Finite Group Databasebeta

← C2×#26930 #6443521

Subgroups — C2×#26930 #6443521

Order 512.

2976 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#481C211yesmaximal, characteristic, complemented
2C22×#460C211yesmaximal, characteristic, complemented
3C2×#2428C211yesmaximal, characteristic
4C2×#2360C211yesmaximal, characteristic, complemented
5#26930C2116yesmaximal, direct product factor
6C2×#2088C211yesmaximal, characteristic, complemented
7C2×#2041C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1968C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1923C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1865C211yesmaximal, characteristic, complemented
16C2×C4×#102C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C22×#127C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121—21no—
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#481—28no—
28C2×#481C2218yescomplemented
29C2×#460—28no—
30C2×#460C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2428—24no—
46#2428C2218yes—
47C2×#394—21no—
48C2×#392—21no—
49#2360—24no—
50#2360C2218yescomplemented
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389—21no—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#387—21no—
57C2×#386—21no—
58C2×#385—21no—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4C2211yescharacteristic
62#2088C2218yescomplemented
63#2041C2218yescomplemented
64#2000C2218yescomplemented
65#2000C2218yescomplemented
66#1968C2218yescomplemented
67#1926C2218yescomplemented
68#1923C2218yescomplemented
69#1877C2218yescomplemented
70#1874C2218yescomplemented
71#1865C2218yescomplemented
72C4×#102C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16—42no—
94C22×SD16—42no—
95C22×SD16C2314yes—
96C22×SD16C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C2×#127—24no—
102C2×#127—22no—
103C2×#127—42no—
104C2×#127C2314yes—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—22no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8C2314yes—
109C2×#121—22no—
110C2×#121—22no—
111C2×#121—28no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—42no—
115C2×#121—42no—
116C2×#121—48no—
117C2×#121C2314yes—
118C2×#121C2314yes—
119C2×C4×Q8—22no—
120C2×C4×Q8—24no—
121C2×C4×Q8—42no—
122C2×C4×Q8C2314yes—
123C2×C4×D4—24no—
124C2×C4×D4—22no—
125C2×C4×D4—42no—
126C2×C4×D4C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—22no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#481—232no—
154#460—232no—
155C2×#106—24no—
156C2×#106—24no—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—24no—
169C2×#102—42no—
170C2×#102D418yescomplemented
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—42no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C4×C8—42no—
182C2×C4×C8C2314yes—
183#394—28no—
184#392—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389—28no—
192#389C2314yes—
193#389C2314yes—
194#387—28no—
195#386—28no—
196#385—28no—
197C4×C4⋊C4—22no—
198C4×C4⋊C4C2314yes—
199C4×C22⋊C4—28no—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8#4114yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4—82no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4C2×D414yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—82no—
277C23×C4—82no—
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—28no—
289C2×SD16—28no—
290C2×SD16—44no—
291C2×SD16—44no—
292C2×SD16—416no—
293C2×SD16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8C2×D414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310#127—28no—
311#127—44no—
312#127—48no—
313C22⋊Q8—216no—
314C22⋊Q8—28no—
315C22⋊Q8—28no—
316#121—28no—
317#121—28no—
318#121—44no—
319#121—44no—
320#121—48no—
321#121—48no—
322#121—432no—
323C4×Q8—28no—
324C4×Q8—44no—
325C4×Q8—48no—
326C4×D4—28no—
327C4×D4—44no—
328C4×D4—48no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—48no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—82no—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4#4114yes—
356C2×C4⋊C4#4114yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4SD1618yescomplemented
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—44no—
385C2×C42—82no—
386C2×C42C2×D412yes—
387C2×C42C2×D412yes—
388C2×C42C2412yes—
389C2×C42C2412yes—
390#106—28no—
391#106—28no—
392C4⋊C8—28no—
393#103—28no—
394#103—44no—
395#102—28no—
396#102—28no—
397#102—28no—
398#102—28no—
399#102—44no—
400#102C2×D4116yescomplemented
401C22⋊C8—28no—
402C22⋊C8—44no—
403C4×C8—44no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95C2×D414yes—
