Finite Group Databasebeta

← C11×#18048 #14595241

Subgroups — C11×#18048 #14595241

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2971C211yesmaximal, characteristic, complemented
2C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
3D4×C11×M16C211yesmaximal, characteristic, complemented
4C11×#1594C211yesmaximal, characteristic, complemented
5C11×#1589C211yesmaximal, characteristic, complemented
6C11×#1588C211yesmaximal, characteristic, complemented
7C11×#1586C211yesmaximal, characteristic, complemented
8C11×#1583C211yesmaximal, characteristic, complemented
9C11×#1581C211yesmaximal, characteristic, complemented
10C11×SD16⋊C8C211yesmaximal, characteristic, complemented
11C8×C11×SD16C211yesmaximal, characteristic, complemented
12C11×#1569C211yesmaximal, characteristic, complemented
13C11×#1490C211yesmaximal, characteristic, complemented
14C11×#1489C211yesmaximal, characteristic, complemented
15C11×#1455C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C411yescharacteristic
17C22×C11×M16—21no—
18C4×C11×#41C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic, complemented
21C8×Q8×C11C2211yescharacteristic, complemented
22C11×#442C411yescharacteristic
23C11×#442C411yescharacteristic
24C11×#440C411yescharacteristic
25C11×#440C411yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×D8C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#436—21no—
31C11×#436—21no—
32C11×#436C2211yescharacteristic
33C11×#436C2211yescharacteristic
34C11×#436C2211yescharacteristic, complemented
35C11×#436C2211yescharacteristic, complemented
36C11×#435—21no—
37C11×#435—21no—
38C8×D4×C11C2211yescharacteristic
39C8×D4×C11C2211yescharacteristic
40C11×#432—21no—
41C11×#432C2211yescharacteristic
42C11×#428C411yescharacteristic
43C11×#423C2211yescharacteristic
44C11×#418C411yescharacteristic
45C11×#417C411yescharacteristic
46C11×#407—21no—
47C4×C11×M16—21no—
48C4×C11×M16C2211yescharacteristic
49C4×C11×M16C2211yescharacteristic
50C4×C11×M16C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×#335C2211yescharacteristic, complemented
53C11×#334C2211yescharacteristic, complemented
54C11×#334C2211yescharacteristic, complemented
55C11×Q8⋊C8C2211yescharacteristic, complemented
56C11×Q8⋊C8C2211yescharacteristic, complemented
57C11×D4⋊C8C2211yescharacteristic
58C11×D4⋊C8C2211yescharacteristic
59C11×D4⋊C8C2211yescharacteristic
60C11×D4⋊C8C2211yescharacteristic
61C11×D4⋊C8C2211yescharacteristic, complemented
62C11×D4⋊C8C2211yescharacteristic, complemented
63C11×#322C2211yescharacteristic, complemented
64C11×#322C2211yescharacteristic, complemented
65C11×#322C2211yescharacteristic, complemented
66C82×C11C2211yescharacteristic, complemented
67C2×C11×#41C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C23×C4×C11—21no—
70C11×AGL(1,ℤ/8)—24no—
71C2×C11×SD16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C2×C11×D8C2×C411yescharacteristic
74C2×C11×D8C2×C411yescharacteristic
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—44no—
82C2×C11×M16C2×C411yescharacteristic
83C2×C11×M16C2×C411yescharacteristic
84C2×C11×M16D411yescharacteristic
85C2×C11×M16D411yescharacteristic
86C22×C8×C11—21no—
87C22×C8×C11—21no—
88C4×Q8×C11C2×C411yescharacteristic
89C4×Q8×C11C2311yescharacteristic
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11C2×C411yescharacteristic
95C4×D4×C11C2×C411yescharacteristic
96C4×D4×C11C2×C411yescharacteristic
97C4×D4×C11C2311yescharacteristic
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C11×#117C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#107C2×C411yescharacteristic
107C11×#107C2×C411yescharacteristic
108C11×#106C2×C411yescharacteristic
109C11×#106C2×C411yescharacteristic
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#103C2×C411yescharacteristic
118C11×#103C2×C411yescharacteristic
119C11×#102C2×C411yescharacteristic
120C11×#102C2×C411yescharacteristic
121C11×#102C2×C411yescharacteristic
122C11×#102C2×C411yescharacteristic
123C11×#102C2×C411yescharacteristic
124C11×#102C2×C411yescharacteristic
