Finite Group Databasebeta

← C2×#27270 #6440744

Subgroups — C2×#27270 #6440744

Order 512.

3280 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#486C211yesmaximal, characteristic, complemented
2C22×#417C211yesmaximal, characteristic, complemented
3C2×#2431C211yesmaximal, characteristic
4C2×#2440C211yesmaximal, characteristic, complemented
5#27270C2116yesmaximal, direct product factor
6C2×#2071C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2041C211yesmaximal, characteristic, complemented
9C2×#2024C211yesmaximal, characteristic, complemented
10C2×#1959C211yesmaximal, characteristic, complemented
11C2×#1936C211yesmaximal, characteristic, complemented
12C2×#1933C211yesmaximal, characteristic, complemented
13C2×#1895C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1788C211yesmaximal, characteristic, complemented
16C2×#1753C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×#127C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C22×#121C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C2×#486—28no—
26C2×#486C2218yescomplemented
27C2×#417—28no—
28C2×#417C2218yescomplemented
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×#97C2211yescharacteristic
43C22×C4×C8C2211yescharacteristic
44#2440—24no—
45#2440C2218yescomplemented
46#2431—24no—
47#2431C2218yes—
48C2×#398—21no—
49C2×#395—21no—
50C2×#392—21no—
51C2×#392—21no—
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#386—21no—
57C2×#386—21no—
58C2×#385—21no—
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2071C2218yescomplemented
63#2042C2218yescomplemented
64#2041C2218yescomplemented
65#2024C2218yescomplemented
66#1959C2218yescomplemented
67#1936C2218yescomplemented
68#1933C2218yescomplemented
69#1895C2218yescomplemented
70#1874C2218yescomplemented
71#1788C2218yescomplemented
72#1753C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8—21no—
88C23×Q8C2311yescharacteristic
89C23×D4—21no—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4—21no—
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4—21no—
96C24×C4—21no—
97C24×C4C2311yescharacteristic
98C22×M16—24no—
99C22×M16—24no—
100C22×M16—42no—
101C22×M16C2314yes—
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8—42no—
109C2×C4⋊Q8C2314yes—
110C2×#127—24no—
111C2×#127—22no—
112C2×#127—42no—
113C2×#127C2314yes—
114C2×#124—24no—
115C2×#124—22no—
116C2×#124—42no—
117C2×#124C2314yes—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—48no—
120C2×#121—22no—
121C2×#121—24no—
122C2×#121—24no—
123C2×#121C2314yes—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—22no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
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⋊C4D411yescharacteristic
146C22×C22⋊C4D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#486—232no—
150#417—232no—
151C2×#103—24no—
152C2×#103—24no—
153C2×#103—24no—
154C2×#103—42no—
155C2×#103C2314yes—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#102—24no—
160C2×#102—24no—
161C2×#102—24no—
162C2×#102—24no—
163C2×#102—42no—
164C2×#102—42no—
165C2×#102—42no—
166C2×#102D418yescomplemented
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8C2314yes—
177C2×#97—42no—
178C2×#97C2314yes—
179C2×C4×C8—24no—
180C2×C4×C8C2314yes—
181#398—28no—
182#395—28no—
183#392—28no—
184#392—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389C2314yes—
192#389C2314yes—
193#386—28no—
194#386—28no—
195#385—28no—
196#384—22no—
197#384C2314yes—
198#380—22no—
199#380C2314yes—
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
218C2×#41—232no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—28no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—48no—
226C2×#41—416no—
227C2×#41—48no—
228C2×#41—416no—
229C2×#41—416no—
230C2×#41—48no—
231C22×Q8—21no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—44no—
239C22×Q8—44no—
240C22×Q8—82no—
241C22×Q8#4114yes—
242C22×Q8C2412yes—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—82no—
269C22×D4—82no—
270C22×D4—82no—
271C22×D4—82no—
272C22×D4C2×D414yes—
273C22×D4C2412yes—
274C22×D4C2412yes—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—82no—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D412yes—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4#4114yes—
300C23×C4#4114yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C2×M16—28no—
304C2×M16—28no—
305C2×M16—44no—
306C2×M16—416no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8C2×D414yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—28no—
324C4⋊Q8—44no—
325C4⋊Q8—48no—
326#127—28no—
327#127—44no—
328#127—48no—
329#124—28no—
330#124—44no—
331#124—48no—
332C22⋊Q8—432no—
333#121—28no—
334#121—28no—
335#121—48no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—48no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—82no—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—82no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4C2×D414yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393C2×C42C2412yes—
394C2×C42C2412yes—
395#103—28no—
396#103—28no—
397#103—28no—
398#103—44no—
399#102—28no—
400#102—28no—
401#102—28no—
