Finite Group Databasebeta

← #356095

Subgroups — #356095

Order 512.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#417C211yesmaximal, characteristic
2C2×#2339C211yesmaximal, characteristic
3C2×#1788C211yesmaximal, characteristic
4C2×#1762C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6C2×#1753C211yesmaximal, characteristic, complemented
7C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
8#10932C211yesmaximal, characteristic, complemented
9#10932C211yesmaximal, characteristic, complemented
10#10928C211yesmaximal, characteristic, complemented
11#10926C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10722C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C2×#417—24no—
22C2×#417—24no—
23C2×#417C418yescomplemented
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35#2339—24no—
36#2339C418yescomplemented
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#386—21no—
40C2×#386—21no—
41C2×#381—21no—
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4—21no—
47C2×C4×C22⋊C4C2211yescharacteristic
48C22×#95—21no—
49#1788C418yescomplemented
50#1762—24no—
51C4×#102—24no—
52#1753—24no—
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63#1436—21no—
64#1436—21no—
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67C22⋊#95—21no—
68C22×#41—22no—
69C22×#41—22no—
70C22×#41—22no—
71C22×#41—22no—
72C22×#41—22no—
73C22×#41—22no—
74C22×#41—22no—
75C22×#41—41no—
76C22×#41—41no—
77C22×#41—41no—
78C22×#41—41no—
79C22×#41C2×C414yes—
80C22×#41C2×C414yes—
81C22×#41C2×C414yes—
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4—21no—
87C24×C4—21no—
88C24×C4—21no—
89C24×C4C2311yescharacteristic
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—22no—
93C22×M16—22no—
94C22×M16—41no—
95C22×M16—41no—
96C22×M16C2×C414yescomplemented
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C2×C4×D4—22no—
102C2×C4×D4—22no—
103C2×C4×D4—22no—
104C2×C4×D4—22no—
105C2×C4×D4—22no—
106C2×C4×D4—22no—
107C2×C4×D4—41no—
108C2×C4×D4—41no—
109C2×C4×D4—41no—
110C2×C4×D4—41no—
111C2×C4×D4C2×C414yescomplemented
112C2×C4×D4C2×C414yescomplemented
113C22×C4⋊C4—22no—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—22no—
117C22×C4⋊C4—41no—
118C22×C4⋊C4—41no—
119C22×C4⋊C4C2×C414yescomplemented
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4D411yescharacteristic
131C22×C22⋊C4D411yescharacteristic
132C22×C42—21no—
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#417—232no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—41no—
142C2×#103—41no—
143C2×#103—41no—
144C2×#103—41no—
145C2×#103C2×C414yescomplemented
146C2×#103C2×C414yescomplemented
147C2×#103C2×C414yescomplemented
148C2×#103C2×C414yescomplemented
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—22no—
153C2×#102—22no—
154C2×#102—22no—
155C2×#102C2×C414yes—
156C2×#102C2×C414yes—
157C2×#102C2×C414yescomplemented
158C2×#102C2×C414yescomplemented
159C2×#102D414yes—
160C2×#102D414yes—
161C2×C22⋊C8—22no—
162C2×C22⋊C8—22no—
163C2×C22⋊C8C2×C414yescomplemented
164C2×#97—22no—
165C2×#97—22no—
166C2×#97—41no—
167C2×C4×C8—22no—
168C2×C4×C8—22no—
169C2×C4×C8—41no—
170#391—22no—
171#391—22no—
172#391C2×C414yescomplemented
173#391C2×C414yescomplemented
174#386—28no—
175#386—28no—
176#381—28no—
177#380—22no—
178#380—22no—
179#380C2×C414yes—
180#380C2×C414yescomplemented
181C4×C4⋊C4—22no—
182C4×C4⋊C4—22no—
183C4×C4⋊C4—41no—
184C4×C4⋊C4—41no—
185C4×C22⋊C4—44no—
186C4×C22⋊C4C2×C414yes—
187C4×C22⋊C4D414yes—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—28no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95D411yescharacteristic
202C2×#95D411yescharacteristic
203#340—22no—
204#340—22no—
205#340—22no—
206#340—22no—
207#340—41no—
208#340—41no—
209#340—41no—
210#340—41no—
211#336—22no—
212#336—22no—
213C25—21no—
214C25C2×D411yescharacteristic
215C2×#41—28no—
216C2×#41—28no—
217C2×#41—28no—
218C2×#41—28no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—28no—