125C11×C22⋊C8—21no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8—21no—
131C11×C22⋊C8—21no—
132C11×#97—21no—
133C11×#97—21no—
134C11×#97C2×C411yescharacteristic
135C11×#97C2×C411yescharacteristic
136C11×#97D411yescharacteristic
137C11×#97D411yescharacteristic
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11C2311yescharacteristic
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145C4×C8×C11C2311yescharacteristic
146#18048C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—21no—
148C11×#41—22no—
149C11×#41—41no—
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C22×C411yescharacteristic
156C2×D4×C11C22×C411yescharacteristic
157C2×D4×C11C22×C411yescharacteristic
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—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C11×SD16—22no—
172C11×SD16M1614yescomplemented
173C11×D8—22no—
174C11×D8—22no—
175C11×M16—22no—
176C11×M16—22no—
177C11×M16—41no—
178C11×M16—41no—
179C11×M16—42no—
180C11×M16—42no—
181C11×M16—42no—
182C11×M16—42no—
183C11×M16—42no—
184C11×M16—42no—
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—42no—
192C2×C8×C11—42no—
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C22×C411yescharacteristic
195C2×C8×C11C22×C411yescharacteristic
196C2×C8×C11C22×C411yescharacteristic
197C2×C8×C11C2×D411yescharacteristic
198C2×C8×C11C2×D411yescharacteristic
199C2×C8×C11C2×D411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4C22×C411yescharacteristic
205C11×C4⋊C4C22×C411yescharacteristic
206C11×C4⋊C4C22×C411yescharacteristic
207C11×C4⋊C4C22×C411yescharacteristic
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11C22×C411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11#4111yescharacteristic
221C42×C11C2411yescharacteristic
222#2971C2×C1111yescharacteristic, complemented
223C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
224D4×M16C2×C1111yescharacteristic, complemented
225#1594C2×C1111yescharacteristic, complemented
226#1589C2×C1111yescharacteristic, complemented
227#1588C2×C1111yescharacteristic, complemented
228#1586C2×C1111yescharacteristic, complemented
229#1583C2×C1111yescharacteristic, complemented
230#1581C2×C1111yescharacteristic, complemented
231SD16⋊C8C2×C1111yescharacteristic, complemented
232C8×SD16C2×C1111yescharacteristic, complemented
233#1569C2×C1111yescharacteristic, complemented
234#1490C2×C1111yescharacteristic, complemented
235#1489C2×C1111yescharacteristic, complemented
236#1455C2×C1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—81no—
243C23×C11C4×D411yescharacteristic
244Q8×C11—21no—
245Q8×C11C2×M1612yescomplemented
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—42no—
252D4×C11—42no—
253D4×C11C2×M1612yes—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—81no—
275C2×C4×C11C4×D411yescharacteristic
276C2×C4×C11C4×D411yescharacteristic
277C2×C4×C11C4×D411yescharacteristic
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C8×C11—22no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11C2×M1612yescomplemented
294C8×C11AGL(1,ℤ/8)12yescomplemented
295C2×AGL(1,ℤ/8)C4×C1111yescharacteristic
296C22×M16—21no—
297C4×#41C22×C1111yescharacteristic
298C2×C4×D4C22×C1111yescharacteristic
299C8×Q8C22×C1111yescharacteristic, complemented
300C8×Q8C22×C1111yescharacteristic, complemented
301#442C4×C1111yescharacteristic
302#442C4×C1111yescharacteristic
303#440C4×C1111yescharacteristic
304#440C4×C1111yescharacteristic
305C4×SD16C22×C1111yescharacteristic
306C4×SD16C22×C1111yescharacteristic
307C4×D8C22×C1111yescharacteristic
308C4×D8C22×C1111yescharacteristic
309#436—21no—
310#436—21no—
311#436C22×C1111yescharacteristic
312#436C22×C1111yescharacteristic
313#436C22×C1111yescharacteristic, complemented
314#436C22×C1111yescharacteristic, complemented
315#435—21no—
316#435—21no—
317C8×D4C22×C1111yescharacteristic
318C8×D4C22×C1111yescharacteristic
319#432—21no—
320#432C22×C1111yescharacteristic
321#428C4×C1111yescharacteristic
322#423C22×C1111yescharacteristic
323#418C4×C1111yescharacteristic
324#417C4×C1111yescharacteristic
325#407—21no—
326C4×M16—21no—
