Finite Group Databasebeta

← #6344726

Subgroups — #6344726

Order 512.

1922 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60558C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3C22×#436C211yesmaximal, characteristic, complemented
4#17942C214yesmaximal, complemented
5#17938C214yesmaximal, complemented
6#17935C212yesmaximal, complemented
7#17933C212yesmaximal, complemented
8#17930C212yesmaximal, complemented
9#17928C212yesmaximal, complemented
10#17891C214yesmaximal, complemented
11#17871C214yesmaximal, complemented
12#17807C211yesmaximal, characteristic, complemented
13#17466C211yesmaximal, characteristic, complemented
14#17448C211yesmaximal, characteristic, complemented
15#17323C211yesmaximal, characteristic, complemented
16C23×M16—21no—
17#3444C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19#3114C414yes—
20#3110C412yes—
21#3109C412yes—
22#3105C2214yes—
23#3101C2212yes—
24#3100C2212yes—
25#3092C412yes—
26#3077C412yes—
27#3036C412yes—
28#3003C412yes—
29#2966—21no—
30#2966—21no—
31#2966C2212yescomplemented
32#2966C2212yescomplemented
33#2965—21no—
34#2965C2212yescomplemented
35C8×#41—21no—
36C8×#41C2212yescomplemented
37#2960C2211yescharacteristic, complemented
38#2960C2211yescharacteristic, complemented
39C4×AGL(1,ℤ/8)C2214yes—
40#2931C2211yescharacteristic, complemented
41#2931C2211yescharacteristic, complemented
42#2929—21no—
43#2929—21no—
44C2×#436—21no—
45C2×#436—21no—
46C2×#436—21no—
47C2×#436—21no—
48C2×#436—21no—
49C2×#436—21no—
50C2×#436C2212yes—
51C2×#436C2212yes—
52C2×#436C2212yes—
53C2×#436C2212yes—
54C2×#436C2212yes—
55C2×#436C2212yes—
56#2922—21no—
57#2920C2211yescharacteristic
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60C22×C4⋊C8C2211yescharacteristic
61C22×C22⋊C8—21no—
62C4×#131—21no—
63C22×C4×C8C2211yescharacteristic
64#1594C2218yescomplemented
65#1592C2218yescomplemented
66#1590C2218yescomplemented
67#1589C2218yescomplemented
68#1588C2218yescomplemented
69#1586C2218yescomplemented
70#1583C2218yescomplemented
71#1581C2218yescomplemented
72#1573C2214yescomplemented
73#1571C2212yescomplemented
74#1570C2212yescomplemented
75#1565C2214yescomplemented
76#1490C2214yes—
77#1486C2212yes—
78#1486C2212yes—
79#1483C2214yescomplemented
80#1481C2212yescomplemented
81#1480C2212yescomplemented
82#1478C2214yes—
83#1477C2214yescomplemented
84#1452C2212yescomplemented
85#1451C2212yescomplemented
86#1451C2212yescomplemented
87#1450C2212yescomplemented
88C8×M16C2212yescomplemented
89C8×M16C2212yescomplemented
90C23×D4C2×C411yescharacteristic
91C24×C4—21no—
92C2×AGL(1,ℤ/8)C2×C414yes—
93C2×#131—21no—
94C2×#131—21no—
95C22×M16—22no—
96C22×M16—22no—
97C22×M16—22no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—48no—
102C23×C8—21no—
103C23×C8D411yescharacteristic
104C23×C8D411yescharacteristic
105#533C2×C411yescharacteristic
106#533C2×C411yescharacteristic
107#533C2311yescharacteristic
108#532C2×C411yescharacteristic
109#532C2×C411yescharacteristic
110#532C2311yescharacteristic
111#529—21no—
112#529—21no—
113#529—21no—
114#529—21no—
115#529C2×C412yes—
116#529C2312yes—
117#525—21no—
118#525—21no—
119#525C2×C412yes—
120C4×#41—21no—
121C4×#41—21no—
122C4×#41C2312yes—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4C2×C412yes—
130C2×C4×D4C2×C412yes—
131C2×C4×D4C2×C412yes—
132C2×C4×D4C2312yes—
133C2×C4×D4C2312yes—
134C2×C4×D4C2312yes—
135C22×C4⋊C4C2×C411yescharacteristic
136C22×C22⋊C4—21no—
137C22×C42C2311yescharacteristic
138#484C2×C414yes—
139#483C2×C414yes—
140#481C2×C414yes—
141#480C2×C414yes—
142#478C2×C418yes—
143#476C2×C414yes—
144#474C2×C414yes—
145#463C2×C418yes—
146#461C2×C414yes—
147#459C2×C414yes—
148#450C2×C414yes—
149#450C2×C414yes—
