Finite Group Databasebeta

← C11×#23860 #14601053

Subgroups — C11×#23860 #14601053

Order 2816.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×D42×C11C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#447C211yesmaximal, characteristic, complemented
6C11×#2407C211yesmaximal, characteristic, complemented
7C11×#2014C211yesmaximal, characteristic, complemented
8C11×#2011C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic, complemented
14C11×#1870C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C23×D4×C11—21no—
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C2×C11×AGL(1,ℤ/8)—24no—
21C2×C11×AGL(1,ℤ/8)—24no—
22C2×C11×AGL(1,ℤ/8)—24no—
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic, complemented
25C22×C11×SD16C2211yescharacteristic, complemented
26C22×C11×D8C2211yescharacteristic
27C22×C11×D8C2211yescharacteristic, complemented
28C22×C11×D8C2211yescharacteristic, complemented
29C22×C11×M16C2211yescharacteristic, complemented
30D42×C11—24no—
31D42×C11—24no—
32C2×C11×#127C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic, complemented
34C2×C11×#121—21no—
35C2×C11×#121C2211yescharacteristic
36C2×C11×#121C2211yescharacteristic
37C2×C11×#121C2211yescharacteristic, complemented
38C2×C11×#120—21no—
39C2×C11×#120—21no—
40C2×C4×D4×C11C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C11×#450—24no—
43C11×#449—24no—
44C11×#447—24no—
45C2×C11×#103C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C11×C22⋊C8C2211yescharacteristic, complemented
55C2×C11×C22⋊C8C2211yescharacteristic, complemented
56C11×#394—21no—
57C11×#392—21no—
58C11×#391C2211yescharacteristic, complemented
59C11×#390C2211yescharacteristic, complemented
60C11×#386—21no—
61C11×#385—21no—
62C11×#380C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C11×#336C2211yescharacteristic, complemented
66C11×#336C2211yescharacteristic, complemented
67C25×C11—21no—
68C25×C11—21no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C22×Q8×C11C2311yescharacteristic
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—28no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—22no—
83C22×D4×C11—22no—
84C22×D4×C11—22no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—22no—
91C22×D4×C11—21no—
92C22×D4×C11—41no—
93C22×D4×C11—41no—
94C22×D4×C11—41no—
95C22×D4×C11—41no—
96C22×D4×C11—44no—
97C22×D4×C11—44no—
98C22×D4×C11D411yescharacteristic
99C22×D4×C11D414yescomplemented
100C22×D4×C11C2311yescharacteristic
101C22×D4×C11C2311yescharacteristic
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11—21no—
105C23×C4×C11—21no—
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C11×AGL(1,ℤ/8)—232no—
109C2×C11×SD16—22no—
110C2×C11×SD16—22no—
111C2×C11×SD16—22no—
112C2×C11×SD16—22no—
113C2×C11×SD16—22no—
114C2×C11×SD16—22no—
115C2×C11×SD16—22no—
116C2×C11×SD16—41no—
117C2×C11×SD16D414yescomplemented
118C2×C11×D8—22no—
119C2×C11×D8—22no—
120C2×C11×D8—22no—
121C2×C11×D8—22no—
122C2×C11×D8—22no—
123C2×C11×D8—22no—
124C2×C11×D8—22no—
125C2×C11×D8—41no—
126C2×C11×D8D414yescomplemented
127C2×C11×M16—22no—
128C2×C11×M16—22no—
129C2×C11×M16—22no—
130C22×C8×C11C2311yescharacteristic
131C22×C8×C11C2311yescharacteristic
132C22×C8×C11C2311yescharacteristic
133C22×C8×C11C2311yescharacteristic
134C11×#127—22no—
135C11×#127—22no—
136C11×C22⋊Q8—22no—
137C11×C22⋊Q8—41no—
138C11×#121—28no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—22no—
