Finite Group Databasebeta

← C2×#62016 #10578809

Subgroups — C2×#62016 #10578809

Order 512.

6910 conjugacy classes of subgroups.

The subgroup lattice has 1197 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic, complemented
2C2×#3561C211yesmaximal, characteristic, complemented
3#62016C2132yesmaximal, direct product factor
4C2×#3397C212yesmaximal, complemented
5C2×#3376C212yesmaximal, complemented
6C2×#3321C212yesmaximal, complemented
7C2×#3320C212yesmaximal, complemented
8C2×#3297C212yesmaximal, complemented
9C2×D4×SD16C212yesmaximal, complemented
10C2×#3265C212yesmaximal, complemented
11C2×#3264C212yesmaximal, complemented
12C2×#3257C212yesmaximal, complemented
13C2×#3246C211yesmaximal, characteristic, complemented
14C2×#3221C212yesmaximal, complemented
15C2×#3213C211yesmaximal, characteristic, complemented
16C2×#3118C212yesmaximal, complemented
17C2×#3110C211yesmaximal, characteristic, complemented
18C2×#3042C212yesmaximal, complemented
19C22×#463C211yesmaximal, characteristic, complemented
20C2×#2992C211yesmaximal, characteristic, complemented
21C22×AGL(1,ℤ/8)C2212yes—
22C23×SD16C2211yescharacteristic
23C23×SD16C2212yescomplemented
24C23×D8C2211yescharacteristic
25#3561—28no—
26#3561C22116yescomplemented
27C2×#563—21no—
28C2×#562—21no—
29#3519—28no—
30#3519C22116yescomplemented
31C2×#556C2212yescomplemented
32C2×#555C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic, complemented
34C2×#553—21no—
35C2×#553C2212yes—
36C2×#551—22no—
37C2×#550C2211yescharacteristic, complemented
38C2×D4×Q8C2212yescomplemented
39C2×#548C2212yescomplemented
40C2×#546—21no—
41C2×#546—22no—
42C2×#546C2212yescomplemented
43C2×D42C2212yes—
44C2×D42C2211yescharacteristic, complemented
45C2×#543—21no—
46C2×#542—22no—
47C2×#542C2212yescomplemented
48C2×#540C2212yescomplemented
49C2×#538—22no—
50C2×#538—21no—
51C2×#536C2212yescomplemented
52C2×#533C2211yescharacteristic, complemented
53C2×#532C2211yescharacteristic
54C2×#529C2211yescharacteristic
55C22×#124C2211yescharacteristic, complemented
56C2×#525—21no—
57C22×#121—21no—
58C2×#518C2212yescomplemented
59C22×C4×D4C2211yescharacteristic
60#3397C22132yescomplemented
61#3376C22132yescomplemented
62#3321C22132yescomplemented
63#3320C22132yescomplemented
64#3297C22132yescomplemented
65D4×SD16C22132yescomplemented
66#3265C22132yescomplemented
67#3264C22132yescomplemented
68#3257C22132yescomplemented
69#3246C22116yescomplemented
70#3221C22132yescomplemented
71#3213C22116yescomplemented
72C2×#496C2212yescomplemented
73C2×#496C2212yescomplemented
74C2×#492C2212yescomplemented
75C2×#491C2212yescomplemented
76C2×#489C2212yescomplemented
77C2×#488C2212yescomplemented
78#3118C22132yescomplemented
79#3110C22116yescomplemented
80C2×#484C2212yescomplemented
81C2×#485C2212yescomplemented
82C2×#482C2212yescomplemented
83C2×#479C2212yescomplemented
84C2×#475C2212yescomplemented
85C2×#478C2212yescomplemented
86C2×#476C2212yescomplemented
87C2×#474C2211yescharacteristic, complemented
88C2×#474C2211yescharacteristic, complemented
89C2×#469C2212yescomplemented
90C2×#468C2212yescomplemented
91C2×#466C2212yescomplemented
92C2×#465C2212yescomplemented
93C2×#465C2212yescomplemented
94C2×#465C2212yescomplemented
95#3042C22132yescomplemented
96C2×#460C2212yescomplemented
97C2×#460C2212yescomplemented
