Finite Group Databasebeta

← C2×#6520234 #72316170

Subgroups — C2×#6520234 #72316170

Order 1024.

23141 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3213C212yesmaximal, complemented
2C22×#3109C212yesmaximal, complemented
3C2×#35166C211yesmaximal, characteristic, complemented
4C22×#2544C211yesmaximal, characteristic, complemented
5#6520234C2132yesmaximal, direct product factor
6C2×#28475C218yesmaximal, complemented
7C2×#28430C218yesmaximal, complemented
8C2×#28310C212yesmaximal, complemented
9C2×#28305C212yesmaximal, complemented
10C2×#25731C212yesmaximal, complemented
11C2×#25721C212yesmaximal, complemented
12C2×#20534C211yesmaximal, characteristic, complemented
13C22×#537—22no—
14C22×#532C2212yes—
15C23×#127C2211yescharacteristic
16C23×#124C2211yescharacteristic
17C23×#124C2211yescharacteristic
18C23×C4×D4C2211yescharacteristic
19C2×#3213—232no—
20C2×#3213C22132yescomplemented
21C22×#496C2214yescomplemented
22C22×#496C2214yescomplemented
23C22×#493C2214yes—
24C22×#489C2214yescomplemented
25C2×#3109—232no—
26C2×#3109C22132yescomplemented
27C22×#481C2214yes—
28C22×#476C2214yescomplemented
29C22×#463C2218yescomplemented
30C22×#459C2214yescomplemented
31C22×#448C2214yes—
32C22×#447C2214yes—
33C22×#447C2214yes—
34C22×#442C2218yescomplemented
35C22×#432C2212yes—
36C2×#2856C2212yes—
37C2×#2856C2212yes—
38#35166—28no—
39#35166C22116yescomplemented
40C2×#2542C2214yescomplemented
41C2×#2541C2214yescomplemented
42C2×#2540—24no—
43C2×#2544—24no—
44C2×#2544—28no—
45C2×#2544C2218yes—
46C2×#2544C22116yescomplemented
47C2×#2656—22no—
48C22×#394—22no—
49C22×#391C2211yescharacteristic
50C22×#390C2211yescharacteristic
51C22×#386—22no—
52C22×C4×C4⋊C4C2211yescharacteristic
53#28475C221128yescomplemented
54#28430C221128yescomplemented
55#28310C22132yescomplemented
56#28305C22132yescomplemented
57#25731C22132yescomplemented
58#25721C22132yescomplemented
59C2×#2096C2214yescomplemented
60C2×#2094C2214yescomplemented
61C2×#2012C2218yescomplemented
62C2×#2014C2214yescomplemented
63C2×#2011C2218yes—
64C2×#2011C2214yescomplemented
65C2×#1972C2218yescomplemented
66C2×#1968C2218yescomplemented
67C2×#1959C2214yescomplemented
68C2×#1957C2214yes—
69#20534C22116yescomplemented
70C2×#1771C2218yescomplemented
71C2×#1749C2212yes—
72C2×C4×C22⋊C8C2212yes—
73C23×#41—22no—
74C24×Q8C2311yescharacteristic
75C24×D4—22no—
76C24×D4C2311yescharacteristic
77C24×D4C2311yescharacteristic
78C25×C4—21no—
79C23×SD16C2318yes—
80C23×D8C2318yes—
81C23×D8C2318yes—
82C2×#537—232no—
83C2×#537—432no—
84C2×#532—28no—
85C2×#532—216no—
86C2×#532—216no—
87C2×#532C23116yes—
88C22×C4⋊Q8C2312yes—
89C22×#127—24no—
90C22×#127—22no—
91C22×#127—48no—
92C22×#127C2312yes—
93C22×#127C2314yes—
94C22×#127C2312yes—
95C22×#127C2312yes—
96C22×#127C2318yes—
97C22×#124—22no—
98C22×#124—24no—
99C22×#124—24no—
100C22×#124—22no—
101C22×#124—22no—
102C22×#124—216no—
103C22×#124—48no—
104C22×#124C2314yes—
105C22×#124C2318yes—
106C22×#124C2314yes—
107C22×#124C2318yes—
