Finite Group Databasebeta

← C11×#23035 #14600228

Subgroups — C11×#23035 #14600228

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2363C211yesmaximal, characteristic
5C11×#2360C211yesmaximal, characteristic, complemented
6C11×#1973C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1874C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1863C211yesmaximal, characteristic, complemented
14C11×#1776C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#468C418yescomplemented
25C4×C11×SD16—24no—
26C11×#428—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#390—21no—
43C11×#390C2211yescharacteristic
44C11×#389—21no—
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#387—21no—
49C11×#386—21no—
50C11×#385—21no—
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4—21no—
54C4×C11×C22⋊C4—21no—
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16C2×C414yescomplemented
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16C2×C414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2×C414yescomplemented
80C11×#121—22no—
81C11×#121C2×C414yes—
82C4×Q8×C11—22no—
83C4×Q8×C11—41no—
84C4×D4×C11—22no—
85C4×D4×C11—41no—
86C11×#117—22no—
87C11×#117—41no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—41no—
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×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⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#107—22no—
116C11×#107—22no—
117C11×#107C2×C414yescomplemented
118C11×#106—22no—
119C11×#106D414yescomplemented
120C11×#103—22no—
121C11×#103—41no—
122C11×#103C2×C414yescomplemented
123C11×#102—22no—
124C11×#102—41no—
125C11×#102C2×C414yescomplemented
126C11×C22⋊C8—22no—
127C11×#97—22no—
128C4×C8×C11—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#23035C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11C22×C412yes—
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—21no—
165C22×C4×C11—21no—
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×C11C22×C412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4112yes—
179C22×C4×C11C2411yescharacteristic
180C11×SD16—28no—
181C11×M16—28no—
182C2×C8×C11—21no—
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×C11C22×C412yes—
191C2×C8×C11C22×C412yes—
192C2×C8×C11C2×D412yes—
193C2×C8×C11#4112yes—
194C11×C4⋊C4—24no—
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⋊C4—81no—
207C11×C4⋊C4C22×C412yes—
208C11×C4⋊C4C22×C412yes—
209C11×C4⋊C4C2×D412yes—
210C11×C4⋊C4C2×D412yes—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C42×C11—42no—
225C42×C11—81no—
226C42×C11—81no—
227C2×#468C2×C1111yescharacteristic
228C2×C4×SD16C2×C1111yescharacteristic, complemented
229C2×#428C2×C1111yescharacteristic, complemented
230#2363C2×C1111yescharacteristic
231#2360C2×C1111yescharacteristic, complemented
232#1973C2×C1111yescharacteristic, complemented
233#1942C2×C1111yescharacteristic, complemented
234#1927C2×C1111yescharacteristic, complemented
235#1925C2×C1111yescharacteristic, complemented
236#1874C2×C1111yescharacteristic
237#1873C2×C1111yescharacteristic, complemented
238#1864C2×C1111yescharacteristic, complemented
239#1863C2×C1111yescharacteristic, complemented
240#1776C2×C1111yescharacteristic, complemented
241#1753C2×C1111yescharacteristic, complemented
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—22no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C4×D412yes—
256C23×C11C22×D411yescharacteristic
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—41no—
260Q8×C11—41no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—84no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
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—21no—
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—41no—
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—84no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11#13712yes—
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C112−1+411yescharacteristic
314C8×C11—22no—
315C8×C11—41no—
316C8×C11—41no—
317C8×C11C4×D414yes—
318C22×SD16C22×C1111yescharacteristic
319C22×M16C22×C1111yescharacteristic
320C2×C22⋊Q8C22×C1111yescharacteristic
321C2×#121C22×C1111yescharacteristic
322C2×C4×Q8C22×C1111yescharacteristic
323C2×C4×D4C22×C1111yescharacteristic
324C2×#117C22×C1111yescharacteristic
325C22×C4⋊C4C22×C1111yescharacteristic
326#468C4×C1118yescomplemented
327C4×SD16—24no—
328#428—24no—
329C2×#107C22×C1111yescharacteristic
330C2×#107C22×C1111yescharacteristic
331C2×#107C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1111yescharacteristic
341C2×#97C22×C1111yescharacteristic
342C2×C4×C8C22×C1111yescharacteristic
343#391C22×C1111yescharacteristic
344#390—21no—
345#390C22×C1111yescharacteristic
346#389—21no—
347#389C22×C1111yescharacteristic
348#389C22×C1111yescharacteristic
349#388—21no—
350#387—21no—
351#386—21no—
352#385—21no—
353C4×C4⋊C4C22×C1111yescharacteristic
354C4×C4⋊C4C22×C1111yescharacteristic
355C4×C22⋊C4—21no—
356C4×C22⋊C4—21no—
357C4×C22⋊C4C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#336C22×C1111yescharacteristic
363#336C22×C1111yescharacteristic
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11D4211yescharacteristic
380C22×C11#54711yescharacteristic
381C22×C11C2×#13711yescharacteristic
382C22×C11#57511yescharacteristic
383C22×C11#57611yescharacteristic
384C22×C11#57711yescharacteristic