98C2×#463C2212yes—
99C2×#463C2212yes—
100C2×#463C2212yes—
101C2×#463C2212yescomplemented
102C2×#463C2212yescomplemented
103C2×#463C2212yescomplemented
104C2×#463C2212yescomplemented
105C2×#463C2212yescomplemented
106C2×#463C22116yescomplemented
107C2×#461C2211yescharacteristic, complemented
108C2×#461C2212yescomplemented
109C2×#461C2212yescomplemented
110C2×#461C2212yescomplemented
111C2×#461C2211yescharacteristic, complemented
112C2×#459C2212yescomplemented
113C2×#449C2212yescomplemented
114C2×#449C2212yescomplemented
115C2×#448C2212yescomplemented
116C2×#448C2212yescomplemented
117C2×#448C2212yescomplemented
118C2×#450C2212yes—
119C2×#450C2212yescomplemented
120C2×#447C2212yes—
121C2×#447C2212yescomplemented
122#2992C22116yescomplemented
123C2×#446C2212yescomplemented
124C2×#442C2212yes—
125C2×#440C2212yescomplemented
126C2×#440C2212yescomplemented
127C2×#440C2212yescomplemented
128C2×C4×SD16C2212yescomplemented
129C2×C4×D8C2212yescomplemented
130C2×#435C2212yescomplemented
131C2×#435C2212yescomplemented
132C2×C8×D4C2212yescomplemented
133C2×#433C2212yescomplemented
134C2×#432C2211yescharacteristic, complemented
135C2×#424C2212yescomplemented
136C22×C4⋊C8C2211yescharacteristic, complemented
137C2×#419C2212yescomplemented
138C2×#416C2212yescomplemented
139C22×#103C2211yescharacteristic, complemented
140C22×#102C2211yescharacteristic, complemented
141C22×#41—21no—
142C22×#41—21no—
143C22×#41C2312yes—
144C23×Q8C2311yescharacteristic
145C23×Q8C2312yes—
146C23×D4—22no—
147C23×D4—21no—
148C23×D4C2311yescharacteristic
149C23×D4C2312yes—
150C23×D4C2311yescharacteristic
151C24×C4—21no—
152C2×AGL(1,ℤ/8)—48no—
153C2×AGL(1,ℤ/8)C23116yes—
154C22×SD16—44no—
155C22×SD16—48no—
156C22×SD16C2312yes—
157C22×SD16C2312yes—
158C22×SD16C2312yes—
159C22×SD16C2312yes—
160C22×SD16C2312yes—
161C22×SD16C2312yes—
162C22×SD16C2312yes—
163C22×SD16C2312yes—
164C22×SD16C2318yes—
165C22×SD16C23116yescomplemented
166C22×D8—44no—
167C22×D8C2312yes—
168C22×D8C2312yes—
169C22×D8C2312yes—
170C22×D8C2312yes—
171C22×D8C2318yes—
172C22×M16C2312yes—
173C23×C8C2311yescharacteristic
174C23×C8C2311yescharacteristic
175C23×C8C2312yes—
176#563—216no—
177#562—216no—
178#556—28no—
179#556C23116yescomplemented
180#555—24no—
181#555C2318yescomplemented
182#554—24no—
183#554C2318yescomplemented
184#553—216no—
185#553—28no—
186#553C23116yes—
187#551—232no—
188#550—24no—
189#550C2318yescomplemented
190D4×Q8—28no—
191D4×Q8C23116yescomplemented
192#548—28no—
193#548C23116yescomplemented
194#546—216no—
195#546—232no—
196#546—28no—
197#546C23116yescomplemented
198D42—28no—
199D42—24no—
200D42C23116yes—
201D42C2318yescomplemented
202#543—216no—
203#542—232no—
204#542—28no—
205#542C23116yescomplemented
206#540—28no—
207#540C23116yescomplemented
208#538—232no—
209#538—216no—
210#536—28no—
211#536C23116yescomplemented
212#533—24no—
213#533C2318yescomplemented
214#532—24no—
215#532C2318yes—
216C2×C4⋊Q8—22no—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2312yes—
222C2×#127C2311yescharacteristic
223#529D418yes—
224#529C2318yes—
225C2×#126—22no—
226C2×#126—22no—
227C2×#126—22no—
228C2×#126—22no—
229C2×#126D412yes—
230C2×#125—21no—
231C2×#125D411yescharacteristic
232C2×#125C2312yes—
233C2×#124—22no—
234C2×#124—22no—
235C2×#124—22no—
236C2×#124—21no—
237C2×#124—21no—
238C2×#124—24no—
