Finite Group Databasebeta

← C2×#7613946 #72264530

Subgroups — C2×#7613946 #72264530

Order 1024.

15329 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3399C212yesmaximal, complemented
2C2×#45354C212yesmaximal, complemented
3#7613946C2132yesmaximal, direct product factor
4C2×#31224C212yesmaximal, complemented
5C2×#31223C212yesmaximal, complemented
6C2×#28270C212yesmaximal, complemented
7C2×#28467C212yesmaximal, complemented
8C2×#28257C212yesmaximal, complemented
9C2×#24202C212yesmaximal, complemented
10C2×#24196C212yesmaximal, complemented
11C2×#26268C214yesmaximal, complemented
12C2×#24738C214yesmaximal, complemented
13C2×#22670C212yesmaximal, complemented
14C2×#21716C211yesmaximal, characteristic, complemented
15C2×#21697C211yesmaximal, characteristic, complemented
16C2×#21694C211yesmaximal, characteristic, complemented
17C22×#559C2212yes—
18C22×#550C2212yes—
19C2×#3399—232no—
20C2×#3399C22132yescomplemented
21C22×#496C2214yes—
22C22×#495C2211yescharacteristic
23C22×#493C2211yescharacteristic
24C22×#460C2212yes—
25C22×#463C2214yes—
26C22×#463C2214yes—
27C22×#459C2214yes—
28C22×#459C2212yes—
29C22×#446C2212yes—
30C22×#442C2214yes—
31C22×#442C2212yes—
32C22×#442C2211yescharacteristic
33C22×#441C2211yescharacteristic
34C22×C4×SD16C2212yes—
35C22×C4×D8C2212yes—
36C2×#2708—24no—
37C2×#2686—24no—
38#45354—216no—
39#45354C22132yescomplemented
40C2×#2581C2212yes—
41C2×#2580C2212yes—
42C2×#2544C2214yes—
43C2×#2406—24no—
44C2×#2447C2214yes—
45C2×#2445C2214yes—
46C2×#2443—24no—
47C2×#2399C2211yescharacteristic
48C2×D4×C4⋊C4C2214yes—
49C2×#2328C2212yes—
50C2×#2326C2212yes—
51#31224C22132yescomplemented
52#31223C22132yescomplemented
53#28467C22132yescomplemented
54#28270C22132yescomplemented
55#28257C22132yescomplemented
56#26268C22164yescomplemented
57#24738C22164yescomplemented
58#24202C22132yescomplemented
59#24196C22132yescomplemented
60C2×#2066C2214yes—
61C2×#2065C2214yes—
62C2×#2055C2214yes—
63C2×#2054C2214yes—
64C2×#2042C2214yes—
65C2×#2041C2214yes—
66C2×#2015C2214yes—
67C2×#2011C2214yes—
68#22670C22132yescomplemented
69#21716C22116yescomplemented
70#21697C22116yescomplemented
71#21694C22116yescomplemented
72C2×#1985C2212yes—
73C2×#1973C2214yes—
74C2×#1972C2211yescharacteristic
75C2×#1972C2212yes—
76C2×#1971C2211yescharacteristic
77C2×#1970C2212yes—
78C2×#1968C2212yes—
79C2×#1961C2212yes—
80C2×#1959C2212yes—
81C2×#1943C2214yes—
82C2×#1940C2212yes—
83C2×#1940C2212yes—
84C2×#1879C2214yes—
85C2×#1877C2214yes—
86C2×#1864C2214yes—
87C2×#1864C2214yes—
88C2×#1846C2211yescharacteristic
89C2×#1844C2211yescharacteristic
90C2×#1843C2211yescharacteristic
91C2×#1805C2212yes—
92C2×#1804C2212yes—
93C2×#1802C2214yes—
94C2×#1770C2212yes—
95C2×#1770C2212yes—
96C2×#1726C2211yescharacteristic
97C23×#41—22no—
98C23×Q16C2311yescharacteristic
99C23×SD16C2312yes—
100C23×SD16C2314yes—
101C23×D8C2312yes—