327C4×M16C22×C1111yescharacteristic
328C4×M16C22×C1111yescharacteristic
329C4×M16C22×C1111yescharacteristic
330#335C22×C1111yescharacteristic, complemented
331#335C22×C1111yescharacteristic, complemented
332#334C22×C1111yescharacteristic, complemented
333#334C22×C1111yescharacteristic, complemented
334Q8⋊C8C22×C1111yescharacteristic, complemented
335Q8⋊C8C22×C1111yescharacteristic, complemented
336D4⋊C8C22×C1111yescharacteristic
337D4⋊C8C22×C1111yescharacteristic
338D4⋊C8C22×C1111yescharacteristic
339D4⋊C8C22×C1111yescharacteristic
340D4⋊C8C22×C1111yescharacteristic, complemented
341D4⋊C8C22×C1111yescharacteristic, complemented
342#322C22×C1111yescharacteristic, complemented
343#322C22×C1111yescharacteristic, complemented
344#322C22×C1111yescharacteristic, complemented
345C82C22×C1111yescharacteristic, complemented
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—84no—
359C22×C11C2×C4×D411yescharacteristic
360C4×C11—21no—
361C4×C11—22no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11C22×M1611yescharacteristic
370C4×C11#56811yescharacteristic
371C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
372C4×C11#57511yescharacteristic
373C2×#41C2×C4×C1111yescharacteristic
374C22×D4C2×C4×C1111yescharacteristic
375C23×C4—21no—
376AGL(1,ℤ/8)—24no—
377C2×SD16C2×C4×C1111yescharacteristic
378C2×SD16C2×C4×C1111yescharacteristic
379C2×D8C2×C4×C1111yescharacteristic
380C2×D8C2×C4×C1111yescharacteristic
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—44no—
388C2×M16C2×C4×C1111yescharacteristic
389C2×M16C2×C4×C1111yescharacteristic
390C2×M16D4×C1111yescharacteristic
391C2×M16D4×C1111yescharacteristic
392C22×C8—21no—
393C22×C8—21no—
394C4×Q8C2×C4×C1111yescharacteristic
395C4×Q8C23×C1111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C2×C4×C1111yescharacteristic
401C4×D4C2×C4×C1111yescharacteristic
402C4×D4C2×C4×C1111yescharacteristic
403C4×D4C23×C1111yescharacteristic
404C4×D4C23×C1111yescharacteristic
405C4×D4C23×C1111yescharacteristic
406#117—21no—
407#117C2×C4×C1111yescharacteristic
408C2×C4⋊C4C2×C4×C1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C42—21no—
411C2×C42C23×C1111yescharacteristic
412#107C2×C4×C1111yescharacteristic
413#107C2×C4×C1111yescharacteristic
414#106C2×C4×C1111yescharacteristic
415#106C2×C4×C1111yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C1111yescharacteristic
420C4⋊C8C23×C1111yescharacteristic
421C4⋊C8C23×C1111yescharacteristic
422C4⋊C8C23×C1111yescharacteristic
423#103C2×C4×C1111yescharacteristic
424#103C2×C4×C1111yescharacteristic
425#102C2×C4×C1111yescharacteristic
426#102C2×C4×C1111yescharacteristic
427#102C2×C4×C1111yescharacteristic
428#102C2×C4×C1111yescharacteristic
429#102C2×C4×C1111yescharacteristic
430#102C2×C4×C1111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438#97—21no—
439#97—21no—
440#97C2×C4×C1111yescharacteristic
441#97C2×C4×C1111yescharacteristic
442#97D4×C1111yescharacteristic
443#97D4×C1111yescharacteristic
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C1111yescharacteristic
447C4×C8C23×C1111yescharacteristic
448C4×C8C23×C1111yescharacteristic
449C4×C8C23×C1111yescharacteristic
450C4×C8C23×C1111yescharacteristic
451C4×C8C23×C1111yescharacteristic
452C2×C11—41no—
453C2×C11—42no—
454C2×C11—81no—
455C2×C11—81no—
456C2×C11D4×M1611yescharacteristic
457C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
458C2×C11#295611yescharacteristic
459C24—21no—
460#41—22no—
461#41—41no—
462C2×Q8C22×C4×C1111yescharacteristic
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4C22×C4×C1111yescharacteristic
468C2×D4C22×C4×C1111yescharacteristic
469C2×D4C22×C4×C1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4C22×C4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C11×#4111yescharacteristic
483SD16—22no—
484SD16C11×M1614yescomplemented
485D8—22no—
486D8—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16—42no—
492M16—42no—
493M16—42no—
494M16—42no—
495M16—42no—
496M16—42no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—42no—
505C2×C8C22×C4×C1111yescharacteristic