150#447C2×C414yes—
151#447C2×C414yes—
152#446—21no—
153#446—21no—
154#446C2312yescomplemented
155#446C2312yescomplemented
156C8×Q8—21no—
157C8×Q8—21no—
158C8×Q8C2312yescomplemented
159C8×Q8C2312yescomplemented
160#442C2×C418yes—
161#440C2×C418yes—
162C4×SD16C2318yes—
163C4×D8C2318yes—
164#436—22no—
165#436—22no—
166#436—22no—
167#436—22no—
168#436—22no—
169#436—22no—
170#436—22no—
171#436—22no—
172#436—22no—
173#436—22no—
174#436—22no—
175#436—22no—
176#436—21no—
177#436—21no—
178#436C2314yes—
179#436C2314yes—
180#436C2314yes—
181#436C2314yes—
182#436C2312yescomplemented
183#436C2312yescomplemented
184#435—22no—
185#435—22no—
186#435—22no—
187#435—22no—
188C8×D4—22no—
189C8×D4—22no—
190C8×D4—22no—
191C8×D4—22no—
192C8×D4—21no—
193C8×D4—21no—
194C8×D4C2312yescomplemented
195C8×D4C2312yescomplemented
196#433—22no—
197#433—22no—
198#432—21no—
199#432—21no—
200#432—21no—
201#432C2×C412yes—
202#432C2×C412yes—
203#432C2312yes—
204#431—21no—
205#431—22no—
206#431—22no—
207#431C2312yes—
208#431C2312yes—
209#431C2312yes—
210#431C2312yes—
211#431C2312yes—
212#428C2×C414yes—
213#424—21no—
214#424—21no—
215#423—21no—
216#423C2×C412yes—
217#423C2311yescharacteristic
218#423C2311yescharacteristic
219C2×C4⋊C8—21no—
220C2×C4⋊C8—21no—
221C2×C4⋊C8—21no—
222C2×C4⋊C8C2312yes—
223C2×C4⋊C8C2312yes—
224C2×C4⋊C8C2312yes—
225#418C2×C414yes—
226#417C2×C414yes—
227#408—21no—
228#408—21no—
229#407—21no—
230#407—21no—
231#407C2×C412yes—
232C2×C22⋊C8—22no—
233C2×C22⋊C8—22no—
234C2×C22⋊C8—22no—
235C2×C22⋊C8—22no—
236C2×C22⋊C8—22no—
237C2×C22⋊C8—22no—
238#405—21no—
239#405—21no—
240#405—22no—
241#405—22no—
242C4×M16—21no—
243C4×M16—22no—
244C4×M16C2312yes—
245C4×M16C2312yes—
246C2×C4×C8—22no—
247C2×C4×C8D411yescharacteristic
248C2×C4×C8D411yescharacteristic
249C2×C4×C8D411yescharacteristic
250C2×C4×C8D411yescharacteristic
251C2×C4×C8D411yescharacteristic
252C2×C4×C8D411yescharacteristic
253C2×C4×C8C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259#335C2318yescomplemented
260#334C2318yescomplemented
261Q8⋊C8C2318yescomplemented
262D4⋊C8C2318yes—
263D4⋊C8C2318yes—
264D4⋊C8C2318yescomplemented
265#322C2314yescomplemented
266#322C2314yescomplemented
267#322C2314yescomplemented
268C82C2314yescomplemented
269C25—21no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41C22×C412yes—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—44no—
277C22×D4C22×C412yes—
278C22×D4C22×C412yes—
279C22×D4C22×C412yes—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4C22×C411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4#4111yescharacteristic
292AGL(1,ℤ/8)—48no—
293C2×SD16C22×C418yes—
294C2×D8C22×C418yes—
295#131—44no—
296#131—44no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—22no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—48no—
307C2×M16—48no—
308C2×M16—48no—
309C2×M16—48no—
310C2×M16—48no—
311C2×M16—48no—
312C2×M16C22×C414yes—
313C22×C8—24no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—42no—
320C22×C8—44no—
321C22×C8C2×D411yescharacteristic
322C22×C8C2×D411yescharacteristic
323C22×C8C2×D411yescharacteristic
324C22×C8C2×D411yescharacteristic
325C22×C8C2×D411yescharacteristic
326C22×C8C2×D411yescharacteristic
327C22×C8C2×D411yescharacteristic
328C22×C8C2×D411yescharacteristic
329C22×C8C2×D411yescharacteristic
330C22×C8C2×D411yescharacteristic
331C22×C8C2×D411yescharacteristic
332C22×C8C2×D411yescharacteristic
333C4⋊Q8C22×C411yescharacteristic
334C4⋊Q8C22×C411yescharacteristic
335C4⋊Q8C22×C411yescharacteristic
336#127C22×C411yescharacteristic
337#126—22no—
338#126—22no—
339#125—21no—
340#125—21no—
341#125C22×C412yes—
342#124—21no—
343#124—21no—
344#124C22×C412yes—
345#123—22no—