102C23×D8C2311yescharacteristic
103C23×D8C2314yes—
104C23×D8C2312yes—
105C2×#559—28no—
106C2×#559—216no—
107C2×#559—48no—
108C2×#559C23116yes—
109C2×#550—216no—
110C2×#550—28no—
111C2×#550—48no—
112C2×#550C23116yes—
113C22×#127C2314yes—
114C22×#127C2312yes—
115C22×#124—22no—
116C22×#124C2312yes—
117C22×#124C2314yes—
118C22×#123—24no—
119C22×#123—24no—
120C22×#121—24no—
121C22×#121—22no—
122C22×C4×Q8C2312yes—
123C22×C4×Q8C2312yes—
124C22×C4×D4—22no—
125C22×C4×D4C2312yes—
126C22×C4×D4C2314yes—
127C22×C4×D4C2314yes—
128C22×C4×D4C2314yes—
129C23×C4⋊C4—24no—
130#3399—2256no—
131C2×#496—232no—
132C2×#496C23132yes—
133C2×#495—28no—
134C2×#495C2318yes—
135C2×#493D4116yes—
136C2×#493C2318yes—
137C2×#460—216no—
138C2×#460C23116yes—
139C2×#463—232no—
140C2×#463—416no—
141C2×#463C23132yes—
142C2×#463C23132yes—
143C2×#459—232no—
144C2×#459—216no—
145C2×#459C23116yes—
146C2×#459C23132yes—
147C2×#446—216no—
148C2×#446C23116yes—
149C2×#442—232no—
150C2×#442—44no—
151C2×#442—48no—
152C2×#442C23132yes—
153C2×#442C2318yes—
154C2×#442C23116yes—
155C2×#441—44no—
156C2×#441C2318yes—
157C2×C4×SD16—216no—
158C2×C4×SD16C23116yes—
159C2×C4×D8—216no—
160C2×C4×D8C23116yes—
161C22×#107C2312yes—
162C22×#106C2312yes—
163C22×#106C2312yes—
164C22×#106C2311yescharacteristic
165C22×#106C2311yescharacteristic
166C22×C4⋊C8C2312yes—
167C22×C4⋊C8C2314yes—
168C22×C4⋊C8C2312yes—
169C22×C4⋊C8C2312yes—
170C22×#103C2312yes—
171C22×#103C2314yes—
172C22×#103C2312yes—
173C22×#102C2312yes—
174C22×#102C2314yes—
175C22×#102C2314yes—
176C22×#102C2314yes—
177C22×#102C2314yes—
178C22×#102C2314yes—
179C22×#102C2312yes—
180C22×#97C2314yes—
181C22×#97C2311yescharacteristic
182C22×#97C2311yescharacteristic
183C22×#97C2311yescharacteristic
184C22×C4×C8C2311yescharacteristic
185C22×C4×C8C2311yescharacteristic
186C22×C4×C8C2311yescharacteristic
187#2708—264no—
188#2686—264no—
189#2581—28no—
190#2581C23116yes—
191#2580—28no—
192#2580C23116yes—
193#2544—216no—
194#2544C23132yes—
195#2447—216no—
196#2447C23132yes—
197#2445—216no—
198#2445C23132yes—
199#2443—264no—
200#2406—264no—
201#2399D418yes—
202#2399C2318yes—
203C2×#400—22no—
204C2×#399—22no—
205C2×#398D414yes—
206C2×#397—24no—
207C2×#397—24no—
208C2×#395—22no—
209C2×#395D414yes—
210C2×#394—24no—
211C2×#394—24no—
212C2×#394—24no—
213C2×#394—24no—
214C2×#393—22no—
215D4×C4⋊C4—216no—
216D4×C4⋊C4C23132yes—
217#2328—28no—
218#2328C23116yes—
219#2326—28no—
220#2326C23116yes—
221C2×#391C2312yes—
222C2×#391C2314yes—
223C2×#390C2312yes—
224C2×#390C2314yes—
225C2×#390C2314yes—
226C2×#389C2314yes—
227C2×#389C2314yes—
228C2×#388—24no—
229C2×#387—24no—
230C2×#386—24no—
231C2×#386—24no—
232C2×#386—24no—
233C2×#386—24no—
234C2×#386—24no—
235C2×#385—24no—
236C2×#385—24no—
237C2×#385—24no—
238C2×#385—24no—
239C2×#385—24no—
240C2×#384C2312yes—
241C2×#382C2312yes—
242C2×#381—24no—
243C2×#380—24no—