108C22×C22⋊Q8—28no—
109C22×#121—22no—
110C22×#121—24no—
111C22×#121—24no—
112C22×#121—28no—
113C22×#121C2314yes—
114C22×C4×D4—22no—
115C22×C4×D4—24no—
116C22×C4×D4—22no—
117C22×C4×D4—216no—
118C22×C4×D4C2314yes—
119C22×C4×D4C2318yes—
120C22×C4×D4C2314yes—
121C23×C4⋊C4D412yes—
122C23×C4⋊C4C2311yescharacteristic
123C23×C22⋊C4—21no—
124C23×C22⋊C4—21no—
125C23×C22⋊C4—22no—
126C23×C22⋊C4—21no—
127C23×C22⋊C4—22no—
128C23×C42C2311yescharacteristic
129C23×C42C2311yescharacteristic
130C23×C42C2311yescharacteristic
131#3213—2256no—
132C2×#496—232no—
133C2×#496—416no—
134C2×#496C23132yescomplemented
135C2×#496C23132yescomplemented
136C2×#493—416no—
137C2×#493C23132yes—
138C2×#489—232no—
139C2×#489C23132yescomplemented
140#3109—2256no—
141C2×#481—232no—
142C2×#481C23132yes—
143C2×#476—232no—
144C2×#476C23132yescomplemented
145C2×#463—264no—
146C2×#463C23164yescomplemented
147C2×#459—232no—
148C2×#459C23132yescomplemented
149C2×#448—232no—
150C2×#448C23132yes—
151C2×#447—232no—
152C2×#447—232no—
153C2×#447C23132yes—
154C2×#447C23132yes—
155C2×#442—264no—
156C2×#442C23164yescomplemented
157C2×#432D4132yescomplemented
158C2×#432C23116yes—
159C22×#106C2318yes—
160C22×C4⋊C8C2314yes—
161C22×#103C2318yes—
162C22×#102C2318yes—
163C22×#102C2318yes—
164C22×#102C2318yes—
165C22×C22⋊C8C2314yes—
166C22×#97C2314yes—
167C22×#97C2314yes—
168C22×C4×C8C2314yes—
169#2856—28no—
170#2856—28no—
171#2856C23116yes—
172#2856C23116yes—
173#2656—232no—
174#2544—232no—
175#2544—264no—
176#2544C23164yes—
177#2542—216no—
178#2542C23132yescomplemented
179#2541—216no—
180#2541C23132yescomplemented
181#2540—264no—
182C2×#399—28no—
183C2×#394—216no—
184C2×#394—232no—
185C2×#392—28no—
186C2×#391—24no—
187C2×#391—22no—
188C2×#391C2314yes—
189C2×#391C2318yes—
190C2×#390—24no—
191C2×#390—24no—
192C2×#390—24no—
193C2×#390—22no—
194C2×#390C2314yes—
195C2×#390C2314yes—
196C2×#390C2314yes—
197C2×#390C2318yes—
198C2×#386—216no—
199C2×#386—232no—
200C2×#384C2312yes—
201C2×#384C2312yes—
202C2×C4×C4⋊C4D414yes—
203C2×C4×C4⋊C4D418yes—
204C2×C4×C4⋊C4C2318yes—
205C2×C4×C4⋊C4C2314yes—
206C22×#95—22no—
207C22×#95D412yes—
208#2096C23132yescomplemented
209#2094C23132yescomplemented
210#2014C23132yescomplemented
211#2012C23164yescomplemented
212#2011C23164yes—
213#2011C23132yescomplemented
214#1972C23164yescomplemented
215#1968C23164yescomplemented
216#1959C23132yescomplemented
217#1957C23132yes—
218#1771C23164yescomplemented
219#1749C23116yes—
220C4×C22⋊C8C23116yes—
221C2×#336C2314yes—
222C2×#336C2314yes—
223C26—21no—
224C26—21no—
225C22×#41—216no—
226C22×#41—432no—
227C22×#41—416no—
228C23×Q8—22no—
229C23×Q8—21no—
230C23×Q8—22no—
231C23×Q8—28no—
232C23×Q8—44no—
233C23×Q8—44no—
234C23×Q8C2412yes—
235C23×Q8C2414yes—
236C23×D4—28no—
237C23×D4—24no—
238C23×D4—22no—
239C23×D4—21no—
240C23×D4—28no—
241C23×D4—28no—
242C23×D4—22no—
243C23×D4—21no—
244C23×D4—22no—
245C23×D4—28no—
246C23×D4—216no—
247C23×D4—22no—
248C23×D4—24no—
249C23×D4—24no—
250C23×D4—44no—
