Finite Group Databasebeta

← C11×#13996 #14591189

Subgroups — C11×#13996 #14591189

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C2×C11×#386C211yesmaximal, characteristic
3C2×C11×#386C211yesmaximal, characteristic
4C2×C11×#385C211yesmaximal, characteristic, complemented
5C2×C11×#381C211yesmaximal, characteristic, complemented
6C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C11×#95C211yesmaximal, characteristic, complemented
8C11×#1445C212yesmaximal, complemented
9C11×#1439C212yesmaximal, complemented
10C11×#1437C212yesmaximal, complemented
11C11×C4⋊#95C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C2×C11×#123—24no—
17C2×C11×#123—24no—
18C2×C11×#123C418yescomplemented
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2212yes—
29C11×#386—24no—
30C11×#386—24no—
31C11×#385—24no—
32C11×#381—24no—
33C4×C11×C22⋊C4—24no—
34C2×C11×#95—24no—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C2×C11×#95C2212yes—
40C2×C11×#95C2212yes—
41C2×C11×#95C2212yes—
42C2×C11×#95C2212yes—
43C2×C11×#95C2211yescharacteristic
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11C2×C414yes—
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—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—24no—
63C23×C4×C11—24no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—42no—
67C23×C4×C11—42no—
68C23×C4×C11C2×C414yes—
69C23×C4×C11D414yes—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2312yes—
77C23×C4×C11C2312yes—
78C23×C4×C11C2311yescharacteristic
79C11×#123—232no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—42no—
85C2×C11×C4⋊C4C2×C418yescomplemented
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4—42no—
99C2×C11×C22⋊C4—42no—
100C2×C11×C22⋊C4C2×C414yes—
101C2×C11×C22⋊C4C2×C418yescomplemented
102C2×C11×C22⋊C4D414yes—
103C2×C11×C22⋊C4D414yes—
104C2×C11×C22⋊C4D414yes—
105C2×C42×C11—24no—
106C2×C42×C11—24no—
107C2×C42×C11—42no—
108C11×#95—24no—
109C11×#95—24no—
110C11×#95—24no—
111C11×#95—24no—
112C11×#95—24no—
113C11×#95—24no—
114C11×#95—24no—
115C11×#95—22no—
116C11×#95—22no—
117#13996C1111yesmaximal, 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—21no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11C22×C412yes—
133C24×C11C22×C412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11C2×D412yes—
137C24×C11C2×D412yes—
138C24×C11#4112yes—
139C24×C11#4112yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—28no—
156C22×C4×C11—28no—
157C22×C4×C11—28no—
158C22×C4×C11—28no—
159C22×C4×C11—28no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—28no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—44no—
200C22×C4×C11—48no—
201C22×C4×C11—48no—
202C22×C4×C11—48no—
203C22×C4×C11—48no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11C22×C414yes—
211C22×C4×C11C22×C412yes—
212C22×C4×C11C22×C414yes—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11#4114yes—
219C22×C4×C11#4114yes—
220C11×C4⋊C4—216no—
221C11×C4⋊C4—48no—
222C11×C22⋊C4—28no—
223C11×C22⋊C4—216no—
224C11×C22⋊C4—48no—
225C11×C22⋊C4—44no—
226C11×C22⋊C4—44no—
227C11×C22⋊C4—44no—
228C11×C22⋊C4C22⋊C4116yescomplemented
229C42×C11—48no—
230C22×#123C2×C1111yescharacteristic
231C2×#386C2×C1111yescharacteristic
232C2×#386C2×C1111yescharacteristic
233C2×#385C2×C1111yescharacteristic, complemented
234C2×#381C2×C1111yescharacteristic, complemented
235C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
236C22×#95C2×C1111yescharacteristic, complemented
237#1445C2×C1112yescomplemented
238#1439C2×C1112yescomplemented
239#1437C2×C1112yescomplemented
240C4⋊#95C2×C1112yescomplemented
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—42no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11C2×C22⋊C414yes—
281C23×C11C4×D414yes—
282C23×C11C4×D414yes—
283C23×C11#12114yes—
284C23×C11#12114yes—
