Finite Group Databasebeta

← C2×#30603 #7501242

Subgroups — C2×#30603 #7501242

Order 512.

2758 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#463C211yesmaximal, characteristic, complemented
3C2×#2426C211yesmaximal, characteristic, complemented
4C2×#2422C211yesmaximal, characteristic, complemented
5#30603C2116yesmaximal, direct product factor
6C2×#2094C211yesmaximal, characteristic, complemented
7C2×#2088C211yesmaximal, characteristic, complemented
8C2×#2054C211yesmaximal, characteristic, complemented
9C2×#2042C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#1999C211yesmaximal, characteristic
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1880C211yesmaximal, characteristic, complemented
14C2×#1864C211yesmaximal, characteristic, complemented
15C2×#1850C211yesmaximal, characteristic, complemented
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C22×#123—21no—
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#465—28no—
28C2×#465C2218yescomplemented
29C2×#463—28no—
30C2×#463C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2426—24no—
45#2426C2218yescomplemented
46#2422—24no—
47#2422C2218yescomplemented
48C2×#397—21no—
49C2×#396—21no—
50C2×#394—21no—
51C2×#394—21no—
52C2×#390—21no—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#385—21no—
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2094C2218yescomplemented
63#2088C2218yescomplemented
64#2054C2218yescomplemented
65#2042C2218yescomplemented
66#2035C2218yescomplemented
67#1999C2218yes—
68#1893C2218yescomplemented
69#1880C2218yescomplemented
70#1864C2218yescomplemented
71#1850C2218yescomplemented
72#1803C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4C2311yescharacteristic
86C22×SD16—42no—
87C22×SD16—42no—
88C22×SD16D418yescomplemented
89C22×SD16C2314yes—
90C22×D8—24no—
91C22×D8—42no—
92C22×D8—42no—
93C22×D8C2314yes—
94C23×C8—24no—
95C23×C8—42no—
96C23×C8—42no—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2314yes—
102C2×#124—24no—
103C2×#124—22no—
104C2×#124—42no—
105C2×#124C2314yes—
106C2×#123—28no—
107C2×#123—48no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8C2314yes—
112C2×#121—22no—
113C2×#121—22no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—42no—
117C2×#121—42no—
118C2×#121C2314yes—
119C2×#121C2314yes—
120C2×C4×Q8—22no—
121C2×C4×Q8—24no—
122C2×C4×Q8—42no—
123C2×C4×Q8C2314yes—
124C2×C4×D4—24no—
125C2×C4×D4—22no—
126C2×C4×D4—42no—
127C2×C4×D4C2314yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
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⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4D411yescharacteristic
151C22×C22⋊C4D411yescharacteristic
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#465—232no—
156#463—232no—
157C2×#106—24no—
158C2×#106—42no—
159C2×#106C2314yes—
160C2×#106C2314yes—
161C2×C4⋊C8—24no—
162C2×C4⋊C8—42no—
163C2×C4⋊C8C2314yes—
164C2×C4⋊C8C2314yes—
165C2×#103—24no—
166C2×#103—24no—
167C2×#103—42no—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—24no—
174C2×#102—42no—
175C2×#102—42no—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×C22⋊C8—42no—
182C2×C22⋊C8C2314yes—
183#397—28no—
184#396—28no—
185#394—28no—
186#394—28no—
187#390—28no—
188#390—22no—
189#390—22no—
190#390C2314yes—
191#390C2314yes—
192#389—22no—
193#389—22no—
194#389C2314yes—
195#389C2314yes—
196#388—28no—
197#385—28no—
198#384—22no—
199#384C2314yes—
200#380—22no—
201#380C2314yes—
202C4×C22⋊C4D414yes—
203C4×C22⋊C4C2314yes—
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×Q8C2×D414yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—22no—
232C22×D4—22no—
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—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—82no—
246C22×D4—82no—
247C22×D4C2×D414yes—
248C22×D4C2412yes—
249C22×D4C2412yes—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—24no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4—82no—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C2×SD16—416no—
275C2×SD16—44no—
276C2×SD16—44no—
277C2×SD16C2×D4116yescomplemented
278C2×D8—28no—
279C2×D8—44no—
280C2×D8—44no—
281C2×D8—416no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—28no—
294C22×C8—44no—
295C22×C8—44no—
296C22×C8—416no—
297C22×C8C2×D414yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302#124—28no—
303#124—44no—
304#124—48no—
305#123—432no—
306C22⋊Q8—28no—
307C22⋊Q8—44no—
308C22⋊Q8—48no—
309#121—28no—
310#121—28no—
311#121—44no—
312#121—44no—
313#121—48no—
314#121—48no—
315C4×Q8—28no—
316C4×Q8—44no—
317C4×Q8—48no—
318C4×D4—28no—
319C4×D4—44no—
320C4×D4—48no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—82no—
346C2×C4⋊C4—82no—
347C2×C4⋊C4#4114yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—44no—