251C23×D4—44no—
252C23×D4—44no—
253C23×D4—416no—
254C23×D4—416no—
255C23×D4—88no—
256C23×D4C2412yes—
257C23×D4C2414yes—
258C23×D4C2412yes—
259C23×D4C2414yes—
260C23×D4C2414yes—
261C24×C4—21no—
262C24×C4—21no—
263C24×C4—24no—
264C24×C4—28no—
265C24×C4—24no—
266C24×C4—48no—
267C24×C4—88no—
268C24×C4C2×D411yescharacteristic
269C24×C4C2×D412yes—
270C24×C4C2×D411yescharacteristic
271C24×C4C2×D412yes—
272C24×C4C2411yescharacteristic
273C22×SD16—232no—
274C22×SD16—416no—
275C22×SD16—416no—
276C22×SD16C24132yes—
277C22×D8—232no—
278C22×D8—232no—
279C22×D8—232no—
280C22×D8—416no—
281C22×D8—416no—
282C22×D8—416no—
283C22×D8C24132yes—
284C22×D8C24132yes—
285C23×C8C2418yes—
286#537—4256no—
287#532—264no—
288#532—264no—
289#532—464no—
290C2×C4⋊Q8—24no—
291C2×C4⋊Q8—28no—
292C2×C4⋊Q8—28no—
293C2×C4⋊Q8C2418yes—
294C2×#127—216no—
295C2×#127—28no—
296C2×#127—28no—
297C2×#127—28no—
298C2×#127—216no—
299C2×#127—24no—
300C2×#127—24no—
301C2×#127—24no—
302C2×#127—48no—
303C2×#127—48no—
304C2×#127—48no—
305C2×#127—432no—
306C2×#127—432no—
307C2×#127—416no—
308C2×#127C2418yes—
309C2×#127C24116yes—
310C2×#127C2418yes—
311C2×#127C2418yes—
312C2×#124—216no—
313C2×#124—28no—
314C2×#124—216no—
315C2×#124—216no—
316C2×#124—28no—
317C2×#124—216no—
318C2×#124—216no—
319C2×#124—264no—
320C2×#124—216no—
321C2×#124—48no—
322C2×#124—432no—
323C2×#124—432no—
324C2×#124—416no—
325C2×#124—416no—
326C2×#124—432no—
327C2×#124—416no—
328C2×#124C24116yes—
329C2×#124C24116yes—
330C2×C22⋊Q8—264no—
331C2×C22⋊Q8—464no—
332C2×#121—28no—
333C2×#121—232no—
334C2×#121—232no—
335C2×#121—216no—
336C2×#121—264no—
337C2×#121—216no—
338C2×#121—216no—
339C2×#121—464no—
340C2×#121—432no—
341C2×#121—416no—
342C2×#121—432no—
343C2×#121C24116yes—
344C2×C4×D4—216no—
345C2×C4×D4—28no—
346C2×C4×D4—216no—
347C2×C4×D4—28no—
348C2×C4×D4—264no—
349C2×C4×D4—216no—
350C2×C4×D4—216no—
351C2×C4×D4—216no—
352C2×C4×D4—216no—
353C2×C4×D4—416no—
354C2×C4×D4—432no—
355C2×C4×D4—416no—
356C2×C4×D4C24116yes—
357C2×C4×D4C24116yes—
358C22×C4⋊C4—216no—
359C22×C4⋊C4—28no—
360C22×C4⋊C4—22no—
361C22×C4⋊C4—24no—
362C22×C4⋊C4—24no—
363C22×C4⋊C4—22no—
364C22×C4⋊C4—21no—
365C22×C4⋊C4C2×D418yes—
366C22×C4⋊C4C2×D4116yes—
367C22×C4⋊C4C2414yes—
368C22×C4⋊C4C2414yes—
369C22×C4⋊C4C2412yes—
370C22×C22⋊C4—24no—
371C22×C22⋊C4—28no—
372C22×C22⋊C4—28no—
373C22×C22⋊C4—28no—
374C22×C22⋊C4—24no—
375C22×C22⋊C4—28no—
376C22×C22⋊C4—24no—
377C22×C22⋊C4—28no—
378C22×C22⋊C4—216no—
379C22×C22⋊C4—28no—
380C22×C22⋊C4—24no—
381C22×C22⋊C4—24no—
382C22×C22⋊C4—28no—
383C22×C22⋊C4—216no—
384C22×C22⋊C4—416no—
385C22×C22⋊C4—48no—
386C22×C22⋊C4—48no—
387C22×C22⋊C4—48no—
388C22×C22⋊C4—88no—
389C22×C42—44no—
390C22×C42—44no—
391C22×C42C2×D414yes—
392C22×C42C2×D414yes—
393C22×C42C2×D412yes—
394C22×C42C2×D412yes—
395C22×C42C2×D412yes—
396C22×C42C2×D414yes—
397C22×C42C2×D4116yes—
398C22×C42C2412yes—
399C22×C42C2412yes—
400C22×C42C2414yes—
401C22×C42C2414yes—
402C22×C42C2412yes—
403C22×C42C2414yes—