143C11×#121—41no—
144C11×#121D414yescomplemented
145C11×#120—28no—
146C11×#120—28no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C4×D4×C11—22no—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4D411yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—21no—
162C2×C11×C22⋊C4—21no—
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4D411yescharacteristic
165C2×C11×C22⋊C4D411yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C11×#103—22no—
168C11×#102—22no—
169C11×#102—22no—
170C11×#102—22no—
171C11×#102—22no—
172C11×#102—22no—
173C11×#102—41no—
174C11×#102—41no—
175C11×C22⋊C8—22no—
176C11×C22⋊C8—22no—
177C11×C22⋊C8—22no—
178C11×#95—21no—
179C11×#95—21no—
180C11×#95—21no—
181#23860C1111yesmaximal, characteristic, direct product factor, Sylow
182C24×C11—21no—
183C24×C11—24no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—24no—
188C24×C11—42no—
189C24×C11—42no—
190C24×C11—42no—
191C24×C11—42no—
192C24×C11—42no—
193C24×C11—42no—
194C24×C11—42no—
195C24×C11—42no—
196C24×C11—81no—
197C24×C11—81no—
198C24×C11—81no—
199C24×C11—81no—
200C24×C11C2×D411yescharacteristic
201C24×C11C2×D411yescharacteristic
202C11×#41—28no—
203C11×#41—44no—
204C11×#41—44no—
205C11×#41—44no—
206C2×Q8×C11—21no—
207C2×Q8×C11—21no—
208C2×Q8×C11—21no—
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11C2×D412yescomplemented
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—28no—
215C2×D4×C11—24no—
216C2×D4×C11—24no—
217C2×D4×C11—24no—
218C2×D4×C11—24no—
219C2×D4×C11—24no—
220C2×D4×C11—24no—
221C2×D4×C11—22no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—44no—
241C2×D4×C11—44no—
242C2×D4×C11—44no—
243C2×D4×C11—42no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—42no—
248C2×D4×C11—42no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—432no—
252C2×D4×C11—44no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—42no—
256C2×D4×C11—42no—
257C2×D4×C11—42no—
258C2×D4×C11—42no—
259C2×D4×C11—44no—
260C2×D4×C11—42no—
261C2×D4×C11—42no—
262C2×D4×C11—42no—
263C2×D4×C11—81no—
264C2×D4×C11—81no—
265C2×D4×C11—81no—
266C2×D4×C11C2×D412yes—
267C2×D4×C11C2×D412yes—
268C2×D4×C11C2×D412yes—
269C2×D4×C11C2×D412yes—
270C2×D4×C11C2×D412yes—
271C2×D4×C11C2×D412yescomplemented
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—24no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D412yes—
296C22×C4×C11C2×D412yes—
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C11×SD16—28no—
300C11×SD16—28no—
301C11×SD16—44no—
302C11×D8—28no—
303C11×D8—28no—
304C11×D8—44no—
305C11×M16—28no—
306C2×C8×C11—21no—
307C2×C8×C11—21no—
308C2×C8×C11—21no—
309C2×C8×C11—21no—
310C2×C8×C11—21no—
311C2×C8×C11—21no—
312C2×C8×C11—21no—
313C2×C8×C11—21no—
314C2×C8×C11—21no—
315C2×C8×C11—21no—
316C2×C8×C11C2×D412yescomplemented
317C2×C8×C11C2×D412yescomplemented
318C11×C4⋊C4—22no—
319C11×C4⋊C4—21no—
320C11×C4⋊C4—21no—
321C11×C4⋊C4—21no—
322C11×C4⋊C4—21no—
323C11×C4⋊C4—21no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4C2×D412yes—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—24no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—42no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—81no—
335C11×C22⋊C4—81no—
336C42×C11—21no—
337C42×C11—21no—
338C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
339C2×D42C2×C1111yescharacteristic, complemented
