Finite Group Databasebeta

← C2×#23575 #6432011

Subgroups — C2×#23575 #6432011

Order 512.

4102 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C22×#442C211yesmaximal, characteristic, complemented
3C22×#440C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#23575C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2035C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#2025C211yesmaximal, characteristic, complemented
11C2×#2012C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic, complemented
13C2×#1999C211yesmaximal, characteristic
14C2×#1763C211yesmaximal, characteristic, complemented
15C2×#1762C211yesmaximal, characteristic, complemented
16C2×#1749C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C2×#529—24no—
20C2×#529—28no—
21C2×#529—28no—
22C2×#529C2218yescomplemented
23C22×#126—21no—
24C22×#125C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#123—21no—
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4—21no—
32C22×C4×D4—21no—
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117—21no—
36C23×C42C2211yescharacteristic
37C2×#442—28no—
38C2×#442C2218yescomplemented
39C2×#440—28no—
40C2×#440C2218yescomplemented
41C22×#107C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53C22×#97C2211yescharacteristic
54C22×#97C2211yescharacteristic
55C4×#121—24no—
56C4×#121C2218yescomplemented
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#386—21no—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4—21no—
64#2059C2218yescomplemented
65#2042C2218yescomplemented
66#2035C2218yescomplemented
67#2033C2218yescomplemented
68#2025C2218yescomplemented
69#2012C2218yescomplemented
70#2000C2218yescomplemented
71#1999C2218yes—
72#1763C2218yescomplemented
73#1762C2218yescomplemented
74#1749C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4—21no—
88C24×C4D411yescharacteristic
89C24×C4D411yescharacteristic
90C24×C4C2311yescharacteristic
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16—24no—
94C22×SD16C2314yes—
95C22×D8—24no—
96C22×D8—24no—
97C22×D8—24no—
98C22×D8C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103#529—264no—
104#529—232no—
105#529—232no—
106C2×#126—216no—
107C2×#126—28no—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125—22no—
111C2×#125C2314yes—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—22no—
115C2×#124C2314yes—
116C2×#123—216no—
117C2×#123—28no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8C2314yes—
122C2×#121—24no—
123C2×#121—24no—
124C2×#121—22no—
125C2×#121—22no—
126C2×#121—24no—
127C2×#121—24no—
128C2×#121C2314yes—
129C2×#121C2314yes—
130C2×C4×Q8—24no—
131C2×C4×Q8—22no—
132C2×C4×Q8D418yescomplemented
133C2×C4×Q8C2314yes—
134C2×C4×D4—216no—
135C2×C4×D4—28no—
136C2×C4×D4—28no—
137C2×C4×D4—22no—
138C2×C4×D4—24no—
139C2×C4×D4—22no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—48no—
143C2×C4×D4D418yescomplemented
144C2×C4×D4C2314yes—
145C2×C4×D4C2314yes—
146C2×#117—216no—
147C2×#117—28no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C42—21no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—21no—
172C22×C42D411yescharacteristic
173C22×C42D411yescharacteristic
174C22×C42D414yes—
175C22×C42C2311yescharacteristic
176C22×C42C2314yes—
177C22×C42C2311yescharacteristic
178#442—232no—
179#440—232no—
180C2×#107—24no—
181C2×#107C2314yes—
182C2×#106—24no—
183C2×#106C2314yes—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—24no—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#102—24no—
191C2×#102—24no—
192C2×#102—24no—
193C2×#102—24no—
194C2×#102—24no—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×C22⋊C8—24no—
201C2×C22⋊C8—24no—
202C2×C22⋊C8C2314yes—
203C2×C22⋊C8C2314yes—
204C2×#97—24no—
205C2×#97—24no—
206C2×#97C2314yes—
207C2×#97C2314yes—
208#390—22no—
209#390C2314yes—
210#389—22no—
211#389C2314yes—
212#388—28no—
213#386—28no—
214#380—22no—
215#380C2314yes—
216C4×C4⋊C4—22no—
217C4×C4⋊C4C2314yes—
218C4×C22⋊C4—28no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25—21no—
230C25C2×D411yescharacteristic
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4C2×D414yes—
260C22×D4#4114yes—
261C22×D4C2412yes—
262C22×D4C2412yes—
263C23×C4—24no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—28no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4C2×D412yes—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D414yes—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D414yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C2×SD16—232no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—28no—
303C2×D8—232no—
304C2×D8—28no—
305C2×D8—28no—
306C2×D8—28no—
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#4114yes—
318C22×C8#4114yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323#126—264no—
324#125—216no—
325#125—28no—
326#125—28no—
327#124—216no—
328#124—28no—
329#124—28no—
330#123—264no—
331C22⋊Q8—216no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334#121—216no—
335#121—216no—
336#121—28no—
337#121—28no—
338#121—28no—
339#121—28no—
340C4×Q8—216no—
341C4×Q8—28no—
342C4×Q8C2×D4116yescomplemented
343C4×D4—264no—
344C4×D4—216no—
345C4×D4—28no—
346C4×D4—28no—
347C4×D4—28no—
348C4×D4—432no—
349C4×D4—48no—
350C4×D4C2×D4116yescomplemented
351#117—264no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4#4114yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C42—24no—
403C2×C42—28no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—216no—
