Finite Group Databasebeta

← C11×#24347 #14601540

Subgroups — C11×#24347 #14601540

Order 2816.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2058C211yesmaximal, characteristic, complemented
7C11×#2025C211yesmaximal, characteristic, complemented
8C11×#2023C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1985C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic
12C11×#1879C211yesmaximal, characteristic
13C11×#1864C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C11×#554—24no—
18C11×#554—24no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4—21no—
32C11×#478—24no—
33C11×#442—24no—
34C2×C11×#107C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#97C2211yescharacteristic
45C11×#396—21no—
46C11×#396—21no—
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#384C2211yescharacteristic
52C11×#380—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8Q814yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8—22no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125—22no—
83C11×#125D414yes—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8—44no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11D414yes—
98C2×C11×C4⋊C4—28no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#106—22no—
130C11×#106—22no—
131C11×C4⋊C8—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#97—22no—
139C11×#95—21no—
140C11×#95—21no—
141#24347C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C2×Q8×C11—24no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—41no—
148C2×Q8×C11—81no—
149C2×Q8×C11—81no—
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×C11C2×D412yes—
159C2×D4×C11C2×Q812yes—
160C2×D4×C11C2×Q812yes—
161C2×D4×C11#4112yes—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C11×D8—28no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11C2×Q812yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
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—42no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—81no—
221C11×C4⋊C4C2×D412yes—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2×D412yes—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11C2×D412yes—
237C42×C11C2×D412yes—
238C2×#554C2×C1111yescharacteristic, complemented
239C2×#478C2×C1111yescharacteristic, complemented
240C2×#442C2×C1111yescharacteristic
241#2538C2×C1111yescharacteristic, complemented
242#2059C2×C1111yescharacteristic, complemented
243#2058C2×C1111yescharacteristic, complemented
244#2025C2×C1111yescharacteristic, complemented
245#2023C2×C1111yescharacteristic, complemented
246#1992C2×C1111yescharacteristic, complemented
247#1985C2×C1111yescharacteristic, complemented
248#1879C2×C1111yescharacteristic
249#1879C2×C1111yescharacteristic
250#1864C2×C1111yescharacteristic, complemented
251#1862C2×C1111yescharacteristic, complemented
252#1802C2×C1111yescharacteristic, complemented
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11C22×D411yescharacteristic
268Q8×C11—44no—
269Q8×C11—84no—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11C22⋊Q814yescomplemented
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—48no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—84no—
313C2×C4×C11—84no—
314C2×C4×C11—84no—
315C2×C4×C11#12012yes—
316C2×C4×C11#12012yes—
317C2×C4×C11AGL(1,ℤ/8)12yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C22×Q811yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C112−1+411yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C8×C11—22no—
325C8×C11—41no—
326C8×C11—41no—
327C8×C11—41no—
328C22×D8C22×C1111yescharacteristic
329#554—24no—
330#554—24no—
331C2×C4⋊Q8C22×C1111yescharacteristic
332C2×#125C22×C1111yescharacteristic
333C2×#125C22×C1111yescharacteristic
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8—21no—
336C2×C22⋊Q8—21no—
337C2×C22⋊Q8—21no—
338C2×C4×Q8C22×C1111yescharacteristic
339C2×C4×D4C22×C1111yescharacteristic
340C2×C4×D4C22×C1111yescharacteristic
341C2×C4×D4C22×C1111yescharacteristic
342C2×C4×D4C22×C1111yescharacteristic
343C22×C4⋊C4—21no—
344#478—24no—
345#442—24no—
346C2×#107C22×C1111yescharacteristic
347C2×#106C22×C1111yescharacteristic
348C2×#106C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#97C22×C1111yescharacteristic
357#396—21no—
358#396—21no—
359#390C22×C1111yescharacteristic
360#390C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#389C22×C1111yescharacteristic
363#384C22×C1111yescharacteristic
364#380—21no—
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375C22×C11—24no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11C2×#12011yescharacteristic
390C22×C11#54811yescharacteristic
391C22×C11D4×Q811yescharacteristic
392C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57611yescharacteristic
