Finite Group Databasebeta

← #354198

Subgroups — #354198

Order 512.

2148 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34065C211yesmaximal, characteristic
2C2×C4×#117C211yesmaximal, characteristic, complemented
3C2×#1897C211yesmaximal, characteristic
4C2×#1896C211yesmaximal, characteristic
5C2×#1759C211yesmaximal, characteristic, complemented
6C2×C4×#104C211yesmaximal, characteristic, complemented
7#20377C211yesmaximal, characteristic, complemented
8#10924C211yesmaximal, characteristic, complemented
9#10923C211yesmaximal, characteristic, complemented
10#10879C211yesmaximal, characteristic, complemented
11#10878C211yesmaximal, characteristic, complemented
12#10720C211yesmaximal, characteristic, complemented
13#10719C211yesmaximal, characteristic, complemented
14#10701C211yesmaximal, characteristic, complemented
15C4×#339C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C2×#407C2211yescharacteristic
26C2×#407C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28C2×C4×M16C2211yescharacteristic
29#2324C414yescomplemented
30#2323C414yescomplemented
31#2322—22no—
32#2321—22no—
33#2297C2211yescharacteristic
34#2296C2211yescharacteristic
35#2293—22no—
36#2290—22no—
37#2280C2211yescharacteristic
38C4×#117—24no—
39C4×#117—24no—
40C4×#117C2211yescharacteristic
41C2×C4×C4⋊C4—22no—
42C2×C4×C22⋊C4—22no—
43C2×#376C2211yescharacteristic
44C2×#376C2211yescharacteristic
45C2×C43C2211yescharacteristic
46C2×C43C2211yescharacteristic
47#1897C418yescomplemented
48#1896C418yescomplemented
49#1759—24no—
50C4×#104—24no—
51#1750—22no—
52#1750—22no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67C22×#41C2311yescharacteristic
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74#525—22no—
75#525—22no—
76#525C2×C414yes—
77#525C2×C414yes—
78C2×#123—21no—
79C2×C22⋊Q8C2×C412yes—
80C2×#121C2×C412yes—
81C2×#120—21no—
82C4×#41—22no—
83C4×#41—22no—
84C4×#41—22no—
85C4×#41—22no—
86C2×C4×Q8C2×C412yescomplemented
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4C2×C412yescomplemented
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—21no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117C2×C414yes—
101C2×#117C2×C414yescomplemented
102C2×#117D412yes—
103C2×#117D412yes—
104C2×#117C2311yescharacteristic
105C2×#117C2311yescharacteristic
106C2×#117C2311yescharacteristic
107C22×C4⋊C4—21no—
108C22×C4⋊C4D412yes—
109C22×C22⋊C4—21no—
110C22×C22⋊C4D412yes—
111C22×C42—21no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42—22no—
116C22×C42—22no—
117C22×C42—22no—
118C22×C42—22no—
119C22×C42—21no—
120C22×C42C2×C414yescomplemented
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126C22×C42C2311yescharacteristic
127C2×#104—22no—
128C2×#104—22no—
129C2×#104—22no—
130C2×#104—22no—
131C2×#104—22no—
132C2×#104—22no—
133C2×#104—22no—
134C2×#104—22no—
135C2×#104C2×C414yes—
136C2×#104C2×C414yes—
137C2×#104C2×C414yescomplemented
138C2×#104C2×C414yescomplemented
139#407—22no—
140#407—22no—
141#407C2×C414yescomplemented
142#407C2×C414yescomplemented
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C4×M16—22no—
146C4×M16—22no—
147C4×M16—22no—
148C4×M16—22no—
149C2×#97—21no—
150C2×#97—21no—
151C2×C4×C8—21no—
152C2×C4×C8—21no—
153#391C2×C412yescomplemented
154#390—24no—
155#390C2×C412yescomplemented
156#389—24no—
157#389C2×C414yescomplemented
158#388—24no—
159#388—24no—
160#388—24no—
161#387—24no—
162#386—22no—
163#386—24no—
164#385—22no—
165#385—24no—
166#381—21no—
167#380C2×C414yes—
168#379—21no—
169C4×C4⋊C4—216no—
170C4×C4⋊C4—22no—
171C4×C4⋊C4C2×C414yescomplemented
172C4×C22⋊C4—216no—
173C4×C22⋊C4—22no—
174C4×C22⋊C4—22no—
175C4×C22⋊C4—22no—
176#376—22no—
177#376—22no—
178#376—22no—
179#376—21no—
180#376D414yescomplemented
181C2×#95—22no—
182C2×#95—22no—
183C43—22no—
184C43—22no—
185C43—22no—
186C43—21no—
187C43D414yescomplemented
188#339—22no—
189#339—22no—
190#339—22no—
191#339—22no—
192#339—22no—
193#339—22no—
194#339—22no—
195#339—22no—