223C2×#41—28no—
224C2×#41—44no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—44no—
230C2×#41—44no—
231C2×#41—44no—
232C2×#41—44no—
233C2×#41—44no—
234C2×#41—44no—
235C2×#41—44no—
236C2×#41—44no—
237C2×#41—44no—
238C2×#41—44no—
239C2×#41—44no—
240C2×#41—44no—
241C2×#41—44no—
242C2×#41C42116yescomplemented
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8C22×C412yes—
255C22×Q8C22×C412yes—
256C22×Q8C22×C412yes—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4C22×C412yes—
272C22×D4C22×C412yes—
273C22×D4C22×C412yes—
274C22×D4C2×D412yes—
275C22×D4C2×D412yes—
276C22×D4#4112yes—
277C22×D4#4112yes—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4—81no—
316C23×C4—81no—
317C23×C4—81no—
318C23×C4—81no—
319C23×C4—81no—
320C23×C4—81no—
321C23×C4C22×C412yes—
322C23×C4C22×C412yes—
323C23×C4C22×C412yes—
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D412yes—
330C23×C4#4112yes—
331C23×C4#4112yes—
332C23×C4C2411yescharacteristic
333C2×M16—28no—
334C2×M16—28no—
335C2×M16—44no—
336C2×M16—44no—
337C2×M16—44no—
338C2×M16—44no—
339C2×M16—44no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8C22×C412yes—
363C22×C8C22×C412yes—
364C22×C8C22×C412yes—
365C22×C8C22×C412yes—
366C22×C8C2×D412yes—
367C22×C8C2×D412yes—
368C4×D4—28no—
369C4×D4—28no—
370C4×D4—44no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—44no—
374C4×D4—44no—
375C4×D4—44no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4C22×C412yes—
412C2×C4⋊C4C22×C412yes—
413C2×C4⋊C4C22×C412yes—
414C2×C4⋊C4C22×C412yes—
415C2×C4⋊C4C22×C412yes—
416C2×C4⋊C4C22×C412yes—
417C2×C4⋊C4C2×D412yes—
418C2×C4⋊C4C2×D412yes—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—41no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—81no—
434C2×C22⋊C4—81no—
435C2×C22⋊C4C22⋊C414yes—
436C2×C22⋊C4C22⋊C414yes—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42—42no—
448C2×C42—42no—
449C2×C42—81no—
450C2×C42—81no—
451C2×C42C22×C412yes—
452C2×C42C22×C412yes—
453C2×C42C2×D412yes—
454C2×C42C2×D412yes—
455#103—28no—
456#103—28no—
457#103—44no—
458#103—44no—
459#102—28no—
460#102—28no—
461#102—28no—
462#102C22⋊C4116yescomplemented
463C22⋊C8—28no—
464#97—44no—
465C4×C8—44no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—81no—
477#95—81no—
478#95C22⋊C414yes—
479#95C22⋊C414yes—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—41no—
500C24—41no—
501C24—41no—
502C24—41no—
503C24—41no—
504C24—41no—
505C24—41no—
506C24—41no—
507C24C2×C22⋊C412yes—
508C24C4×D412yes—
509C24C4×D412yes—
510C24C22×D411yescharacteristic
511#41—232no—
512#41—416no—
513#41—416no—
514#41—416no—
515#41—416no—
516#41—416no—
517#41—416no—
518#41—416no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8C2×C4214yes—
547C2×D4—216no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4C2×C4214yes—
576C2×D4C2×C22⋊C414yes—
577C2×D4#11714yes—
578C2×D4C4×D414yes—
579C2×D4C4×D414yes—
580C2×D4C4×D414yes—
581C2×D4C4×D414yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
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—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—216no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—48no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—48no—
648C22×C4—48no—
649C22×C4—48no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—48no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—48no—
694C22×C4—84no—
695C22×C4—84no—
696C22×C4—84no—
697C22×C4—84no—
698C22×C4—84no—
699C22×C4—84no—
700C22×C4—84no—
701C22×C4—84no—
702C22×C4—84no—
703C22×C4—84no—
704C22×C4—84no—
705C22×C4—84no—
706C22×C4—84no—
707C22×C4—84no—
708C22×C4—84no—
709C22×C4C2×C4214yes—
710C22×C4C2×C22⋊C412yes—
711C22×C4C2×C22⋊C412yes—
712C22×C4C2×C22⋊C412yes—
713C22×C4C2×C22⋊C412yes—
714C22×C4C2×C22⋊C412yes—
715C22×C4#11714yes—
716C22×C4C4×D414yes—
717C22×C4C4×D414yes—
718C22×C4C4×D412yes—
719C22×C4C4×D412yes—
