
404C2×H(5,𝔽2)C22×C1111yescharacteristic
405#577—24no—
406#577C4×C1118yescomplemented
407C2×#137—21no—
408C2×#137C22×C1111yescharacteristic
409C2×AGL(1,ℤ/8)—21no—
410C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
411C2×#135—21no—
412C2×#135C22×C1111yescharacteristic
413C22×SD16—21no—
414C22×SD16C22×C1111yescharacteristic
415C2×#131C22×C1111yescharacteristic
416C2×#131C22×C1111yescharacteristic
417C2×#131C22×C1111yescharacteristic, complemented
418#520C22×C1111yescharacteristic
419#520C22×C1111yescharacteristic, complemented
420#444—24no—
421#440—21no—
422#440—21no—
423C4×Q16—21no—
424C4×D8—21no—
425C2×#108C22×C1111yescharacteristic, complemented
426C2×#107C22×C1111yescharacteristic, complemented
427C2×#104C22×C1111yescharacteristic
428C2×#104C22×C1111yescharacteristic
429C2×#104C22×C1111yescharacteristic, complemented
430#419—21no—
431#419C22×C1111yescharacteristic, complemented
432#418—21no—
433#418C22×C1111yescharacteristic
434#417—21no—
435#417—21no—
436#417C22×C1111yescharacteristic
437#417C22×C1111yescharacteristic
438#417C22×C1111yescharacteristic
439#417C22×C1111yescharacteristic, complemented
440#416—21no—
441#416—21no—
442#416C22×C1111yescharacteristic
443C2×#103—21no—
444C2×#103C22×C1111yescharacteristic, complemented
445C2×#102—21no—
446C2×#102C22×C1111yescharacteristic
447C2×#101C22×C1111yescharacteristic, complemented
448C2×#100C22×C1111yescharacteristic
449#405C22×C1111yescharacteristic, complemented
450C2×#97C22×C1111yescharacteristic, complemented
451#391C22×C1111yescharacteristic, complemented
452#390C22×C1111yescharacteristic
453#343C22×C1111yescharacteristic, complemented
454#343C22×C1111yescharacteristic, complemented
455#341C22×C1111yescharacteristic, complemented
456#339C22×C1111yescharacteristic, complemented
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—82no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11—161no—
473C22×C11—164no—
474C22×C11#51811yescharacteristic
475C22×C11D4211yescharacteristic
476C22×C11#54611yescharacteristic
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—22no—
480C4×C11—42no—
481C4×C11—41no—
482C4×C11—41no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11C22×C22⋊C411yescharacteristic
487C4×C11C2×C4×D411yescharacteristic
488C4×C11D4211yescharacteristic
489C4×C11#54611yescharacteristic
4902−1+4—22no—
4912−1+4—22no—
4922−1+4—41no—
4932−1+4C2×C4×C1114yescomplemented
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—41no—
497H(5,𝔽2)C2×C4×C1114yescomplemented
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—41no—
503C2×#41C23×C1111yescharacteristic
504C2×#41C23×C1111yescharacteristic
505C2×#41C23×C1111yescharacteristic
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C23×C1111yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4C23×C1111yescharacteristic
513#137—22no—
514#137—28no—
515#137C2×C4×C1114yescomplemented
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—28no—
518AGL(1,ℤ/8)C2×C4×C1114yescomplemented
519#135—28no—
520#135C2×C4×C1114yes—
521#135D4×C1114yes—
522C2×Q16—21no—
523C2×Q16D4×C1111yescharacteristic
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—28no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—22no—
530C2×SD16C2×C4×C1114yescomplemented
531C2×SD16D4×C1111yescharacteristic
532C2×SD16D4×C1111yescharacteristic
533C2×D8—21no—
534C2×D8D4×C1111yescharacteristic
535#131—22no—
536#131—22no—
537#131—22no—
538#131—41no—
539#131—41no—
540#131C2×C4×C1114yescomplemented
541C2×M16—21no—
542C2×M16—21no—
543C2×M16—21no—