404#496—2128no—
405#496—464no—
406#493—464no—
407#489—2128no—
408#481—2128no—
409#476—2128no—
410#463—2256no—
411#459—2128no—
412#448—2128no—
413#447—2128no—
414#447—2128no—
415#442—2256no—
416#432C2×D41128yescomplemented
417C2×#106—232no—
418C2×#106C24132yes—
419C2×C4⋊C8C2×D4132yescomplemented
420C2×C4⋊C8C24116yes—
421C2×#103—232no—
422C2×#103C24132yes—
423C2×#102—232no—
424C2×#102—232no—
425C2×#102—232no—
426C2×#102C24132yes—
427C2×#102C24132yes—
428C2×#102C24132yes—
429C2×C22⋊C8C2×D4132yes—
430C2×C22⋊C8C24116yes—
431C2×#97—48no—
432C2×#97C2×D4132yescomplemented
433C2×#97C24116yes—
434C2×#97C24116yes—
435C2×C4×C8—48no—
436C2×C4×C8C24116yes—
437#399—264no—
438#394—2128no—
439#392—264no—
440#391—28no—
441#391—216no—
442#391C24116yes—
443#390—28no—
444#390—28no—
445#390—232no—
446#390—232no—
447#390—28no—
448#390—216no—
449#390C24116yes—
450#390C24116yes—
451#390C24116yes—
452#386—2128no—
453#384—24no—
454#384—24no—
455#384C2418yes—
456#384C2418yes—
457C4×C4⋊C4C2×D4132yes—
458C4×C4⋊C4C2×D4116yes—
459C4×C4⋊C4C24116yes—
460C2×#95—216no—
461C2×#95—28no—
462C2×#95C2×D418yes—
463C2×#95C2×D4116yes—
464#336C24116yes—
465#336C24116yes—
466C25—28no—
467C25—24no—
468C25—22no—
469C25—24no—
470C25—22no—
471C25—24no—
472C25—48no—
473C25—44no—
474C25—48no—
475C25—44no—
476C25—44no—
477C25—44no—
478C25—48no—
479C25—44no—
480C25—48no—
481C25C22×D411yescharacteristic
482C2×#41—4128no—
483C2×#41—464no—
484C2×#41—8128no—
485C22×Q8—28no—
486C22×Q8—24no—
487C22×Q8—22no—
488C22×Q8—28no—
489C22×Q8—216no—
490C22×Q8—28no—
491C22×Q8—28no—
492C22×Q8—48no—
493C22×Q8—48no—
494C22×Q8—416no—
495C22×Q8—44no—
496C22×Q8—48no—
497C22×Q8—44no—
498C22×Q8—48no—
499C22×Q8—44no—
500C22×Q8—48no—
501C22×Q8—48no—
502C22×Q8—832no—
503C22×Q8C2514yes—
504C22×D4—28no—
505C22×D4—216no—
506C22×D4—216no—
507C22×D4—216no—
508C22×D4—28no—
509C22×D4—24no—
510C22×D4—22no—
511C22×D4—216no—
512C22×D4—28no—
513C22×D4—28no—
514C22×D4—28no—
515C22×D4—216no—
516C22×D4—24no—
517C22×D4—28no—
518C22×D4—24no—
519C22×D4—22no—
520C22×D4—232no—
521C22×D4—28no—
522C22×D4—216no—
523C22×D4—216no—
524C22×D4—24no—
525C22×D4—28no—
526C22×D4—216no—
527C22×D4—28no—
528C22×D4—216no—
529C22×D4—28no—
530C22×D4—48no—
531C22×D4—48no—
532C22×D4—48no—
533C22×D4—464no—
534C22×D4—44no—
535C22×D4—48no—
536C22×D4—432no—
537C22×D4—416no—
538C22×D4—44no—
539C22×D4—48no—
540C22×D4—44no—
541C22×D4—48no—
542C22×D4—416no—
543C22×D4—464no—
544C22×D4—416no—
545C22×D4—432no—
546C22×D4—44no—
547C22×D4—48no—
548C22×D4—48no—
549C22×D4—44no—
550C22×D4—48no—
551C22×D4—48no—
552C22×D4—432no—
553C22×D4—464no—
554C22×D4—416no—
555C22×D4—832no—
556C22×D4—88no—
557C22×D4—816no—
558C22×D4—88no—
559C22×D4—88no—
560C22×D4—88no—
561C22×D4—88no—
562C22×D4—832no—
563C22×D4—8128no—
564C22×D4H(5,𝔽2)18yes—
565C22×D4C2518yes—
566C22×D4C2514yes—
567C22×D4C2514yes—
568C23×C4—28no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—28no—
572C23×C4—24no—
573C23×C4—24no—
574C23×C4—22no—
575C23×C4—24no—
576C23×C4—22no—