395C22×C11#57711yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—41no—
400C4×C11—42no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11C2×C22⋊Q811yescharacteristic
409C4×C11#53611yescharacteristic
410C4×C11#54811yescharacteristic
411C4×C11D4×Q811yescharacteristic
412C22×Q8—21no—
413C22×Q8D4×C1111yescharacteristic
414C22×D4C23×C1111yescharacteristic
415C22×D4C23×C1111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C2×D8—22no—
421C2×D8—22no—
422C2×D8Q8×C1114yescomplemented
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429#125—22no—
430#125—22no—
431#125—22no—
432#125D4×C1114yes—
433C22⋊Q8—28no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436C22⋊Q8—44no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4D4×C1114yes—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C1111yescharacteristic
458C2×C4⋊C4D4×C1111yescharacteristic
459C2×C4⋊C4D4×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C4⋊C4C23×C1111yescharacteristic
463C2×C4⋊C4C23×C1111yescharacteristic
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C42C23×C1111yescharacteristic
475C2×C42C23×C1111yescharacteristic
476C2×C42C23×C1111yescharacteristic
477#107—22no—
478#106—22no—
479#106—22no—
480C4⋊C8—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#97—22no—
488#95—21no—
489#95—21no—
490C2×C11—44no—
491C2×C11—82no—
492C2×C11#240911yescharacteristic
493C2×C11#300611yescharacteristic
494C2×C11#301211yescharacteristic
495C2×C11#336611yescharacteristic
496C2×C11#337611yescharacteristic
497C2×C11#338411yescharacteristic
498C2×C11#338911yescharacteristic
499C24—21no—
500C24—21no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—41no—
505C2×Q8—81no—
506C2×Q8—81no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4C2×D4×C1112yes—
516C2×D4C2×Q8×C1112yes—
517C2×D4C2×Q8×C1112yes—
518C2×D4C11×#4112yes—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C2×D4×C1111yescharacteristic
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C24×C1111yescharacteristic
544D8—28no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C2×Q8×C1112yes—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4C2×D4×C1112yes—
579C4⋊C4C2×D4×C1112yes—
580C4⋊C4C2×D4×C1112yes—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42C2×D4×C1112yes—
594C42C2×D4×C1112yes—
595C11#2434711yescharacteristic, direct product factor, Sylow
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C1111yescharacteristic
611Q8—44no—
612Q8—84no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—22no—
618D4—41no—
619D4—41no—
620D4C11×C22⋊Q814yescomplemented
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4C11×#12012yes—
659C2×C4C11×#12012yes—
660C2×C4C11×AGL(1,ℤ/8)12yes—
661C2×C4C22×D4×C1111yescharacteristic
662C2×C4C22×D4×C1111yescharacteristic
663C2×C4C22×Q8×C1111yescharacteristic
664C2×C4C2×C11×#4111yescharacteristic
665C2×C4C11×2−1+411yescharacteristic
666C2×C4C11×2−1+411yescharacteristic
667C8—22no—
668C8—41no—
669C8—41no—
670C8—41no—
671C22—24no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C11×#12011yescharacteristic
686C22C11×#54811yescharacteristic
687C22D4×Q8×C1111yescharacteristic
688C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
689C22C11×#57511yescharacteristic
690C22C11×#57611yescharacteristic
691C22C11×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×C11×C22⋊Q811yescharacteristic
705C4C11×#53611yescharacteristic
706C4C11×#54811yescharacteristic
707C4D4×Q8×C1111yescharacteristic
708C2—44no—
709C2—82no—
710C2C11×#240911yescharacteristic
711C2C11×#300611yescharacteristic
712C2C11×#301211yescharacteristic
713C2C11×#336611yescharacteristic
714C2C11×#337611yescharacteristic
715C2C11×#338411yescharacteristic
716C2C11×#338911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#554C2semidirect
2. C2×C11×#478C2semidirect
4. C11×#2538C2semidirect
5. C11×#2059C2semidirect
6. C11×#2058C2semidirect
7. C11×#2025C2semidirect
8. C11×#2023C2semidirect
9. C11×#1992C2semidirect
10. C11×#1985C2semidirect
13. C11×#1864C2semidirect
14. C11×#1862C2semidirect
15. C11×#1802C2semidirect
73. C2×C11×D8Q8semidirect
141. #24347C11direct (N × H)
238. C2×#554C2×C11semidirect
239. C2×#478C2×C11semidirect
241. #2538C2×C11semidirect
242. #2059C2×C11semidirect
243. #2058C2×C11semidirect
244. #2025C2×C11semidirect
245. #2023C2×C11semidirect
246. #1992C2×C11semidirect
247. #1985C2×C11semidirect
250. #1864C2×C11semidirect
251. #1862C2×C11semidirect
252. #1802C2×C11semidirect
277. D4×C11C22⋊Q8semidirect
422. C2×D8Q8×C11semidirect
595. C11#24347direct (N × H)
620. D4C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4782
C2×C11×#4422
C11×#25382
C11×#20592
C11×#20582
C11×#20252
C11×#20232
C11×#19922
C11×#19852
C11×#18792
C11×#18642
C11×#18622
C11×#18022
#2434711