Finite Group Databasebeta

← C2×#25375 #6444136

Subgroups — C2×#25375 #6444136

Order 512.

2998 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#495C211yesmaximal, characteristic
2C22×#464C211yesmaximal, characteristic, complemented
3C22×#464C211yesmaximal, characteristic, complemented
4C22×#461C211yesmaximal, characteristic, complemented
5C2×#2545C211yesmaximal, characteristic, complemented
6C2×#2367C211yesmaximal, characteristic, complemented
7#25375C2116yesmaximal, direct product factor
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2055C211yesmaximal, characteristic, complemented
10C2×#2016C211yesmaximal, characteristic, complemented
11C2×#2012C211yesmaximal, characteristic
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1939C211yesmaximal, characteristic, complemented
14C2×#1878C211yesmaximal, characteristic, complemented
15C2×#1879C211yesmaximal, characteristic
16C2×C4×#103C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×D8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C2×#495—28no—
31C2×#495C2218yes—
32C2×#464—28no—
33C2×#464—28no—
34C2×#464C2218yescomplemented
35C2×#464C2218yescomplemented
36C2×#461—28no—
37C2×#461C2218yescomplemented
38C22×C4⋊C8C2211yescharacteristic
39C22×C4⋊C8C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×C4×C8C2211yescharacteristic
50#2545—24no—
51#2545C2218yescomplemented
52C2×#396—21no—
53C2×#396—21no—
54#2367—24no—
55#2367C2218yescomplemented
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#388—21no—
61C2×#388—21no—
62C2×#388—21no—
63C2×#388—21no—
64C2×#385—21no—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4—21no—
68#2055C2218yescomplemented
69#2055C2218yescomplemented
70#2016C2218yescomplemented
71#2012C2218yes—
72#1983C2218yescomplemented
73#1939C2218yescomplemented
74#1879C2218yes—
75#1878C2218yescomplemented
76C4×#103C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C22×Q16—24no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16—42no—
93C22×Q16C2314yes—
94C22×Q16C2314yes—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C22×D8—24no—
108C22×D8—24no—
109C22×D8—42no—
110C22×D8C2314yes—
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113C23×C8C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2314yes—
119C2×#124—24no—
120C2×#124—22no—
121C2×#124—22no—
122C2×#124—22no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—24no—
126C2×#124—42no—
127C2×#124D418yes—
128C2×#124C2314yes—
129C2×#124C2314yes—
130C2×#124C2314yes—
131C2×C4×Q8—22no—
132C2×C4×Q8—22no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—42no—
137C2×C4×Q8C2314yes—
138C2×C4×Q8C2314yes—
139C2×C4×D4—24no—
140C2×C4×D4—22no—
141C2×C4×D4—42no—
142C2×C4×D4C2314yes—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4D411yescharacteristic
148C22×C4⋊C4D411yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C42—21no—
164C22×C42—21no—
165C22×C42—21no—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#495—232no—
170#464—232no—
171#464—232no—
172#461—232no—
173C2×C4⋊C8—24no—
174C2×C4⋊C8—24no—
175C2×C4⋊C8—24no—
176C2×C4⋊C8C2314yes—
177C2×C4⋊C8C2314yes—
178C2×C4⋊C8C2314yes—
179C2×#103—24no—
180C2×#103—24no—
181C2×#103—24no—
182C2×#103—42no—
183C2×#103D418yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102—24no—
190C2×#102—24no—
191C2×#102—42no—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×C4×C8—24no—
196C2×C4×C8C2314yes—
197#396—28no—
198#396—28no—
199#391—22no—
200#391—22no—
201#391C2314yes—
202#391C2314yes—
203#390—22no—
204#390—22no—
205#390C2314yes—
206#390C2314yes—
207#388—28no—
208#388—28no—
209#388—28no—
210#388—28no—
211#385—28no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4D414yes—
214C4×C4⋊C4C2314yes—
215C4×C4⋊C4C2314yes—
216C4×C22⋊C4—28no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25—21no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8C2×D414yes—
250C22×Q8C2×D414yes—
251C22×Q8C2412yes—
252C22×Q8C2412yes—
253C22×Q8C2412yes—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—21no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4C2×D414yes—
268C22×D4C2412yes—
269C22×D4C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—82no—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2411yescharacteristic
287C2×Q16—28no—
288C2×Q16—28no—
289C2×Q16—28no—
290C2×Q16—28no—
291C2×Q16—44no—
292C2×Q16—44no—
293C2×Q16—416no—
294C2×Q16—416no—
295C2×SD16—28no—
296C2×SD16—28no—
297C2×SD16—28no—
298C2×SD16—28no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×SD16—44no—
302C2×SD16—44no—
303C2×SD16—44no—
304C2×SD16—416no—
305C2×SD16—416no—
306C2×SD16—416no—
307C2×D8—28no—
308C2×D8—28no—
309C2×D8—44no—
310C2×D8—416no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8C2×D414yes—
322C22×C8#4114yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—28no—
328C4⋊Q8—44no—
329C4⋊Q8—48no—
330#124—28no—
331#124—216no—
332#124—28no—
333#124—28no—
334#124—28no—
335#124—44no—
336#124—48no—
337#124—48no—
