Finite Group Databasebeta

← #220122

Subgroups — #220122

Order 512.

1341 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#22469C211yesmaximal, characteristic, complemented
3D4×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×#1580C211yesmaximal, characteristic, complemented
5C2×C8×D8C211yesmaximal, characteristic, complemented
6#9660C211yesmaximal, characteristic, complemented
7#9655C211yesmaximal, characteristic, complemented
8#8947C211yesmaximal, characteristic, complemented
9#8947C211yesmaximal, characteristic, complemented
10#8945C211yesmaximal, characteristic, complemented
11#8945C211yesmaximal, characteristic, complemented
12#8597C211yesmaximal, characteristic, complemented
13#8312C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15#8146C211yesmaximal, characteristic, complemented
16C22×AGL(1,ℤ/8)C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C4×AGL(1,ℤ/8)—24no—
20C4×AGL(1,ℤ/8)—24no—
21C2×#442C411yescharacteristic
22C2×#442C411yescharacteristic
23C2×#440C411yescharacteristic
24C2×#440C411yescharacteristic
25C2×C4×SD16C2211yescharacteristic
26C2×C4×SD16C2211yescharacteristic
27C2×C4×D8C2211yescharacteristic
28C2×C4×D8C2211yescharacteristic
29C2×C8×D4C2211yescharacteristic
30C2×C8×D4C2211yescharacteristic
31C2×C8×D4C2211yescharacteristic, complemented
32C2×C8×D4C2211yescharacteristic, complemented
33C2×#428C411yescharacteristic
34C2×#417C411yescharacteristic
35C2×#418C411yescharacteristic
36C22×C22⋊C8—21no—
37C2×C4×M16C2211yescharacteristic
38#1984C2211yescharacteristic, complemented
39#1984C2211yescharacteristic, complemented
40#1954C2211yescharacteristic
41#1954C2211yescharacteristic
42#1869—21no—
43#1869—21no—
44#1869—21no—
45#1869—21no—
46#1817—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779—21no—
50C4×C22⋊C8C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52C2×#336—21no—
53#1580—24no—
54C8×D8—24no—
55C2×#335C2211yescharacteristic, complemented
56C2×#334C2211yescharacteristic, complemented
57C2×Q8⋊C8C2211yescharacteristic, complemented
58C2×Q8⋊C8C2211yescharacteristic, complemented
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic, complemented
64C2×D4⋊C8C2211yescharacteristic, complemented
65C2×#322C2211yescharacteristic, complemented
66C2×C82C2211yescharacteristic, complemented
67#1277C2211yescharacteristic, complemented
68#1277C2211yescharacteristic, complemented
69#1273C2211yescharacteristic, complemented
70#1273C2211yescharacteristic, complemented
71C22×#41C2×C411yescharacteristic
72C23×D4C2×C411yescharacteristic
73C24×C4—21no—
74C2×AGL(1,ℤ/8)—24no—
75C2×AGL(1,ℤ/8)—24no—
76C2×AGL(1,ℤ/8)C818yescomplemented
77C22×SD16C2×C411yescharacteristic
78C22×SD16C2×C411yescharacteristic
79C22×D8C2×C411yescharacteristic
80C22×D8C2×C411yescharacteristic
81C22×M16C2×C411yescharacteristic
82C22×M16C2×C411yescharacteristic
83C23×C8—21no—
84C23×C8—21no—
85C23×C8—21no—
86C23×C8—21no—
87C4×#41—22no—
88C4×#41—22no—
89C4×#41—41no—
90C4×#41—41no—
91C2×C4×Q8C2×C411yescharacteristic
92C2×C4×Q8C2311yescharacteristic
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×C4×D4—41no—
100C2×C4×D4—41no—
101C2×C4×D4C2×C411yescharacteristic
102C2×C4×D4C2×C411yescharacteristic
103C2×C4×D4C2×C411yescharacteristic
104C2×C4×D4C2311yescharacteristic
105C2×C4×D4C2311yescharacteristic
106C2×C4×D4C2311yescharacteristic
107C2×#117—21no—
108C2×#117C2×C411yescharacteristic
109C22×C4⋊C4C2×C411yescharacteristic
110C22×C22⋊C4—21no—
111C22×C42—21no—
112C22×C42C2311yescharacteristic
113#442—24no—
114#442—24no—
115#440—24no—
116#440—24no—
117C4×SD16—22no—
118C4×SD16—22no—
119C4×SD16—22no—
120C4×SD16—22no—
121C4×D8—22no—
122C4×D8—22no—
123C4×D8D414yes—
124C4×D8D414yes—
125C8×D4—22no—
126C8×D4—22no—
127C8×D4—22no—
128C8×D4—22no—
129C8×D4—41no—
130C8×D4—41no—
131C8×D4—41no—
132C8×D4—41no—
133#428—24no—
134C2×#107C2×C411yescharacteristic
135C2×#107C2×C411yescharacteristic
136C2×#106C2×C411yescharacteristic
137C2×#106C2×C411yescharacteristic
138C2×C4⋊C8C2311yescharacteristic
139C2×C4⋊C8C2311yescharacteristic
140C2×C4⋊C8C2311yescharacteristic
141C2×C4⋊C8C2311yescharacteristic
142#418—24no—
143#417—24no—
144C2×#103C2×C411yescharacteristic
145C2×#103C2×C411yescharacteristic
146C2×#102C2×C411yescharacteristic
147C2×#102C2×C411yescharacteristic
