Finite Group Databasebeta

← C11×#22659 #14599852

Subgroups — C11×#22659 #14599852

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C11×#2352C211yesmaximal, characteristic
5D4×C11×C4⋊C4C211yesmaximal, characteristic
6C11×#1949C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1854C211yesmaximal, characteristic, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1852C211yesmaximal, characteristic, complemented
12C11×#1847C211yesmaximal, characteristic, complemented
13C11×#1809C211yesmaximal, characteristic, complemented
14C11×#1808C211yesmaximal, characteristic, complemented
15C11×#1776C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#435C418yescomplemented
25C11×#428—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106—24no—
31C2×C11×#106C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C11×#389—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#385—21no—
46C11×#385—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16C2×C414yescomplemented
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11C2×C414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—44no—
79C4×D4×C11C2×C414yes—
80C4×D4×C11Q814yes—
81C11×#117—22no—
82C11×#117—41no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C11×#107—22no—
115C11×#107—22no—
116C11×#107—22no—
117C11×#107—41no—
118C11×#106—22no—
119C11×#106—22no—
120C11×#106—22no—
121C11×#106—22no—
122C11×#106—41no—
123C11×#106D414yescomplemented
124C11×C4⋊C8C2×C414yescomplemented
125C11×C22⋊C8C2×C414yescomplemented
126C11×C22⋊C8C2×C414yescomplemented
127C11×#97C2×C414yescomplemented
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136#22659C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D411yescharacteristic
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11C4⋊C414yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11—81no—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×Q812yes—
174C22×C4×C11C2×Q812yes—
175C22×C4×C11C2411yescharacteristic
176C11×M16—28no—
177C2×C8×C11—28no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C2×C8×C11C22×C412yes—
187C2×C8×C11C22×C412yes—
188C2×C8×C11C2×D412yes—
189C2×C8×C11#4112yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
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—21no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—81no—
209C11×C4⋊C4C4⋊C414yes—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4C4⋊C414yes—
218C11×C22⋊C4C4⋊C414yes—
219C42×C11—42no—
220C42×C11—42no—
221C42×C11—81no—
222C42×C11C22×C412yes—
223C42×C11C2×Q812yes—
224C2×#435C2×C1111yescharacteristic
225C2×#428C2×C1111yescharacteristic, complemented
226C22×#106C2×C1111yescharacteristic, complemented
227#2352C2×C1111yescharacteristic
228D4×C4⋊C4C2×C1111yescharacteristic
229#1949C2×C1111yescharacteristic, complemented
230#1948C2×C1111yescharacteristic, complemented
231#1854C2×C1111yescharacteristic, complemented
232#1853C2×C1111yescharacteristic, complemented
233#1853C2×C1111yescharacteristic, complemented
234#1852C2×C1111yescharacteristic, complemented
235#1847C2×C1111yescharacteristic, complemented
236#1809C2×C1111yescharacteristic, complemented
237#1808C2×C1111yescharacteristic, complemented
238#1776C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C2×C4⋊C412yes—
250C23×C11C2×C4⋊C412yes—
251C23×C11AGL(1,ℤ/8)12yes—
252C23×C11#13712yes—
253C23×C11C22×D411yescharacteristic
254D4×C11—28no—
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—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—84no—
296C2×C4×C11—84no—
297C2×C4×C11—84no—
298C2×C4×C11C2×C4⋊C412yes—
299C2×C4×C11C2×C4⋊C412yes—
300C2×C4×C11C2×C4⋊C412yes—