196#339C2×C414yescomplemented
197#339C2×C414yescomplemented
198#339C2×C414yescomplemented
199#339C2×C414yescomplemented
200#336—22no—
201#336—22no—
202C25C2×D411yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41C22×C412yes—
214C2×#41C22×C412yes—
215C22×Q8C22×C411yescharacteristic
216C22×D4—21no—
217C22×D4—22no—
218C22×D4C22×C411yescharacteristic
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—22no—
236C23×C4—48no—
237C23×C4C22×C412yes—
238C23×C4C22×C412yes—
239C23×C4C22×C412yes—
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4#4112yes—
245C23×C4#4112yes—
246C23×C4C2411yescharacteristic
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16C22×C412yes—
268C2×M16C22×C412yes—
269C2×M16C22×C412yes—
270C2×M16C22×C412yes—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275#123—24no—
276#123—24no—
277C22⋊Q8—24no—
278C22⋊Q8C4218yescomplemented
279#121—24no—
280#121C4218yescomplemented
281#120—24no—
282#120—24no—
283C4×Q8—24no—
284C4×Q8—24no—
285C4×D4—28no—
286C4×D4—28no—
287C4×D4—24no—
288C4×D4—24no—
289C4×D4—44no—
290C4×D4—44no—
291#117—28no—
292#117—28no—
293#117—21no—
294#117—21no—
295#117—28no—
296#117—28no—
297#117—28no—
298#117—28no—
299#117—24no—
300#117—24no—
301#117—24no—
302#117—24no—
303#117—21no—
304#117—21no—
305#117—21no—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—42no—
312#117—42no—
313#117C22×C412yes—
314#117C22×C412yes—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4C22⋊C414yes—
324C2×C4⋊C4C22⋊C414yes—
325C2×C4⋊C4C22×C412yes—
326C2×C4⋊C4C22×C412yes—
327C2×C4⋊C4C22×C412yes—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4C22⋊C414yes—
342C2×C22⋊C4C22⋊C414yes—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—28no—
346C2×C42—28no—
347C2×C42—24no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—22no—
369C2×C42—28no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—24no—
373C2×C42—48no—
374C2×C42—48no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42C22×C412yes—
378C2×C42C22×C412yes—
379C2×C42C22×C412yes—
380C2×C42C22×C412yes—
381C2×C42C22×C412yes—
382C2×C42C22×C412yes—
383C2×C42C2×D412yes—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C2×C42C2×D412yes—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42C2×D412yes—
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42#4112yes—
393C2×C42#4112yes—
394C2×C42#4112yes—
395C2×C42#4112yes—
396C2×C42#4112yes—
397C2×C42#4112yes—
398#104—28no—
399#104—28no—
400#104—28no—
401#104—28no—
402C22⋊C8—28no—
403C22⋊C8—28no—
404#97—42no—
405#97—42no—
406C4×C8—42no—
407C4×C8—42no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—44no—
420C24C2×C22⋊C412yes—
421C24C4×D412yes—
422C24C4×D412yes—
423C24C22×D411yescharacteristic
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×C4212yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—28no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—84no—
459C2×D4C2×C4212yes—
460C22×C4—28no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—216no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—416no—
513C22×C4—416no—
514C22×C4—416no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—44no—
523C22×C4—84no—
524C22×C4C2×C4214yes—
525C22×C4C2×C22⋊C414yes—
526C22×C4C2×C22⋊C412yes—
527C22×C4C2×C22⋊C412yes—
528C22×C4C2×C22⋊C412yes—
529C22×C4#11714yes—
530C22×C4C4×D414yes—
531C22×C4C4×D414yes—
532C22×C4C4×D412yes—
533C22×C4C4×D412yes—
534C22×C4#12014yes—
535C22×C4#12314yes—
536C22×C4C23×C411yescharacteristic
537C22×C4C23×C411yescharacteristic
538C22×C4C23×C411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550M16—22no—
551M16—22no—
552M16—22no—
553M16—22no—
554M16—22no—
555M16—22no—
556M16—22no—
557M16—22no—
558M16—41no—
559M16—41no—
560M16—41no—
561M16—41no—
562M16—41no—
563M16—41no—
564M16—41no—
565M16—41no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C4⋊C4—216no—
579C4⋊C4—22no—
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—44no—
588C4⋊C4—84no—
