Finite Group Databasebeta

← #14660616

Subgroups — #14660616

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077135C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic, complemented
3C2×#10622853C211yesmaximal, characteristic, complemented
4#13071198C211yesmaximal, characteristic, complemented
5C2×#10622197C211yesmaximal, characteristic, complemented
6#13068327C211yesmaximal, characteristic, complemented
7C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C2×C11×AGL(1,ℤ/8)—22no—
11C2×C11×AGL(1,ℤ/8)—22no—
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×AGL(1,ℤ/8)—22no—
15C2×C11×AGL(1,ℤ/8)C414yescomplemented
16C22×C11×SD16—21no—
17C22×C11×D8—21no—
18C22×C11×M16C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10622860—22no—
24#10622853—22no—
25#10622853—22no—
26#10622846—22no—
27#10622845—22no—
28#10622838—21no—
29#10622834—22no—
30#10622834—22no—
31C2×#66898—22no—
32#10622828—22no—
33#10622828—21no—
34#10622828—22no—
35C2×#66896—22no—
36#10622197—22no—
37#10622193—22no—
38C25×C11—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41C2×C412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11D411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2×C412yes—
65C22×D4×C11D412yes—
66C22×D4×C11D412yes—
67C22×D4×C11D411yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C11×AGL(1,ℤ/8)—28no—
71C11×AGL(1,ℤ/8)—28no—
72C11×AGL(1,ℤ/8)—28no—
73C11×AGL(1,ℤ/8)—28no—
74C2×C11×SD16—24no—
75C2×C11×SD16—24no—
76C2×C11×SD16—24no—
77C2×C11×D8—24no—
78C2×C11×D8—24no—
79C2×C11×D8—24no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16C2×C412yes—
84C2×C11×M16D412yes—
85C2×C11×M16D412yes—
86C22×C8×C11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11D412yes—
91#66979—21no—
92#66979—21no—
93#66979—21no—
94#66979—21no—
95#66979—21no—
96#66979—21no—
97#66979—21no—
98#66979—21no—
99#66979—21no—
100#66979—21no—
101#66979—21no—
102#66979D412yes—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11D412yes—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C22×C11⋊C8D412yes—
116#66899—24no—
117#66898—28no—
118#66896—28no—
119#66896—24no—
120#11030—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—41no—
126C24×C11—41no—
127C24×C11—41no—
128C24×C11—41no—
129C24×C11—84no—
130C24×C11C2×D411yescharacteristic
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—41no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C22⋊C412yescomplemented
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—21no—
172C2×D4×C11—22no—
173C2×D4×C11—21no—
174C2×D4×C11—22no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11—41no—
180C2×D4×C11—41no—
181C2×D4×C11—41no—
182C2×D4×C11—41no—
183C2×D4×C11—41no—
184C2×D4×C11—41no—
185C2×D4×C11—41no—
186C2×D4×C11—41no—
187C2×D4×C11—41no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11C22⋊C414yes—
192C2×D4×C11C22⋊C412yescomplemented
193C22×C4×C11—21no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—41no—
197C22×C4×C11—41no—
198C22×C4×C11—41no—
199C22×C4×C11—41no—
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11#4111yescharacteristic
211C22×C4×C11#4111yescharacteristic
212C22×C4×C11#4111yescharacteristic
213C22×C4×C11#4111yescharacteristic
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—41no—
217C11×SD16—216no—
218C11×D8—216no—
219C11×M16—22no—
220C11×M16—22no—
221C11×M16—22no—
222C11×M16C22⋊C414yescomplemented
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—41no—
230C22⋊Dic11—41no—
231C22⋊Dic11—41no—
232C22⋊Dic11—88no—
233C4⋊Dic11—22no—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236C4⋊Dic11—41no—
237C4⋊Dic11—41no—
238C4⋊Dic11—41no—
239C4×Dic11—22no—
240C4×Dic11—41no—
241C4×Dic11—41no—
242C4×Dic11—41no—
243C4×Dic11—41no—
244C4×Dic11—41no—
245#4318—41no—
246#4318—41no—
247#4318—41no—
248#4318—41no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8—22no—
251C2×C11⋊C8—22no—
252C22×AGL(1,ℤ/8)D1111yescharacteristic
253#2896—111no—
254C2×#418—111no—
255C2×#410—111no—
256#2309—111no—
257C2×#344—111no—
258#1733—111no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11—42no—
262C23×C11—48no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—41no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—82no—
272C23×C11—84no—
273C23×C11—84no—
274C23×C11—84no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11C4×D411yescharacteristic
279C23×C11#12011yescharacteristic
280C23×C11#12011yescharacteristic