577C23×C4—216no—
578C23×C4—216no—
579C23×C4—44no—
580C23×C4—44no—
581C23×C4—44no—
582C23×C4—44no—
583C23×C4—44no—
584C23×C4—432no—
585C23×C4—44no—
586C23×C4—48no—
587C23×C4—44no—
588C23×C4—44no—
589C23×C4—44no—
590C23×C4—416no—
591C23×C4—432no—
592C23×C4—416no—
593C23×C4—816no—
594C23×C4—832no—
595C23×C4—864no—
596C23×C4#12718yes—
597C23×C4#12718yes—
598C23×C4AGL(1,ℤ/8)116yes—
599C23×C4C22×D414yes—
600C23×C4C22×D414yes—
601C23×C4C22×D412yes—
602C23×C4C22×D412yes—
603C23×C4C22×D411yescharacteristic
604C23×C4C22×D412yes—
605C23×C4C22×D418yes—
606C23×C4C22×D414yes—
607C23×C4C22×D418yes—
608C23×C4C22×D414yes—
609C23×C4C22×D418yes—
610C23×C4C2512yes—
611C23×C4C2511yescharacteristic
612C2×SD16—264no—
613C2×SD16—432no—
614C2×SD16—432no—
615C2×SD16—864no—
616C2×D8—264no—
617C2×D8—264no—
618C2×D8—264no—
619C2×D8—432no—
620C2×D8—4128no—
621C2×D8—432no—
622C2×D8—432no—
623C2×D8—864no—
624C22×C8—216no—
625C22×C8—216no—
626C22×C8C22×D4132yes—
627C22×C8C25116yes—
628C4⋊Q8—216no—
629C4⋊Q8—216no—
630C4⋊Q8—416no—
631#127—232no—
632#127—216no—
633#127—216no—
634#127—416no—
635#127—416no—
636#127—416no—
637#127—432no—
638#127—464no—
639#127—416no—
640#127—88no—
641#127—88no—
642#124—232no—
643#124—232no—
644#124—232no—
645#124—416no—
646#124—432no—
647#124—464no—
648#124—464no—
649#124—432no—
650#124—464no—
651C22⋊Q8—4256no—
652#121—232no—
653#121—232no—
654#121—4256no—
655#121—4128no—
656#121—432no—
657#121—464no—
658#121—4128no—
659C4×D4—232no—
660C4×D4—232no—
661C4×D4—232no—
662C4×D4—232no—
663C4×D4—464no—
664C4×D4—432no—
665C4×D4—432no—
666C4×D4—464no—
667C2×C4⋊C4—232no—
668C2×C4⋊C4—264no—
669C2×C4⋊C4—28no—
670C2×C4⋊C4—216no—
671C2×C4⋊C4—28no—
672C2×C4⋊C4—28no—
673C2×C4⋊C4—24no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—28no—
676C2×C4⋊C4—216no—
677C2×C4⋊C4—216no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—416no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4—48no—
682C2×C4⋊C4—48no—
683C2×C4⋊C4—416no—
684C2×C4⋊C4C22×D4132yes—
685C2×C4⋊C4C2514yes—
686C2×C4⋊C4C2518yes—
687C2×C22⋊C4—216no—
688C2×C22⋊C4—216no—
689C2×C22⋊C4—232no—
690C2×C22⋊C4—216no—
691C2×C22⋊C4—216no—
692C2×C22⋊C4—216no—
693C2×C22⋊C4—232no—
694C2×C22⋊C4—232no—
695C2×C22⋊C4—232no—
696C2×C22⋊C4—432no—
697C2×C22⋊C4—432no—
698C2×C22⋊C4—464no—
699C2×C22⋊C4—416no—
700C2×C22⋊C4—432no—
701C2×C22⋊C4—416no—
702C2×C22⋊C4—416no—
703C2×C22⋊C4—432no—
704C2×C22⋊C4—432no—
705C2×C22⋊C4—416no—
706C2×C22⋊C4—416no—
707C2×C22⋊C4—432no—
708C2×C22⋊C4—816no—
709C2×C22⋊C4—832no—
710C2×C42—28no—
711C2×C42—28no—
712C2×C42—48no—
713C2×C42—48no—
714C2×C42—48no—
715C2×C42—48no—
716C2×C42—44no—
717C2×C42—44no—
718C2×C42#127116yes—
719C2×C42#127132yes—
720C2×C42C22×D414yes—
721C2×C42C22×D414yes—
722C2×C42C22×D418yes—
723C2×C42C22×D418yes—
724C2×C42C22×D418yes—
725C2×C42C22×D414yes—
726C2×C42C22×D418yes—
727C2×C42C22×D418yes—
728C2×C42C22×D4132yes—
729C2×C42C2514yes—
730C2×C42C2514yes—
731C2×C42C2514yes—
732#106—264no—
733C4⋊C8C22×D4164yescomplemented