148C2×#102C2×C411yescharacteristic
149C2×#102C2×C411yescharacteristic
150C2×#102C2×C411yescharacteristic
151C2×#102C2×C411yescharacteristic
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C22⋊C8—21no—
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160C2×C22⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8—44no—
164C2×C22⋊C8D411yescharacteristic
165C2×C22⋊C8D411yescharacteristic
166C4×M16—22no—
167C4×M16—22no—
168C2×#97C2×C411yescharacteristic
169C2×#97C2×C411yescharacteristic
170C2×C4×C8C2311yescharacteristic
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176#336—21no—
177#336—21no—
178#336—21no—
179#336—21no—
180#336—21no—
181#336—21no—
182#336—21no—
183#336D411yescharacteristic
184#336D411yescharacteristic
185#335—22no—
186#334—22no—
187Q8⋊C8—41no—
188Q8⋊C8—41no—
189D4⋊C8—22no—
190D4⋊C8—22no—
191D4⋊C8—22no—
192D4⋊C8—22no—
193D4⋊C8—41no—
194D4⋊C8—41no—
195#322—22no—
196C82—22no—
197C25—21no—
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—22no—
201C2×#41—41no—
202C2×#41—41no—
203C2×#41C2×C814yescomplemented
204C22×Q8C22×C411yescharacteristic
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—22no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4C2×C814yescomplemented
213C22×D4C22×C411yescharacteristic
214C22×D4C22×C411yescharacteristic
215C22×D4C22×C411yescharacteristic
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—81no—
229C23×C4—81no—
230C23×C4C22×C411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4#4111yescharacteristic
233AGL(1,ℤ/8)—232no—
234C2×SD16—22no—
235C2×SD16—22no—
236C2×SD16—22no—
237C2×SD16—22no—
238C2×SD16C2×C814yescomplemented
239C2×SD16C2×C814yescomplemented
240C2×D8—22no—
241C2×D8—22no—
242C2×D8C22⋊C414yes—
243C2×D8C2×C814yes—
244C2×D8C2×C814yescomplemented
245C2×D8M1614yes—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—41no—
251C2×M16C2×C814yescomplemented
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—42no—
259C22×C8—42no—
260C22×C8—42no—
261C22×C8—42no—
262C22×C8—42no—
263C22×C8—42no—
264C22×C8—42no—
265C22×C8—42no—
266C22×C8—81no—
267C22×C8—81no—
268C22×C8—81no—
269C22×C8—81no—
270C22×C8C22×C411yescharacteristic
271C22×C8C22×C411yescharacteristic
272C22×C8C22×C411yescharacteristic
273C22×C8C22×C411yescharacteristic
274C22×C8C2×D411yescharacteristic
275C22×C8C2×D411yescharacteristic
276C22×C8C2×D411yescharacteristic
277C22×C8C2×D411yescharacteristic
278C4×Q8—22no—
279C4×Q8—21no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—41no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—42no—
296C4×D4—42no—
297C4×D4—41no—
298C4×D4—41no—
299C4×D4—41no—
300C4×D4—42no—
301C4×D4—42no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4—42no—
305C4×D4—42no—
306C4×D4C2×D412yes—
307C4×D4C2×D412yes—
308C4×D4C2×D412yes—
309C4×D4C2×D412yes—
310#117—22no—
311#117—42no—
312#117—42no—
313#117—41no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42C22×C411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42#4111yescharacteristic
344C2×C42C2411yescharacteristic
345#107—22no—
346#107C22⋊C414yes—
347#106—22no—
348#106—22no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357#103—22no—
358#103—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362#102—22no—
363#102C22⋊C414yes—
364#102C22⋊C414yes—
365C22⋊C8—22no—
366C22⋊C8—41no—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—42no—
374C22⋊C8—42no—
375C22⋊C8—81no—
376C22⋊C8—81no—
377C22⋊C8—81no—
378#97—22no—
379#97—22no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8—21no—
387C4×C8—21no—
388C4×C8—21no—
389C4×C8—21no—
390C4×C8C2×D412yes—
391C4×C8C2×D412yes—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—24no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24—81no—
401C24—81no—
402C24C4×D411yescharacteristic
403#41—28no—
404#41—44no—
405#41—44no—
406#41—44no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8C22×C812yes—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—24no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4C2×C22⋊C412yes—
435C2×D4C2×C22⋊C412yes—
436C2×D4C22×C812yes—
437C2×D4C22×C812yes—
438C2×D4C22×C812yes—
439C2×D4C2×M1612yes—
440C2×D4C2×M1612yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
500C22×C4C22×C812yes—
501C22×C4#13112yes—
502C22×C4C23×C411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C2×#4111yescharacteristic