281C23×C11#12111yescharacteristic
282C23×C11#12111yescharacteristic
283C23×C11#12111yescharacteristic
284C23×C11#12711yescharacteristic
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—41no—
288Q8×C11—41no—
289D4×C11—22no—
290D4×C11—24no—
291D4×C11—24no—
292D4×C11—22no—
293D4×C11—42no—
294D4×C11—42no—
295D4×C11—42no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—41no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—41no—
305C2×C4×C11—22no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C2×C22⋊C411yescharacteristic
314C2×C4×C11C2×C22⋊C411yescharacteristic
315C2×C4×C11C4×D411yescharacteristic
316C2×C4×C11C4×D411yescharacteristic
317C2×C4×C11C4×D411yescharacteristic
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12011yescharacteristic
321C2×C4×C11#12011yescharacteristic
322C2×C4×C11#12011yescharacteristic
323C2×C4×C11#12011yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12111yescharacteristic
331C2×C4×C11#12111yescharacteristic
332C2×C4×C11#12111yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12311yescharacteristic
336C2×C4×C11#12311yescharacteristic
337C2×C4×C11#12411yescharacteristic
338C2×C4×C11#12411yescharacteristic
339C2×C4×C11#12711yescharacteristic
340C2×Dic11—44no—
341C2×Dic11—44no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—82no—
346C8×C11—24no—
347C11⋊C8—42no—
348C22×#41C2×D1111yescharacteristic
349C23×D4C2×D1111yescharacteristic
350C2×AGL(1,ℤ/8)—22no—
351C2×AGL(1,ℤ/8)—22no—
352C2×AGL(1,ℤ/8)—22no—
353C2×AGL(1,ℤ/8)—22no—
354C2×AGL(1,ℤ/8)—22no—
355C2×AGL(1,ℤ/8)Dic1114yescomplemented
356C22×SD16—21no—
357C22×D8—21no—
358C22×M16—111no—
359C22×M16C2×D1111yescharacteristic
360C2×#117—111no—
361C2×#117—111no—
362C2×#117—111no—
363#419—221no—
364#418—222no—
365#418—222no—
366#418—221no—
367#417—222no—
368#416—222no—
369C2×#102—222no—
370#410—222no—
371#410—222no—
372C2×#99—222no—
373#390—222no—
374#390—222no—
375#379—222no—
376#344—222no—
377#339—222no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—48no—
386C22×C11—42no—
387C22×C11—44no—
388C22×C11—82no—
389C22×C11—84no—
390C22×C11—82no—
391C22×C11—84no—
392C22×C11—84no—
393C22×C11—84no—
394C22×C11—84no—
395C22×C11—84no—
396C22×C11—82no—
397C22×C11#38611yescharacteristic
398C22×C11#38611yescharacteristic
399C22×C11#39011yescharacteristic
400C22×C11#39211yescharacteristic
401C22×C11#39211yescharacteristic
402C22×C11#39211yescharacteristic
403C22×C11#39411yescharacteristic
404C4×C11—42no—
405C4×C11#37911yescharacteristic
406C4×C11#38611yescharacteristic
407C4×C11#38611yescharacteristic
408C4×C11#39011yescharacteristic
409C4×C11#39211yescharacteristic
410C4×C11#39411yescharacteristic
411C4×C11#39411yescharacteristic
412C4×C11#39411yescharacteristic
413Dic11—82no—
414Dic11—82no—
415Dic11—82no—
416C25—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41C2×Dic1112yes—
428C2×#41C22⋊D1112yes—
429C22×Q8C22⋊D1111yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C2×Dic1112yes—
443C22×D4C22⋊D1112yes—
444C22×D4C22⋊D1112yes—
445C22×D4C22⋊D1111yescharacteristic
446C23×C4—21no—
447C23×C4C22×D1111yescharacteristic
448AGL(1,ℤ/8)—28no—
449AGL(1,ℤ/8)—28no—
450AGL(1,ℤ/8)—28no—
451AGL(1,ℤ/8)—28no—
452C2×SD16—24no—
453C2×SD16—24no—
454C2×SD16—24no—
455C2×D8—24no—
456C2×D8—24no—
457C2×D8—24no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—221no—
462C2×M16—221no—
463C2×M16—221no—
464C2×M16—221no—
465C2×M16—221no—
466C2×M16—221no—
467C2×M16C2×Dic1112yes—
468C2×M16C22⋊D1112yes—
469C2×M16C22⋊D1112yes—
470C22×C8—21no—
471C22×C8—112no—
472#117—112no—
473#117—221no—
474#117—221no—
475#117—221no—
476#117—221no—
477#117—221no—
478#117—221no—
479#117—221no—
480#117—221no—
481#117—221no—
482#117—221no—
483#117—221no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—228no—
491C2×C42—221no—
492C2×C42—221no—
493C2×C42—221no—
494#103—224no—
495#102—228no—
496#102—224no—
497#99—228no—
498C2×C11—21no—
499C2×C11—21no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—21no—
503C2×C11—21no—
504C2×C11—84no—
505C2×C11—82no—
506C2×C11#143811yescharacteristic
507C2×C11#200812yes—
508C24—22no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—41no—
513C24—41no—
514C24—41no—
515C24—41no—
516C24—84no—
517C24D4×D1111yescharacteristic
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8C22⋊Dic1112yescomplemented
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4C22⋊Dic1114yes—
579C2×D4C22⋊Dic1112yescomplemented