734#103—264no—
735#102—264no—
736#102—264no—
737#102—264no—
738C22⋊C8C22×D4164yes—
739#97—416no—
740#97C22×D4164yescomplemented
741C4×C8—416no—
742#95—232no—
743#95C22×D4132yes—
744C24—24no—
745C24—22no—
746C24—22no—
747C24—216no—
748C24—24no—
749C24—28no—
750C24—24no—
751C24—28no—
752C24—416no—
753C24—48no—
754C24—432no—
755C24—464no—
756C24—416no—
757C24—48no—
758C24—48no—
759C24—48no—
760C24—48no—
761C24—44no—
762C24—44no—
763C24—416no—
764C24—48no—
765C24—48no—
766C24—416no—
767C24—48no—
768C24—44no—
769C24—48no—
770C24—44no—
771C24—48no—
772C24—44no—
773C24—48no—
774C24—416no—
775C24—416no—
776C24—48no—
777C24—816no—
778C24—832no—
779C24—832no—
780C24—816no—
781C24—832no—
782C24—816no—
783C24—816no—
784C24—816no—
785C24C2×#12714yes—
786C24C2×AGL(1,ℤ/8)18yes—
787C24C23×D412yes—
788C24C23×D411yescharacteristic
789#41—8256no—
790C2×Q8—28no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—432no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8—44no—
798C2×Q8—416no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—432no—
802C2×Q8—832no—
803C2×Q8—816no—
804C2×Q8—832no—
805C2×Q8—832no—
806C2×D4—216no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—24no—
812C2×D4—28no—
813C2×D4—216no—
814C2×D4—28no—
815C2×D4—216no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—232no—
819C2×D4—464no—
820C2×D4—48no—
821C2×D4—432no—
822C2×D4—464no—
823C2×D4—464no—
824C2×D4—432no—
825C2×D4—48no—
826C2×D4—48no—
827C2×D4—432no—
828C2×D4—432no—
829C2×D4—464no—
830C2×D4—48no—
831C2×D4—44no—
832C2×D4—416no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—44no—
836C2×D4—416no—
837C2×D4—44no—
838C2×D4—48no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—44no—
842C2×D4—416no—
843C2×D4—432no—
844C2×D4—432no—
845C2×D4—432no—
846C2×D4—464no—
847C2×D4—432no—
848C2×D4—832no—
849C2×D4—816no—
850C2×D4—832no—
851C2×D4—8128no—
852C2×D4—816no—
853C2×D4—832no—
854C2×D4—832no—
855C2×D4—832no—
856C2×D4—816no—
857C2×D4—816no—
858C2×D4—816no—
859C2×D4—816no—
860C2×D4—8256no—
861C2×D4—864no—
862C2×D4—1632no—
863C2×D4—1632no—
864C2×D4C2×H(5,𝔽2)18yes—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—232no—
868C22×C4—28no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—216no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—232no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—216no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—28no—
885C22×C4—48no—
886C22×C4—416no—
887C22×C4—48no—
888C22×C4—432no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—464no—
893C22×C4—48no—
894C22×C4—416no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—48no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—416no—
905C22×C4—432no—
906C22×C4—432no—
907C22×C4—832no—
908C22×C4—864no—
909C22×C4—864no—
910C22×C4—816no—
911C22×C4—8128no—
912C22×C4—816no—
913C22×C4—816no—
914C22×C4C2×#12714yes—
915C22×C4C2×#12718yes—
916C22×C4C2×#12718yes—
917C22×C4C2×#12718yes—
918C22×C4C2×#127116yes—