385C4×C11—22no—
386C4×C11—22no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11C2×C4×D411yescharacteristic
398C4×C11#52011yescharacteristic
399C4×C11#54811yescharacteristic
400C4×C11#55311yescharacteristic
401C22×Q8C23×C1111yescharacteristic
402C22×D4—21no—
403C22×D4C23×C1111yescharacteristic
404C23×C4—21no—
405C23×C4—21no—
406C23×C4C23×C1111yescharacteristic
407C2×SD16—22no—
408C2×SD16—22no—
409C2×SD16C2×C4×C1114yescomplemented
410C2×M16—22no—
411C2×M16—22no—
412C2×M16C2×C4×C1114yescomplemented
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22⋊Q8—22no—
418C22⋊Q8C2×C4×C1114yescomplemented
419#121—22no—
420#121C2×C4×C1114yes—
421C4×Q8—22no—
422C4×Q8—41no—
423C4×D4—22no—
424C4×D4—41no—
425#117—22no—
426#117—41no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4D4×C1111yescharacteristic
447C2×C22⋊C4D4×C1111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C1111yescharacteristic
453C2×C42C23×C1111yescharacteristic
454#107—22no—
455#107—22no—
456#107C2×C4×C1114yescomplemented
457#106—22no—
458#106D4×C1114yescomplemented
459#103—22no—
460#103—41no—
461#103C2×C4×C1114yescomplemented
462#102—22no—
463#102—41no—
464#102C2×C4×C1114yescomplemented
465C22⋊C8—22no—
466#97—22no—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C1111yescharacteristic
475#95D4×C1111yescharacteristic
476C2×C11—42no—
477C2×C11—82no—
478C2×C11#236111yescharacteristic
479C2×C11C4×#13711yescharacteristic
480C2×C11#294611yescharacteristic
481C2×C11#326611yescharacteristic
482C2×C11#326811yescharacteristic
483C2×C11#335111yescharacteristic
484C2×C11#335711yescharacteristic
485C24—21no—
486C24C2×D4×C1111yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8C22×C4×C1112yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4C22×C4×C1112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C22×C4×C1112yes—
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C11×#4112yes—
526C22×C4C24×C1111yescharacteristic
527SD16—28no—
528M16—28no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8C22×C4×C1112yes—
538C2×C8C22×C4×C1112yes—
539C2×C8C2×D4×C1112yes—
540C2×C8C11×#4112yes—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C22×C4×C1112yes—
555C4⋊C4C22×C4×C1112yes—
556C4⋊C4C2×D4×C1112yes—
557C4⋊C4C2×D4×C1112yes—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—42no—
572C42—81no—
573C42—81no—
574C11#2303511yescharacteristic, direct product factor, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C4×D4×C1112yes—
589C23C22×D4×C1111yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594D4—22no—
595D4—22no—
596D4—41no—
597D4—41no—
598D4—84no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4C4×D4×C1112yes—
640C2×C4C11×#13712yes—
641C2×C4C23×C4×C1111yescharacteristic
642C2×C4C22×D4×C1111yescharacteristic
643C2×C4C2×C11×#4111yescharacteristic
644C2×C4C2×C11×#4111yescharacteristic
645C2×C4C11×H(5,𝔽2)11yescharacteristic
646C2×C4C11×2−1+411yescharacteristic
647C8—22no—
648C8—41no—
649C8—41no—
650C8C4×D4×C1114yes—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22C2×C4×D4×C1111yescharacteristic
666C22D42×C1111yescharacteristic
667C22C11×#54711yescharacteristic
668C22C2×C11×#13711yescharacteristic
669C22C11×#57511yescharacteristic
670C22C11×#57611yescharacteristic
671C22C11×#57711yescharacteristic
672C4—22no—
673C4—22no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—41no—
678C4—42no—
679C4—41no—
680C4—41no—
681C4—42no—
682C4—81no—
683C4—81no—
684C4C2×C4×D4×C1111yescharacteristic
685C4C11×#52011yescharacteristic
686C4C11×#54811yescharacteristic
687C4C11×#55311yescharacteristic
688C2—42no—
689C2—82no—
690C2C11×#236111yescharacteristic
691C2C4×C11×#13711yescharacteristic
692C2C11×#294611yescharacteristic
693C2C11×#326611yescharacteristic
694C2C11×#326811yescharacteristic
695C2C11×#335111yescharacteristic
696C2C11×#335711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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. C2×C4×C11×SD16C2semidirect
3. C2×C11×#428C2semidirect
5. C11×#2360C2semidirect
6. C11×#1973C2semidirect
7. C11×#1942C2semidirect
8. C11×#1927C2semidirect
9. C11×#1925C2semidirect
11. C11×#1873C2semidirect
12. C11×#1864C2semidirect
13. C11×#1863C2semidirect
14. C11×#1776C2semidirect
15. C11×#1753C2semidirect
24. C11×#468C4semidirect
70. C2×C11×SD16C2×C4semidirect
73. C2×C11×M16C2×C4semidirect
79. C11×C22⋊Q8C2×C4semidirect
117. C11×#107C2×C4semidirect
119. C11×#106D4semidirect
122. C11×#103C2×C4semidirect
125. C11×#102C2×C4semidirect
137. #23035C11direct (N × H)
228. C2×C4×SD16C2×C11semidirect
229. C2×#428C2×C11semidirect
231. #2360C2×C11semidirect
232. #1973C2×C11semidirect
233. #1942C2×C11semidirect
234. #1927C2×C11semidirect
235. #1925C2×C11semidirect
237. #1873C2×C11semidirect
238. #1864C2×C11semidirect
239. #1863C2×C11semidirect
240. #1776C2×C11semidirect
241. #1753C2×C11semidirect
326. #468C4×C11semidirect
409. C2×SD16C2×C4×C11semidirect
412. C2×M16C2×C4×C11semidirect
418. C22⋊Q8C2×C4×C11semidirect
456. #107C2×C4×C11semidirect
458. #106D4×C11semidirect
461. #103C2×C4×C11semidirect
464. #102C2×C4×C11semidirect
574. C11#23035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4682
C2×C4×C11×SD162
C2×C11×#4282
C11×#23632
C11×#23602
C11×#19732
C11×#19422
C11×#19272
C11×#19252
C11×#18742
C11×#18732
C11×#18642
C11×#18632
C11×#17762
C11×#17532
#2303511