239C2×#124—21no—
240C2×#124D411yescharacteristic
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2318yescomplemented
245#525—216no—
246C2×#123—22no—
247C2×#123—22no—
248C2×#123—22no—
249C2×#123—22no—
250C2×#123—22no—
251C2×#123—22no—
252C2×#123—22no—
253C2×#123D412yes—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—22no—
258C2×C22⋊Q8—22no—
259C2×C22⋊Q8—22no—
260C2×C22⋊Q8—22no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8—22no—
263C2×C22⋊Q8—22no—
264C2×C22⋊Q8D411yescharacteristic
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×#121—22no—
268C2×#121—21no—
269C2×#121—22no—
270C2×#121—21no—
271C2×#121—216no—
272C2×#121—21no—
273C2×#121—21no—
274C2×#121—22no—
275C2×#121—22no—
276C2×#121—22no—
277C2×#121—22no—
278C2×#121—22no—
279C2×#121D411yescharacteristic
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#120—22no—
285C2×#120—22no—
286C2×#120—22no—
287C2×#120—22no—
288#518—28no—
289#518C23116yescomplemented
290C2×C4×Q8—21no—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4—22no—
295C2×C4×D4—22no—
296C2×C4×D4—22no—
297C2×C4×D4—22no—
298C2×C4×D4—22no—
299C2×C4×D4—21no—
300C2×C4×D4—21no—
301C2×C4×D4—24no—
302C2×C4×D4—21no—
303C2×C4×D4C2312yes—
304C2×C4×D4C2318yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×#117—21no—
315C2×#117—21no—
316C2×#117—22no—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C22×C4⋊C4—21no—
320C22×C4⋊C4C2311yescharacteristic
321C22×C22⋊C4—21no—
322C22×C22⋊C4—21no—
323C22×C22⋊C4—21no—
324C22×C22⋊C4—22no—
325C22×C22⋊C4—22no—
326C22×C22⋊C4—22no—
327C22×C42C2311yescharacteristic
328#496C23116yescomplemented
329#496C23116yescomplemented
330#492C23116yescomplemented
331#491C23116yescomplemented
332#489C23116yescomplemented
333#488C23116yescomplemented
334#485C23116yescomplemented
335#484C23116yescomplemented
336#482C23116yescomplemented
337#479C23116yescomplemented
338#478C23116yescomplemented
339#476C23116yescomplemented
340#475C23116yescomplemented
341#474C2318yescomplemented
342#474C2318yescomplemented
343#469C23116yescomplemented
344#468C23116yescomplemented
345#466C23116yescomplemented
346#465C23116yescomplemented
347#465C23116yescomplemented
348#465C23116yescomplemented
349#463C23116yes—
350#463C23116yes—
351#463C23116yes—
352#463C23116yescomplemented
353#463C23116yescomplemented
354#463C23116yescomplemented
355#463C23116yescomplemented
356#463C23116yescomplemented
357#461C2318yescomplemented
358#461C2318yescomplemented
359#461C23116yescomplemented
360#461C23116yescomplemented
361#461C23116yescomplemented
362#460C23116yescomplemented
363#460C23116yescomplemented
364#459C23116yescomplemented
365#450C23116yes—
366#450C23116yescomplemented
367#449C23116yescomplemented
368#449C23116yescomplemented
369#448C23116yescomplemented
370#448C23116yescomplemented
371#448C23116yescomplemented
372#447C23116yes—
373#447C23116yescomplemented
374#446C23116yescomplemented
375#442C23116yes—
376#440C23116yescomplemented
377#440C23116yescomplemented
378#440C23116yescomplemented
379C4×SD16C23116yescomplemented
380C4×D8C23116yescomplemented
381#435C23116yescomplemented
382#435C23116yescomplemented
383C8×D4C23116yescomplemented
384#433C23116yescomplemented
385#432C2318yescomplemented
386C2×#107C2312yes—
387C2×#107C2312yes—
388C2×#106C2312yes—
389C2×#106C2312yes—
390#424C23116yescomplemented