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—441no—
590C22×C4D4×D1111yescharacteristic
591C22×C4D4×D1111yescharacteristic
592C22×C4D4×D1111yescharacteristic
593C22×C4#434111yescharacteristic
594C22×C4#434111yescharacteristic
595C22×C4#434111yescharacteristic
596C22×C4#434111yescharacteristic
597C22×C4C22×Dic1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604SD16—216no—
605D8—216no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—441no—
610M16—441no—
611M16—441no—
612M16—441no—
613M16C22⋊Dic1114yescomplemented
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8—222no—
620C4⋊C4—222no—
621C4⋊C4—222no—
622C4⋊C4—222no—
623C4⋊C4—441no—
624C4⋊C4—441no—
625C4⋊C4—441no—
626C22⋊C4—222no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—441no—
630C22⋊C4—441no—
631C22⋊C4—441no—
632C22⋊C4—888no—
633C42—222no—
634C42—441no—
635C42—441no—
636C42—441no—
637C42—441no—
638C42—441no—
639C11#1103011yescharacteristic, complemented, Sylow
640C23—24no—
641C23—22no—
642C23—42no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—42no—
652C23—82no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23D4×Dic1111yescharacteristic
660C23#6699011yescharacteristic
661C23#6699011yescharacteristic
662C23#6699111yescharacteristic
663C23#6699211yescharacteristic
664C23#6699211yescharacteristic
665C23#6699311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—24no—
671D4—22no—
672D4—22no—
673D4—24no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—41no—
684D4—42no—
685D4—41no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—444no—
694C2×C4—444no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—882no—
699C2×C4D4×Dic1111yescharacteristic
700C2×C4D4×Dic1111yescharacteristic
701C2×C4D4×Dic1111yescharacteristic
702C2×C4#6698811yescharacteristic
703C2×C4#6698811yescharacteristic
704C2×C4#6698811yescharacteristic
705C2×C4#6698811yescharacteristic
706C2×C4#6698911yescharacteristic
707C2×C4#6698911yescharacteristic
708C2×C4#6699011yescharacteristic
709C2×C4#6699011yescharacteristic
710C2×C4#6699111yescharacteristic
711C2×C4#6699111yescharacteristic
712C2×C4#6699111yescharacteristic
713C2×C4#6699211yescharacteristic
714C2×C4#6699211yescharacteristic
715C2×C4#6699211yescharacteristic
716C2×C4#6699211yescharacteristic
717C2×C4#6699211yescharacteristic
718C2×C4#6699211yescharacteristic
719C2×C4#6699311yescharacteristic
720C2×C4C2×C22⋊Dic1111yescharacteristic
721C2×C4C2×C22⋊Dic1111yescharacteristic
722C2×C4C2×C22⋊Dic1111yescharacteristic
723C2×C4#6700611yescharacteristic
724C2×C4#6700611yescharacteristic
725C2×C4#6700611yescharacteristic
726C2×C4#6700611yescharacteristic
727C8—24no—
728C8—442no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—48no—
737C22—42no—
738C22—44no—
739C22—82no—
740C22—84no—
741C22—84no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—82no—
746C22—84no—
747C22—82no—
748C22#1062283311yescharacteristic
749C22#1062283311yescharacteristic
750C22#1062283411yescharacteristic
751C22#1062283511yescharacteristic
752C22#1062283611yescharacteristic
753C22#1062283611yescharacteristic
754C22#1062283611yescharacteristic
755C4—42no—
756C4—882no—
757C4—882no—
758C4—882no—
759C4#1062283311yescharacteristic
760C4#1062283311yescharacteristic
761C4#1062283411yescharacteristic
762C4#1062283511yescharacteristic
763C4#1062283511yescharacteristic
764C4#1062283511yescharacteristic
765C4#1062283611yescharacteristic
766C4#1062286011yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—84no—
774C2—82no—
775C2#1306685711yescharacteristic
776C2#1306966712yes—
subgroupG/H
centerC22#10622836
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC22×C11#392
cosocleC23×C4×C11C23
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#11030
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13077135C2semidirect
2. C2×#10622828C2semidirect
3. C2×#10622853C2semidirect
4. #13071198C2semidirect
5. C2×#10622197C2semidirect
6. #13068327C2semidirect
15. C2×C11×AGL(1,ℤ/8)C4semidirect
152. C2×Q8×C11C22⋊C4semidirect
192. C2×D4×C11C22⋊C4semidirect
222. C11×M16C22⋊C4semidirect
355. C2×AGL(1,ℤ/8)Dic11semidirect
539. C2×Q8C22⋊Dic11semidirect
579. C2×D4C22⋊Dic11semidirect
613. M16C22⋊Dic11semidirect
639. C11#11030semidirect

Maximal subgroups

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

subgroupindex
#130771352
C2×#106228282
C2×#106228532
#130711982
C2×#106221972
#130683272
C22×C11×AGL(1,ℤ/8)2
#1103011