506C2×C8C22×C4×C1111yescharacteristic
507C2×C8C22×C4×C1111yescharacteristic
508C2×C8C22×C4×C1111yescharacteristic
509C2×C8C2×D4×C1111yescharacteristic
510C2×C8C2×D4×C1111yescharacteristic
511C2×C8C2×D4×C1111yescharacteristic
512C2×C8C2×D4×C1111yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4C22×C4×C1111yescharacteristic
517C4⋊C4C22×C4×C1111yescharacteristic
518C4⋊C4C22×C4×C1111yescharacteristic
519C4⋊C4C22×C4×C1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42C22×C4×C1111yescharacteristic
531C42C2×D4×C1111yescharacteristic
532C42C11×#4111yescharacteristic
533C42C24×C1111yescharacteristic
534C11#1804811yescharacteristic, direct product factor, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—42no—
539C23—42no—
540C23—81no—
541C23C4×D4×C1111yescharacteristic
542Q8—21no—
543Q8C2×C11×M1612yescomplemented
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—42no—
550D4—42no—
551D4C2×C11×M1612yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4C4×D4×C1111yescharacteristic
574C2×C4C4×D4×C1111yescharacteristic
575C2×C4C4×D4×C1111yescharacteristic
576C2×C4C23×C4×C1111yescharacteristic
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8C2×C11×M1612yescomplemented
592C8C11×AGL(1,ℤ/8)12yescomplemented
593C22—21no—
594C22—22no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—84no—
606C22C2×C4×D4×C1111yescharacteristic
607C4—21no—
608C4—22no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4C22×C11×M1611yescharacteristic
617C4C11×#56811yescharacteristic
618C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
619C4C11×#57511yescharacteristic
620C2—41no—
621C2—42no—
622C2—81no—
623C2—81no—
624C2D4×C11×M1611yescharacteristic
625C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
626C2C11×#295611yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC42C24×C11
socleC22×C11C2×C4×D4
prime radicalC2×C11×AGL(1,ℤ/8)C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2971C2semidirect
3. D4×C11×M16C2semidirect
4. C11×#1594C2semidirect
5. C11×#1589C2semidirect
6. C11×#1588C2semidirect
7. C11×#1586C2semidirect
8. C11×#1583C2semidirect
9. C11×#1581C2semidirect
10. C11×SD16⋊C8C2semidirect
11. C8×C11×SD16C2semidirect
12. C11×#1569C2semidirect
13. C11×#1490C2semidirect
14. C11×#1489C2semidirect
15. C11×#1455C2semidirect
20. C8×Q8×C11C22semidirect
21. C8×Q8×C11C22semidirect
34. C11×#436C22semidirect
35. C11×#436C22semidirect
51. C11×#335C22semidirect
52. C11×#335C22semidirect
53. C11×#334C22semidirect
54. C11×#334C22semidirect
55. C11×Q8⋊C8C22semidirect
56. C11×Q8⋊C8C22semidirect
61. C11×D4⋊C8C22semidirect
62. C11×D4⋊C8C22semidirect
63. C11×#322C22semidirect
64. C11×#322C22semidirect
65. C11×#322C22semidirect
66. C82×C11C22semidirect
146. #18048C11direct (N × H)
172. C11×SD16M16semidirect
222. #2971C2×C11semidirect
224. D4×M16C2×C11semidirect
225. #1594C2×C11semidirect
226. #1589C2×C11semidirect
227. #1588C2×C11semidirect
228. #1586C2×C11semidirect
229. #1583C2×C11semidirect
230. #1581C2×C11semidirect
231. SD16⋊C8C2×C11semidirect
232. C8×SD16C2×C11semidirect
233. #1569C2×C11semidirect
234. #1490C2×C11semidirect
235. #1489C2×C11semidirect
236. #1455C2×C11semidirect
245. Q8×C11C2×M16semidirect
293. C8×C11C2×M16semidirect
294. C8×C11AGL(1,ℤ/8)semidirect
299. C8×Q8C22×C11semidirect
300. C8×Q8C22×C11semidirect
313. #436C22×C11semidirect
314. #436C22×C11semidirect
330. #335C22×C11semidirect
331. #335C22×C11semidirect
332. #334C22×C11semidirect
333. #334C22×C11semidirect
334. Q8⋊C8C22×C11semidirect
335. Q8⋊C8C22×C11semidirect
340. D4⋊C8C22×C11semidirect
341. D4⋊C8C22×C11semidirect
342. #322C22×C11semidirect
343. #322C22×C11semidirect
344. #322C22×C11semidirect
345. C82C22×C11semidirect
484. SD16C11×M16semidirect
534. C11#18048direct (N × H)
543. Q8C2×C11×M16semidirect
591. C8C2×C11×M16semidirect
592. C8C11×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
C11×#29712
C4×C11×AGL(1,ℤ/8)2
D4×C11×M162
C11×#15942
C11×#15892
C11×#15882
C11×#15862
C11×#15832
C11×#15812
C11×SD16⋊C82
C8×C11×SD162
C11×#15692
C11×#14902
C11×#14892
C11×#14552
#1804811