391C2×C4⋊C8C2312yes—
392C2×C4⋊C8C2312yes—
393C2×C4⋊C8C2312yes—
394C2×C4⋊C8C2312yes—
395C2×C4⋊C8C2311yescharacteristic
396C2×C4⋊C8C2311yescharacteristic
397C2×C4⋊C8C2318yescomplemented
398#419C23116yescomplemented
399#416C23116yescomplemented
400C2×#103C2312yes—
401C2×#103C2312yes—
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#103C2312yes—
405C2×#103C2312yes—
406C2×#103C2312yes—
407C2×#103C2312yes—
408C2×#103C2318yescomplemented
409C2×#102C2312yes—
410C2×#102C2312yes—
411C2×#102C2312yes—
412C2×#102C2312yes—
413C2×#102C2312yes—
414C2×#102C2312yes—
415C2×#102C2312yes—
416C2×#102C2312yes—
417C2×#102C2318yescomplemented
418C2×C22⋊C8C2312yes—
419C2×C22⋊C8C2312yes—
420C2×C22⋊C8C2312yes—
421C2×#97C2312yes—
422C2×#97C2312yes—
423C2×C4×C8C2312yes—
424C25—21no—
425C25—21no—
426C25—22no—
427C2×#41—28no—
428C2×#41—28no—
429C2×#41—24no—
430C2×#41—44no—
431C2×#41—44no—
432C2×#41—84no—
433C2×#41—84no—
434C2×#41C2418yes—
435C22×Q8—21no—
436C22×Q8—22no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—22no—
440C22×Q8—24no—
441C22×Q8—42no—
442C22×Q8—44no—
443C22×Q8—42no—
444C22×Q8—44no—
445C22×Q8C2×D411yescharacteristic
446C22×Q8C2412yes—
447C22×Q8C2412yes—
448C22×Q8C2414yes—
449C22×Q8C2418yes—
450C22×D4—24no—
451C22×D4—28no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—216no—
458C22×D4—28no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4—21no—
463C22×D4—24no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—21no—
468C22×D4—22no—
469C22×D4—42no—
470C22×D4—44no—
471C22×D4—42no—
472C22×D4—42no—
473C22×D4—84no—
474C22×D4—88no—
475C22×D4C2×D412yes—
476C22×D4C2×D411yescharacteristic
477C22×D4C2411yescharacteristic
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2414yes—
481C22×D4C2418yes—
482C22×D4C2411yescharacteristic
483C22×D4C2414yes—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—22no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—21no—
496C23×C4—28no—
497C23×C4—84no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2412yes—
502AGL(1,ℤ/8)—432no—
503C2×SD16—28no—
504C2×SD16—28no—
505C2×SD16—44no—
506C2×SD16—44no—
507C2×SD16—44no—
508C2×SD16—44no—
509C2×SD16—44no—
510C2×SD16—44no—
511C2×SD16—416no—
512C2×SD16—432no—
513C2×SD16C2418yes—
514C2×SD16C2418yes—
515C2×SD16C2418yes—
516C2×SD16C2418yes—
517C2×SD16C2418yes—
518C2×SD16C2418yes—
519C2×SD16C2418yes—
520C2×SD16C2418yes—
521C2×D8—28no—
522C2×D8—44no—
523C2×D8—44no—
524C2×D8—44no—
525C2×D8—416no—
526C2×D8C2418yes—
527C2×D8C2418yes—
528C2×D8C2418yes—
529C2×D8C2418yes—
530C2×M16—44no—
531C2×M16C2418yes—
532C22×C8—42no—
533C22×C8—42no—
534C22×C8—44no—
535C22×C8C2412yes—
536C22×C8C2412yes—
537C22×C8C2412yes—
538C22×C8C2412yes—
539C22×C8C2414yes—
540C22×C8C2414yes—
541C22×C8C2418yes—
542C4⋊Q8—216no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—24no—
547C4⋊Q8C2414yes—
548C4⋊Q8C2418yes—
549C4⋊Q8C2414yes—
550C4⋊Q8C2414yes—
551#127—22no—
552#127—24no—
553#127C2414yes—
554#127C2418yes—
555#126—216no—
556#126—216no—
557#126—216no—
558#126—216no—
559#126C2×D4116yes—
560#125—28no—
561#125—24no—
562#125C2×D418yes—
563#125C2418yes—
564#124—216no—
565#124—216no—
566#124—216no—
567#124—24no—
568#124—24no—
569#124—28no—
570#124—28no—
571#124—28no—
572#124—24no—
573#124C2×D418yes—
574#124C2418yes—
575#124C2418yes—
576#124C2418yes—
577#123—216no—