340C2×#449C2×C1111yescharacteristic, complemented
341C2×#450C2×C1111yescharacteristic, complemented
342C2×#447C2×C1111yescharacteristic, complemented
343#2407C2×C1111yescharacteristic, complemented
344#2014C2×C1111yescharacteristic, complemented
345#2011C2×C1111yescharacteristic, complemented
346#2000C2×C1111yescharacteristic, complemented
347#1999C2×C1111yescharacteristic, complemented
348#1895C2×C1111yescharacteristic, complemented
349#1879C2×C1111yescharacteristic, complemented
350#1877C2×C1111yescharacteristic, complemented
351#1870C2×C1111yescharacteristic, complemented
352#1786C2×C1111yescharacteristic, complemented
353C23×C11—21no—
354C23×C11—22no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—21no—
358C23×C11—21no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11—21no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—21no—
367C23×C11—21no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—48no—
372C23×C11—48no—
373C23×C11—48no—
374C23×C11—48no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—84no—
398C23×C11—84no—
399C23×C11—84no—
400C23×C11—84no—
401C23×C11—84no—
402C23×C11—84no—
403C23×C11—84no—
404C23×C11—84no—
405C23×C11—84no—
406C23×C11—84no—
407C23×C11#12012yes—
408C23×C11AGL(1,ℤ/8)12yescomplemented
409C23×C11C22×D411yescharacteristic
410Q8×C11—22no—
411Q8×C11—22no—
412Q8×C11—41no—
413Q8×C11—41no—
414D4×C11—28no—
415D4×C11—22no—
416D4×C11—22no—
417D4×C11—22no—
418D4×C11—22no—
419D4×C11—22no—
420D4×C11—22no—
421D4×C11—22no—
422D4×C11—22no—
423D4×C11—22no—
424D4×C11—48no—
425D4×C11—48no—
426D4×C11—48no—
427D4×C11—48no—
428D4×C11—48no—
429D4×C11—48no—
430D4×C11—41no—
431D4×C11—41no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—41no—
436D4×C11—84no—
437D4×C11—84no—
438D4×C11#12014yes—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—48no—
456C2×C4×C11—48no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11#12012yes—
472C2×C4×C11AGL(1,ℤ/8)12yescomplemented
473C2×C4×C11C22×D411yescharacteristic
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11C22×D411yescharacteristic
476C2×C4×C11C22×D411yescharacteristic
477C2×C4×C11H(5,𝔽2)11yescharacteristic
478C2×C4×C11H(5,𝔽2)11yescharacteristic
479C8×C11—22no—
480C8×C11—22no—
481C8×C11—41no—
482C8×C11—41no—
483C22×#41C22×C1111yescharacteristic, complemented
484C23×D4—21no—
485C23×D4C22×C1111yescharacteristic
486C23×D4C22×C1111yescharacteristic
487C2×AGL(1,ℤ/8)—24no—
488C2×AGL(1,ℤ/8)—24no—
489C2×AGL(1,ℤ/8)—24no—
490C22×SD16C22×C1111yescharacteristic
491C22×SD16C22×C1111yescharacteristic, complemented
492C22×SD16C22×C1111yescharacteristic, complemented
493C22×D8C22×C1111yescharacteristic
494C22×D8C22×C1111yescharacteristic, complemented
495C22×D8C22×C1111yescharacteristic, complemented
496C22×M16C22×C1111yescharacteristic, complemented
497D42—24no—
498D42—24no—
499C2×#127C22×C1111yescharacteristic
500C2×C22⋊Q8C22×C1111yescharacteristic, complemented
501C2×#121—21no—
502C2×#121C22×C1111yescharacteristic
503C2×#121C22×C1111yescharacteristic
504C2×#121C22×C1111yescharacteristic, complemented
505C2×#120—21no—
506C2×#120—21no—
507C2×C4×D4C22×C1111yescharacteristic
508C2×C4×D4C22×C1111yescharacteristic
509#450—24no—
510#449—24no—
511#447—24no—
512C2×#103C22×C1111yescharacteristic, complemented
513C2×#102C22×C1111yescharacteristic
514C2×#102C22×C1111yescharacteristic
515C2×#102C22×C1111yescharacteristic, complemented