244C2×C4×C4⋊C4C2312yes—
245C2×C4×C4⋊C4C2312yes—
246C2×#376C2311yescharacteristic
247#2066C23132yes—
248#2065C23132yes—
249#2055C23132yes—
250#2054C23132yes—
251#2042C23132yes—
252#2041C23132yes—
253#2015C23132yes—
254#2011C23132yes—
255#1985C23116yes—
256#1973C23132yes—
257#1972C2318yes—
258#1972C23116yes—
259#1971C2318yes—
260#1970C23116yes—
261#1968C23116yes—
262#1961C23116yes—
263#1959C23116yes—
264#1943C23132yes—
265#1940C23116yes—
266#1940C23116yes—
267#1879C23132yes—
268#1877C23132yes—
269#1864C23132yes—
270#1864C23132yes—
271#1846C2318yes—
272#1844C2318yes—
273#1843C2318yes—
274#1805C23116yes—
275#1804C23116yes—
276#1802C23132yes—
277#1770C23116yes—
278#1770C23116yes—
279C2×#340C2314yes—
280C2×#340C2314yes—
281C2×#336C2314yes—
282C2×#336C2314yes—
283#1726C2318yes—
284C22×#41—216no—
285C22×#41—416no—
286C22×#41—816no—
287C23×Q8C2×D412yes—
288C23×Q8C2412yes—
289C23×D4—22no—
290C23×D4—22no—
291C23×D4—24no—
292C23×D4—24no—
293C23×D4C2412yes—
294C23×D4C2414yes—
295C24×C4—24no—
296C24×C4—22no—
297C24×C4—24no—
298C24×C4—24no—
299C22×Q16—24no—
300C22×Q16—42no—
301C22×Q16—42no—
302C22×Q16C2414yes—
303C22×SD16—216no—
304C22×SD16—28no—
305C22×SD16—28no—
306C22×SD16—28no—
307C22×SD16—48no—
308C22×SD16—48no—
309C22×SD16C2418yes—
310C22×SD16C24116yes—
311C22×D8—216no—
312C22×D8—28no—
313C22×D8—24no—
314C22×D8—28no—
315C22×D8—44no—
316C22×D8—42no—
317C22×D8—44no—
318C22×D8—42no—
319C22×D8—48no—
320C22×D8—48no—
321C22×D8C2×D4116yes—
322C22×D8C2×D4116yes—
323C22×D8C2418yes—
324C22×D8C24116yes—
325C22×D8C2414yes—
326C22×D8C2418yes—
327C23×C8C2411yescharacteristic
328C23×C8C2414yes—
329C23×C8C2411yescharacteristic
330C23×C8C2411yescharacteristic
331C23×C8C2411yescharacteristic
332#559—264no—
333#559—432no—
334#559—464no—
335#550—264no—
336#550—432no—
337#550—464no—
338C2×#127—216no—
339C2×#127—24no—
340C2×#127—28no—
341C2×#127—28no—
342C2×#127—48no—
343C2×#127C2×D4116yes—
344C2×#127C24116yes—
345C2×#127C2418yes—
346C2×#124—216no—
347C2×#124—216no—
348C2×#124—24no—
349C2×#124—28no—
350C2×#124—28no—
351C2×#124—28no—
352C2×#124—48no—
353C2×#124—416no—
354C2×#124C2418yes—
355C2×#124C24116yes—
356C2×#123—232no—
357C2×#123—232no—
358C2×#123—432no—
359C2×#123—816no—
360C2×#121—232no—
361C2×#121—216no—
362C2×#121—416no—
363C2×#121—432no—
364C2×C4×Q8—28no—
365C2×C4×Q8—24no—
366C2×C4×Q8—28no—
367C2×C4×Q8—28no—
368C2×C4×Q8—28no—
369C2×C4×Q8C2×D418yes—
370C2×C4×Q8C2418yes—
371C2×C4×Q8C2418yes—
372C2×C4×D4—216no—
373C2×C4×D4—216no—
374C2×C4×D4—216no—
375C2×C4×D4—24no—
376C2×C4×D4—28no—
377C2×C4×D4—28no—
378C2×C4×D4—28no—
379C2×C4×D4—28no—
380C2×C4×D4—216no—
381C2×C4×D4—28no—
382C2×C4×D4—216no—
383C2×C4×D4—48no—
384C2×C4×D4—48no—
385C2×C4×D4—416no—
386C2×C4×D4C24116yes—
387C2×C4×D4C2418yes—
388C2×C4×D4C24116yes—
389C2×C4×D4C24116yes—
390C22×C4⋊C4—24no—
391C22×C4⋊C4—22no—
392C22×C4⋊C4—24no—
393C22×C4⋊C4—24no—