578#123—216no—
579#123—216no—
580#123—216no—
581#123—216no—
582#123—216no—
583#123—216no—
584#123C2×D4116yes—
585C22⋊Q8—28no—
586C22⋊Q8—216no—
587C22⋊Q8—28no—
588C22⋊Q8—24no—
589C22⋊Q8—24no—
590C22⋊Q8—216no—
591C22⋊Q8—216no—
592C22⋊Q8—216no—
593C22⋊Q8—216no—
594C22⋊Q8—216no—
595C22⋊Q8—216no—
596C22⋊Q8—216no—
597C22⋊Q8C2×D418yes—
598C22⋊Q8C2418yes—
599C22⋊Q8C2418yes—
600#121—216no—
601#121—28no—
602#121—216no—
603#121—28no—
604#121—24no—
605#121—24no—
606#121—24no—
607#121—24no—
608#121—28no—
609#121—28no—
610#121—216no—
611#121—216no—
612#121—216no—
613#121—216no—
614#121—216no—
615#121C2×D418yes—
616#121C2418yes—
617#121C2418yes—
618#121C2418yes—
619#121C2418yes—
620#120—216no—
621#120—216no—
622#120—216no—
623#120—216no—
624C4×Q8—28no—
625C4×Q8—24no—
626C4×Q8—24no—
627C4×Q8C2×D414yes—
628C4×Q8C2418yes—
629C4×Q8C2418yes—
630C4×Q8C2414yes—
631C4×D4—216no—
632C4×D4—216no—
633C4×D4—216no—
634C4×D4—216no—
635C4×D4—216no—
636C4×D4—22no—
637C4×D4—28no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—28no—
641C4×D4—22no—
642C4×D4—28no—
643C4×D4—24no—
644C4×D4—24no—
645C4×D4—24no—
646C4×D4—24no—
647C4×D4C2×D418yes—
648C4×D4C2×D414yes—
649C4×D4C2414yes—
650C4×D4C2414yes—
651C4×D4C2414yes—
652C4×D4C2414yes—
653C4×D4C2418yes—
654C4×D4C2418yes—
655C4×D4C2418yes—
656C4×D4C2418yes—
657C4×D4C2418yes—
658C4×D4C2414yes—
659#117—28no—
660#117—24no—
661#117—28no—
662#117—216no—
663#117C2×D418yes—
664#117C2418yes—
665#117C2418yes—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D412yes—
684C2×C4⋊C4C2×D412yes—
685C2×C4⋊C4C2×D412yes—
686C2×C4⋊C4C2×D412yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—28no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—28no—
710C2×C22⋊C4—28no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—216no—
717C2×C22⋊C4—216no—
718C2×C22⋊C4—216no—
719C2×C22⋊C4C2×D412yes—
720C2×C22⋊C4C2×D412yes—
721C2×C22⋊C4C2×D412yes—
722C2×C22⋊C4C2×D412yes—
723C2×C22⋊C4C2×D412yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2414yes—
734#107C2418yes—
735#107C2418yes—
736#106C2418yes—
737#106C2418yes—
738C4⋊C8C2418yes—
739C4⋊C8C2418yes—
740C4⋊C8C2414yes—
741C4⋊C8C2418yes—
742C4⋊C8C2418yes—
743C4⋊C8C2414yes—
744#103C2418yes—
745#103C2418yes—
746#103C2418yes—
747#103C2418yes—
748#103C2418yes—
749#103C2418yes—
750#103C2418yes—
751#103C2418yes—
752#102C2418yes—
753#102C2418yes—
754#102C2418yes—
755#102C2418yes—
756#102C2418yes—
757#102C2418yes—
758#102C2418yes—
759#102C2418yes—
760C22⋊C8C2418yes—
761C22⋊C8C2418yes—
762C22⋊C8C2418yes—
763#97C2418yes—
764#97C2418yes—
765C4×C8C2418yes—
766C24—21no—
767C24—22no—
768C24—21no—
769C24—22no—
770C24—24no—
771C24—24no—
772C24—28no—
773C24—44no—
774C24—48no—
775C24—44no—
776C24—44no—
777C24—82no—
778C24—82no—
779C24—84no—
780C24—84no—
781C24—82no—
782C24C22×D412yes—
783C24C22×D411yescharacteristic
784#41—48no—
785#41—48no—
786#41—816no—
787#41—88no—
788#41—816no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—42no—
800C2×Q8—44no—
801C2×Q8—48no—
802C2×Q8—44no—
803C2×Q8—48no—
804C2×Q8—82no—
805C2×Q8—84no—
806C2×Q8—82no—
807C2×Q8—82no—
808C2×Q8—84no—
809C2×Q8—88no—
810C2×Q8C22×D414yes—
811C2×Q8C2514yes—
812C2×Q8C2514yes—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—216no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—21no—
822C2×D4—28no—
823C2×D4—24no—