285C23×C11#12414yes—
286C23×C11#12714yes—
287C23×C11C23×C411yescharacteristic
288C23×C11C22×D411yescharacteristic
289C23×C11C22×D411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4112yes—
295C23×C11C2×#4112yes—
296C23×C11H(5,𝔽2)12yes—
297C23×C112−1+412yes—
298D4×C11—416no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—416no—
325C2×C4×C11—416no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—42no—
331C2×C4×C11—41no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—41no—
336C2×C4×C11—42no—
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—416no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11C2×C22⋊C418yes—
356C2×C4×C11#12314yescomplemented
357C23×D4C22×C1111yescharacteristic
358C24×C4C22×C1111yescharacteristic
359C24×C4C22×C1111yescharacteristic
360C24×C4C22×C1111yescharacteristic
361C2×#123—24no—
362C2×#123—24no—
363C2×#123C4×C1118yescomplemented
364C22×C4⋊C4C22×C1112yes—
365C22×C4⋊C4C22×C1112yes—
366C22×C22⋊C4C22×C1111yescharacteristic
367C22×C22⋊C4C22×C1111yescharacteristic
368C22×C22⋊C4C22×C1112yes—
369C22×C22⋊C4C22×C1112yes—
370C22×C22⋊C4C22×C1111yescharacteristic
371C22×C22⋊C4C22×C1111yescharacteristic
372C22×C22⋊C4C22×C1111yescharacteristic
373C22×C42C22×C1112yes—
374#386—24no—
375#386—24no—
376#385—24no—
377#381—24no—
378C4×C22⋊C4—24no—
379C2×#95—24no—
380C2×#95C22×C1111yescharacteristic
381C2×#95C22×C1112yes—
382C2×#95C22×C1112yes—
383C2×#95C22×C1112yes—
384C2×#95C22×C1112yes—
385C2×#95C22×C1112yes—
386C2×#95C22×C1112yes—
387C2×#95C22×C1112yes—
388C2×#95C22×C1111yescharacteristic
389C22×C11—24no—
390C22×C11—28no—
391C22×C11—28no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—28no—
395C22×C11—28no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—42no—
400C22×C11—44no—
401C22×C11—44no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—82no—
407C22×C11—82no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11#39018yes—
411C22×C11C22×C22⋊C411yescharacteristic
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C4×#4112yes—
415C22×C11#52012yes—
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×#12111yescharacteristic
418C22×C11C2×#12311yescharacteristic
419C22×C11#52511yescharacteristic
420C22×C11C2×#12411yescharacteristic
421C22×C11#52912yes—
422C22×C11C2×#12711yescharacteristic
423C22×C11#53411yescharacteristic
424C22×C11#53611yescharacteristic
425C22×C11#53912yes—
426C22×C11#54612yes—
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#54712yes—
432C22×C11#55112yes—
433C22×C11#55212yes—
434C4×C11—28no—
435C4×C11—24no—
436C4×C11—42no—
437C4×C11—44no—
438C4×C11—44no—
439C4×C11—44no—
440C4×C11—42no—
441C4×C11—81no—
442C4×C11—81no—
443C25C23×C1111yescharacteristic
444C25C23×C1111yescharacteristic
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4C2×C4×C1114yes—
452C23×C4—22no—
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—42no—
466C23×C4—42no—
467C23×C4C2×C4×C1114yes—
468C23×C4D4×C1114yes—
469C23×C4C23×C1111yescharacteristic
470C23×C4C23×C1111yescharacteristic
471C23×C4C23×C1112yes—
472C23×C4C23×C1111yescharacteristic
473C23×C4C23×C1112yes—
474C23×C4C23×C1111yescharacteristic
475C23×C4C23×C1112yes—
476C23×C4C23×C1112yes—
477C23×C4C23×C1111yescharacteristic
478#123—232no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4C2×C4×C1118yescomplemented
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4C2×C4×C1114yes—
500C2×C22⋊C4C2×C4×C1118yescomplemented
501C2×C22⋊C4D4×C1114yes—
502C2×C22⋊C4D4×C1114yes—
503C2×C22⋊C4D4×C1114yes—
504C2×C42—24no—
505C2×C42—24no—
506C2×C42—42no—
507#95—24no—
508#95—24no—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—22no—
515#95—22no—
516C2×C11—28no—
517C2×C11—82no—
518C2×C11C2×#39011yescharacteristic
519C2×C11C4×#12311yescharacteristic
520C2×C11#232211yescharacteristic
521C2×C11#233912yes—