394C22×C4⋊C4—232no—
395C22×C4⋊C4—816no—
396C22×C4⋊C4C2×D414yes—
397C22×C4⋊C4C2×D412yes—
398C22×C4⋊C4C2×D414yes—
399C22×C4⋊C4C2×D414yes—
400C22×C4⋊C4C2412yes—
401C22×C4⋊C4C2412yes—
402C22×C4⋊C4C2414yes—
403C22×C22⋊C4—22no—
404C22×C22⋊C4—24no—
405C22×C22⋊C4—24no—
406C22×C22⋊C4—24no—
407C22×C22⋊C4—24no—
408C22×C22⋊C4—24no—
409C22×C22⋊C4—24no—
410C22×C22⋊C4—24no—
411C22×C22⋊C4—24no—
412C22×C22⋊C4—24no—
413C22×C22⋊C4—24no—
414C22×C22⋊C4—24no—
415C22×C42—22no—
416C22×C42C2411yescharacteristic
417C22×C42C2414yes—
418C22×C42C2411yescharacteristic
419C22×C42C2411yescharacteristic
420#496—2128no—
421#495—232no—
422#493C2×D4164yes—
423#463—2128no—
424#463—464no—
425#460—264no—
426#459—2128no—
427#459—264no—
428#446—264no—
429#442—2128no—
430#442—416no—
431#442—432no—
432#441—416no—
433C4×SD16—264no—
434C4×D8—264no—
435C2×#107—28no—
436C2×#107C2418yes—
437C2×#106—28no—
438C2×#106—42no—
439C2×#106—42no—
440C2×#106—44no—
441C2×#106C2418yes—
442C2×#106C2418yes—
443C2×#106C2414yes—
444C2×#106C2414yes—
445C2×C4⋊C8—216no—
446C2×C4⋊C8—28no—
447C2×C4⋊C8—28no—
448C2×C4⋊C8—44no—
449C2×C4⋊C8C2418yes—
450C2×C4⋊C8C2418yes—
451C2×C4⋊C8C24116yes—
452C2×C4⋊C8C2418yes—
453C2×#103—28no—
454C2×#103—44no—
455C2×#103—48no—
456C2×#103C2418yes—
457C2×#103C24116yes—
458C2×#103C2418yes—
459C2×#102—216no—
460C2×#102—216no—
461C2×#102—28no—
462C2×#102—216no—
463C2×#102—44no—
464C2×#102—48no—
465C2×#102—48no—
466C2×#102C24116yes—
467C2×#102C24116yes—
468C2×#102C2418yes—
469C2×#102C24116yes—
470C2×#102C24116yes—
471C2×#102C24116yes—
472C2×#102C2418yes—
473C2×#97—216no—
474C2×#97—24no—
475C2×#97—24no—
476C2×#97—42no—
477C2×#97C24116yes—
478C2×#97C2414yes—
479C2×#97C2414yes—
480C2×#97C2414yes—
481C2×C4×C8—24no—
482C2×C4×C8C2×D418yes—
483C2×C4×C8#4118yescomplemented
484C2×C4×C8C2414yes—
485C2×C4×C8C2414yes—
486C2×C4×C8C2414yes—
487#400—216no—
488#399—216no—
489#398C2×D4132yes—
490#397—232no—
491#397—232no—
492#395—216no—
493#395C2×D4132yes—
494#394—232no—
495#394—232no—
496#394—232no—
497#394—232no—
498#393—216no—
499#391—28no—
500#391—24no—
501#391C2418yes—
502#391C24116yes—
503#390—28no—
504#390—24no—
505#390—28no—
506#390C2418yes—
507#390C24116yes—
508#390C24116yes—
509#389—28no—
510#389—28no—
511#389C24116yes—
512#389C24116yes—
513#388—232no—
514#387—232no—
515#386—232no—
516#386—232no—
517#386—232no—
518#386—232no—
519#386—232no—
520#385—232no—
521#385—232no—
522#385—232no—
523#385—232no—
524#385—232no—
525#384—24no—
526#384C2418yes—
527#382—24no—
528#382C2418yes—
529#381—232no—
530#380—232no—
531C4×C4⋊C4C2×D418yes—
532C4×C4⋊C4C2×D418yes—
533C4×C4⋊C4C2418yes—
534C4×C4⋊C4C2418yes—
535#376C2×D414yes—
536#376C2414yes—
537C2×#95—24no—
538C2×#95—22no—
539C2×#95—24no—
540C2×#95—24no—
541C2×#95—24no—
542C2×#95—22no—
543C2×#95—24no—
544C2×#95C2×D412yes—
545C2×#95C2×D412yes—
546C2×#95C2×D414yes—
547C2×#95C2×D412yes—