346#123—22no—
347#123—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8C22×C412yes—
353C22⋊Q8C22×C412yes—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121C22×C412yes—
359#121C22×C412yes—
360#120—22no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C22×C412yes—
366C4×Q8C2412yes—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4C22×C414yes—
390C4×D4C22×C414yes—
391C4×D4C22×C414yes—
392C4×D4C22×C412yes—
393C4×D4C2414yes—
394C4×D4C2412yes—
395#117—21no—
396#117—21no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117C22×C412yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C22×C412yes—
405C2×C4⋊C4C22×C412yes—
406C2×C4⋊C4C22×C412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C42—22no—
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42#4111yescharacteristic
421C2×C42#4111yescharacteristic
422C2×C42#4111yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#107C22×C418yes—
427#106C22×C418yes—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8C22×C414yes—
440C4⋊C8C22×C414yes—
441C4⋊C8C2412yes—
442C4⋊C8C2412yes—
443C4⋊C8C2414yes—
444#103C22×C418yes—
445#102C22×C418yes—
446#102C22×C418yes—
447#102C22×C418yes—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8C22×C414yes—
461C22⋊C8C22×C414yes—
462#97—22no—
463#97—22no—
464#97—22no—
465#97—22no—
466#97C22×C414yes—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8C2×D411yescharacteristic
471C4×C8C2×D411yescharacteristic
472C4×C8C2×D411yescharacteristic
473C4×C8C2×D411yescharacteristic
474C4×C8C2×D411yescharacteristic
475C4×C8C2×D411yescharacteristic
476C4×C8C2×D411yescharacteristic
477C4×C8C2×D411yescharacteristic
478C4×C8C2×D411yescharacteristic
479C4×C8C2×D411yescharacteristic
480C4×C8C2×D411yescharacteristic
481C4×C8C2×D411yescharacteristic
482C4×C8C2414yes—
483C4×C8C2414yes—
484C4×C8C2411yescharacteristic
485C4×C8C2411yescharacteristic
486C4×C8C2411yescharacteristic
487C4×C8C2411yescharacteristic
488C24—22no—
489C24—22no—
490C24—22no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24C4×D411yescharacteristic
495#41—28no—
496#41—44no—
497#41—42no—
498#41—42no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C23×C412yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4C23×C414yes—
518C2×D4C23×C412yes—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4C4×D411yescharacteristic
544C22×C4C4×D411yescharacteristic
545C22×C4C4×D411yescharacteristic
546C22×C4C4×D411yescharacteristic
547C22×C4C4×D411yescharacteristic
548C22×C4C4×D411yescharacteristic
549C22×C4C4×D411yescharacteristic
550C22×C4C4×D411yescharacteristic
551C22×C4C4×D411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4C2×#4111yescharacteristic
561SD16—48no—
562D8—48no—
563M16—28no—
564M16—48no—
565M16—48no—
566M16—44no—
567M16—44no—
568M16—42no—
569M16—42no—
570M16—48no—
571M16—48no—
572M16—44no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—44no—
589C2×C8—44no—
590C2×C8—44no—
591C2×C8—44no—
592C2×C8—44no—
593C2×C8AGL(1,ℤ/8)14yescomplemented
594C2×C8C23×C418yes—
595C2×C8C22×D411yescharacteristic
596C2×C8C22×D411yescharacteristic
597C2×C8C22×D411yescharacteristic
598C2×C8C22×D411yescharacteristic
599C2×C8C22×D411yescharacteristic
600C2×C8C22×D411yescharacteristic
601C2×C8C22×D411yescharacteristic
602C2×C8C22×D411yescharacteristic
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4C23×C412yes—
617C4⋊C4C23×C412yes—
618C4⋊C4C23×C414yes—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42C4×D411yescharacteristic
636C42C4×D411yescharacteristic
637C42C4×D411yescharacteristic
638C42C4×D411yescharacteristic
639C42C4×D411yescharacteristic
640C42C4×D411yescharacteristic
641C42C23×C411yescharacteristic