410#95C2×D414yes—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24C2×SD1614yes—
434C24C22×D412yes—
435C24C22×D411yescharacteristic
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8C2×#4114yes—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—84no—
483C2×D4—84no—
484C2×D4—816no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—816no—
488C2×D4—816no—
489C2×D4—816no—
490C2×D4C22×D414yes—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—48no—
545C22×C4—84no—
546C22×C4—816no—
547C22×C4—84no—
548C22×C4—816no—
549C22×C4C2×SD1614yes—
550C22×C4C2×SD1614yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D412yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2×#4112yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4C2511yescharacteristic
564SD16—416no—
565SD16—416no—
566C2×C8—28no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—44no—
579C2×C8—44no—
580C2×C8—44no—
581C2×C8C22×D414yes—
582C4⋊C4—216no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—48no—
598C4⋊C4—84no—
599C4⋊C4C22×D414yes—
600C4⋊C4C2×#4114yes—
601C4⋊C4C2×#4114yes—
602C22⋊C4—216no—
603C22⋊C4—44no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—84no—
609C22⋊C4C2×SD16116yescomplemented
610C42—24no—
611C42—24no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—48no—
617C42—84no—
618C23—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—48no—
635C23—48no—
636C23—48no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23#52512yes—
660C23D4212yes—
661C23#54612yes—
662C23C22×SD1614yes—
663C23C22×SD1612yes—
664C23#57512yes—
665C23#57612yes—
666C23#57712yes—
667C23C23×D411yescharacteristic
668Q8—24no—
669Q8—24no—
670Q8—42no—
671Q8—42no—
672Q8—48no—
673D4—24no—
674D4—24no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—48no—
682D4—816no—
683D4—816no—
684D4—816no—
685D4—816no—
686D4—84no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—816no—
733C2×C4—816no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4#52512yes—
737C2×C4#53214yes—
738C2×C4#54014yes—
739C2×C4D4212yes—
740C2×C4#54614yes—
741C2×C4#54612yes—
742C2×C4#55314yes—
743C2×C4C22×SD1614yes—
744C2×C4C22×SD1614yes—
745C2×C4C23×D411yescharacteristic
746C2×C4C22×#4111yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4111yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C8—24no—
752C8—42no—
753C8—42no—
754C8—42no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—416no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—816no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—168no—
779C22#246414yes—
780C22#310314yes—
781C22#311914yes—
782C22#327314yes—
783C22D4×SD1614yes—
784C22#329514yes—
785C22#331714yes—
786C22C2×#52511yescharacteristic
787C22C2×D4211yescharacteristic
788C22C2×#54611yescharacteristic
789C22C23×SD1611yescharacteristic
790C22C2×#57511yescharacteristic
791C22C2×#57611yescharacteristic
792C22C2×#57711yescharacteristic
793C4—24no—
794C4—24no—
795C4—42no—
796C4—44no—
797C4—42no—
798C4—44no—
799C4—44no—
800C4—44no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4#246414yes—
805C4C2×#53211yescharacteristic
806C4C2×#54011yescharacteristic
807C4C2×#54611yescharacteristic
808C4C2×#55311yescharacteristic
809C2—44no—
810C2—84no—
811C2—162no—
812C2#2693018yesdirect product factor
813C2C2×#246411yescharacteristic
814C2C2×#310311yescharacteristic
815C2C2×#311911yescharacteristic
816C2C2×#327311yescharacteristic
817C2C2×D4×SD1611yescharacteristic
818C2C2×#329511yescharacteristic
819C2C2×#331711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#481C2semidirect
2. C22×#460C2semidirect
4. C2×#2360C2semidirect
5. #26930C2direct (N × H)
6. C2×#2088C2semidirect
7. C2×#2041C2semidirect
8. C2×#2000C2semidirect
9. C2×#2000C2semidirect
10. C2×#1968C2semidirect
11. C2×#1926C2semidirect
12. C2×#1923C2semidirect
13. C2×#1877C2semidirect
14. C2×#1874C2semidirect
15. C2×#1865C2semidirect
16. C2×C4×#102C2semidirect
28. C2×#481C22semidirect
30. C2×#460C22semidirect
50. #2360C22semidirect
62. #2088C22semidirect
63. #2041C22semidirect
64. #2000C22semidirect
65. #2000C22semidirect
66. #1968C22semidirect
67. #1926C22semidirect
68. #1923C22semidirect
69. #1877C22semidirect
70. #1874C22semidirect
71. #1865C22semidirect
72. C4×#102C22semidirect
170. C2×#102D4semidirect
375. C2×C22⋊C4SD16semidirect
400. #102C2×D4semidirect
609. C22⋊C4C2×SD16semidirect
812. C2#26930direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4812
C22×#4602
C2×#24282
C2×#23602
#269302
C2×#20882
C2×#20412
C2×#20002
C2×#19682
C2×#19262
C2×#19232
C2×#18772
C2×#18742
C2×#18652
C2×C4×#1022