548C2×#95C2×D412yes—
549#340C24116yes—
550#340C24116yes—
551#336C24116yes—
552#336C24116yes—
553C25—24no—
554C25—22no—
555C2×#41—464no—
556C2×#41—864no—
557C2×#41—8128no—
558C22×Q8—28no—
559C22×Q8—22no—
560C22×Q8—24no—
561C22×Q8—24no—
562C22×Q8—24no—
563C22×Q8—24no—
564C22×Q8—24no—
565C22×Q8—24no—
566C22×Q8—48no—
567C22×Q8C22×D418yes—
568C22×Q8C2514yes—
569C22×D4—216no—
570C22×D4—216no—
571C22×D4—24no—
572C22×D4—28no—
573C22×D4—28no—
574C22×D4—24no—
575C22×D4—22no—
576C22×D4—216no—
577C22×D4—216no—
578C22×D4—28no—
579C22×D4—24no—
580C22×D4—28no—
581C22×D4—28no—
582C22×D4—24no—
583C22×D4—24no—
584C22×D4—28no—
585C22×D4—24no—
586C22×D4—28no—
587C22×D4—24no—
588C22×D4—416no—
589C22×D4—416no—
590C22×D4—416no—
591C22×D4—88no—
592C22×D4—88no—
593C22×D4—88no—
594C22×D4—88no—
595C22×D4—88no—
596C22×D4C22×D4116yes—
597C22×D4C2514yes—
598C22×D4C2518yes—
599C23×C4—22no—
600C23×C4—24no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—216no—
604C23×C4—216no—
605C23×C4—216no—
606C23×C4—28no—
607C23×C4—416no—
608C23×C4—416no—
609C23×C4—416no—
610C23×C4—48no—
611C23×C4—416no—
612C23×C4—88no—
613C23×C4—88no—
614C23×C4—88no—
615C23×C4—88no—
616C23×C4—88no—
617C23×C4—88no—
618C23×C4C22×D412yes—
619C23×C4C22×D414yes—
620C23×C4C22×D414yes—
621C23×C4C22×D412yes—
622C23×C4C22×D412yes—
623C23×C4C2511yescharacteristic
624C2×Q16—28no—
625C2×Q16—44no—
626C2×Q16—44no—
627C2×Q16—416no—
628C2×SD16—232no—
629C2×SD16—216no—
630C2×SD16—216no—
631C2×SD16—216no—
632C2×SD16—416no—
633C2×SD16—416no—
634C2×SD16—432no—
635C2×SD16—832no—
636C2×D8—232no—
637C2×D8—264no—
638C2×D8—216no—
639C2×D8—28no—
640C2×D8—216no—
641C2×D8—432no—
642C2×D8—48no—
643C2×D8—44no—
644C2×D8—48no—
645C2×D8—44no—
646C2×D8—416no—
647C2×D8—416no—
648C2×D8—416no—
649C2×D8—832no—
650C2×D8C22×D4132yes—
651C2×D8C22×D4132yes—
652C22×C8—22no—
653C22×C8—22no—
654C22×C8—22no—
655C22×C8—22no—
656C22×C8—28no—
657C22×C8—28no—
658C22×C8—22no—
659C22×C8—22no—
660C22×C8—22no—
661C22×C8—28no—
662C22×C8C22×D414yes—
663C22×C8C22×D414yes—
664C22×C8C2×#4114yes—
665C22×C8C2×#4114yes—
666C22×C82−1+414yes—
667C22×C8C2518yes—
668C22×C8C2512yes—
669C22×C8C2512yes—
670C22×C8C2512yes—
671C22×C8C2512yes—
672#127—232no—
673#127—232no—
674#127—216no—
675#127—416no—
676#127—432no—
677#127C22×D4132yes—
678#124—232no—
679#124—216no—
680#124—216no—
681#124—416no—
682#124—432no—
683#124—464no—
684#124—416no—
685#123—4128no—
686#123—864no—
687#121—464no—
688#121—4128no—
689C4×Q8—232no—
690C4×Q8—216no—
691C4×Q8—216no—
692C4×Q8—216no—
693C4×Q8—216no—
694C4×Q8—416no—
695C4×D4—232no—
696C4×D4—232no—
697C4×D4—216no—
698C4×D4—232no—
699C4×D4—216no—
700C4×D4—232no—
701C4×D4—416no—
702C4×D4—416no—
703C4×D4—432no—
704C4×D4—432no—
705C4×D4—464no—
706C4×D4—416no—
707C4×D4—432no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—216no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—216no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—216no—