516C2×#102C22×C1111yescharacteristic, complemented
517C2×#102C22×C1111yescharacteristic, complemented
518C2×#102C22×C1111yescharacteristic, complemented
519C2×#102C22×C1111yescharacteristic, complemented
520C2×C22⋊C8C22×C1111yescharacteristic, complemented
521C2×C22⋊C8C22×C1111yescharacteristic, complemented
522C2×C22⋊C8C22×C1111yescharacteristic, complemented
523#394—21no—
524#392—21no—
525#391C22×C1111yescharacteristic, complemented
526#390C22×C1111yescharacteristic, complemented
527#386—21no—
528#385—21no—
529#380C22×C1111yescharacteristic, complemented
530#340C22×C1111yescharacteristic, complemented
531#340C22×C1111yescharacteristic, complemented
532#336C22×C1111yescharacteristic, complemented
533#336C22×C1111yescharacteristic, complemented
534C22×C11—22no—
535C22×C11—24no—
536C22×C11—22no—
537C22×C11—22no—
538C22×C11—22no—
539C22×C11—22no—
540C22×C11—22no—
541C22×C11—41no—
542C22×C11—42no—
543C22×C11—41no—
544C22×C11—42no—
545C22×C11—41no—
546C22×C11—42no—
547C22×C11—41no—
548C22×C11—42no—
549C22×C11—41no—
550C22×C11—41no—
551C22×C11—42no—
552C22×C11—41no—
553C22×C11—41no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—816no—
565C22×C11—816no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11—81no—
570C22×C11—81no—
571C22×C11—81no—
572C22×C11—81no—
573C22×C11—81no—
574C22×C11—81no—
575C22×C11—81no—
576C22×C11—81no—
577C22×C11—81no—
578C22×C11C2×#12011yescharacteristic
579C22×C11D4211yescharacteristic
580C22×C11D4211yescharacteristic
581C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
582C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
583C22×C11#57611yescharacteristic
584C22×C11#57711yescharacteristic
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—41no—
588C4×C11—42no—
589C4×C11—42no—
590C4×C11—41no—
591C4×C11—81no—
592C4×C11—81no—
593C4×C11C2×#12011yescharacteristic
594C4×C11#53411yescharacteristic
595C4×C11D4211yescharacteristic
596C4×C11D4211yescharacteristic
597C25—21no—
598C25—21no—
599C2×#41—22no—
600C2×#41—22no—
601C2×#41—22no—
602C2×#41—22no—
603C2×#41—41no—
604C2×#41—41no—
605C22×Q8C23×C1111yescharacteristic
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—28no—
609C22×D4—21no—
610C22×D4—21no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—22no—
621C22×D4—21no—
622C22×D4—41no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4—41no—
626C22×D4—44no—
627C22×D4—44no—
628C22×D4D4×C1111yescharacteristic
629C22×D4D4×C1114yescomplemented
630C22×D4C23×C1111yescharacteristic
631C22×D4C23×C1111yescharacteristic
632C22×D4C23×C1111yescharacteristic
633C22×D4C23×C1111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638AGL(1,ℤ/8)—232no—
639C2×SD16—22no—
640C2×SD16—22no—
641C2×SD16—22no—
642C2×SD16—22no—
643C2×SD16—22no—
644C2×SD16—22no—
645C2×SD16—22no—
646C2×SD16—41no—
647C2×SD16D4×C1114yescomplemented
648C2×D8—22no—
649C2×D8—22no—
650C2×D8—22no—
651C2×D8—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×D8—22no—
655C2×D8—41no—
656C2×D8D4×C1114yescomplemented
657C2×M16—22no—
658C2×M16—22no—
659C2×M16—22no—
660C22×C8C23×C1111yescharacteristic
661C22×C8C23×C1111yescharacteristic
662C22×C8C23×C1111yescharacteristic
663C22×C8C23×C1111yescharacteristic
664#127—22no—
665#127—22no—
666C22⋊Q8—22no—
667C22⋊Q8—41no—
668#121—28no—
669#121—22no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—41no—
674#121D4×C1114yescomplemented