720C22×C4AGL(1,ℤ/8)12yes—
721C22×C4#13712yes—
722C22×C4C23×C411yescharacteristic
723C22×C4C23×C411yescharacteristic
724C22×C4C23×C411yescharacteristic
725C22×C4C22×D411yescharacteristic
726C22×C4C22×D411yescharacteristic
727C22×C4C22×D411yescharacteristic
728C22×C4C2×#4111yescharacteristic
729C22×C4C2×#4111yescharacteristic
730C22×C4C2×#4111yescharacteristic
731C22×C4C2×#4111yescharacteristic
732C22×C4H(5,𝔽2)11yescharacteristic
733C22×C4H(5,𝔽2)11yescharacteristic
734C22×C4H(5,𝔽2)11yescharacteristic
735C22×C4H(5,𝔽2)11yescharacteristic
736M16—416no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—22no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—22no—
746C2×C8—22no—
747C2×C8—22no—
748C2×C8—22no—
749C2×C8—22no—
750C2×C8—22no—
751C2×C8—22no—
752C2×C8—41no—
753C2×C8—41no—
754C2×C8—41no—
755C2×C8—41no—
756C2×C8—41no—
757C2×C8—41no—
758C2×C8—41no—
759C2×C8—41no—
760C2×C8—41no—
761C2×C8—41no—
762C2×C8—41no—
763C2×C8—41no—
764C2×C8C2×C22⋊C414yes—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—22no—
775C4⋊C4—22no—
776C4⋊C4—22no—
777C4⋊C4—22no—
778C4⋊C4—48no—
779C4⋊C4—41no—
780C4⋊C4—41no—
781C4⋊C4—41no—
782C4⋊C4—41no—
783C4⋊C4—41no—
784C4⋊C4—41no—
785C4⋊C4—41no—
786C4⋊C4—41no—
787C4⋊C4—41no—
788C4⋊C4—41no—
789C4⋊C4C2×C22⋊C414yes—
790C22⋊C4—28no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—84no—
796C42—22no—
797C42—22no—
798C42—22no—
799C42—22no—
800C42—22no—
801C42—22no—
802C42—22no—
803C42—22no—
804C42—84no—
805C42—84no—
806C23—24no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—24no—
812C23—22no—
813C23—24no—
814C23—22no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—41no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—41no—
848C23—42no—
849C23—42no—
850C23—41no—
851C23—41no—
852C23—42no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—41no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—42no—
863C23—42no—
864C23—41no—
865C23—41no—
866C23—42no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23C4×C22⋊C414yes—
876C23C22×C22⋊C411yescharacteristic
877C23C2×C4×D411yescharacteristic
878C23C2×C4×D411yescharacteristic
879C23D4211yescharacteristic
880C23D4211yescharacteristic
881C23#54611yescharacteristic
882C23#54611yescharacteristic
883C23C2×AGL(1,ℤ/8)11yescharacteristic
884C23C2×#13711yescharacteristic
885C23#57511yescharacteristic
886C23#57511yescharacteristic
887C23#57611yescharacteristic
888C23#57711yescharacteristic
889C23#57711yescharacteristic
890C23#57811yescharacteristic
891Q8—24no—
892Q8—24no—
893Q8—42no—
894Q8—42no—
895Q8—42no—
896Q8—42no—
897Q8—42no—
898Q8—42no—
899D4—24no—
900D4—24no—
901D4—24no—
902D4—24no—
903D4—24no—
904D4—24no—
905D4—24no—
906D4—432no—
907D4C4×C22⋊C418yescomplemented
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—432no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—816no—
980C2×C4—816no—
981C2×C4—816no—
982C2×C4—81no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—81no—
992C2×C4—81no—
993C2×C4—81no—
994C2×C4—81no—
995C2×C4—81no—
996C2×C4—81no—
997C2×C4—81no—
998C2×C4—81no—
999C2×C4—81no—
1000C2×C4—81no—
1001C2×C4—81no—
1002C2×C4C4×C22⋊C414yes—
1003C2×C4#41714yescomplemented
1004C2×C4C22×C4211yescharacteristic
1005C2×C4C22×C22⋊C411yescharacteristic
1006C2×C4C2×#11711yescharacteristic
1007C2×C4C2×#11711yescharacteristic
1008C2×C4C2×C4×D411yescharacteristic
1009C2×C4C2×C4×D411yescharacteristic
1010C2×C4C2×C4×D411yescharacteristic
1011C2×C4C2×C4×D411yescharacteristic
1012C2×C4C2×C4×D411yescharacteristic
1013C2×C4C2×C4×D411yescharacteristic
1014C2×C4#51811yescharacteristic
1015C2×C4#51811yescharacteristic
1016C2×C4#51811yescharacteristic
1017C2×C4#51811yescharacteristic
1018C2×C4#51811yescharacteristic
1019C2×C4#51811yescharacteristic
1020C2×C4D4211yescharacteristic
1021C2×C4D4211yescharacteristic
1022C2×C4#54611yescharacteristic
1023C2×C4#54611yescharacteristic
1024C2×C4#54611yescharacteristic