824C2×D4—21no—
825C2×D4—22no—
826C2×D4—24no—
827C2×D4—22no—
828C2×D4—28no—
829C2×D4—24no—
830C2×D4—28no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—48no—
844C2×D4—416no—
845C2×D4—42no—
846C2×D4—48no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—48no—
850C2×D4—84no—
851C2×D4—82no—
852C2×D4—84no—
853C2×D4—84no—
854C2×D4—82no—
855C2×D4—816no—
856C2×D4—84no—
857C2×D4—84no—
858C2×D4—84no—
859C2×D4—84no—
860C2×D4—832no—
861C2×D4C22×D418yes—
862C2×D4C22×D414yes—
863C2×D4H(5,𝔽2)14yes—
864C2×D4C2514yes—
865C2×D4C2512yes—
866C2×D4C2514yes—
867C2×D4C2512yes—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—28no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—28no—
886C22×C4—28no—
887C22×C4—28no—
888C22×C4—28no—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—84no—
895C22×C4—82no—
896C22×C4—82no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—816no—
902C22×C4—82no—
903C22×C4—84no—
904C22×C4—82no—
905C22×C4C22×D412yes—
906C22×C4C22×D414yes—
907C22×C4C22×D414yes—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D412yes—
916C22×C4C22×D414yes—
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2511yescharacteristic
920SD16—216no—
921SD16—216no—
922SD16—48no—
923SD16—48no—
924SD16—48no—
925SD16—48no—
926SD16—48no—
927SD16—48no—
928D8—216no—
929D8—48no—
930D8—48no—
931D8—48no—
932M16—48no—
933C2×C8—24no—
934C2×C8—24no—
935C2×C8—24no—
936C2×C8—24no—
937C2×C8—44no—
938C2×C8—44no—
939C2×C8—48no—
940C2×C8C2514yes—
941C2×C8C2514yes—
942C2×C8C2514yes—
943C2×C8C2514yes—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—24no—
949C4⋊C4—28no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4C22×D414yes—
962C4⋊C4C22×D414yes—
963C4⋊C4C22×D418yes—
964C4⋊C4C22×D418yes—
965C4⋊C4C22×D418yes—
966C4⋊C4C22×D418yes—
967C4⋊C4C2514yes—
968C4⋊C4C2514yes—
969C4⋊C4C2512yes—
970C4⋊C4C2512yes—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—24no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—24no—
978C22⋊C4—28no—
979C22⋊C4—24no—
980C22⋊C4—28no—
981C22⋊C4—24no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4C22×D418yes—
993C22⋊C4C22×D418yes—
994C22⋊C4C22×D418yes—
995C22⋊C4C22×D418yes—
996C22⋊C4C22×D418yes—
997C42—28no—
998C42—28no—
999C42—28no—
1000C42C22×D412yes—
1001C42C22×D414yes—
1002C42C22×D412yes—
1003C42C22×D414yes—
1004C42C22×D414yes—
1005C42C2514yes—
1006C42C2512yes—
1007C42C2512yes—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—22no—
1018C23—48no—
1019C23—416no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—44no—
1024C23—44no—
1025C23—44no—
1026C23—42no—
1027C23—44no—
1028C23—44no—
1029C23—48no—
1030C23—42no—
1031C23—44no—
1032C23—48no—
1033C23—84no—
1034C23—84no—
1035C23—88no—
1036C23—88no—
1037C23—84no—
1038C23—816no—
1039C23—168no—
1040C23—1616no—
1041C23#57714yes—
1042C23C23×D414yes—
1043C23C23×D412yes—
1044C23C23×D411yescharacteristic
1045Q8—24no—
1046Q8—24no—
1047Q8—24no—
1048Q8—24no—
1049Q8—44no—
1050Q8—44no—
1051Q8—44no—
1052Q8—88no—
1053Q8—84no—
1054Q8—84no—
1055Q8—84no—
1056D4—216no—
1057D4—24no—
1058D4—22no—
1059D4—24no—
1060D4—22no—
1061D4—24no—
1062D4—24no—
1063D4—22no—
1064D4—24no—
1065D4—44no—
1066D4—416no—
1067D4—48no—
1068D4—48no—
1069D4—416no—
1070D4—42no—
1071D4—44no—
1072D4—44no—
1073D4—84no—
1074D4—88no—
1075D4—84no—
1076D4—88no—
1077D4—88no—
1078D4—88no—