675#120—28no—
676#120—28no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—22no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4D4×C1111yescharacteristic
683C2×C4⋊C4C23×C1111yescharacteristic
684C2×C4⋊C4C23×C1111yescharacteristic
685C2×C4⋊C4C23×C1111yescharacteristic
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4D4×C1111yescharacteristic
695C2×C22⋊C4D4×C1111yescharacteristic
696C2×C42C23×C1111yescharacteristic
697#103—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708#95—21no—
709#95—21no—
710#95—21no—
711C2×C11—42no—
712C2×C11—42no—
713C2×C11—44no—
714C2×C11—82no—
715C2×C11—82no—
716C2×C11—82no—
717C2×C11#240311yescharacteristic
718C2×C11#300311yescharacteristic
719C2×C11#301211yescharacteristic
720C2×C11#326411yescharacteristic
721C2×C11#326511yescharacteristic
722C2×C11#327211yescharacteristic
723C2×C11#327411yescharacteristic
724C24—21no—
725C24—24no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—24no—
730C24—42no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—81no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24C2×D4×C1111yescharacteristic
743C24C2×D4×C1111yescharacteristic
744#41—28no—
745#41—44no—
746#41—44no—
747#41—44no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8C2×D4×C1112yescomplemented
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—432no—
794C2×D4—44no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—44no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4C2×D4×C1112yes—
809C2×D4C2×D4×C1112yes—
810C2×D4C2×D4×C1112yes—
811C2×D4C2×D4×C1112yes—
812C2×D4C2×D4×C1112yes—
813C2×D4C2×D4×C1112yescomplemented
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—24no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4C2×D4×C1111yescharacteristic
835C22×C4C2×D4×C1111yescharacteristic
836C22×C4C2×D4×C1111yescharacteristic
837C22×C4C2×D4×C1112yes—
838C22×C4C2×D4×C1112yes—
839C22×C4C2×D4×C1111yescharacteristic
840C22×C4C24×C1111yescharacteristic
841SD16—28no—
842SD16—28no—
843SD16—44no—
844D8—28no—
845D8—28no—
846D8—44no—
847M16—28no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8C2×D4×C1112yescomplemented
859C2×C8C2×D4×C1112yescomplemented
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—42no—
867C4⋊C4C2×D4×C1112yes—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—22no—
871C22⋊C4—24no—
872C22⋊C4—22no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C42—21no—
879C42—21no—
880C11#2386011yescharacteristic, direct product factor, Sylow
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23C11×#12012yes—
936C23C11×AGL(1,ℤ/8)12yescomplemented
937C23C22×D4×C1111yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4C11×#12014yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4C11×#12012yes—
1000C2×C4C11×AGL(1,ℤ/8)12yescomplemented
1001C2×C4C22×D4×C1111yescharacteristic
1002C2×C4C22×D4×C1111yescharacteristic
1003C2×C4C22×D4×C1111yescharacteristic
1004C2×C4C22×D4×C1111yescharacteristic
1005C2×C4C11×H(5,𝔽2)11yescharacteristic
1006C2×C4C11×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×C11×#12011yescharacteristic
1056C22D42×C1111yescharacteristic
1057C22D42×C1111yescharacteristic
1058C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
1059C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
1060C22C11×#57611yescharacteristic
1061C22C11×#57711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×C11×#12011yescharacteristic
