Finite Group Databasebeta

← #220123

Subgroups — #220123

Order 512.

1323 conjugacy classes of subgroups.

The subgroup lattice has 792 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#22530C211yesmaximal, characteristic, complemented
3D4×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×SD16⋊C8C211yesmaximal, characteristic, complemented
5C2×C8×SD16C211yesmaximal, characteristic, complemented
6#9659C211yesmaximal, characteristic, complemented
7#9657C211yesmaximal, characteristic, complemented
8#8948C211yesmaximal, characteristic, complemented
9#8948C211yesmaximal, characteristic, complemented
10#8947C211yesmaximal, characteristic, complemented
11#8947C211yesmaximal, 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
19C2×C8×Q8C2211yescharacteristic, complemented
20C2×C8×Q8C2211yescharacteristic, complemented
21C4×AGL(1,ℤ/8)—24no—
22C4×AGL(1,ℤ/8)—24no—
23C2×#442C411yescharacteristic
24C2×#442C411yescharacteristic
25C2×#440C411yescharacteristic
26C2×#440C411yescharacteristic
27C2×C4×SD16C2211yescharacteristic
28C2×C4×SD16C2211yescharacteristic
29C2×C4×D8C2211yescharacteristic
30C2×C4×D8C2211yescharacteristic
31C2×C8×D4C2211yescharacteristic
32C2×C8×D4C2211yescharacteristic
33C2×#428C411yescharacteristic
34C2×#417C411yescharacteristic
35C2×#418C411yescharacteristic
36C22×C22⋊C8—21no—
37C2×C4×M16C2211yescharacteristic
38#1954—21no—
39#1954—21no—
40#1954C2211yescharacteristic
41#1954C2211yescharacteristic
42#1954C2211yescharacteristic, complemented
43#1954C2211yescharacteristic, complemented
44#1869—21no—
45#1869—21no—
46#1797—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779—21no—
50C4×C22⋊C8—21no—
51C4×C22⋊C8C2211yescharacteristic
52C4×C22⋊C8C2211yescharacteristic
53SD16⋊C8—24no—
54C8×SD16—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—
85C4×#41—22no—
86C4×#41—22no—
87C4×#41—41no—
88C4×#41—41no—
89C2×C4×Q8C2×C411yescharacteristic
90C2×C4×Q8C2311yescharacteristic
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—41no—
98C2×C4×D4—41no—
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×C4×D4C2311yescharacteristic
103C2×C4×D4C2311yescharacteristic
104C2×C4×D4C2311yescharacteristic
105C2×#117—21no—
106C2×#117C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C22⋊C4—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C8×Q8—22no—
112C8×Q8—22no—
113C8×Q8—41no—
114C8×Q8—41no—
115#442—24no—
116#442—24no—
117#440—24no—
118#440—24no—
119C4×SD16—22no—
120C4×SD16—22no—
121C4×SD16D414yes—
122C4×SD16D414yes—
123C4×D8—22no—
124C4×D8—22no—
125C4×D8—22no—
126C4×D8—22no—
127C8×D4—22no—
128C8×D4—22no—
129C8×D4—41no—
130C8×D4—41no—
131#428—24no—
132C2×#107C2×C411yescharacteristic
133C2×#107C2×C411yescharacteristic
134C2×#106C2×C411yescharacteristic
135C2×#106C2×C411yescharacteristic
136C2×C4⋊C8—21no—
137C2×C4⋊C8—21no—
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—21no—
164C2×C22⋊C8—21no—
165C2×C22⋊C8—44no—
166C2×C22⋊C8D411yescharacteristic
167C2×C22⋊C8D411yescharacteristic
168C4×M16—22no—
169C4×M16—22no—
170C2×#97C2×C411yescharacteristic
171C2×#97C2×C411yescharacteristic
172C2×C4×C8—21no—
173C2×C4×C8—21no—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180#336—21no—
181#336—21no—
182#336—21no—
183#336D411yescharacteristic
184#336D411yescharacteristic
185#335—22no—
186#334—22no—
187Q8⋊C8—22no—
188Q8⋊C8—22no—
189D4⋊C8—22no—
190D4⋊C8—22no—
191D4⋊C8—41no—
192D4⋊C8—41no—
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×C814yes—
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×SD16C22⋊C414yes—
237C2×SD16C2×C814yes—
238C2×SD16C2×C814yescomplemented
239C2×SD16M1614yes—
240C2×D8—22no—
241C2×D8—22no—
242C2×D8—22no—
243C2×D8—22no—
244C2×D8C2×C814yes—
245C2×D8C2×C814yescomplemented
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—81no—
263C22×C8—81no—
264C22×C8C22×C411yescharacteristic
265C22×C8C22×C411yescharacteristic
266C22×C8C22×C411yescharacteristic
267C22×C8C22×C411yescharacteristic
268C22×C8C2×D411yescharacteristic
269C22×C8C2×D411yescharacteristic
270C22×C8C2×D411yescharacteristic
271C22×C8C2×D411yescharacteristic
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—22no—
275C4×Q8—41no—
276C4×Q8C2×D412yes—
277C4×Q8C2×D412yes—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—42no—
292C4×D4—42no—
293C4×D4—41no—
294C4×D4—41no—
295C4×D4—41no—
296C4×D4—42no—
297C4×D4—42no—
298C4×D4—42no—
299C4×D4—42no—
300C4×D4—42no—
301C4×D4—42no—
302C4×D4C2×D412yes—
303C4×D4C2×D412yes—
304#117—22no—
305#117—42no—
306#117—42no—
307#117—41no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4C22×C411yescharacteristic
314C2×C4⋊C4C22×C411yescharacteristic
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42C22×C411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42#4111yescharacteristic
338C2×C42C2411yescharacteristic
339#107—22no—
340#107—22no—
341#106—22no—
342#106C22⋊C414yes—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—42no—
352C4⋊C8—42no—
353#103—22no—
354#103C22⋊C414yes—
355#102—22no—