722C2×C4⋊C4—216no—
723C2×C4⋊C4—48no—
724C2×C4⋊C4—48no—
725C2×C4⋊C4—416no—
726C2×C4⋊C4—48no—
727C2×C4⋊C4—864no—
728C2×C4⋊C4—88no—
729C2×C4⋊C4—88no—
730C2×C4⋊C4C22×D418yes—
731C2×C4⋊C4C22×D4116yes—
732C2×C4⋊C4C22×D4116yes—
733C2×C4⋊C4C22×D4116yes—
734C2×C4⋊C4C2514yes—
735C2×C4⋊C4C2514yes—
736C2×C4⋊C4C2518yes—
737C2×C22⋊C4—216no—
738C2×C22⋊C4—216no—
739C2×C22⋊C4—28no—
740C2×C22⋊C4—216no—
741C2×C22⋊C4—216no—
742C2×C22⋊C4—216no—
743C2×C22⋊C4—216no—
744C2×C22⋊C4—216no—
745C2×C22⋊C4—216no—
746C2×C22⋊C4—216no—
747C2×C22⋊C4—216no—
748C2×C22⋊C4—216no—
749C2×C22⋊C4—416no—
750C2×C22⋊C4—416no—
751C2×C22⋊C4—416no—
752C2×C22⋊C4—416no—
753C2×C22⋊C4—48no—
754C2×C22⋊C4—416no—
755C2×C22⋊C4—416no—
756C2×C22⋊C4—88no—
757C2×C22⋊C4—88no—
758C2×C22⋊C4—88no—
759C2×C22⋊C4—88no—
760C2×C22⋊C4—88no—
761C2×C42—28no—
762C2×C42—28no—
763C2×C42—22no—
764C2×C42—22no—
765C2×C42—28no—
766C2×C42—48no—
767C2×C42C22×D418yes—
768C2×C42C22×D412yes—
769C2×C42C22×D412yes—
770C2×C42C22×D414yes—
771C2×C42C22×D412yes—
772C2×C42C2×#4114yes—
773C2×C42H(5,𝔽2)14yes—
774C2×C42H(5,𝔽2)14yes—
775C2×C42C2518yes—
776C2×C42C2512yes—
777C2×C42C2512yes—
778C2×C42C2512yes—
779#107—216no—
780#106—216no—
781#106—44no—
782#106—48no—
783#106—44no—
784C4⋊C8—232no—
785C4⋊C8—216no—
786C4⋊C8—216no—
787C4⋊C8—48no—
788#103—216no—
789#103—48no—
790#103—416no—
791#102—232no—
792#102—232no—
793#102—216no—
794#102—232no—
795#102—416no—
796#102—48no—
797#102—416no—
798#97—232no—
799#97—28no—
800#97—28no—
801#97—44no—
802C4×C8—28no—
803C4×C8C22×D4116yes—
804C4×C8C2×#41116yescomplemented
805#95—216no—
806#95—216no—
807#95—216no—
808#95—216no—
809#95—28no—
810#95—28no—
811#95—216no—
812#95C22×D4116yes—
813#95C22×D418yes—
814#95C22×D418yes—
815#95C22×D418yes—
816#95C22×D418yes—
817C24—28no—
818C24—216no—
819C24—24no—
820C24—48no—
821C24—48no—
822C24—48no—
823C24—48no—
824C24—48no—
825C24—48no—
826C24—48no—
827C24—48no—
828C24—44no—
829C24—44no—
830C24—44no—
831C24C23×D411yescharacteristic
832#41—8256no—
833C2×Q8—216no—
834C2×Q8—24no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—24no—
838C2×Q8—24no—
839C2×Q8—24no—
840C2×Q8—416no—
841C2×Q8—432no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—48no—
846C2×Q8—48no—
847C2×Q8—48no—
848C2×Q8—48no—
849C2×D4—24no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—28no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—28no—
857C2×D4—24no—
858C2×D4—28no—
859C2×D4—24no—
860C2×D4—216no—
861C2×D4—232no—
862C2×D4—232no—
863C2×D4—232no—
864C2×D4—232no—
865C2×D4—432no—
866C2×D4—432no—
867C2×D4—432no—
868C2×D4—44no—
869C2×D4—48no—
870C2×D4—48no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—44no—
875C2×D4—416no—
876C2×D4—48no—
877C2×D4—416no—
878C2×D4—48no—
879C2×D4—816no—
880C2×D4—832no—
881C2×D4—816no—
882C2×D4—832no—
883C2×D4—816no—