544C2×M16C23×C1111yescharacteristic
545C2×M16C23×C1111yescharacteristic
546C2×M16C23×C1111yescharacteristic
547C2×M16C23×C1111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C1111yescharacteristic
552C22×C8C23×C1111yescharacteristic
553C4×Q8—21no—
554C4×Q8—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—41no—
558C4×D4—41no—
559#117—21no—
560#117—21no—
561#117C23×C1111yescharacteristic
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4C23×C1111yescharacteristic
565C2×C4⋊C4C23×C1111yescharacteristic
566C2×C22⋊C4—41no—
567C2×C42C23×C1111yescharacteristic
568#108—22no—
569#107—21no—
570#107—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#103—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#103—21no—
579#103—21no—
580#103—21no—
581#103—21no—
582#103D4×C1111yescharacteristic
583#103D4×C1111yescharacteristic
584#102—21no—
585#102—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102D4×C1111yescharacteristic
593#102D4×C1111yescharacteristic
594#101—41no—
595#100—41no—
596#97—22no—
597#97—21no—
598C4×C8—21no—
599#95—41no—
600C2×C11—21no—
601C2×C11—21no—
602C2×C11—42no—
603C2×C11—42no—
604C2×C11—42no—
605C2×C11—82no—
606C2×C11D4×C22⋊C411yescharacteristic
607C2×C11#328811yescharacteristic
608C2×C11#328911yescharacteristic
609C24—21no—
610C24—41no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—24no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—44no—
622#41—42no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—44no—
627#41C22×C4×C1112yes—
628#41C22×C4×C1112yes—
629#41C22×C4×C1112yes—
630#41C2×D4×C1112yes—
631#41C2×D4×C1112yes—
632#41C11×#4112yes—
633C2×Q8—21no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—41no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8C22×C4×C1112yes—
644C2×Q8C2×D4×C1111yescharacteristic
645C2×Q8C2×D4×C1111yescharacteristic
646C2×Q8C2×D4×C1111yescharacteristic
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—41no—
664C2×D4C22×C4×C1112yes—
665C2×D4C2×D4×C1111yescharacteristic
666C2×D4C2×D4×C1111yescharacteristic
667C2×D4C2×D4×C1111yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4C24×C1111yescharacteristic
681Q16—24no—
682Q16C11×C22⋊C414yescomplemented
683SD16—24no—
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16C11×C22⋊C414yescomplemented
688SD16C11×C22⋊C414yescomplemented
689D8—24no—
690D8C11×C22⋊C414yescomplemented
691M16—21no—
692M16—24no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—21no—
698M16—21no—
699M16—42no—
700M16—42no—
701M16C22×C4×C1112yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—24no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—42no—
710C2×C8—42no—
711C2×C8C22×C4×C1112yes—
712C2×C8C2×D4×C1111yescharacteristic
713C2×C8C2×D4×C1111yescharacteristic
714C2×C8C2×D4×C1111yescharacteristic
715C2×C8C2×D4×C1111yescharacteristic
716C2×C8C2×D4×C1112yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—41no—
722C4⋊C4—41no—
723C4⋊C4C2×D4×C1111yescharacteristic
724C4⋊C4C2×D4×C1111yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—41no—
727C22⋊C4—41no—
728C22⋊C4—82no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—41no—
733C42—41no—
734C11#2246411yescharacteristic, direct product factor, Sylow
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23C11×H(5,𝔽2)11yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8C2×C11×C22⋊C412yes—
756Q8C2×C11×C22⋊C412yes—
757Q8C4×D4×C1112yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4C2×C11×C22⋊C412yes—
775D4C2×C11×C22⋊C412yes—
776D4C4×D4×C1112yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—161no—