338#124C2×D4116yes—
339C4×Q8—28no—
340C4×Q8—28no—
341C4×Q8—28no—
342C4×Q8—44no—
343C4×Q8—48no—
344C4×Q8—48no—
345C4×D4—28no—
346C4×D4—44no—
347C4×D4—48no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—82no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—44no—
402C2×C42—44no—
403C2×C42—82no—
404C2×C42C2×D412yes—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D414yes—
408C2×C42#4114yes—
409C2×C42C2412yes—
410C2×C42C2412yes—
411C2×C42C2412yes—
412C4⋊C8—28no—
413C4⋊C8—28no—
414C4⋊C8—28no—
415#103—28no—
416#103—28no—
417#103—28no—
418#103—44no—
419#103C2×D4116yes—
420#102—28no—
421#102—28no—
422#102—44no—
423C4×C8—28no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95C2×D414yes—
430#95C2×D414yes—
431C24—24no—
432C24—22no—
433C24—22no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24C22×D411yescharacteristic
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—44no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8C22×D414yes—
486C2×Q8C22×D414yes—
487C2×D4—24no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4C22×D414yes—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
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—22no—
537C22×C4—48no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—48no—
554C22×C4—84no—
555C22×C4—816no—
556C22×C4#12114yes—
557C22×C4#12114yes—
558C22×C4#13514yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4C2511yescharacteristic
573Q16—416no—
574Q16—416no—
575SD16—416no—
576SD16—416no—
577SD16—416no—
578D8—416no—
579C2×C8—28no—
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—44no—
592C2×C8—44no—
593C2×C8C22×D414yes—
594C2×C8C2×#4114yes—
595C4⋊C4—24no—
596C4⋊C4—28no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—44no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—42no—
607C4⋊C4—48no—
608C4⋊C4—42no—
609C4⋊C4C22×D414yes—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—84no—
621C42—24no—
622C42—24no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—48no—
628C42—48no—
629C42—84no—
630C42#12118yes—
631C42C22×D414yes—
632C42C2×#4114yes—
633C23—24no—
634C23—48no—
635C23—42no—
636C23—42no—
637C23—48no—
638C23—48no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23C2×#12112yes—
662C23D4212yes—
663C23#55012yes—
664C23C2×#13512yes—
665C23#57512yes—
666C23#57712yes—
667C23#57812yes—
668C23C23×D411yescharacteristic
669Q8—24no—
670Q8—24no—
671Q8—24no—
672Q8—24no—
673Q8—42no—
674Q8—48no—
675Q8—48no—
676Q8—42no—
677Q8—42no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—84no—
684D4—24no—
685D4—24no—
686D4—42no—
687D4—42no—
688D4—48no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—84no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—816no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C2×#12114yes—
741C2×C4C2×#12114yes—
742C2×C4C2×#12112yes—
743C2×C4#53214yes—
744C2×C4#54014yes—
745C2×C4D4212yes—
746C2×C4D4214yes—
747C2×C4#54614yes—
748C2×C4#55012yes—
749C2×C4C2×#13514yes—
750C2×C4C23×D411yescharacteristic
751C2×C4C23×D411yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C8—24no—
757C8—24no—
758C8—42no—
759C8—42no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—816no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—168no—
776C22#242814yes—
777C22#303514yes—
778C22#304614yes—
779C22#327714yes—
780C22#328214yes—
781C22#339314yes—
782C22#340114yes—
783C22C22×#12111yescharacteristic
784C22C2×D4211yescharacteristic
785C22C2×#55011yescharacteristic
786C22C22×#13511yescharacteristic
787C22C2×#57511yescharacteristic
788C22C2×#57711yescharacteristic
789C22C2×#57811yescharacteristic
790C4—24no—
791C4—24no—
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#242814yes—
803C4C2×#53211yescharacteristic
804C4C2×#54011yescharacteristic
805C4C2×D4211yescharacteristic
806C4C2×#54611yescharacteristic
807C2—84no—
808C2—162no—
809C2#2537518yesdirect product factor
810C2C2×#242811yescharacteristic
811C2C2×#303511yescharacteristic
812C2C2×#304611yescharacteristic
813C2C2×#327711yescharacteristic
814C2C2×#328211yescharacteristic
815C2C2×#339311yescharacteristic
816C2C2×#340111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#464C2semidirect
3. C22×#464C2semidirect
4. C22×#461C2semidirect
5. C2×#2545C2semidirect
6. C2×#2367C2semidirect
7. #25375C2direct (N × H)
8. C2×#2055C2semidirect
9. C2×#2055C2semidirect
10. C2×#2016C2semidirect
12. C2×#1983C2semidirect
13. C2×#1939C2semidirect
14. C2×#1878C2semidirect
16. C2×C4×#103C2semidirect
34. C2×#464C22semidirect
35. C2×#464C22semidirect
37. C2×#461C22semidirect
51. #2545C22semidirect
55. #2367C22semidirect
68. #2055C22semidirect
69. #2055C22semidirect
70. #2016C22semidirect
72. #1983C22semidirect
73. #1939C22semidirect
75. #1878C22semidirect
76. C4×#103C22semidirect
809. C2#25375direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4952
C22×#4642
C22×#4612
C2×#25452
C2×#23672
#253752
C2×#20552
C2×#20162
C2×#20122
C2×#19832
C2×#19392
C2×#18782
C2×#18792
C2×C4×#1032