Finite Group Databasebeta

← C11×#14016 #14591209

Subgroups — C11×#14016 #14591209

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C2×C11×#386C211yesmaximal, characteristic
3C2×C11×#386C211yesmaximal, characteristic
4C2×C11×#385C211yesmaximal, characteristic, complemented
5C22×C11×#95C211yesmaximal, characteristic, complemented
6C11×#1442C212yesmaximal, complemented
7C11×#1439C212yesmaximal, complemented
8C11×#1436C212yesmaximal, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C11×C22⋊#95C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11—24no—
19C2×C4×D4×C11—24no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2212yes—
28C22×C42×C11C2211yescharacteristic
29C11×#386—24no—
30C11×#386C418yescomplemented
31C11×#385—24no—
32C2×C11×#95—24no—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C2×C11×#95C2212yes—
40C2×C11×#95C2212yes—
41C2×C11×#95C2212yes—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C22×D4×C11D414yes—
50C22×D4×C11Q814yes—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—24no—
60C23×C4×C11—24no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—24no—
64C23×C4×C11—42no—
65C23×C4×C11—42no—
66C23×C4×C11—42no—
67C23×C4×C11—42no—
68C23×C4×C11—42no—
69C23×C4×C11C2×C414yescomplemented
70C23×C4×C11D414yes—
71C23×C4×C11C2312yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2312yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C4×D4×C11—232no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—42no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4—42no—
100C2×C11×C22⋊C4—42no—
101C2×C11×C22⋊C4—42no—
102C2×C11×C22⋊C4C2×C414yescomplemented
103C2×C11×C22⋊C4C2×C418yescomplemented
104C2×C11×C22⋊C4D414yes—
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11—22no—
108C11×#95—24no—
109C11×#95—24no—
110C11×#95—24no—
111C11×#95—24no—
112C11×#95—24no—
113C11×#95—42no—
114C11×#95—42no—
115C11×#95—42no—
116C11×#95C2×C418yescomplemented
117#14016C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11C22×C412yes—
131C24×C11C22×C412yes—
132C24×C11C2×D412yes—
133C24×C11C2×D412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11C2×Q812yes—
137C24×C11C2×Q812yes—
138C24×C11#4112yes—
139C24×C11#4112yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11C4⋊C4116yescomplemented
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—22no—
155C22×C4×C11—28no—
156C22×C4×C11—28no—
157C22×C4×C11—28no—
158C22×C4×C11—28no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—28no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—48no—
198C22×C4×C11—44no—
199C22×C4×C11—48no—
200C22×C4×C11—48no—
201C22×C4×C11—48no—
202C22×C4×C11—48no—
203C22×C4×C11—48no—
204C22×C4×C11—48no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11—48no—
210C22×C4×C11—44no—
211C22×C4×C11—44no—
212C22×C4×C11C22×C414yes—
213C22×C4×C11C22×C414yes—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×Q812yes—
221C22×C4×C11#4114yes—
222C22×C4×C11#4114yes—
223C11×C4⋊C4—28no—
224C11×C4⋊C4—48no—
225C11×C22⋊C4—28no—
226C11×C22⋊C4—28no—
227C11×C22⋊C4—28no—
228C11×C22⋊C4—48no—
229C11×C22⋊C4—48no—
230C11×C22⋊C4—44no—
231C42×C11—28no—
232C22×C4×D4C2×C1111yescharacteristic
233C2×#386C2×C1111yescharacteristic
234C2×#386C2×C1111yescharacteristic
235C2×#385C2×C1111yescharacteristic, complemented
236C22×#95C2×C1111yescharacteristic, complemented
237#1442C2×C1112yescomplemented
238#1439C2×C1112yescomplemented
239#1436C2×C1112yescomplemented
240C22⋊#95C2×C1111yescharacteristic, complemented
241C22⋊#95C2×C1111yescharacteristic, complemented
242C22⋊#95C2×C1112yescomplemented
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11C2×C4⋊C414yes—
282C23×C11C2×C4⋊C414yes—
283C23×C11C4×D414yes—
284C23×C11C4×D414yes—
285C23×C11#12014yes—
286C23×C11C22⋊Q814yes—
287C23×C11C22⋊Q814yes—