301C2×C4×C11C2×C4⋊C412yes—
302C2×C4×C11C23×C411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×Q811yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C112−1+411yescharacteristic
308C8×C11—22no—
309C8×C11—22no—
310C8×C11—22no—
311C8×C11C4×D414yescomplemented
312C22×M16C22×C1111yescharacteristic
313C23×C8C22×C1111yescharacteristic
314C2×C4×D4—21no—
315C2×C4×D4C22×C1111yescharacteristic
316C2×#117C22×C1111yescharacteristic
317C22×C4⋊C4C22×C1111yescharacteristic
318C22×C4⋊C4C22×C1111yescharacteristic
319C22×C4⋊C4C22×C1111yescharacteristic
320#435C4×C1118yescomplemented
321#428—24no—
322C2×#107C22×C1111yescharacteristic
323C2×#107C22×C1111yescharacteristic
324C2×#107C22×C1111yescharacteristic
325C2×#107C22×C1111yescharacteristic
326C2×#106—24no—
327C2×#106C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329C2×#106C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334C2×C22⋊C8C22×C1111yescharacteristic
335C2×C22⋊C8C22×C1111yescharacteristic
336C2×#97C22×C1111yescharacteristic
337#389—21no—
338#388—21no—
339#387—21no—
340#386—21no—
341#385—21no—
342#385—21no—
343#384C22×C1111yescharacteristic
344#382C22×C1111yescharacteristic
345#380C22×C1111yescharacteristic
346#380C22×C1111yescharacteristic
347#380C22×C1111yescharacteristic
348#380C22×C1111yescharacteristic
349C4×C4⋊C4C22×C1111yescharacteristic
350C4×C4⋊C4C22×C1111yescharacteristic
351C4×C22⋊C4—21no—
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11#42814yescomplemented
372C22×C11C22×C4⋊C411yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54711yescharacteristic
375C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C11C2×#13711yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57711yescharacteristic
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11C2×C4×D411yescharacteristic
392C4×C11#52011yescharacteristic
393C4×C11D4×Q811yescharacteristic
394C4×C11#55411yescharacteristic
395C22×D4D4×C1111yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C23×C1111yescharacteristic
400C23×C4C23×C1111yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16C2×C4×C1114yescomplemented
404C22×C8—22no—
405C22×C8—22no—
406C22×C8C2×C4×C1114yescomplemented
407C22×C8C23×C1111yescharacteristic
408C22×C8C23×C1111yescharacteristic
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C4×D4—44no—
412C4×D4C2×C4×C1114yes—
413C4×D4Q8×C1114yes—
414#117—22no—
415#117—41no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4D4×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4D4×C1111yescharacteristic
442C2×C22⋊C4D4×C1111yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C1111yescharacteristic
447#107—22no—
448#107—22no—
449#107—22no—
450#107—41no—
451#106—22no—
452#106—22no—
453#106—22no—
454#106—22no—
455#106—41no—
456#106D4×C1114yescomplemented
457C4⋊C8C2×C4×C1114yescomplemented
458C22⋊C8C2×C4×C1114yescomplemented
459C22⋊C8C2×C4×C1114yescomplemented
460#97C2×C4×C1114yescomplemented
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C2×C11—24no—
470C2×C11—42no—
471C2×C11D4×C4⋊C411yescharacteristic
472C2×C11C2×#42811yescharacteristic
473C2×C11#291211yescharacteristic
474C2×C11#326511yescharacteristic
475C2×C11#326611yescharacteristic
476C2×C11#334411yescharacteristic
477C2×C11#334511yescharacteristic
478C24C2×D4×C1111yescharacteristic
479C24C2×D4×C1111yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4C11×C4⋊C414yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C22×C4×C1112yes—
509C22×C4C22×C4×C1112yes—
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C2×D4×C1111yescharacteristic
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×Q8×C1112yes—