385C2×C42C2×D412yes—
386C2×C42C2×D412yes—
387C2×C42C2412yes—
388C2×C42C2412yes—
389#106—28no—
390#106—44no—
391C4⋊C8—28no—
392C4⋊C8—44no—
393#103—28no—
394#103—28no—
395#103—44no—
396#102—28no—
397#102—28no—
398#102—28no—
399#102—44no—
400#102—44no—
401C22⋊C8—44no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95C2×D414yes—
406#95C2×D414yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24AGL(1,ℤ/8)14yes—
430C24C22×D412yes—
431C24C22×D411yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8C22×D414yes—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—816no—
477C2×D4—816no—
478C2×D4C22×D414yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
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—48no—
511C22×C4—48no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—84no—
533C22×C4—816no—
534C22×C4#13514yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C42−1+412yes—
547C22×C4C2511yescharacteristic
548SD16—416no—
549D8—416no—
550C2×C8—28no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—416no—
563C2×C8—44no—
564C2×C8—44no—
565C2×C8—44no—
566C2×C8C22×D414yes—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4C2×#4114yes—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—84no—
601C42—24no—
602C42—24no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—48no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—48no—
623C23—42no—
624C23—42no—
625C23—48no—
626C23—48no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23#53712yes—
650C23D4212yes—
651C23#54612yes—
652C23C2×#13512yes—
653C23C2×AGL(1,ℤ/8)14yes—
654C23C2×AGL(1,ℤ/8)12yes—
655C23#57712yes—
656C23#57712yes—
657C23C23×D411yescharacteristic
658Q8—24no—
659Q8—24no—
660Q8—48no—
661Q8—42no—
662Q8—42no—
663D4—24no—
664D4—24no—
665D4—48no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—816no—
673D4—816no—
674D4—84no—
675C2×C4—22no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—44no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—48no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—816no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4#53414yes—
725C2×C4#53712yes—
726C2×C4#54014yes—
727C2×C4D4212yes—
728C2×C4#54612yes—
729C2×C4#54714yes—
730C2×C4#56214yes—
731C2×C4C2×#13514yes—
732C2×C4C23×D411yescharacteristic
733C2×C4C22×#4111yescharacteristic
734C2×C4C2×H(5,𝔽2)11yescharacteristic
735C2×C4C2×H(5,𝔽2)11yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4C2×2−1+411yescharacteristic
738C8—24no—
739C8—42no—
740C8—42no—
741C8—42no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—416no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—816no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—168no—
766C22#267114yes—
767C22#324714yes—
768C22#326314yes—
769C22#326514yes—
770C22#328414yes—
771C22#330114yes—
772C22#330614yes—
773C22C2×#53711yescharacteristic
774C22C2×D4211yescharacteristic
775C22C2×#54611yescharacteristic
776C22C22×#13511yescharacteristic
777C22C22×AGL(1,ℤ/8)11yescharacteristic
778C22C2×#57711yescharacteristic
779C22C2×#57711yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—42no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4#267114yes—
792C4C2×#53411yescharacteristic
793C4C2×#54011yescharacteristic
794C4C2×#54711yescharacteristic
795C4C2×#56211yescharacteristic
796C2—44no—
797C2—84no—
798C2—162no—
799C2#3060318yesdirect product factor
800C2C2×#267111yescharacteristic
801C2C2×#324711yescharacteristic
802C2C2×#326311yescharacteristic
803C2C2×#326511yescharacteristic
804C2C2×#328411yescharacteristic
805C2C2×#330111yescharacteristic
806C2C2×#330611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
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×#465C2semidirect
2. C22×#463C2semidirect
3. C2×#2426C2semidirect
4. C2×#2422C2semidirect
5. #30603C2direct (N × H)
6. C2×#2094C2semidirect
7. C2×#2088C2semidirect
8. C2×#2054C2semidirect
9. C2×#2042C2semidirect
10. C2×#2035C2semidirect
12. C2×#1893C2semidirect
13. C2×#1880C2semidirect
14. C2×#1864C2semidirect
15. C2×#1850C2semidirect
16. C2×#1803C2semidirect
28. C2×#465C22semidirect
30. C2×#463C22semidirect
45. #2426C22semidirect
47. #2422C22semidirect
62. #2094C22semidirect
63. #2088C22semidirect
64. #2054C22semidirect
65. #2042C22semidirect
66. #2035C22semidirect
68. #1893C22semidirect
69. #1880C22semidirect
70. #1864C22semidirect
71. #1850C22semidirect
72. #1803C22semidirect
88. C22×SD16D4semidirect
277. C2×SD16C2×D4semidirect
799. C2#30603direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×#4632
C2×#24262
C2×#24222
#306032
C2×#20942
C2×#20882
C2×#20542
C2×#20422
C2×#20352
C2×#19992
C2×#18932
C2×#18802
C2×#18642
C2×#18502
C2×#18032