Finite Group Databasebeta

← C11×#23143 #14600336

Subgroups — C11×#23143 #14600336

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#469C211yesmaximal, characteristic
2C11×#2363C211yesmaximal, characteristic, complemented
3C11×#2361C211yesmaximal, characteristic, complemented
4C11×#1936C211yesmaximal, characteristic, complemented
5C11×#1934C211yesmaximal, characteristic, complemented
6C11×#1920C211yesmaximal, characteristic, complemented
7C11×#1920C211yesmaximal, characteristic, complemented
8C11×#1879C211yesmaximal, characteristic, complemented
9C11×#1879C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C11×#1762C211yesmaximal, characteristic, complemented
13C4×C11×#102C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#469C418yescomplemented
26C2×C11×#106C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388—21no—
42C11×#388—21no—
43C11×#386—21no—
44C11×#386—21no—
45C11×#385—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4—21no—
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C2×C11×D8—41no—
69C2×C11×D8—41no—
70C2×C11×D8C2×C414yescomplemented
71C2×C11×M16—41no—
72C2×C11×M16—41no—
73C2×C11×M16C2×C414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#121—22no—
79C11×#121—22no—
80C11×#121C2×C414yescomplemented
81C11×#121C2×C414yescomplemented
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C4×D4×C11—44no—
87C11×#117—22no—
88C11×#117—41no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#106C2×C414yescomplemented
117C11×#102—22no—
118C11×#102—22no—
119C11×#102—41no—
120C11×#102—41no—
121C11×#102C2×C414yescomplemented
122C11×#102C2×C414yescomplemented
123C11×C22⋊C8—22no—
124C11×#97—41no—
125C4×C8×C11—41no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#23143C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—81no—
151C2×D4×C11—81no—
152C2×D4×C11C22×C412yes—
153C2×D4×C11C22×C412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C11×D8—44no—
182C11×M16—44no—
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×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C22×C412yes—
194C2×C8×C11C22×C412yes—
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—21no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C4⋊C4#4112yes—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—81no—
220C11×C22⋊C4—81no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C42×C11—42no—
227C42×C11—81no—
228C2×#469C2×C1111yescharacteristic
229#2363C2×C1111yescharacteristic, complemented
230#2361C2×C1111yescharacteristic, complemented
231#1936C2×C1111yescharacteristic, complemented
232#1934C2×C1111yescharacteristic, complemented
233#1920C2×C1111yescharacteristic, complemented
234#1920C2×C1111yescharacteristic, complemented
235#1879C2×C1111yescharacteristic, complemented
236#1879C2×C1111yescharacteristic, complemented
237#1875C2×C1111yescharacteristic, complemented
238#1874C2×C1111yescharacteristic, complemented
239#1762C2×C1111yescharacteristic, complemented
240C4×#102C2×C1111yescharacteristic, complemented
241#1753C2×C1111yescharacteristic, complemented
242#1736C2×C1111yescharacteristic, complemented
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C4×D412yes—
264C23×C11C22×D411yescharacteristic
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—48no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—84no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
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—41no—
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—84no—
311C2×C4×C11—84no—
312C2×C4×C11—84no—
313C2×C4×C11C4×D412yes—
314C2×C4×C11AGL(1,ℤ/8)12yes—
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C8×C11—22no—
322C8×C11—22no—
323C8×C11—41no—
324C8×C11—41no—
325C22×D8C22×C1111yescharacteristic
326C22×M16C22×C1111yescharacteristic
327C2×#121C22×C1111yescharacteristic
328C2×#121C22×C1111yescharacteristic
329C2×C4×D4—21no—
330C2×C4×D4C22×C1111yescharacteristic
331C2×C4×D4C22×C1111yescharacteristic
332C2×#117C22×C1111yescharacteristic
333C22×C4⋊C4C22×C1111yescharacteristic
334#469C4×C1118yescomplemented
335C2×#106C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×C22⋊C8C22×C1111yescharacteristic
343C2×#97C22×C1111yescharacteristic
344C2×C4×C8C22×C1111yescharacteristic
345#390—21no—
346#390C22×C1111yescharacteristic
347#390C22×C1111yescharacteristic
348#389C22×C1111yescharacteristic
349#389C22×C1111yescharacteristic
350#388—21no—
351#388—21no—
352#386—21no—
353#386—21no—
354#385—21no—
355C4×C4⋊C4C22×C1111yescharacteristic
356C4×C4⋊C4C22×C1111yescharacteristic
357C4×C22⋊C4—21no—
358C4×C22⋊C4C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11C2×C4×D411yescharacteristic
391C22×C11#54611yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C11#57511yescharacteristic
395C22×C11#57611yescharacteristic
396C22×C11#57711yescharacteristic
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—42no—
405C4×C11—41no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11C4×#4111yescharacteristic
409C4×C11#51811yescharacteristic
410C4×C11#55311yescharacteristic
411C4×C11#55311yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C23×C1111yescharacteristic