288C23×C11#12314yes—
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11C22×D411yescharacteristic
293C23×C11C22×Q811yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4112yes—
297C23×C11C2×#4112yes—
298C23×C11H(5,𝔽2)12yes—
299C23×C11H(5,𝔽2)12yes—
300D4×C11—232no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—24no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—416no—
328C2×C4×C11—416no—
329C2×C4×C11—416no—
330C2×C4×C11—416no—
331C2×C4×C11—42no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—42no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11C2×C4⋊C414yes—
359C2×C4×C11#12314yes—
360C23×D4C22×C1111yescharacteristic
361C24×C4C22×C1111yescharacteristic
362C24×C4C22×C1111yescharacteristic
363C24×C4C22×C1111yescharacteristic
364C24×C4C22×C1111yescharacteristic
365C2×C4×D4—24no—
366C2×C4×D4—24no—
367C2×C4×D4—24no—
368C22×C4⋊C4C22×C1111yescharacteristic
369C22×C4⋊C4C22×C1112yes—
370C22×C22⋊C4C22×C1111yescharacteristic
371C22×C22⋊C4C22×C1111yescharacteristic
372C22×C22⋊C4C22×C1112yes—
373C22×C22⋊C4C22×C1111yescharacteristic
374C22×C22⋊C4C22×C1111yescharacteristic
375C22×C22⋊C4C22×C1112yes—
376C22×C42C22×C1111yescharacteristic
377#386—24no—
378#386C4×C1118yescomplemented
379#385—24no—
380C2×#95—24no—
381C2×#95C22×C1112yes—
382C2×#95C22×C1112yes—
383C2×#95C22×C1112yes—
384C2×#95C22×C1112yes—
385C2×#95C22×C1112yes—
386C2×#95C22×C1112yes—
387C2×#95C22×C1112yes—
388C2×#95C22×C1112yes—
389C2×#95C22×C1112yes—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—28no—
393C22×C11—28no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—28no—
397C22×C11—28no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—44no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11#38518yes—
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C4×#4112yes—
416C22×C11#51812yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×C22⋊Q811yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×#12311yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52912yes—
424C22×C11#53411yescharacteristic
425C22×C11#53511yescharacteristic
426C22×C11#53812yes—
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#54612yes—
430C22×C11#54612yes—
431C22×C11#55312yes—
432C22×C11#55312yes—
433C22×C11#55412yes—
434C22×C11#55412yes—
435C4×C11—24no—
436C4×C11—24no—
437C4×C11—44no—
438C4×C11—44no—
439C4×C11—42no—
440C4×C11—44no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—82no—
444C25C23×C1111yescharacteristic
445C25C23×C1111yescharacteristic
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4C2×C4×C1114yes—
451C22×D4D4×C1114yes—
452C22×D4Q8×C1114yes—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4C2×C4×C1114yescomplemented
472C23×C4D4×C1114yes—
473C23×C4C23×C1112yes—
474C23×C4C23×C1112yes—
475C23×C4C23×C1112yes—
476C23×C4C23×C1111yescharacteristic
477C23×C4C23×C1111yescharacteristic
478C23×C4C23×C1111yescharacteristic
479C23×C4C23×C1112yes—
480C23×C4C23×C1111yescharacteristic
481C23×C4C23×C1111yescharacteristic
482C4×D4—232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4C2×C4×C1114yescomplemented
505C2×C22⋊C4C2×C4×C1118yescomplemented
506C2×C22⋊C4D4×C1114yes—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—24no—
515#95—42no—
516#95—42no—
517#95—42no—
518#95C2×C4×C1118yescomplemented
519C2×C11—28no—
520C2×C11—44no—
521C2×C11C2×#38511yescharacteristic
522C2×C11C4×#12311yescharacteristic
523C2×C11#232111yescharacteristic
524C2×C11#234912yes—
525C2×C11#236412yes—
526C2×C11#240411yescharacteristic
527C2×C11#240511yescharacteristic
528C2×C11#244412yes—
529C2×C11#245012yes—
530C2×C11#248711yescharacteristic
531C2×C11#257911yescharacteristic
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C1112yes—
545C24C22×C4×C1112yes—
546C24C2×D4×C1112yes—
547C24C2×D4×C1112yes—