884C2×D4—816no—
885C2×D4—816no—
886C2×D4—864no—
887C2×D4—1632no—
888C2×D4C23×D4116yes—
889C22×C4—28no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—28no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—28no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—432no—
904C22×C4—432no—
905C22×C4—432no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—416no—
917C22×C4—432no—
918C22×C4—816no—
919C22×C4—816no—
920C22×C4—816no—
921C22×C4—816no—
922C22×C4—816no—
923C22×C4—816no—
924C22×C4—864no—
925C22×C4—832no—
926C22×C4—864no—
927C22×C4—1632no—
928C22×C4D4218yes—
929C22×C4#55018yes—
930C22×C4C23×D414yes—
931C22×C4C23×D418yes—
932C22×C4C23×D418yes—
933C22×C4C23×D414yes—
934C22×C4C23×D414yes—
935C22×C4C23×D412yes—
936C22×C4C23×D411yescharacteristic
937C22×C4C22×#4112yes—
938C22×C4C2×H(5,𝔽2)12yes—
939C22×C4C2×H(5,𝔽2)12yes—
940C22×C4C2×2−1+412yes—
941C22×C4#58512yes—
942C22×C4C2611yescharacteristic
943Q16—416no—
944SD16—432no—
945SD16—832no—
946D8—264no—
947D8—432no—
948D8—416no—
949D8—832no—
950C2×C8—22no—
951C2×C8—22no—
952C2×C8—22no—
953C2×C8—22no—
954C2×C8—28no—
955C2×C8—28no—
956C2×C8—28no—
957C2×C8—22no—
958C2×C8—22no—
959C2×C8—28no—
960C2×C8—22no—
961C2×C8—28no—
962C2×C8—416no—
963C2×C8—44no—
964C2×C8#547116yes—
965C2×C8C23×D414yes—
966C2×C8C23×D414yes—
967C2×C8C22×#4114yes—
968C2×C8C22×#4114yes—
969C2×C8C2×2−1+414yes—
970C4⋊C4—216no—
971C4⋊C4—232no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—416no—
979C4⋊C4—416no—
980C4⋊C4—432no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—416no—
984C4⋊C4—48no—
985C4⋊C4—816no—
986C4⋊C4—816no—
987C22⋊C4—432no—
988C22⋊C4—432no—
989C22⋊C4—432no—
990C22⋊C4—432no—
991C22⋊C4—416no—
992C22⋊C4—432no—
993C22⋊C4—432no—
994C22⋊C4—816no—
995C22⋊C4—816no—
996C22⋊C4—816no—
997C22⋊C4—816no—
998C22⋊C4—816no—
999C42—28no—
1000C42—28no—
1001C42—22no—
1002C42—22no—
1003C42—216no—
1004C42—24no—
1005C42—416no—
1006C42D4218yes—
1007C42#55018yes—
1008C42C23×D414yes—
1009C42C22×#4114yes—
1010C42C2×H(5,𝔽2)14yes—
1011C42C2×H(5,𝔽2)14yes—
1012C23—216no—
1013C23—48no—
1014C23—48no—
1015C23—48no—
1016C23—48no—
1017C23—48no—
1018C23—432no—
1019C23—432no—
1020C23—432no—
1021C23—48no—
1022C23—44no—
1023C23—48no—
1024C23—48no—
1025C23—44no—
1026C23—44no—
1027C23—816no—
1028C23—816no—
1029C23—816no—
1030C23—816no—
1031C23—88no—
1032C23—88no—
1033C23—88no—
1034C23—816no—
1035C23—816no—
1036C23C2×D4212yes—
1037C23C2×#55012yes—
1038C23#349712yes—
1039C23#358518yes—
1040C23C24×D411yescharacteristic
1041Q8—432no—
1042Q8—44no—
1043Q8—44no—
1044Q8—44no—
1045Q8—44no—
1046Q8—88no—
1047D4—216no—
1048D4—216no—
1049D4—48no—
1050D4—44no—
1051D4—44no—
1052D4—48no—
1053D4—44no—
1054D4—432no—
1055D4—44no—
1056D4—832no—
1057D4—832no—
1058D4—864no—
1059D4—88no—
1060D4—1632no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—216no—
