Finite Group Databasebeta

← C11×#25960 #14603153

Subgroups — C11×#25960 #14603153

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic
3C11×#2442C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#2092C211yesmaximal, characteristic, complemented
6C11×#2067C211yesmaximal, characteristic, complemented
7C11×#2065C211yesmaximal, characteristic, complemented
8C11×#2025C211yesmaximal, characteristic, complemented
9C11×#1864C211yesmaximal, characteristic, complemented
10C11×#1862C211yesmaximal, characteristic, complemented
11C11×#1852C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1807C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4—21no—
23C11×#478—24no—
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#106C2211yescharacteristic, complemented
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×C4⋊C8C2211yescharacteristic, complemented
29C2×C11×C4⋊C8C2211yescharacteristic, complemented
30C2×C11×#102—24no—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C11×#400—21no—
41C11×#398—21no—
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic, complemented
45C11×#389C2211yescharacteristic, complemented
46C11×#386—21no—
47C11×#386—21no—
48C11×#385—21no—
49C11×#382C2211yescharacteristic, complemented
50C11×#380—21no—
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C11×#379—21no—
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—41no—
67C22×D4×C11—41no—
68C22×D4×C11Q814yes—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#125—22no—
83C11×#125—41no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C2×C11×C4⋊C4—22no—
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—41no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
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×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—44no—
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107—22no—
115C11×#107—41no—
116C11×#106—22no—
117C11×#106—41no—
118C11×C4⋊C8—22no—
119C11×C4⋊C8—41no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102—41no—
127C11×#102D414yes—
128C11×C22⋊C8—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#25960C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—24no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11C2×D411yescharacteristic
148C2×D4×C11—28no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—44no—
159C2×D4×C11—44no—
160C2×D4×C11—44no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11C2×D412yes—
164C2×D4×C11C2×Q812yes—
165C2×D4×C11C2×Q812yes—
166C2×D4×C11#4112yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×Q812yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—44no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4—81no—
223C11×C4⋊C4C2×D412yes—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C2×#478C2×C1111yescharacteristic, complemented
239C22×#102C2×C1111yescharacteristic
240#2442C2×C1111yescharacteristic, complemented
241D4×C22⋊C4C2×C1111yescharacteristic
242#2092C2×C1111yescharacteristic, complemented
243#2067C2×C1111yescharacteristic, complemented
244#2065C2×C1111yescharacteristic, complemented
245#2025C2×C1111yescharacteristic, complemented
246#1864C2×C1111yescharacteristic, complemented
247#1862C2×C1111yescharacteristic, complemented
248#1852C2×C1111yescharacteristic, complemented
249#1850C2×C1111yescharacteristic, complemented
250#1807C2×C1111yescharacteristic, complemented
251#1804C2×C1111yescharacteristic, complemented
252#1786C2×C1111yescharacteristic
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—48no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—48no—
273C23×C11—84no—
274C23×C11—84no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11C22⋊Q812yes—
279C23×C11#13512yes—
280C23×C11AGL(1,ℤ/8)12yes—
281C23×C11C22×D411yescharacteristic
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11C22⋊Q814yes—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—84no—
328C2×C4×C11—84no—
329C2×C4×C11—84no—
330C2×C4×C11C22⋊Q812yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×Q811yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C8×C11—22no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C23×D4C22×C1111yescharacteristic
342C23×C8C22×C1111yescharacteristic
343C2×#125C22×C1111yescharacteristic, complemented
344C2×C4×D4C22×C1111yescharacteristic
345C2×C4×D4C22×C1111yescharacteristic
346C22×C4⋊C4C22×C1111yescharacteristic
347C22×C22⋊C4—21no—
348#478—24no—
349C2×#107C22×C1111yescharacteristic, complemented
350C2×#107C22×C1111yescharacteristic, complemented
351C2×#106C22×C1111yescharacteristic, complemented
352C2×#106C22×C1111yescharacteristic, complemented
353C2×C4⋊C8C22×C1111yescharacteristic, complemented
354C2×C4⋊C8C22×C1111yescharacteristic, complemented
355C2×#102—24no—
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×#102C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365#400—21no—
366#398—21no—
367#390C22×C1111yescharacteristic
368#390C22×C1111yescharacteristic
369#389C22×C1111yescharacteristic, complemented
370#389C22×C1111yescharacteristic, complemented
371#386—21no—
372#386—21no—
373#385—21no—
374#382C22×C1111yescharacteristic, complemented
375#380—21no—
376#380C22×C1111yescharacteristic
377#380C22×C1111yescharacteristic
378#379—21no—
379C4×C22⋊C4C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic, complemented
381#340C22×C1111yescharacteristic, complemented
382#340C22×C1111yescharacteristic, complemented
383#340C22×C1111yescharacteristic, complemented
384#336C22×C1111yescharacteristic, complemented
385#336C22×C1111yescharacteristic, complemented
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—24no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—816no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11#47814yescomplemented