1079D4—88no—
1080D4—88no—
1081D4C2×H(5,𝔽2)14yes—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—28no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—28no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—44no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—88no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—88no—
1116C2×C4—88no—
1117C2×C4—88no—
1118C2×C4—88no—
1119C2×C4—84no—
1120C2×C4—88no—
1121C2×C4—84no—
1122C2×C4C23×D412yes—
1123C2×C4C23×D414yes—
1124C2×C4C23×D414yes—
1125C2×C4C23×D412yes—
1126C2×C4C23×D412yes—
1127C2×C4C23×D412yes—
1128C2×C4C23×D412yes—
1129C2×C4C23×D414yes—
1130C2×C4C23×D411yescharacteristic
1131C2×C4C2×H(5,𝔽2)12yes—
1132C2×C4#58512yes—
1133C2×C4C2611yescharacteristic
1134C8—24no—
1135C8—24no—
1136C8—24no—
1137C8—24no—
1138C22—28no—
1139C22—22no—
1140C22—22no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—48no—
1146C22—48no—
1147C22—42no—
1148C22—42no—
1149C22—44no—
1150C22—42no—
1151C22—44no—
1152C22—44no—
1153C22—42no—
1154C22—44no—
1155C22—42no—
1156C22—44no—
1157C22—44no—
1158C22—816no—
1159C22—84no—
1160C22—88no—
1161C22—88no—
1162C22—168no—
1163C22—1616no—
1164C22#348812yes—
1165C22C2×#57714yes—
1166C22C2×#57712yes—
1167C22#358512yes—
1168C22C24×D411yescharacteristic
1169C4—24no—
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—24no—
1174C4—22no—
1175C4—22no—
1176C4—24no—
1177C4—44no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—42no—
1182C4—44no—
1183C4#348812yes—
1184C4C22×H(5,𝔽2)11yescharacteristic
1185C4C2×#58511yescharacteristic
1186C2—24no—
1187C2—44no—
1188C2—44no—
1189C2—82no—
1190C2—84no—
1191C2—84no—
1192C2#6201614yesdirect product factor
1193C2C2×#348811yescharacteristic
1194C2C22×#57711yescharacteristic
1195C2C2×#358511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3519C2semidirect
2. C2×#3561C2semidirect
3. #62016C2direct (N × H)
4. C2×#3397C2semidirect
5. C2×#3376C2semidirect
6. C2×#3321C2semidirect
7. C2×#3320C2semidirect
8. C2×#3297C2semidirect
9. C2×D4×SD16C2semidirect
10. C2×#3265C2semidirect
11. C2×#3264C2semidirect
12. C2×#3257C2semidirect
13. C2×#3246C2semidirect
14. C2×#3221C2semidirect
15. C2×#3213C2semidirect
16. C2×#3118C2semidirect
17. C2×#3110C2semidirect
18. C2×#3042C2semidirect
19. C22×#463C2semidirect
20. C2×#2992C2semidirect
23. C23×SD16C22semidirect
26. #3561C22semidirect
30. #3519C22semidirect
31. C2×#556C22semidirect
32. C2×#555C22semidirect
33. C2×#554C22semidirect
37. C2×#550C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×#548C22semidirect
42. C2×#546C22semidirect
44. C2×D42C22semidirect
47. C2×#542C22semidirect
48. C2×#540C22semidirect
51. C2×#536C22semidirect
52. C2×#533C22semidirect
55. C22×#124C22semidirect
58. C2×#518C22semidirect
60. #3397C22semidirect
61. #3376C22semidirect
62. #3321C22semidirect
63. #3320C22semidirect
64. #3297C22semidirect
65. D4×SD16C22semidirect
66. #3265C22semidirect
67. #3264C22semidirect
68. #3257C22semidirect
69. #3246C22semidirect
70. #3221C22semidirect
71. #3213C22semidirect
72. C2×#496C22semidirect
73. C2×#496C22semidirect
74. C2×#492C22semidirect
75. C2×#491C22semidirect
76. C2×#489C22semidirect
77. C2×#488C22semidirect
78. #3118C22semidirect
79. #3110C22semidirect
80. C2×#484C22semidirect
81. C2×#485C22semidirect
82. C2×#482C22semidirect
83. C2×#479C22semidirect