1064C2×C4—216no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—28no—
1072C2×C4—28no—
1073C2×C4—416no—
1074C2×C4—416no—
1075C2×C4—48no—
1076C2×C4—44no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—48no—
1086C2×C4—864no—
1087C2×C4—832no—
1088C2×C4—864no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4—88no—
1092C2×C4—816no—
1093C2×C4—1632no—
1094C2×C4C2×D4218yes—
1095C2×C4C2×D4212yes—
1096C2×C4C2×#54714yes—
1097C2×C4C2×#55018yes—
1098C2×C4C2×#55012yes—
1099C2×C4#349614yes—
1100C2×C4#349712yes—
1101C2×C4#350614yes—
1102C2×C4#354814yes—
1103C2×C4C24×D411yescharacteristic
1104C2×C4C23×#4111yescharacteristic
1105C2×C4C22×H(5,𝔽2)11yescharacteristic
1106C2×C4C22×H(5,𝔽2)11yescharacteristic
1107C2×C4C22×2−1+411yescharacteristic
1108C2×C4C2×#58511yescharacteristic
1109C8—24no—
1110C8—24no—
1111C8—42no—
1112C8—48no—
1113C8C2×#54718yes—
1114C22—416no—
1115C22—416no—
1116C22—416no—
1117C22—88no—
1118C22—88no—
1119C22—88no—
1120C22—88no—
1121C22—864no—
1122C22—88no—
1123C22—84no—
1124C22—88no—
1125C22—84no—
1126C22—84no—
1127C22—1616no—
1128C22#5981514yes—
1129C22#6105818yes—
1130C22#6141418yes—
1131C22#6239218yes—
1132C22C22×D4211yescharacteristic
1133C22C22×#55011yescharacteristic
1134C22C2×#349711yescharacteristic
1135C22C2×#358514yes—
1136C4—28no—
1137C4—28no—
1138C4—44no—
1139C4—48no—
1140C4—48no—
1141C4—84no—
1142C4—88no—
1143C4—84no—
1144C4—84no—
1145C4#5981514yes—
1146C4C22×#54711yescharacteristic
1147C4C2×#354811yescharacteristic
1148C4C2×#349611yescharacteristic
1149C4C2×#350611yescharacteristic
1150C2—816no—
1151C2—164no—
1152C2#761394618yesdirect product factor
1153C2C2×#5981511yescharacteristic
1154C2C2×#6105812yes—
1155C2C2×#6141412yes—
1156C2C2×#6239212yes—
subgroupG/H
center, socleC24C23×D4
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#3399C2semidirect
2. C2×#45354C2semidirect
3. #7613946C2direct (N × H)
4. C2×#31224C2semidirect
5. C2×#31223C2semidirect
6. C2×#28270C2semidirect
7. C2×#28467C2semidirect
8. C2×#28257C2semidirect
9. C2×#24202C2semidirect
10. C2×#24196C2semidirect
11. C2×#26268C2semidirect
12. C2×#24738C2semidirect
13. C2×#22670C2semidirect
14. C2×#21716C2semidirect
15. C2×#21697C2semidirect
16. C2×#21694C2semidirect
20. C2×#3399C22semidirect
39. #45354C22semidirect
51. #31224C22semidirect
52. #31223C22semidirect
53. #28467C22semidirect
54. #28270C22semidirect
55. #28257C22semidirect
56. #26268C22semidirect
57. #24738C22semidirect
58. #24202C22semidirect
59. #24196C22semidirect
68. #22670C22semidirect
69. #21716C22semidirect
70. #21697C22semidirect
71. #21694C22semidirect
483. C2×C4×C8#41semidirect
804. C4×C8C2×#41semidirect
1152. C2#7613946direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#33992
C2×#453542
#76139462
C2×#312242
C2×#312232
C2×#282702
C2×#284672
C2×#282572
C2×#242022
C2×#241962
C2×#262682
C2×#247382
C2×#226702
C2×#217162
C2×#216972
C2×#216942