515C22×C4C2×Q8×C1112yes—
516C22×C4C24×C1111yescharacteristic
517M16—28no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—28no—
525C2×C8C22×C4×C1112yes—
526C2×C8C22×C4×C1112yes—
527C2×C8C22×C4×C1112yes—
528C2×C8C22×C4×C1112yes—
529C2×C8C2×D4×C1112yes—
530C2×C8C11×#4112yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4C11×C4⋊C414yes—
551C4⋊C4C2×D4×C1112yes—
552C4⋊C4C2×D4×C1112yes—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4C11×C4⋊C414yes—
559C22⋊C4C11×C4⋊C414yes—
560C42—42no—
561C42—42no—
562C42—81no—
563C42C22×C4×C1112yes—
564C42C2×Q8×C1112yes—
565C11#2265911yescharacteristic, direct product factor, Sylow
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C11×C4⋊C412yes—
577C23C2×C11×C4⋊C412yes—
578C23C11×AGL(1,ℤ/8)12yes—
579C23C11×#13712yes—
580C23C22×D4×C1111yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4—84no—
625C2×C4C2×C11×C4⋊C412yes—
626C2×C4C2×C11×C4⋊C412yes—
627C2×C4C2×C11×C4⋊C412yes—
628C2×C4C2×C11×C4⋊C412yes—
629C2×C4C23×C4×C1111yescharacteristic
630C2×C4C22×D4×C1111yescharacteristic
631C2×C4C22×Q8×C1111yescharacteristic
632C2×C4C2×C11×#4111yescharacteristic
633C2×C4C11×H(5,𝔽2)11yescharacteristic
634C2×C4C11×2−1+411yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8C4×D4×C1114yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22C11×#42814yescomplemented
653C22C22×C11×C4⋊C411yescharacteristic
654C22D42×C1111yescharacteristic
655C22C11×#54711yescharacteristic
656C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
657C22C2×C11×#13711yescharacteristic
658C22C11×#57711yescharacteristic
659C22C11×#57711yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C2×C4×D4×C1111yescharacteristic
673C4C11×#52011yescharacteristic
674C4D4×Q8×C1111yescharacteristic
675C4C11×#55411yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C11×C4⋊C411yescharacteristic
679C2C2×C11×#42811yescharacteristic
680C2C11×#291211yescharacteristic
681C2C11×#326511yescharacteristic
682C2C11×#326611yescharacteristic
683C2C11×#334411yescharacteristic
684C2C11×#334511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×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
2. C2×C11×#428C2semidirect
3. C22×C11×#106C2semidirect
6. C11×#1949C2semidirect
7. C11×#1948C2semidirect
8. C11×#1854C2semidirect
9. C11×#1853C2semidirect
10. C11×#1853C2semidirect
11. C11×#1852C2semidirect
12. C11×#1847C2semidirect
13. C11×#1809C2semidirect
14. C11×#1808C2semidirect
15. C11×#1776C2semidirect
24. C11×#435C4semidirect
70. C2×C11×M16C2×C4semidirect
73. C22×C8×C11C2×C4semidirect
123. C11×#106D4semidirect
124. C11×C4⋊C8C2×C4semidirect
125. C11×C22⋊C8C2×C4semidirect
126. C11×C22⋊C8C2×C4semidirect
127. C11×#97C2×C4semidirect
136. #22659C11direct (N × H)
225. C2×#428C2×C11semidirect
226. C22×#106C2×C11semidirect
229. #1949C2×C11semidirect
230. #1948C2×C11semidirect
231. #1854C2×C11semidirect
232. #1853C2×C11semidirect
233. #1853C2×C11semidirect
234. #1852C2×C11semidirect
235. #1847C2×C11semidirect
236. #1809C2×C11semidirect
237. #1808C2×C11semidirect
238. #1776C2×C11semidirect
311. C8×C11C4×D4semidirect
320. #435C4×C11semidirect
371. C22×C11#428semidirect
403. C2×M16C2×C4×C11semidirect
406. C22×C8C2×C4×C11semidirect
456. #106D4×C11semidirect
457. C4⋊C8C2×C4×C11semidirect
458. C22⋊C8C2×C4×C11semidirect
459. C22⋊C8C2×C4×C11semidirect
460. #97C2×C4×C11semidirect
565. C11#22659direct (N × H)
638. C8C4×D4×C11semidirect
652. C22C11×#428semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C11×#4282
C22×C11×#1062
C11×#23522
D4×C11×C4⋊C42
C11×#19492
C11×#19482
C11×#18542
C11×#18532
C11×#18522
C11×#18472
C11×#18092
C11×#18082
C11×#17762
#2265911