505SD16—28no—
506SD16—28no—
507D8—28no—
508D8C22⋊C8116yescomplemented
509M16—28no—
510M16—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—22no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—84no—
548C2×C8—84no—
549C2×C8—84no—
550C2×C8—84no—
551C2×C8C2×C22⋊C412yes—
552C2×C8C2×C22⋊C412yes—
553C2×C8C22×C812yes—
554C2×C8C22×C812yes—
555C2×C8C2×M1612yes—
556C2×C8AGL(1,ℤ/8)12yescomplemented
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4C2×C22⋊C412yes—
568C4⋊C4C2×C22⋊C412yes—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—42no—
586C42—42no—
587C42—41no—
588C42—41no—
589C42C22×D411yescharacteristic
590C42C22×D411yescharacteristic
591C42H(5,𝔽2)11yescharacteristic
592C42H(5,𝔽2)11yescharacteristic
593C23—22no—
594C23—22no—
595C23—21no—
596C23—22no—
597C23—22no—
598C23—21no—
599C23—22no—
600C23—22no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—22no—
606C23—48no—
607C23—48no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23C8×D412yes—
628C23C2×C4×D411yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—22no—
640D4—22no—
641D4—48no—
642D4—48no—
643D4—41no—
644D4—41no—
645D4C2×C22⋊C814yes—
646D4C2×C22⋊C814yescomplemented
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4C8×D412yes—
700C2×C4C22×C22⋊C411yescharacteristic
701C2×C4#51811yescharacteristic
702C2×C4D4211yescharacteristic
703C2×C4D4211yescharacteristic
704C2×C4#54611yescharacteristic
705C2×C4#54611yescharacteristic
706C2×C4C23×C811yescharacteristic
707C2×C4C22×M1611yescharacteristic
708C2×C4C2×#13111yescharacteristic
709C2×C4#56811yescharacteristic
710C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
711C2×C4#57511yescharacteristic
712C2×C4#57611yescharacteristic
713C2×C4#57711yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8—42no—
718C8—41no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—81no—
723C8—81no—
724C8—81no—
725C8—81no—
726C8—81no—
727C8C2×C22⋊C814yescomplemented
728C22—22no—
729C22—24no—
730C22—24no—
731C22—22no—
732C22—22no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22D4×C22⋊C411yescharacteristic
758C22C2×C8×D411yescharacteristic
759C22D4×M1611yescharacteristic
760C22C4×AGL(1,ℤ/8)11yescharacteristic
761C22#294611yescharacteristic
762C22#295511yescharacteristic
763C22#295611yescharacteristic
764C4—22no—
765C4—21no—
766C4—21no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—42no—
771C4—41no—
772C4—81no—
773C4—81no—
774C4C22×C22⋊C811yescharacteristic
775C4#288011yescharacteristic
776C4#297211yescharacteristic
777C4#297411yescharacteristic
778C4#326411yescharacteristic
779C4#326711yescharacteristic
780C4#327211yescharacteristic
781C4#327311yescharacteristic
782C2—42no—
783C2—44no—
784C2—44no—
785C2—82no—
786C2C8×AGL(1,ℤ/8)11yescharacteristic
787C2#1785211yescharacteristic
788C2#1804611yescharacteristic
789C2#1805011yescharacteristic
790C2D4×C22⋊C811yescharacteristic
791C2#2244211yescharacteristic
792C2#2245311yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23C2×C4×D4
prime radicalC22×AGL(1,ℤ/8)C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22469C2semidirect
3. D4×C22⋊C8C2semidirect
4. C2×#1580C2semidirect
5. C2×C8×D8C2semidirect
6. #9660C2semidirect
7. #9655C2semidirect
8. #8947C2semidirect
9. #8947C2semidirect
10. #8945C2semidirect
11. #8945C2semidirect
12. #8597C2semidirect
13. #8312C2semidirect
14. #8310C2semidirect
15. #8146C2semidirect
31. C2×C8×D4C22semidirect
32. C2×C8×D4C22semidirect
38. #1984C22semidirect
39. #1984C22semidirect
55. C2×#335C22semidirect
56. C2×#334C22semidirect
57. C2×Q8⋊C8C22semidirect
58. C2×Q8⋊C8C22semidirect
63. C2×D4⋊C8C22semidirect
64. C2×D4⋊C8C22semidirect
65. C2×#322C22semidirect
66. C2×C82C22semidirect
67. #1277C22semidirect
68. #1277C22semidirect
69. #1273C22semidirect
70. #1273C22semidirect
76. C2×AGL(1,ℤ/8)C8semidirect
203. C2×#41C2×C8semidirect
212. C22×D4C2×C8semidirect
238. C2×SD16C2×C8semidirect
239. C2×SD16C2×C8semidirect
244. C2×D8C2×C8semidirect
251. C2×M16C2×C8semidirect
508. D8C22⋊C8semidirect
556. C2×C8AGL(1,ℤ/8)semidirect
646. D4C2×C22⋊C8semidirect
727. C8C2×C22⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×AGL(1,ℤ/8)2
#224692
D4×C22⋊C82
C2×#15802
C2×C8×D82
#96602
#96552
#89472
#89452
#85972
#83122
#83102
#81462