1071C4C11×#53411yescharacteristic
1072C4D42×C1111yescharacteristic
1073C4D42×C1111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C11×#240311yescharacteristic
1081C2C11×#300311yescharacteristic
1082C2C11×#301211yescharacteristic
1083C2C11×#326411yescharacteristic
1084C2C11×#326511yescharacteristic
1085C2C11×#327211yescharacteristic
1086C2C11×#327411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×D42×C11C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#447C2semidirect
6. C11×#2407C2semidirect
7. C11×#2014C2semidirect
8. C11×#2011C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1895C2semidirect
12. C11×#1879C2semidirect
13. C11×#1877C2semidirect
14. C11×#1870C2semidirect
15. C11×#1786C2semidirect
16. C22×C11×#41C22semidirect
24. C22×C11×SD16C22semidirect
25. C22×C11×SD16C22semidirect
27. C22×C11×D8C22semidirect
28. C22×C11×D8C22semidirect
29. C22×C11×M16C22semidirect
33. C2×C11×C22⋊Q8C22semidirect
37. C2×C11×#121C22semidirect
45. C2×C11×#103C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#102C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C11×C22⋊C8C22semidirect
55. C2×C11×C22⋊C8C22semidirect
58. C11×#391C22semidirect
59. C11×#390C22semidirect
62. C11×#380C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
65. C11×#336C22semidirect
66. C11×#336C22semidirect
99. C22×D4×C11D4semidirect
117. C2×C11×SD16D4semidirect
126. C2×C11×D8D4semidirect
144. C11×#121D4semidirect
181. #23860C11direct (N × H)
211. C2×Q8×C11C2×D4semidirect
271. C2×D4×C11C2×D4semidirect
316. C2×C8×C11C2×D4semidirect
317. C2×C8×C11C2×D4semidirect
338. C22×AGL(1,ℤ/8)C2×C11semidirect
339. C2×D42C2×C11semidirect
340. C2×#449C2×C11semidirect
341. C2×#450C2×C11semidirect
342. C2×#447C2×C11semidirect
343. #2407C2×C11semidirect
344. #2014C2×C11semidirect
345. #2011C2×C11semidirect
346. #2000C2×C11semidirect
347. #1999C2×C11semidirect
348. #1895C2×C11semidirect
349. #1879C2×C11semidirect
350. #1877C2×C11semidirect
351. #1870C2×C11semidirect
352. #1786C2×C11semidirect
408. C23×C11AGL(1,ℤ/8)semidirect
472. C2×C4×C11AGL(1,ℤ/8)semidirect
483. C22×#41C22×C11semidirect
491. C22×SD16C22×C11semidirect
492. C22×SD16C22×C11semidirect
494. C22×D8C22×C11semidirect
495. C22×D8C22×C11semidirect
496. C22×M16C22×C11semidirect
500. C2×C22⋊Q8C22×C11semidirect
504. C2×#121C22×C11semidirect
512. C2×#103C22×C11semidirect
515. C2×#102C22×C11semidirect
516. C2×#102C22×C11semidirect
517. C2×#102C22×C11semidirect
518. C2×#102C22×C11semidirect
519. C2×#102C22×C11semidirect
520. C2×C22⋊C8C22×C11semidirect
521. C2×C22⋊C8C22×C11semidirect
522. C2×C22⋊C8C22×C11semidirect
525. #391C22×C11semidirect
526. #390C22×C11semidirect
529. #380C22×C11semidirect
530. #340C22×C11semidirect
531. #340C22×C11semidirect
532. #336C22×C11semidirect
533. #336C22×C11semidirect
629. C22×D4D4×C11semidirect
647. C2×SD16D4×C11semidirect
656. C2×D8D4×C11semidirect
674. #121D4×C11semidirect
753. C2×Q8C2×D4×C11semidirect
813. C2×D4C2×D4×C11semidirect
858. C2×C8C2×D4×C11semidirect
859. C2×C8C2×D4×C11semidirect
880. C11#23860direct (N × H)
936. C23C11×AGL(1,ℤ/8)semidirect
1000. C2×C4C11×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C2×D42×C112
C2×C11×#4492
C2×C11×#4502
C2×C11×#4472
C11×#24072
C11×#20142
C11×#20112
C11×#20002
C11×#19992
C11×#18952
C11×#18792
C11×#18772
C11×#18702
C11×#17862
#2386011