589C4⋊C4C2×C4214yes—
590C22⋊C4—216no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—44no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C42—216no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—416no—
624C42—416no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—44no—
630C42—84no—
631C42C4×D414yes—
632C42C4×D414yes—
633C42C4×D414yes—
634C42C4×D414yes—
635C42C4×D414yes—
636C42C4×D414yes—
637C42#12112yes—
638C42#12112yes—
639C42#12112yes—
640C42#12112yes—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—41no—
659C23—41no—
660C23C4×C22⋊C414yes—
661C23C22×C22⋊C411yescharacteristic
662C23C2×C4×D411yescharacteristic
663C23C2×C4×D411yescharacteristic
664C23C2×#12011yescharacteristic
665C23C2×#12311yescharacteristic
666C23#52511yescharacteristic
667C23#52511yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—41no—
679D4—41no—
680D4—88no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—432no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—88no—
735C2×C4C4×C22⋊C414yes—
736C2×C4#38614yes—
737C2×C4#38614yes—
738C2×C4C22×C4211yescharacteristic
739C2×C4C2×#11711yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C2×C4×D411yescharacteristic
746C2×C4C2×C4×D411yescharacteristic
747C2×C4C2×C4×D411yescharacteristic
748C2×C4C4×#4111yescharacteristic
749C2×C4C4×#4111yescharacteristic
750C2×C4C4×#4111yescharacteristic
751C2×C4C4×#4111yescharacteristic
752C2×C4C4×#4111yescharacteristic
753C2×C4C4×#4111yescharacteristic
754C2×C4C2×#12111yescharacteristic
755C2×C4C2×#12111yescharacteristic
756C2×C4#52511yescharacteristic
757C2×C4#52511yescharacteristic
758C2×C4#52511yescharacteristic
759C2×C4#52511yescharacteristic
760C2×C4#52911yescharacteristic
761C2×C4#52911yescharacteristic
762C2×C4#52911yescharacteristic
763C2×C4#52911yescharacteristic
764C2×C4#53211yescharacteristic
765C2×C4#53211yescharacteristic
766C8—42no—
767C8—42no—
768C8—42no—
769C8—42no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—82no—
789C22C2×C4×C22⋊C411yescharacteristic
790C22C2×#38611yescharacteristic
791C22#229711yescharacteristic
792C22C4×#12011yescharacteristic
793C22C4×#12011yescharacteristic
794C22C4×#12311yescharacteristic
795C22C4×#12311yescharacteristic
796C22#290114yes—
797C4—28no—
798C4—24no—
799C4—24no—
800C4—24no—
801C4—44no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—82no—
808C4—82no—
809C4C42×D411yescharacteristic
810C4C42×D411yescharacteristic
811C4#229011yescharacteristic
812C4#229011yescharacteristic
813C4C4×#12111yescharacteristic
814C4C4×#12111yescharacteristic
815C4C4×#12111yescharacteristic
816C4C4×#12111yescharacteristic
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—44no—
822C2—82no—
823C2C4×#38611yescharacteristic
824C2#2040512yes—
825C2#2098012yes—
826C2#2141912yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#117C2semidirect
5. C2×#1759C2semidirect
6. C2×C4×#104C2semidirect
7. #20377C2semidirect
8. #10924C2semidirect
9. #10923C2semidirect
10. #10879C2semidirect
11. #10878C2semidirect
12. #10720C2semidirect
13. #10719C2semidirect
14. #10701C2semidirect
15. C4×#339C2semidirect
29. #2324C4semidirect
30. #2323C4semidirect
47. #1897C4semidirect
48. #1896C4semidirect
86. C2×C4×Q8C2×C4semidirect
89. C2×C4×D4C2×C4semidirect
101. C2×#117C2×C4semidirect
120. C22×C42C2×C4semidirect
137. C2×#104C2×C4semidirect
138. C2×#104C2×C4semidirect
141. #407C2×C4semidirect
142. #407C2×C4semidirect
153. #391C2×C4semidirect
155. #390C2×C4semidirect
157. #389C2×C4semidirect
171. C4×C4⋊C4C2×C4semidirect
180. #376D4semidirect
187. C43D4semidirect
196. #339C2×C4semidirect
197. #339C2×C4semidirect
198. #339C2×C4semidirect
199. #339C2×C4semidirect
278. C22⋊Q8C42semidirect
280. #121C42semidirect

Maximal subgroups

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

subgroupindex
#340652
C2×C4×#1172
C2×#18972
C2×#18962
C2×#17592
C2×C4×#1042
#203772
#109242
#109232
#108792
#108782
#107202
#107192
#107012
C4×#3392