415C22×D4C23×C1111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4C23×C1111yescharacteristic
420C2×D8—41no—
421C2×D8—41no—
422C2×D8C2×C4×C1114yescomplemented
423C2×M16—41no—
424C2×M16—41no—
425C2×M16C2×C4×C1114yescomplemented
426C22×C8C23×C1111yescharacteristic
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430#121—22no—
431#121—22no—
432#121C2×C4×C1114yescomplemented
433#121C2×C4×C1114yescomplemented
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—44no—
439#117—22no—
440#117—41no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C1111yescharacteristic
462C2×C22⋊C4D4×C1111yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C1111yescharacteristic
467C2×C42C23×C1111yescharacteristic
468#106C2×C4×C1114yescomplemented
469#102—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473#102C2×C4×C1114yescomplemented
474#102C2×C4×C1114yescomplemented
475C22⋊C8—22no—
476#97—41no—
477C4×C8—41no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95D4×C1111yescharacteristic
483#95D4×C1111yescharacteristic
484C2×C11—42no—
485C2×C11—82no—
486C2×C11—82no—
487C2×C11#236411yescharacteristic
488C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
489C2×C11#294611yescharacteristic
490C2×C11#330611yescharacteristic
491C2×C11#330911yescharacteristic
492C2×C11#332511yescharacteristic
493C2×C11#332611yescharacteristic
494C24—21no—
495C24—21no—
496C24C2×D4×C1111yescharacteristic
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4C22×C4×C1112yes—
514C2×D4C22×C4×C1112yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C22×C4×C1112yes—
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C11×#4112yes—
541C22×C4C24×C1111yescharacteristic
542D8—44no—
543M16—44no—
544C2×C8—21no—
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×C8C22×C4×C1112yes—
555C2×C8C22×C4×C1112yes—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4C22×C4×C1112yes—
568C4⋊C4C22×C4×C1112yes—
569C4⋊C4C11×#4112yes—
570C4⋊C4C11×#4112yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42—42no—
588C42—81no—
589C11#2314311yescharacteristic, direct product factor, Sylow
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C4×D4×C1112yes—
611C23C22×D4×C1111yescharacteristic
612D4—22no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—48no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—84no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4—84no—
660C2×C4C4×D4×C1112yes—
661C2×C4C11×AGL(1,ℤ/8)12yes—
662C2×C4C23×C4×C1111yescharacteristic
663C2×C4C2×C11×#4111yescharacteristic
664C2×C4C2×C11×#4111yescharacteristic
665C2×C4C2×C11×#4111yescharacteristic
666C2×C4C11×H(5,𝔽2)11yescharacteristic
667C2×C4C11×H(5,𝔽2)11yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×C4×D4×C1111yescharacteristic
694C22C11×#54611yescharacteristic
695C22C11×#54611yescharacteristic
696C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
697C22C11×#57511yescharacteristic
698C22C11×#57611yescharacteristic
699C22C11×#57711yescharacteristic
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—81no—
710C4—81no—
711C4C4×C11×#4111yescharacteristic
712C4C11×#51811yescharacteristic
713C4C11×#55311yescharacteristic
714C4C11×#55311yescharacteristic
715C2—42no—
716C2—82no—
717C2—82no—
718C2C11×#236411yescharacteristic
719C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
720C2C11×#294611yescharacteristic
721C2C11×#330611yescharacteristic
722C2C11×#330911yescharacteristic
723C2C11×#332511yescharacteristic
724C2C11×#332611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#469C2
LCSG ▷ C2×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
2. C11×#2363C2semidirect
3. C11×#2361C2semidirect
4. C11×#1936C2semidirect
5. C11×#1934C2semidirect
6. C11×#1920C2semidirect
7. C11×#1920C2semidirect
8. C11×#1879C2semidirect
9. C11×#1879C2semidirect
10. C11×#1875C2semidirect
11. C11×#1874C2semidirect
12. C11×#1762C2semidirect
13. C4×C11×#102C2semidirect
14. C11×#1753C2semidirect
15. C11×#1736C2semidirect
25. C11×#469C4semidirect
70. C2×C11×D8C2×C4semidirect
73. C2×C11×M16C2×C4semidirect
80. C11×#121C2×C4semidirect
81. C11×#121C2×C4semidirect
116. C11×#106C2×C4semidirect
121. C11×#102C2×C4semidirect
122. C11×#102C2×C4semidirect
132. #23143C11direct (N × H)
229. #2363C2×C11semidirect
230. #2361C2×C11semidirect
231. #1936C2×C11semidirect
232. #1934C2×C11semidirect
233. #1920C2×C11semidirect
234. #1920C2×C11semidirect
235. #1879C2×C11semidirect
236. #1879C2×C11semidirect
237. #1875C2×C11semidirect
238. #1874C2×C11semidirect
239. #1762C2×C11semidirect
240. C4×#102C2×C11semidirect
241. #1753C2×C11semidirect
242. #1736C2×C11semidirect
334. #469C4×C11semidirect
422. C2×D8C2×C4×C11semidirect
425. C2×M16C2×C4×C11semidirect
432. #121C2×C4×C11semidirect
433. #121C2×C4×C11semidirect
468. #106C2×C4×C11semidirect
473. #102C2×C4×C11semidirect
474. #102C2×C4×C11semidirect
589. C11#23143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4692
C11×#23632
C11×#23612
C11×#19362
C11×#19342
C11×#19202
C11×#18792
C11×#18752
C11×#18742
C11×#17622
C4×C11×#1022
C11×#17532
C11×#17362
#2314311