548C24C2×D4×C1112yes—
549C24C2×D4×C1112yes—
550C24C2×Q8×C1112yes—
551C24C2×Q8×C1112yes—
552C24C11×#4112yes—
553C24C11×#4112yes—
554C24C24×C1111yescharacteristic
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4C11×C4⋊C4116yescomplemented
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—28no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C22×C4×C1114yes—
627C22×C4C22×C4×C1114yes—
628C22×C4C22×C4×C1112yes—
629C22×C4C2×D4×C1112yes—
630C22×C4C2×D4×C1112yes—
631C22×C4C2×D4×C1112yes—
632C22×C4C2×D4×C1112yes—
633C22×C4C2×D4×C1112yes—
634C22×C4C2×Q8×C1112yes—
635C22×C4C11×#4114yes—
636C22×C4C11×#4114yes—
637C4⋊C4—28no—
638C4⋊C4—48no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—44no—
645C42—28no—
646C11#1401611yescharacteristic, direct product factor, Sylow
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×C11×C4⋊C414yes—
686C23C2×C11×C4⋊C414yes—
687C23C4×D4×C1114yes—
688C23C4×D4×C1114yes—
689C23C11×#12014yes—
690C23C11×C22⋊Q814yes—
691C23C11×C22⋊Q814yes—
692C23C11×#12314yes—
693C23C23×C4×C1111yescharacteristic
694C23C22×D4×C1111yescharacteristic
695C23C22×D4×C1111yescharacteristic
696C23C22×D4×C1111yescharacteristic
697C23C22×Q8×C1111yescharacteristic
698C23C2×C11×#4111yescharacteristic
699C23C2×C11×#4111yescharacteristic
700C23C2×C11×#4112yes—
701C23C2×C11×#4112yes—
702C23C11×H(5,𝔽2)12yes—
703C23C11×H(5,𝔽2)12yes—
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C2×C11×C4⋊C414yes—
763C2×C4C11×#12314yes—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—28no—
774C22—24no—
775C22—28no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22C11×#38518yes—
786C22C22×C11×C4⋊C411yescharacteristic
787C22C2×C4×D4×C1111yescharacteristic
788C22C2×C4×D4×C1111yescharacteristic
789C22C4×C11×#4112yes—
790C22C11×#51812yes—
791C22C2×C11×#12011yescharacteristic
792C22C2×C11×C22⋊Q811yescharacteristic
793C22C2×C11×C22⋊Q811yescharacteristic
794C22C2×C11×#12311yescharacteristic
795C22C2×C11×#12311yescharacteristic
796C22C11×#52511yescharacteristic
797C22C11×#52912yes—
798C22C11×#53411yescharacteristic
799C22C11×#53511yescharacteristic
800C22C11×#53812yes—
801C22C11×#54612yes—
802C22C11×#54612yes—
803C22C11×#54612yes—
804C22C11×#54612yes—
805C22C11×#55312yes—
806C22C11×#55312yes—
807C22C11×#55412yes—
808C22C11×#55412yes—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—44no—
817C4—82no—
818C2—28no—
819C2—44no—
820C2C2×C11×#38511yescharacteristic
821C2C4×C11×#12311yescharacteristic
822C2C11×#232111yescharacteristic
823C2C11×#234912yes—
824C2C11×#236412yes—
825C2C11×#240411yescharacteristic
826C2C11×#240511yescharacteristic
827C2C11×#244412yes—
828C2C11×#245012yes—
829C2C11×#248711yescharacteristic
830C2C11×#257911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#385C2semidirect
5. C22×C11×#95C2semidirect
6. C11×#1442C2semidirect
7. C11×#1439C2semidirect
8. C11×#1436C2semidirect
9. C11×C22⋊#95C2semidirect
10. C11×C22⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
30. C11×#386C4semidirect
69. C23×C4×C11C2×C4semidirect
102. C2×C11×C22⋊C4C2×C4semidirect
103. C2×C11×C22⋊C4C2×C4semidirect
116. C11×#95C2×C4semidirect
117. #14016C11direct (N × H)
147. C2×D4×C11C4⋊C4semidirect
235. C2×#385C2×C11semidirect
236. C22×#95C2×C11semidirect
237. #1442C2×C11semidirect
238. #1439C2×C11semidirect
239. #1436C2×C11semidirect
240. C22⋊#95C2×C11semidirect
241. C22⋊#95C2×C11semidirect
242. C22⋊#95C2×C11semidirect
378. #386C4×C11semidirect
471. C23×C4C2×C4×C11semidirect
504. C2×C22⋊C4C2×C4×C11semidirect
505. C2×C22⋊C4C2×C4×C11semidirect
518. #95C2×C4×C11semidirect
561. C2×D4C11×C4⋊C4semidirect
646. C11#14016direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C2×C11×#3862
C2×C11×#3852
C22×C11×#952
C11×#14422
C11×#14392
C11×#14362
C11×C22⋊#952
#1401611