642C42C23×C411yescharacteristic
643C42C23×C411yescharacteristic
644C42C22×D411yescharacteristic
645C42C22×D411yescharacteristic
646C42C22×D411yescharacteristic
647C42C2×#4111yescharacteristic
648C42C2×#4111yescharacteristic
649C42C2×#4111yescharacteristic
650C42C2511yescharacteristic
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—816no—
666C23C2×C4×D411yescharacteristic
667C23C2×C4×D411yescharacteristic
668C23C2×C4×D411yescharacteristic
669Q8—24no—
670Q8—42no—
671Q8—42no—
672D4—24no—
673D4—24no—
674D4—24no—
675D4—44no—
676D4—44no—
677D4—42no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—44no—
682D4—42no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—48no—
706C2×C4—48no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4C2×C4×D411yescharacteristic
718C2×C4C2×C4×D411yescharacteristic
719C2×C4C2×C4×D411yescharacteristic
720C2×C4C2×C4×D411yescharacteristic
721C2×C4C2×C4×D411yescharacteristic
722C2×C4C2×C4×D411yescharacteristic
723C2×C4C2×C4×D411yescharacteristic
724C2×C4C2×C4×D411yescharacteristic
725C2×C4C2×C4×D411yescharacteristic
726C2×C4#56814yes—
727C2×C4C2×AGL(1,ℤ/8)12yes—
728C2×C4#57512yes—
729C2×C4C24×C411yescharacteristic
730C2×C4C23×D411yescharacteristic
731C2×C4C22×#4111yescharacteristic
732C8—28no—
733C8—21no—
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—44no—
740C8—44no—
741C8—42no—
742C8—42no—
743C8C2×AGL(1,ℤ/8)12yes—
744C8C2×AGL(1,ℤ/8)12yes—
745C22—28no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—44no—
757C22—42no—
758C22—88no—
759C22—88no—
760C22—88no—
761C22#293012yes—
762C22C4×AGL(1,ℤ/8)12yes—
763C22#295512yes—
764C22C22×C4×D411yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—42no—
774C4—42no—
775C4—44no—
776C4—42no—
777C4#293012yes—
778C4C4×AGL(1,ℤ/8)12yes—
779C4C2×#56812yes—
780C4C22×AGL(1,ℤ/8)11yescharacteristic
781C4C2×#57511yescharacteristic
782C2—22no—
783C2—22no—
784C2—22no—
785C2—82no—
786C2—84no—
787C2C2×#293011yescharacteristic
788C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
789C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60558C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. C22×#436C2semidirect
4. #17942C2semidirect
5. #17938C2semidirect
6. #17935C2semidirect
7. #17933C2semidirect
8. #17930C2semidirect
9. #17928C2semidirect
10. #17891C2semidirect
11. #17871C2semidirect
12. #17807C2semidirect
13. #17466C2semidirect
14. #17448C2semidirect
15. #17323C2semidirect
31. #2966C22semidirect
32. #2966C22semidirect
34. #2965C22semidirect
36. C8×#41C22semidirect
37. #2960C22semidirect
38. #2960C22semidirect
40. #2931C22semidirect
41. #2931C22semidirect
64. #1594C22semidirect
65. #1592C22semidirect
66. #1590C22semidirect
67. #1589C22semidirect
68. #1588C22semidirect
69. #1586C22semidirect
70. #1583C22semidirect
71. #1581C22semidirect
72. #1573C22semidirect
73. #1571C22semidirect
74. #1570C22semidirect
75. #1565C22semidirect
79. #1483C22semidirect
80. #1481C22semidirect
81. #1480C22semidirect
83. #1477C22semidirect
84. #1452C22semidirect
85. #1451C22semidirect
86. #1451C22semidirect
87. #1450C22semidirect
88. C8×M16C22semidirect
89. C8×M16C22semidirect
154. #446C23semidirect
155. #446C23semidirect
158. C8×Q8C23semidirect
159. C8×Q8C23semidirect
182. #436C23semidirect
183. #436C23semidirect
194. C8×D4C23semidirect
195. C8×D4C23semidirect
259. #335C23semidirect
260. #334C23semidirect
261. Q8⋊C8C23semidirect
264. D4⋊C8C23semidirect
265. #322C23semidirect
266. #322C23semidirect
267. #322C23semidirect
268. C82C23semidirect
593. C2×C8AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#605582
#602042
C22×#4362
#179422
#179382
#179352
#179332
#179302
#179282
#178912
#178712
#178072
#174662
#174482
#173232