919C22×C4C2×#127116yes—
920C22×C4C2×AGL(1,ℤ/8)116yes—
921C22×C4C2×AGL(1,ℤ/8)132yes—
922C22×C4C23×D418yes—
923C22×C4C23×D418yes—
924C22×C4C23×D414yes—
925C22×C4C23×D412yes—
926C22×C4C23×D414yes—
927C22×C4C23×D418yes—
928C22×C4C23×D414yes—
929C22×C4C23×D411yescharacteristic
930C22×C4C2×H(5,𝔽2)14yes—
931C22×C4#58514yes—
932C22×C4C2611yescharacteristic
933SD16—864no—
934D8—4128no—
935D8—864no—
936C2×C8—216no—
937C2×C8—216no—
938C2×C8—264no—
939C2×C8C23×D4132yes—
940C4⋊C4—264no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—432no—
945C4⋊C4—48no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—416no—
949C4⋊C4—432no—
950C22⋊C4—464no—
951C22⋊C4—464no—
952C22⋊C4—432no—
953C22⋊C4—432no—
954C22⋊C4—432no—
955C22⋊C4—432no—
956C22⋊C4—432no—
957C22⋊C4—464no—
958C22⋊C4—832no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—28no—
963C42—48no—
964C42—48no—
965C42C2×#127132yes—
966C42C2×#127116yes—
967C42C23×D418yes—
968C42C23×D418yes—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—216no—
973C23—216no—
974C23—28no—
975C23—28no—
976C23—28no—
977C23—432no—
978C23—464no—
979C23—44no—
980C23—48no—
981C23—48no—
982C23—432no—
983C23—44no—
984C23—416no—
985C23—44no—
986C23—48no—
987C23—44no—
988C23—48no—
989C23—416no—
990C23—48no—
991C23—48no—
992C23—416no—
993C23—44no—
994C23—48no—
995C23—816no—
996C23—832no—
997C23—8128no—
998C23—832no—
999C23—816no—
1000C23—832no—
1001C23—816no—
1002C23—816no—
1003C23—816no—
1004C23—88no—
1005C23—88no—
1006C23—816no—
1007C23—832no—
1008C23—832no—
1009C23—816no—
1010C23—816no—
1011C23—816no—
1012C23—88no—
1013C23—816no—
1014C23—88no—
1015C23—88no—
1016C23—816no—
1017C23—1664no—
1018C23#3151116yes—
1019C23C22×#12714yes—
1020C23C22×#12712yes—
1021C23#348412yes—
1022C23#348712yes—
1023C23C22×AGL(1,ℤ/8)18yes—
1024C23C22×AGL(1,ℤ/8)14yes—
1025C23#358514yes—
1026C23C24×D411yescharacteristic
1027Q8—416no—
1028Q8—816no—
1029Q8—832no—
1030Q8—88no—
1031D4—216no—
1032D4—432no—
1033D4—48no—
1034D4—416no—
1035D4—416no—
1036D4—416no—
1037D4—416no—
1038D4—8128no—
1039D4—816no—
1040D4—832no—
1041D4—832no—
1042D4—864no—
1043D4—816no—
1044D4—88no—
1045D4—1632no—
1046D4—1632no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—232no—
1054C2×C4—216no—
1055C2×C4—232no—
1056C2×C4—216no—
1057C2×C4—28no—
1058C2×C4—216no—
1059C2×C4—216no—
1060C2×C4—28no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—416no—
1064C2×C4—432no—
1065C2×C4—416no—
1066C2×C4—44no—
1067C2×C4—44no—
1068C2×C4—416no—
1069C2×C4—48no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—48no—
1073C2×C4—864no—
1074C2×C4—864no—
1075C2×C4—816no—
1076C2×C4—816no—
1077C2×C4—816no—
1078C2×C4—816no—
1079C2×C4—88no—
1080C2×C4—88no—
1081C2×C4C22×#12714yes—
1082C2×C4C22×#12718yes—
1083C2×C4C22×#12718yes—
1084C2×C4C22×#12712yes—
1085C2×C4#348412yes—
1086C2×C4#348712yes—
1087C2×C4#3488116yes—
1088C2×C4C22×AGL(1,ℤ/8)116yes—
1089C2×C4C24×D412yes—
1090C2×C4C22×H(5,𝔽2)12yes—
1091C2×C4C2×#58512yes—
1092C8—232no—
1093C22—28no—