84. C2×#475C22semidirect
85. C2×#478C22semidirect
86. C2×#476C22semidirect
87. C2×#474C22semidirect
88. C2×#474C22semidirect
89. C2×#469C22semidirect
90. C2×#468C22semidirect
91. C2×#466C22semidirect
92. C2×#465C22semidirect
93. C2×#465C22semidirect
94. C2×#465C22semidirect
95. #3042C22semidirect
96. C2×#460C22semidirect
97. C2×#460C22semidirect
101. C2×#463C22semidirect
102. C2×#463C22semidirect
103. C2×#463C22semidirect
104. C2×#463C22semidirect
105. C2×#463C22semidirect
106. C2×#463C22semidirect
107. C2×#461C22semidirect
108. C2×#461C22semidirect
109. C2×#461C22semidirect
110. C2×#461C22semidirect
111. C2×#461C22semidirect
112. C2×#459C22semidirect
113. C2×#449C22semidirect
114. C2×#449C22semidirect
115. C2×#448C22semidirect
116. C2×#448C22semidirect
117. C2×#448C22semidirect
119. C2×#450C22semidirect
121. C2×#447C22semidirect
122. #2992C22semidirect
123. C2×#446C22semidirect
125. C2×#440C22semidirect
126. C2×#440C22semidirect
127. C2×#440C22semidirect
128. C2×C4×SD16C22semidirect
129. C2×C4×D8C22semidirect
130. C2×#435C22semidirect
131. C2×#435C22semidirect
132. C2×C8×D4C22semidirect
133. C2×#433C22semidirect
134. C2×#432C22semidirect
135. C2×#424C22semidirect
136. C22×C4⋊C8C22semidirect
137. C2×#419C22semidirect
138. C2×#416C22semidirect
139. C22×#103C22semidirect
140. C22×#102C22semidirect
165. C22×SD16C23semidirect
179. #556C23semidirect
181. #555C23semidirect
183. #554C23semidirect
189. #550C23semidirect
191. D4×Q8C23semidirect
193. #548C23semidirect
197. #546C23semidirect
201. D42C23semidirect
205. #542C23semidirect
207. #540C23semidirect
211. #536C23semidirect
213. #533C23semidirect
244. C2×#124C23semidirect
289. #518C23semidirect
328. #496C23semidirect
329. #496C23semidirect
330. #492C23semidirect
331. #491C23semidirect
332. #489C23semidirect
333. #488C23semidirect
334. #485C23semidirect
335. #484C23semidirect
336. #482C23semidirect
337. #479C23semidirect
338. #478C23semidirect
339. #476C23semidirect
340. #475C23semidirect
341. #474C23semidirect
342. #474C23semidirect
343. #469C23semidirect
344. #468C23semidirect
345. #466C23semidirect
346. #465C23semidirect
347. #465C23semidirect
348. #465C23semidirect
352. #463C23semidirect
353. #463C23semidirect
354. #463C23semidirect
355. #463C23semidirect
356. #463C23semidirect
357. #461C23semidirect
358. #461C23semidirect
359. #461C23semidirect
360. #461C23semidirect
361. #461C23semidirect
362. #460C23semidirect
363. #460C23semidirect
364. #459C23semidirect
366. #450C23semidirect
367. #449C23semidirect
368. #449C23semidirect
369. #448C23semidirect
370. #448C23semidirect
371. #448C23semidirect
373. #447C23semidirect
374. #446C23semidirect
376. #440C23semidirect
377. #440C23semidirect
378. #440C23semidirect
379. C4×SD16C23semidirect
380. C4×D8C23semidirect
381. #435C23semidirect
382. #435C23semidirect
383. C8×D4C23semidirect
384. #433C23semidirect
385. #432C23semidirect
390. #424C23semidirect
397. C2×C4⋊C8C23semidirect
398. #419C23semidirect
399. #416C23semidirect
408. C2×#103C23semidirect
417. C2×#102C23semidirect
1192. C2#62016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35192
C2×#35612
#620162
C2×#33972
C2×#33762
C2×#33212
C2×#33202
C2×#32972
C2×D4×SD162
C2×#32652
C2×#32642
C2×#32572
C2×#32462
C2×#32212
C2×#32132
C2×#31182
C2×#31102
C2×#30422
C22×#4632
C2×#29922