356#102—22no—
357#102—22no—
358#102—22no—
359#102—22no—
360#102C22⋊C414yes—
361C22⋊C8—22no—
362C22⋊C8—41no—
363C22⋊C8—42no—
364C22⋊C8—42no—
365C22⋊C8—42no—
366C22⋊C8—42no—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—81no—
372C22⋊C8—81no—
373C22⋊C8—81no—
374C22⋊C8—81no—
375C22⋊C8—81no—
376#97—22no—
377#97—22no—
378C4×C8—21no—
379C4×C8—21no—
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—42no—
389C4×C8—42no—
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×Q8C2×C22⋊C412yes—
411C2×Q8C22×C812yes—
412C2×Q8C2×M1612yes—
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—21no—
427C2×D4—21no—
428C2×D4—24no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4C2×C22⋊C412yes—
437C2×D4C22×C812yes—
438C2×D4C22×C812yes—
439C2×D4C22×C812yes—
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—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—24no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—42no—
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—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
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—
506SD16C22⋊C8116yescomplemented
507D8—28no—
508D8—28no—
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×C8C2×C22⋊C412yes—
550C2×C8C2×C22⋊C412yes—
551C2×C8C22×C812yes—
552C2×C8C22×C812yes—
553C2×C8C2×M1612yes—
554C2×C8AGL(1,ℤ/8)12yescomplemented
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4C2×C22⋊C412yes—
566C4⋊C4C2×C22⋊C412yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C42—21no—
578C42—21no—
579C42—22no—
580C42—22no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—42no—
586C42—42no—
587C42C22×D411yescharacteristic
588C42C22×D411yescharacteristic
589C42H(5,𝔽2)11yescharacteristic
590C42H(5,𝔽2)11yescharacteristic
591C23—22no—
592C23—21no—
593C23—22no—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—22no—
602C23—48no—
603C23—48no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
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—84no—
621C23—84no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23C8×D412yes—
626C23C2×C4×D411yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8C2×C22⋊C814yescomplemented
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—48no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4C2×C22⋊C814yes—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
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—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4C8×D412yes—
698C2×C4C22×C22⋊C411yescharacteristic
699C2×C4#51811yescharacteristic
700C2×C4D4211yescharacteristic
701C2×C4D4211yescharacteristic
702C2×C4#54611yescharacteristic
703C2×C4#54611yescharacteristic
704C2×C4C23×C811yescharacteristic
705C2×C4C22×M1611yescharacteristic
706C2×C4C2×#13111yescharacteristic
707C2×C4#56811yescharacteristic
708C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
709C2×C4#57511yescharacteristic
710C2×C4#57611yescharacteristic
711C2×C4#57711yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—42no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8—41no—
720C8—81no—
721C8—81no—
722C8—81no—
723C8—81no—
724C8—81no—
725C8C2×C22⋊C814yescomplemented
726C22—22no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—816no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22D4×C22⋊C411yescharacteristic
756C22C2×C8×D411yescharacteristic
757C22D4×M1611yescharacteristic
758C22C4×AGL(1,ℤ/8)11yescharacteristic
759C22#294611yescharacteristic
760C22#295511yescharacteristic
761C22#295611yescharacteristic
762C4—22no—
763C4—24no—
764C4—21no—
765C4—21no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4C22×C22⋊C811yescharacteristic
773C4#288011yescharacteristic
774C4#297211yescharacteristic
775C4#297411yescharacteristic
776C4#326511yescharacteristic
777C4#326811yescharacteristic
778C4#327411yescharacteristic
779C4#327511yescharacteristic
780C2—42no—
781C2—44no—
782C2—82no—
783C2—82no—
784C2C8×AGL(1,ℤ/8)11yescharacteristic
785C2#1785211yescharacteristic
786C2#1804811yescharacteristic
787C2#1805211yescharacteristic
788C2D4×C22⋊C811yescharacteristic
789C2#2244311yescharacteristic
790C2#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. #22530C2semidirect
3. D4×C22⋊C8C2semidirect
4. C2×SD16⋊C8C2semidirect
5. C2×C8×SD16C2semidirect
6. #9659C2semidirect
7. #9657C2semidirect
8. #8948C2semidirect
9. #8948C2semidirect
10. #8947C2semidirect
11. #8947C2semidirect
12. #8597C2semidirect
13. #8312C2semidirect
14. #8310C2semidirect
15. #8146C2semidirect
19. C2×C8×Q8C22semidirect
20. C2×C8×Q8C22semidirect
42. #1954C22semidirect
43. #1954C22semidirect
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
238. C2×SD16C2×C8semidirect
245. C2×D8C2×C8semidirect
251. C2×M16C2×C8semidirect
506. SD16C22⋊C8semidirect
554. C2×C8AGL(1,ℤ/8)semidirect
630. Q8C2×C22⋊C8semidirect
725. 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
#225302
D4×C22⋊C82
C2×SD16⋊C82
C2×C8×SD162
#96592
#96572
#89482
#89472
#85972
#83122
#83102
#81462