408C22×C11C2×C22⋊Q811yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11#54611yescharacteristic
411C22×C11C2×#13511yescharacteristic
412C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C4×C11—22no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11C2×C22⋊Q811yescharacteristic
427C4×C11#54311yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430C25—21no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—21no—
434C22×D4—22no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4Q8×C1114yes—
438C22×D4C23×C1111yescharacteristic
439C22×D4C23×C1111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C1111yescharacteristic
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—41no—
447C22×C8C23×C1111yescharacteristic
448C22×C8C23×C1111yescharacteristic
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451#125—22no—
452#125—41no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—41no—
456C4×D4—41no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4D4×C1111yescharacteristic
480C2×C22⋊C4D4×C1111yescharacteristic
481C2×C42C23×C1111yescharacteristic
482C2×C42C23×C1111yescharacteristic
483#107—22no—
484#107—41no—
485#106—22no—
486#106—41no—
487C4⋊C8—22no—
488C4⋊C8—41no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—41no—
495#102—41no—
496#102D4×C1114yes—
497C22⋊C8—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95D4×C1111yescharacteristic
505#95D4×C1111yescharacteristic
506C2×C11—24no—
507C2×C11—44no—
508C2×C11—82no—
509C2×C11#243711yescharacteristic
510C2×C11C2×#47811yescharacteristic
511C2×C11#308111yescharacteristic
512C2×C11#326411yescharacteristic
513C2×C11#328211yescharacteristic
514C2×C11#329711yescharacteristic
515C2×C11#331011yescharacteristic
516C24—21no—
517C24—21no—
518C24—24no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—81no—
524C24—81no—
525C24C2×D4×C1111yescharacteristic
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4C2×D4×C1112yes—
542C2×D4C2×Q8×C1112yes—
543C2×D4C2×Q8×C1112yes—
544C2×D4C11×#4112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4C2×D4×C1111yescharacteristic
565C22×C4C2×D4×C1111yescharacteristic
566C22×C4C2×D4×C1111yescharacteristic
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×Q8×C1112yes—
570C22×C4C11×#4112yes—
571C22×C4C24×C1111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8C2×D4×C1112yes—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C4⋊C4C2×D4×C1112yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C11#2596011yescharacteristic, direct product factor, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—48no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—48no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23C11×C22⋊Q812yes—
643C23C11×#13512yes—
644C23C11×AGL(1,ℤ/8)12yes—
645C23C22×D4×C1111yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4C11×C22⋊Q814yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4C11×C22⋊Q812yes—
695C2×C4C22×D4×C1111yescharacteristic
696C2×C4C22×Q8×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C11×H(5,𝔽2)11yescharacteristic
700C2×C4C11×H(5,𝔽2)11yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22C11×#47814yescomplemented
727C22C2×C11×C22⋊Q811yescharacteristic
728C22D42×C1111yescharacteristic
729C22C11×#54611yescharacteristic
730C22C2×C11×#13511yescharacteristic
731C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
732C22C11×#57611yescharacteristic
733C22C11×#57711yescharacteristic
734C4—22no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C2×C11×C22⋊Q811yescharacteristic
746C4C11×#54311yescharacteristic
747C4C11×#54611yescharacteristic
748C4C11×#55111yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2C11×#243711yescharacteristic
753C2C2×C11×#47811yescharacteristic
754C2C11×#308111yescharacteristic
755C2C11×#326411yescharacteristic
756C2C11×#328211yescharacteristic
757C2C11×#329711yescharacteristic
758C2C11×#331011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×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
1. C2×C11×#478C2semidirect
3. C11×#2442C2semidirect
5. C11×#2092C2semidirect
6. C11×#2067C2semidirect
7. C11×#2065C2semidirect
8. C11×#2025C2semidirect
9. C11×#1864C2semidirect
10. C11×#1862C2semidirect
11. C11×#1852C2semidirect
12. C11×#1850C2semidirect
13. C11×#1807C2semidirect
14. C11×#1804C2semidirect
18. C2×C11×#125C22semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#106C22semidirect
27. C2×C11×#106C22semidirect
28. C2×C11×C4⋊C8C22semidirect
29. C2×C11×C4⋊C8C22semidirect
44. C11×#389C22semidirect
45. C11×#389C22semidirect
49. C11×#382C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
137. #25960C11direct (N × H)
238. C2×#478C2×C11semidirect
240. #2442C2×C11semidirect
242. #2092C2×C11semidirect
243. #2067C2×C11semidirect
244. #2065C2×C11semidirect
245. #2025C2×C11semidirect
246. #1864C2×C11semidirect
247. #1862C2×C11semidirect
248. #1852C2×C11semidirect
249. #1850C2×C11semidirect
250. #1807C2×C11semidirect
251. #1804C2×C11semidirect
343. C2×#125C22×C11semidirect
349. C2×#107C22×C11semidirect
350. C2×#107C22×C11semidirect
351. C2×#106C22×C11semidirect
352. C2×#106C22×C11semidirect
353. C2×C4⋊C8C22×C11semidirect
354. C2×C4⋊C8C22×C11semidirect
369. #389C22×C11semidirect
370. #389C22×C11semidirect
374. #382C22×C11semidirect
380. #340C22×C11semidirect
381. #340C22×C11semidirect
382. #340C22×C11semidirect
383. #340C22×C11semidirect
384. #336C22×C11semidirect
385. #336C22×C11semidirect
407. C22×C11#478semidirect
616. C11#25960direct (N × H)
726. C22C11×#478semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C22×C11×#1022
C11×#24422
D4×C11×C22⋊C42
C11×#20922
C11×#20672
C11×#20652
C11×#20252
C11×#18642
C11×#18622
C11×#18522
C11×#18502
C11×#18072
C11×#18042
C11×#17862
#2596011