1094C22—28no—
1095C22—24no—
1096C22—24no—
1097C22—232no—
1098C22—416no—
1099C22—48no—
1100C22—864no—
1101C22—84no—
1102C22—88no—
1103C22—84no—
1104C22—832no—
1105C22—88no—
1106C22—816no—
1107C22—88no—
1108C22—84no—
1109C22—816no—
1110C22—88no—
1111C22—88no—
1112C22—84no—
1113C22—84no—
1114C22—88no—
1115C22—1632no—
1116C22—1632no—
1117C22—1616no—
1118C22#3556514yes—
1119C22C2×#315118yes—
1120C22C2×#315114yes—
1121C22#6064414yes—
1122C22#6156918yes—
1123C22#6189118yes—
1124C22C23×#12711yescharacteristic
1125C22C2×#348411yescharacteristic
1126C22C2×#348711yescharacteristic
1127C22C23×AGL(1,ℤ/8)12yes—
1128C22C2×#358512yes—
1129C4—216no—
1130C4—28no—
1131C4—28no—
1132C4—24no—
1133C4—48no—
1134C4—88no—
1135C4—84no—
1136C4—84no—
1137C4#3556514yes—
1138C4C2×#348814yes—
1139C2—28no—
1140C2—88no—
1141C2—168no—
1142C2—164no—
1143C2#652023418yesdirect product factor
1144C2C2×#3556511yescharacteristic
1145C2C22×#315111yescharacteristic
1146C2C2×#6064411yescharacteristic
1147C2C2×#6156912yes—
1148C2C2×#6189112yes—
subgroupG/H
center, socleC24C23×D4
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#3213C2semidirect
2. C22×#3109C2semidirect
3. C2×#35166C2semidirect
4. C22×#2544C2semidirect
5. #6520234C2direct (N × H)
6. C2×#28475C2semidirect
7. C2×#28430C2semidirect
8. C2×#28310C2semidirect
9. C2×#28305C2semidirect
10. C2×#25731C2semidirect
11. C2×#25721C2semidirect
12. C2×#20534C2semidirect
20. C2×#3213C22semidirect
21. C22×#496C22semidirect
22. C22×#496C22semidirect
24. C22×#489C22semidirect
26. C2×#3109C22semidirect
28. C22×#476C22semidirect
29. C22×#463C22semidirect
30. C22×#459C22semidirect
34. C22×#442C22semidirect
39. #35166C22semidirect
40. C2×#2542C22semidirect
41. C2×#2541C22semidirect
46. C2×#2544C22semidirect
53. #28475C22semidirect
54. #28430C22semidirect
55. #28310C22semidirect
56. #28305C22semidirect
57. #25731C22semidirect
58. #25721C22semidirect
59. C2×#2096C22semidirect
60. C2×#2094C22semidirect
61. C2×#2012C22semidirect
62. C2×#2014C22semidirect
64. C2×#2011C22semidirect
65. C2×#1972C22semidirect
66. C2×#1968C22semidirect
67. C2×#1959C22semidirect
69. #20534C22semidirect
70. C2×#1771C22semidirect
134. C2×#496C23semidirect
135. C2×#496C23semidirect
139. C2×#489C23semidirect
144. C2×#476C23semidirect
146. C2×#463C23semidirect
148. C2×#459C23semidirect
156. C2×#442C23semidirect
157. C2×#432D4semidirect
178. #2542C23semidirect
180. #2541C23semidirect
208. #2096C23semidirect
209. #2094C23semidirect
210. #2014C23semidirect
211. #2012C23semidirect
213. #2011C23semidirect
214. #1972C23semidirect
215. #1968C23semidirect
216. #1959C23semidirect
218. #1771C23semidirect
416. #432C2×D4semidirect
419. C2×C4⋊C8C2×D4semidirect
432. C2×#97C2×D4semidirect
733. C4⋊C8C22×D4semidirect
740. #97C22×D4semidirect
1143. C2#6520234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#32132
C22×#31092
C2×#351662
C22×#25442
#65202342
C2×#284752
C2×#284302
C2×#283102
C2×#283052
C2×#257312
C2×#257212
C2×#205342