522C2×C11#235912yes—
523C2×C11#241211yescharacteristic
524C2×C11#241311yescharacteristic
525C2×C11#242512yes—
526C2×C11#248812yes—
527C2×C11#250111yescharacteristic
528C2×C11#253911yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24C22×C4×C1112yes—
544C24C22×C4×C1112yes—
545C24C2×D4×C1112yes—
546C24C2×D4×C1112yes—
547C24C2×D4×C1112yes—
548C24C2×D4×C1112yes—
549C24C11×#4112yes—
550C24C11×#4112yes—
551C24C24×C1111yescharacteristic
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4C22×C4×C1114yes—
622C22×C4C22×C4×C1112yes—
623C22×C4C22×C4×C1114yes—
624C22×C4C2×D4×C1114yes—
625C22×C4C2×D4×C1112yes—
626C22×C4C2×D4×C1114yes—
627C22×C4C2×D4×C1114yes—
628C22×C4C2×D4×C1112yes—
629C22×C4C11×#4114yes—
630C22×C4C11×#4114yes—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C22⋊C4—28no—
634C22⋊C4—216no—
635C22⋊C4—48no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4C11×C22⋊C4116yescomplemented
640C42—48no—
641C11#1399611yescharacteristic, direct product factor, Sylow
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C11×C22⋊C414yes—
682C23C4×D4×C1114yes—
683C23C4×D4×C1114yes—
684C23C11×#12114yes—
685C23C11×#12114yes—
686C23C11×#12414yes—
687C23C11×#12714yes—
688C23C23×C4×C1111yescharacteristic
689C23C22×D4×C1111yescharacteristic
690C23C22×D4×C1111yescharacteristic
691C23C22×D4×C1111yescharacteristic
692C23C22×D4×C1111yescharacteristic
693C23C2×C11×#4111yescharacteristic
694C23C2×C11×#4111yescharacteristic
695C23C2×C11×#4112yes—
696C23C2×C11×#4112yes—
697C23C11×H(5,𝔽2)12yes—
698C23C11×2−1+412yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C11×C22⋊C418yes—
757C2×C4C11×#12314yescomplemented
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22C11×#39018yes—
780C22C22×C11×C22⋊C411yescharacteristic
781C22C2×C4×D4×C1111yescharacteristic
782C22C2×C4×D4×C1111yescharacteristic
783C22C4×C11×#4112yes—
784C22C11×#52012yes—
785C22C2×C11×#12111yescharacteristic
786C22C2×C11×#12111yescharacteristic
787C22C2×C11×#12311yescharacteristic
788C22C11×#52511yescharacteristic
789C22C2×C11×#12411yescharacteristic
790C22C11×#52912yes—
791C22C2×C11×#12711yescharacteristic
792C22C11×#53411yescharacteristic
793C22C11×#53611yescharacteristic
794C22C11×#53912yes—
795C22C11×#54612yes—
796C22C11×#54612yes—
797C22C11×#54612yes—
798C22C11×#54712yes—
799C22C11×#54712yes—
800C22C11×#54712yes—
801C22C11×#55112yes—
802C22C11×#55212yes—
803C4—24no—
804C4—28no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C11×#39011yescharacteristic
815C2C4×C11×#12311yescharacteristic
816C2C11×#232211yescharacteristic
817C2C11×#233912yes—
818C2C11×#235912yes—
819C2C11×#241211yescharacteristic
820C2C11×#241311yescharacteristic
821C2C11×#242512yes—
822C2C11×#248812yes—
823C2C11×#250111yescharacteristic
824C2C11×#253911yescharacteristic
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. C2×C11×#381C2semidirect
6. C2×C4×C11×C22⋊C4C2semidirect
7. C22×C11×#95C2semidirect
8. C11×#1445C2semidirect
9. C11×#1439C2semidirect
10. C11×#1437C2semidirect
11. C11×C4⋊#95C2semidirect
18. C2×C11×#123C4semidirect
85. C2×C11×C4⋊C4C2×C4semidirect
101. C2×C11×C22⋊C4C2×C4semidirect
117. #13996C11direct (N × H)
228. C11×C22⋊C4C22⋊C4semidirect
233. C2×#385C2×C11semidirect
234. C2×#381C2×C11semidirect
235. C2×C4×C22⋊C4C2×C11semidirect
236. C22×#95C2×C11semidirect
237. #1445C2×C11semidirect
238. #1439C2×C11semidirect
239. #1437C2×C11semidirect
240. C4⋊#95C2×C11semidirect
356. C2×C4×C11#123semidirect
363. C2×#123C4×C11semidirect
484. C2×C4⋊C4C2×C4×C11semidirect
500. C2×C22⋊C4C2×C4×C11semidirect
639. C22⋊C4C11×C22⋊C4semidirect
641. C11#13996direct (N × H)
757. C2×C4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C2×C11×#3862
C2×C11×#3852
C2×C11×#3812
C2×C4×C11×C22⋊C42
C22×C11×#952
C11×#14452
C11×#14392
C11×#14372
C11×C4⋊#952
#1399611