Finite Group Databasebeta

← #14676897

Subgroups — #14676897

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×#66988C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622559C211yesmaximal, characteristic, complemented
4C2×#10622556C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066882C212yesmaximal, complemented
8#13066859C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10Dic11⋊#95C212yesmaximal, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66988—24no—
24C2×#66988—24no—
25C2×#66988C418yescomplemented
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C11×#386—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32#10622833—24no—
33C4×C22⋊Dic11—24no—
34C2×C11⋊#95—24no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622559—24no—
43#10622556—24no—
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—24no—
56C23×C4×C11—42no—
57C23×C4×C11D414yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—24no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—42no—
74C23×Dic11C2×C414yes—
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2312yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—42no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—42no—
93C2×C22⋊Dic11C2×C414yes—
94C2×C22⋊Dic11C2×C418yescomplemented
95C2×C22⋊Dic11D414yes—
96C2×C22⋊Dic11D414yes—
97C2×C22⋊Dic11D414yes—
98#66988—232no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—42no—
104C2×Dic11⋊C4C2×C418yescomplemented
105C2×C4×Dic11—24no—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—42no—
108C11×#95—22no—
109C11×#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117#13996—111nomaximal, 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—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
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—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—28no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—44no—
174C22×C4×C11—48no—
175C22×C4×C11—48no—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11#4114yes—
180C22×Dic11—28no—
181C22×Dic11—28no—
182C22×Dic11—28no—
183C22×Dic11—28no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—48no—
207C22×Dic11—48no—
208C22×Dic11—44no—
209C22×Dic11—44no—
210C22×Dic11—44no—
211C22×Dic11—44no—
212C22×Dic11—44no—
213C22×Dic11—44no—
214C22×Dic11C22×C414yes—
215C22×Dic11C22×C414yes—
216C22×Dic11C2×D414yes—
217C22×Dic11C2×D414yes—
218C22×Dic11C2×D414yes—
219C22×Dic11#4114yes—
220C11×C22⋊C4—44no—
221C11×C22⋊C4—44no—
222C11×C22⋊C4—44no—
223C22⋊Dic11—216no—
224C22⋊Dic11—28no—
225C22⋊Dic11—48no—
226C22⋊Dic11C22⋊C4116yescomplemented
227Dic11⋊C4—216no—
228Dic11⋊C4—48no—
229C4×Dic11—48no—
230C22×#123—111no—
231C2×#386—111no—
232C2×#386D1111yescharacteristic
233C2×#385—111no—
234C2×#381—111no—
235C2×C4×C22⋊C4—111no—
236C22×#95—111no—
237#1445—112no—
238#1439—112no—
239#1437—112no—
240C4⋊#95—112no—
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—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
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—416no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11#12314yescomplemented
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—416no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—416no—
356C2×Dic11C2×C22⋊C418yes—
357C23×D4C2×D1111yescharacteristic
358C24×C4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×#123—118no—
362C2×#123—224no—
363C2×#123—224no—
364C22×C4⋊C4—112no—
365C22×C4⋊C4—112no—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—112no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4C2×D1111yescharacteristic
372C22×C22⋊C4C2×D1111yescharacteristic
373C22×C42—112no—
374#386—24no—
375#386—224no—
376#385—224no—
377#381—224no—
378C4×C22⋊C4—224no—
379C2×#95—112no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—224no—
387C2×#95C2×D1111yescharacteristic
388C2×#95C2×D1111yescharacteristic
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—24no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—81no—
438C4×C11—81no—
439Dic11—28no—
440Dic11—44no—
441Dic11—44no—
442Dic11—44no—
443C25C22×D1111yescharacteristic
444C25C22×D1111yescharacteristic
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4C4×D1114yes—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4—42no—
456C23×C4—112no—
457C23×C4—114no—
458C23×C4—112no—
459C23×C4—112no—
460C23×C4—112no—
461C23×C4—224no—
462C23×C4—222no—
463C23×C4—222no—
464C23×C4—222no—
465C23×C4—222no—
466C23×C4—222no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—442no—