409C2×C42—28no—
410C2×C42—28no—
411C2×C42—24no—
412C2×C42—44no—
413C2×C42C2×D414yes—
414C2×C42C2×D412yes—
415C2×C42C2×D414yes—
416C2×C42C2×D412yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42C2412yes—
420C2×C42C2412yes—
421#107—28no—
422#106—28no—
423#103—28no—
424#103—28no—
425#103—28no—
426#102—28no—
427#102—28no—
428#102—28no—
429#102—28no—
430#102—28no—
431C22⋊C8—28no—
432C22⋊C8—28no—
433#97—28no—
434#97—28no—
435#95—24no—
436#95—24no—
437#95—24no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24AGL(1,ℤ/8)14yes—
461C24C22×D412yes—
462C24C22×D411yescharacteristic
463C2×Q8—24no—
464C2×Q8—22no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—44no—
472C2×Q8—42no—
473C2×Q8—44no—
474C2×Q8—42no—
475C2×Q8C22×D414yes—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—24no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—24no—
483C2×D4—28no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—432no—
495C2×D4—432no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4C22×D414yes—
509C2×D4C2×#4114yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—28no—
533C22×C4—24no—
534C22×C4—28no—
535C22×C4—216no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—432no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—48no—
575C22×C4—816no—
576C22×C4#12014yes—
577C22×C4#12014yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2511yescharacteristic
591SD16—232no—
592D8—232no—
593C2×C8—28no—
594C2×C8—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—44no—
606C2×C8—44no—
607C2×C8C2×#4114yes—
608C2×C8C2×#4114yes—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—48no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C22×D414yes—
627C4⋊C4C22×D414yes—
628C4⋊C4C2×#4114yes—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C42—28no—
640C42—24no—
641C42—28no—
642C42—216no—
643C42—22no—
644C42—22no—
645C42—48no—
646C42#12018yes—
647C42C22×D414yes—
648C42C22×D414yes—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—22no—
654C23—28no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—48no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—48no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23C2×#12012yes—
691C23#52512yes—
692C23#53212yes—
693C23C2×AGL(1,ℤ/8)14yes—
694C23C2×AGL(1,ℤ/8)12yes—
695C23#57512yes—
696C23#57512yes—
697C23#57512yes—
698C23C23×D411yescharacteristic
699Q8—24no—
700Q8—24no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704D4—24no—
705D4—24no—
706D4—24no—
707D4—24no—
708D4—432no—
709D4—432no—
710D4—48no—
711D4—48no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—416no—
736C2×C4—416no—
737C2×C4—432no—
738C2×C4—48no—
739C2×C4—44no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—816no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4C2×#12014yes—
768C2×C4C2×#12014yes—
769C2×C4C2×#12012yes—
770C2×C4#52512yes—
771C2×C4#52514yes—
772C2×C4#52514yes—
773C2×C4#53212yes—
774C2×C4#53214yes—
775C2×C4#53214yes—
776C2×C4C23×D411yescharacteristic
777C2×C4C23×D411yescharacteristic
778C2×C4C22×#4111yescharacteristic
779C2×C4C22×#4111yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C22×#4111yescharacteristic
782C8—24no—
783C8—24no—
784C8—42no—
785C8—42no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—416no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—816no—
805C22—816no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22#238814yes—
811C22#300514yes—
812C22#300614yes—
813C22#311114yes—
814C22#311414yes—
815C22#318014yes—
816C22#318314yes—
817C22C22×#12011yescharacteristic
818C22C2×#52511yescharacteristic
819C22C2×#53211yescharacteristic
820C22C22×AGL(1,ℤ/8)11yescharacteristic
821C22C2×#57511yescharacteristic
822C22C2×#57511yescharacteristic
823C22C2×#57511yescharacteristic
824C4—24no—
825C4—24no—
826C4—44no—
827C4—42no—
828C4—44no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—82no—
834C4—82no—
835C4#238814yes—
836C4C2×#52511yescharacteristic
837C4C2×#52511yescharacteristic
838C4C2×#53211yescharacteristic
839C4C2×#53211yescharacteristic
840C2—44no—
841C2—84no—
842C2—84no—
843C2#2357518yesdirect product factor
844C2C2×#238811yescharacteristic
845C2C2×#300511yescharacteristic
846C2C2×#300611yescharacteristic
847C2C2×#311411yescharacteristic
848C2C2×#311111yescharacteristic
849C2C2×#318011yescharacteristic
850C2C2×#318311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C22×#442C2semidirect
3. C22×#440C2semidirect
4. C2×C4×#121C2semidirect
5. #23575C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2042C2semidirect
8. C2×#2035C2semidirect
9. C2×#2033C2semidirect
10. C2×#2025C2semidirect
11. C2×#2012C2semidirect
12. C2×#2000C2semidirect
14. C2×#1763C2semidirect
15. C2×#1762C2semidirect
16. C2×#1749C2semidirect
22. C2×#529C22semidirect
38. C2×#442C22semidirect
40. C2×#440C22semidirect
56. C4×#121C22semidirect
64. #2059C22semidirect
65. #2042C22semidirect
66. #2035C22semidirect
67. #2033C22semidirect
68. #2025C22semidirect
69. #2012C22semidirect
70. #2000C22semidirect
72. #1763C22semidirect
73. #1762C22semidirect
74. #1749C22semidirect
132. C2×C4×Q8D4semidirect
143. C2×C4×D4D4semidirect
342. C4×Q8C2×D4semidirect
350. C4×D4C2×D4semidirect
843. C2#23575direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5292
C22×#4422
C22×#4402
C2×C4×#1212
#235752
C2×#20592
C2×#20422
C2×#20352
C2×#20332
C2×#20252
C2×#20122
C2×#20002
C2×#19992
C2×#17632
C2×#17622
C2×#17492