402#102—28no—
403#102—44no—
404#102—44no—
405#102—44no—
406#102C2×D4116yescomplemented
407C22⋊C8—28no—
408#97—44no—
409C4×C8—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95C2×D414yes—
416#95C2×D414yes—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24#12414yes—
440C24C22×D412yes—
441C24C22×D411yescharacteristic
442#41—232no—
443#41—416no—
444#41—416no—
445#41—416no—
446#41—464no—
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—48no—
456C2×Q8—42no—
457C2×Q8—44no—
458C2×Q8—42no—
459C2×Q8—44no—
460C2×Q8—48no—
461C2×Q8—84no—
462C2×Q8—816no—
463C2×Q8C2×#4114yes—
464C2×D4—28no—
465C2×D4—24no—
466C2×D4—28no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—432no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—816no—
501C2×D4—816no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—816no—
505C2×D4C22×D414yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—24no—
515C22×C4—28no—
516C22×C4—24no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—432no—
539C22×C4—48no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—84no—
559C22×C4—816no—
560C22×C4#12414yes—
561C22×C4#12418yes—
562C22×C4AGL(1,ℤ/8)14yes—
563C22×C4#13714yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4114yes—
572C22×C4C2×#4114yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4H(5,𝔽2)12yes—
577C22×C4H(5,𝔽2)12yes—
578C22×C4C2511yescharacteristic
579M16—416no—
580C2×C8—28no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—44no—
594C2×C8—44no—
595C2×C8C22×D414yes—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—48no—
615C4⋊C4—84no—
616C4⋊C4C22×D414yes—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C42—24no—
626C42—24no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—28no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—42no—
646C23—42no—
647C23—48no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23C2×#12414yes—
673C23C2×#12412yes—
674C23D4212yes—
675C23#54612yes—
676C23C2×AGL(1,ℤ/8)12yes—
677C23C2×#13712yes—
678C23#57612yes—
679C23#57712yes—
680C23C23×D411yescharacteristic
681Q8—24no—
682Q8—24no—
683Q8—42no—
684Q8—42no—
685Q8—48no—
686Q8—816no—
687D4—24no—
688D4—24no—
689D4—432no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—48no—
697D4—816no—
698D4—816no—
699D4—816no—
700D4—84no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—216no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—432no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—816no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#52514yes—
750C2×C4C2×#12414yes—
751C2×C4C2×#12412yes—
752C2×C4#53814yes—
753C2×C4D4212yes—
754C2×C4#54614yes—
755C2×C4#54612yes—
756C2×C4#55114yes—
757C2×C4C2×AGL(1,ℤ/8)14yes—
758C2×C4C2×#13714yes—
759C2×C4C23×D411yescharacteristic
760C2×C4C22×#4111yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C22×#4111yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C8—24no—
766C8—42no—
767C8—42no—
768C8—42no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—42no—
773C22—42no—
774C22—416no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—816no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—168no—
793C22#247214yes—
794C22#313614yes—
795C22#314114yes—
796C22#326414yes—
797C22#326614yes—
798C22#333214yes—
799C22#333314yes—
800C22C22×#12411yescharacteristic
801C22C2×D4211yescharacteristic
802C22C2×#54611yescharacteristic
803C22C22×AGL(1,ℤ/8)11yescharacteristic
804C22C22×#13711yescharacteristic
805C22C2×#57611yescharacteristic
806C22C2×#57711yescharacteristic
807C4—24no—
808C4—24no—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#247214yes—
819C4C2×#52511yescharacteristic
820C4C2×#53811yescharacteristic
821C4C2×#54611yescharacteristic
822C4C2×#55111yescharacteristic
823C2—44no—
824C2—84no—
825C2—162no—
826C2#2727018yesdirect product factor
827C2C2×#247211yescharacteristic
828C2C2×#313611yescharacteristic
829C2C2×#314111yescharacteristic
830C2C2×#326411yescharacteristic
831C2C2×#326611yescharacteristic
832C2C2×#333211yescharacteristic
833C2C2×#333311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2431C2
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×#486C2semidirect
2. C22×#417C2semidirect
4. C2×#2440C2semidirect
5. #27270C2direct (N × H)
6. C2×#2071C2semidirect
7. C2×#2042C2semidirect
8. C2×#2041C2semidirect
9. C2×#2024C2semidirect
10. C2×#1959C2semidirect
11. C2×#1936C2semidirect
12. C2×#1933C2semidirect
13. C2×#1895C2semidirect
14. C2×#1874C2semidirect
15. C2×#1788C2semidirect
16. C2×#1753C2semidirect
26. C2×#486C22semidirect
28. C2×#417C22semidirect
45. #2440C22semidirect
62. #2071C22semidirect
63. #2042C22semidirect
64. #2041C22semidirect
65. #2024C22semidirect
66. #1959C22semidirect
67. #1936C22semidirect
68. #1933C22semidirect
69. #1895C22semidirect
70. #1874C22semidirect
71. #1788C22semidirect
72. #1753C22semidirect
166. C2×#102D4semidirect
406. #102C2×D4semidirect
826. C2#27270direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4862
C22×#4172
C2×#24312
C2×#24402
#272702
C2×#20712
C2×#20422
C2×#20412
C2×#20242
C2×#19592
C2×#19362
C2×#19332
C2×#18952
C2×#18742
C2×#17882
C2×#17532