472C23×C4C22⋊D1114yes—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478#123—2232no—
479C2×C4⋊C4—118no—
480C2×C4⋊C4—224no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—224no—
483C2×C4⋊C4—224no—
484C2×C4⋊C4—442no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—224no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—442no—
504C2×C42—224no—
505C2×C42—224no—
506C2×C42—442no—
507#95—22no—
508#95—22no—
509#95—224no—
510#95—224no—
511#95—224no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—224no—
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—21no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24C2×C4×D1112yes—
544C24C2×C4×D1112yes—
545C24#433912yes—
546C24D4×D1112yes—
547C24D4×D1112yes—
548C24D4×D1112yes—
549C24#434112yes—
550C24C2×C22⋊D1112yes—
551C24C23×D1111yescharacteristic
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—21no—
561C22×C4—22no—
562C22×C4—28no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—28no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—114no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—228no—
598C22×C4—228no—
599C22×C4—228no—
600C22×C4—228no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—448no—
620C22×C4—448no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4C2×C4×D1112yes—
628C22×C4#434114yes—
629C22×C4C2×C22⋊D1112yes—
630C22×C4C2×C22⋊D1112yes—
631C4⋊C4—2216no—
632C4⋊C4—448no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—1116no—
637C22⋊C4—2216no—
638C22⋊C4—228no—
639C22⋊C4—448no—
640C42—448no—
641C11#1399611yescharacteristic, complemented, Sylow
642C23—24no—
643C23—24no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
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—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C22⋊C4×D1114yes—
682C23(C22⋊D11)⋊C414yes—
683C23#6693714yes—
684C23#6693814yes—
685C23C4×C22⋊D1114yes—
686C23#6699214yes—
687C23#6699314yes—
688C23C22×C4×D1111yescharacteristic
689C23C2×#433911yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×D4×D1111yescharacteristic
692C23C2×D4×D1111yescharacteristic
693C23C2×#434111yescharacteristic
694C23C2×#434112yes—
695C23#6703712yes—
696C23#41×D1112yes—
697C23#6704312yes—
698C23C22×C22⋊D1111yescharacteristic
699D4—416no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—118no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—4416no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—4416no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4#6698814yescomplemented
758C22—24no—
759C22—28no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—42no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—82no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#1062257018yes—
780C22C2×C22⋊C4×D1111yescharacteristic
781C22C2×(C22⋊D11)⋊C411yescharacteristic
782C22C2×#6693711yescharacteristic
783C22C2×#6693811yescharacteristic
784C22C4×#434112yes—
785C22#1062306912yes—
786C22#1062307712yes—
787C22#1062309512yes—
788C22#1062311812yes—
789C22#1062312212yes—
790C22#1062314112yes—
791C22#1062314112yes—
792C22#1062314212yes—
793C22#1062314212yes—
794C22#1062318112yes—
795C22#1062318612yes—
796C22C2×C4×C22⋊D1111yescharacteristic
797C22C2×#6698811yescharacteristic
798C22C2×#6699211yescharacteristic
799C22C2×#6699311yescharacteristic
800C22#1062333511yescharacteristic
801C22#1062335611yescharacteristic
802C22#1062335911yescharacteristic
803C4—24no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4—228no—
809C4—444no—
810C4—444no—
811C4—444no—
812C2—28no—
813C2—82no—
814C2C2×#1062257011yescharacteristic
815C2C4×#6698811yescharacteristic
816C2#1307128111yescharacteristic
817C2#1307144212yes—
818C2#1307161412yes—
819C2#1307201311yescharacteristic
820C2#1307202411yescharacteristic
821C2#1307216912yes—
822C2#1307294412yes—
823C2#1307308811yescharacteristic
824C2#1307354811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#13996
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#10622559C2semidirect
4. C2×#10622556C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066882C2semidirect
8. #13066859C2semidirect
9. #13066853C2semidirect
10. Dic11⋊#95C2semidirect
25. C2×#66988C4semidirect
94. C2×C22⋊Dic11C2×C4semidirect
104. C2×Dic11⋊C4C2×C4semidirect
226. C22⋊Dic11C22⋊C4semidirect
326. C2×C4×C11#123semidirect
641. C11#13996semidirect
757. C2×C4#66988semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106228332
C2×#106225592
C2×#106225562
C2×C4×C22⋊Dic112
C22×C11⋊#952
#130668822
#130668592
#130668532
Dic11⋊#952
C2×C11×#3862
#1399611