802C2×C4—161no—
803C2×C4C23×C4×C1111yescharacteristic
804C2×C4C22×D4×C1111yescharacteristic
805C2×C4C22×D4×C1111yescharacteristic
806C2×C4C22×D4×C1111yescharacteristic
807C2×C4C2×C11×#4111yescharacteristic
808C2×C4C11×H(5,𝔽2)11yescharacteristic
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C8C2×C11×C22⋊C412yes—
816C8C2×C11×C22⋊C412yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22C11×#51811yescharacteristic
835C22D42×C1111yescharacteristic
836C22C11×#54611yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—41no—
841C4—41no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4C22×C11×C22⋊C411yescharacteristic
847C4C2×C4×D4×C1111yescharacteristic
848C4D42×C1111yescharacteristic
849C4C11×#54611yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C11×C22⋊C411yescharacteristic
857C2C11×#328811yescharacteristic
858C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#577C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#444C2semidirect
3. C11×#2951C2semidirect
4. C11×#2898C2semidirect
5. C11×#2897C2semidirect
6. C11×#1977C2semidirect
7. C11×#1973C2semidirect
8. C11×#1908C2semidirect
9. C11×#1907C2semidirect
10. C11×#1883C2semidirect
11. C11×#1882C2semidirect
12. C11×#1816C2semidirect
13. C11×#1793C2semidirect
14. C11×#1792C2semidirect
15. C11×#1765C2semidirect
19. C11×#577C4semidirect
30. C2×C11×#131C22semidirect
32. C11×#520C22semidirect
38. C2×C11×#108C22semidirect
39. C2×C11×#107C22semidirect
42. C2×C11×#104C22semidirect
44. C11×#419C22semidirect
52. C11×#417C22semidirect
57. C2×C11×#103C22semidirect
60. C2×C11×#101C22semidirect
62. C11×#405C22semidirect
63. C2×C11×#97C22semidirect
64. C11×#391C22semidirect
66. C11×#343C22semidirect
67. C11×#343C22semidirect
68. C11×#341C22semidirect
69. C11×#339C22semidirect
73. C11×2−1+4C2×C4semidirect
77. C11×H(5,𝔽2)C2×C4semidirect
95. C11×#137C2×C4semidirect
98. C11×AGL(1,ℤ/8)C2×C4semidirect
110. C2×C11×SD16C2×C4semidirect
120. C11×#131C2×C4semidirect
180. #22464C11direct (N × H)
254. C11×Q16C22⋊C4semidirect
259. C11×SD16C22⋊C4semidirect
260. C11×SD16C22⋊C4semidirect
262. C11×D8C22⋊C4semidirect
307. C2×#444C2×C11semidirect
308. #2951C2×C11semidirect
309. #2898C2×C11semidirect
310. #2897C2×C11semidirect
311. #1977C2×C11semidirect
312. #1973C2×C11semidirect
313. #1908C2×C11semidirect
314. #1907C2×C11semidirect
315. #1883C2×C11semidirect
316. #1882C2×C11semidirect
317. #1816C2×C11semidirect
318. #1793C2×C11semidirect
319. #1792C2×C11semidirect
320. #1765C2×C11semidirect
406. #577C4×C11semidirect
417. C2×#131C22×C11semidirect
419. #520C22×C11semidirect
425. C2×#108C22×C11semidirect
426. C2×#107C22×C11semidirect
429. C2×#104C22×C11semidirect
431. #419C22×C11semidirect
439. #417C22×C11semidirect
444. C2×#103C22×C11semidirect
447. C2×#101C22×C11semidirect
449. #405C22×C11semidirect
450. C2×#97C22×C11semidirect
451. #391C22×C11semidirect
453. #343C22×C11semidirect
454. #343C22×C11semidirect
455. #341C22×C11semidirect
456. #339C22×C11semidirect
493. 2−1+4C2×C4×C11semidirect
497. H(5,𝔽2)C2×C4×C11semidirect
515. #137C2×C4×C11semidirect
518. AGL(1,ℤ/8)C2×C4×C11semidirect
530. C2×SD16C2×C4×C11semidirect
540. #131C2×C4×C11semidirect
682. Q16C11×C22⋊C4semidirect
687. SD16C11×C22⋊C4semidirect
688. SD16C11×C22⋊C4semidirect
690. D8C11×C22⋊C4semidirect
734. C11#22464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5772
C2×C11×#4442
C11×#29512
C11×#28982
C11×#28972
C11×#19772
C11×#19732
C11×#19082
C11×#19072
C11×#18832
C11×#18822
C11×#18162
C11×#17932
C11×#17922
C11×#17652
#2246411