1025C2×C4#54611yescharacteristic
1026C2×C4#54611yescharacteristic
1027C2×C4#54611yescharacteristic
1028C2×C4#55111yescharacteristic
1029C2×C4#55111yescharacteristic
1030C2×C4#55111yescharacteristic
1031C2×C4#55111yescharacteristic
1032C8—24no—
1033C8—42no—
1034C8—42no—
1035C8—42no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—28no—
1040C22—42no—
1041C22—44no—
1042C22—42no—
1043C22—44no—
1044C22—42no—
1045C22—44no—
1046C22—42no—
1047C22—44no—
1048C22—42no—
1049C22—44no—
1050C22—42no—
1051C22—44no—
1052C22—44no—
1053C22—42no—
1054C22—42no—
1055C22—44no—
1056C22—44no—
1057C22—42no—
1058C22—42no—
1059C22—44no—
1060C22—42no—
1061C22—44no—
1062C22—42no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22C2×C4×C22⋊C411yescharacteristic
1067C22D4×C22⋊C411yescharacteristic
1068C22D4×C22⋊C411yescharacteristic
1069C22D4×C22⋊C411yescharacteristic
1070C22#234211yescharacteristic
1071C22#235811yescharacteristic
1072C22#235811yescharacteristic
1073C22C2×#41711yescharacteristic
1074C22#289611yescharacteristic
1075C22#289711yescharacteristic
1076C22#289811yescharacteristic
1077C22C4×AGL(1,ℤ/8)11yescharacteristic
1078C22C4×AGL(1,ℤ/8)11yescharacteristic
1079C22C4×#13711yescharacteristic
1080C22C4×#13711yescharacteristic
1081C22#294611yescharacteristic
1082C22#294711yescharacteristic
1083C22#295111yescharacteristic
1084C22#295211yescharacteristic
1085C22#326411yescharacteristic
1086C22#326611yescharacteristic
1087C22#326711yescharacteristic
1088C22#326911yescharacteristic
1089C22#327211yescharacteristic
1090C22#327311yescharacteristic
1091C22#327511yescharacteristic
1092C22#327611yescharacteristic
1093C22#330611yescharacteristic
1094C22#330711yescharacteristic
1095C22#331411yescharacteristic
1096C22#331511yescharacteristic
1097C22#332211yescharacteristic
1098C22#332311yescharacteristic
1099C22#333011yescharacteristic
1100C22#333111yescharacteristic
1101C4—24no—
1102C4—24no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4—82no—
1109C4—82no—
1110C4—82no—
1111C4—82no—
1112C4—82no—
1113C4C2×C4×C22⋊C411yescharacteristic
1114C4#227311yescharacteristic
1115C4D4×C22⋊C411yescharacteristic
1116C4#234211yescharacteristic
1117C4#234211yescharacteristic
1118C4#234211yescharacteristic
1119C4#235811yescharacteristic
1120C4#235811yescharacteristic
1121C2—44no—
1122C2—48no—
1123C2C22⋊C4211yescharacteristic
1124C2C4×#41711yescharacteristic
1125C2#2041511yescharacteristic
1126C2#2241911yescharacteristic
1127C2#2242011yescharacteristic
1128C2#2242711yescharacteristic
1129C2#2243111yescharacteristic
1130C2#2244211yescharacteristic
1131C2#2244411yescharacteristic
1132C2#2257811yescharacteristic
1133C2#2258211yescharacteristic
1134C2#2286211yescharacteristic
1135C2#2286611yescharacteristic
1136C2#2287811yescharacteristic
1137C2#2288211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1762C2semidirect
5. C2×C4×#102C2semidirect
6. C2×#1753C2semidirect
7. C22⋊C4×C4⋊C4C2semidirect
8. #10932C2semidirect
9. #10932C2semidirect
10. #10928C2semidirect
11. #10926C2semidirect
12. #10788C2semidirect
13. #10788C2semidirect
14. #10730C2semidirect
15. #10722C2semidirect
23. C2×#417C4semidirect
36. #2339C4semidirect
49. #1788C4semidirect
96. C22×M16C2×C4semidirect
111. C2×C4×D4C2×C4semidirect
112. C2×C4×D4C2×C4semidirect
119. C22×C4⋊C4C2×C4semidirect
145. C2×#103C2×C4semidirect
146. C2×#103C2×C4semidirect
147. C2×#103C2×C4semidirect
148. C2×#103C2×C4semidirect
157. C2×#102C2×C4semidirect
158. C2×#102C2×C4semidirect
163. C2×C22⋊C8C2×C4semidirect
172. #391C2×C4semidirect
173. #391C2×C4semidirect
180. #380C2×C4semidirect
242. C2×#41C42semidirect
462. #102C22⋊C4semidirect
907. D4C4×C22⋊C4semidirect
1003. C2×C4#417semidirect

Maximal subgroups

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

subgroupindex
C22×#4172
C2×#23392
C2×#17882
C2×#17622
C2×C4×#1022
C2×#17532
C22⋊C4×C4⋊C42
#109322
#109282
#109262
#107882
#107302
#107222