Finite Group Databasebeta

← C2×#62546 #10579960

Subgroups — C2×#62546 #10579960

Order 512.

6684 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3508C211yesmaximal, characteristic, complemented
3#62546C2132yesmaximal, direct product factor
4C2×#3370C214yesmaximal, complemented
5C2×#3322C214yesmaximal, complemented
6C2×#3309C214yesmaximal, complemented
7C2×#3319C214yesmaximal, complemented
8C2×#3231C211yesmaximal, characteristic, complemented
9C2×#3228C211yesmaximal, characteristic, complemented
10C2×#3226C211yesmaximal, characteristic, complemented
11C2×#3207C211yesmaximal, characteristic, complemented
12C2×#3207C211yesmaximal, characteristic, complemented
13C2×#3205C211yesmaximal, characteristic, complemented
14C2×#3184C211yesmaximal, characteristic, complemented
15C2×#3182C211yesmaximal, characteristic, complemented
16C2×#3169C211yesmaximal, characteristic, complemented
17C2×#3141C211yesmaximal, characteristic, complemented
18C2×#3138C211yesmaximal, characteristic, complemented
19C2×#3131C211yesmaximal, characteristic, complemented
20C2×#2965C211yesmaximal, characteristic, complemented
21#3511—28no—
22#3511C22116yescomplemented
23#3508—28no—
24#3508C22116yescomplemented
25C2×#559—21no—
26C2×#559C2212yes—
27C2×#556—21no—
28C2×#555C2212yes—
29C2×#554C2212yescomplemented
30C2×#553C2212yes—
31C2×#553C2212yescomplemented
32C2×#550—21no—
33C2×#550C2212yes—
34C2×#548—21no—
35C2×#548—21no—
36C2×#547—21no—
37C2×#546—21no—
38C2×#546—21no—
39C2×#546C2212yes—
40C2×#546C2212yes—
41C2×#542—21no—
42C2×#542—21no—
43C2×#540—21no—
44C2×#540—21no—
45C2×#537—21no—
46C2×#535—21no—
47C2×#533C2211yescharacteristic
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic, complemented
50C2×#532C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#532C2211yescharacteristic
54C2×#532C2211yescharacteristic
55C2×#532C2211yescharacteristic, complemented
56C2×#532C2211yescharacteristic, complemented
57C22×C4⋊Q8C2211yescharacteristic, complemented
58C22×#127C2211yescharacteristic
59C2×#520—21no—
60C2×#518—21no—
61C2×C4×#41C2211yescharacteristic
62#3370C22164yescomplemented
63#3322C22164yescomplemented
64#3319C22164yescomplemented
65#3309C22164yescomplemented
66#3231C22116yescomplemented
67#3228C22116yescomplemented
68#3226C22116yescomplemented
69#3207C22116yescomplemented
70#3207C22116yescomplemented
71#3205C22116yescomplemented
72#3184C22116yescomplemented
73#3182C22116yescomplemented
74#3169C22116yescomplemented
75C2×#500C2211yescharacteristic, complemented
76C2×#500C2211yescharacteristic, complemented
77C2×#498C2211yescharacteristic, complemented
78C2×#493C2211yescharacteristic
79C2×#493C2211yescharacteristic
80C2×#492C2211yescharacteristic, complemented
81#3141C22116yescomplemented
82#3138C22116yescomplemented
83C2×#490C2214yes—
84C2×#489C2214yescomplemented
85#3131C22116yescomplemented
86C2×#488C2214yescomplemented
87C2×#487C2211yescharacteristic, complemented
88C2×#487C2211yescharacteristic, complemented
89C2×#487C2211yescharacteristic, complemented
90C2×#486C2211yescharacteristic
91C2×#486C2211yescharacteristic
92C2×#486C2211yescharacteristic
93C2×#486C2211yescharacteristic
94C2×#486C2211yescharacteristic
95C2×#486C2211yescharacteristic
96C2×#486C2211yescharacteristic, complemented
97C2×#485C2214yes—
98C2×#482C2214yescomplemented
99C2×#480C2214yescomplemented
100C2×#479C2214yescomplemented
101C2×#478C2214yescomplemented
102C2×#474C2214yescomplemented
103C2×#469C2214yescomplemented
104C2×#468C2214yes—
105C2×#466C2214yescomplemented
106C2×#463C2214yescomplemented
107C2×#463C2214yescomplemented
108C2×#459C2214yes—
109C2×#449C2214yescomplemented
110C2×#449C2214yescomplemented
111C2×#447C2214yes—
112#2965C22116yescomplemented
113C2×#446C2212yescomplemented
114C2×#442C2214yescomplemented
115C2×#440C2214yescomplemented
116C2×C4×D8C2214yescomplemented
117C2×#436C2212yes—
118C2×#435C2212yes—
119C2×#435C2212yescomplemented
120C2×#431C2211yescharacteristic
121C2×#431C2211yescharacteristic, complemented
122C2×#431C2211yescharacteristic, complemented
123C2×#417C2214yescomplemented
124C2×#418C2214yes—
125C2×#416C2214yescomplemented
126C2×C4×M16C2211yescharacteristic
127C2×C4×M16C2211yescharacteristic, complemented
128C22×C4×C8C2211yescharacteristic, complemented
129C22×#41—21no—
130C22×#41—21no—
131C22×#41—21no—
132C22×#41—21no—
133C22×#41—21no—
134C22×#41D411yescharacteristic
135C22×#41C2312yes—
136C22×#41C2312yes—
137C23×Q8—21no—
138C23×D4—21no—
139C23×D4—21no—
140C23×D4C2312yes—
141C22×SD16C2314yes—
142C22×D8C2314yes—
143C22×D8C2314yes—
144C22×M16C2312yes—
145C22×M16C2312yes—
146C23×C8C2312yes—
147#559—216no—
148#559—28no—
149#559C23116yes—
150#556—216no—
151#555—28no—
152#555C23116yes—
153#554—28no—
154#554C23116yescomplemented
155#553—28no—
156#553—28no—
157#553C23116yes—
158#553C23116yescomplemented
159#550—216no—
160#550—28no—
161#550C23116yes—
162#548—216no—
163#548—216no—
164#547—216no—
165#546—216no—
166#546—216no—
167#546—28no—
168#546—28no—
169#546C23116yes—
170#546C23116yes—
171#542—216no—
172#542—216no—
173#540—216no—
174#540—216no—
175#537—216no—
176#535—216no—
177#533—24no—
178#533—24no—
179#533—24no—
180#533C2318yes—
181#533C2318yes—
182#533C2318yescomplemented
183#532—24no—
184#532—24no—
185#532—24no—
186#532—24no—
187#532—24no—
188#532—24no—
189#532—24no—
190#532C2318yes—
191#532C2318yes—
192#532C2318yes—
193#532C2318yes—
194#532C2318yes—
195#532C2318yescomplemented
196#532C2318yescomplemented
197C2×C4⋊Q8—21no—
198C2×C4⋊Q8—21no—
199C2×C4⋊Q8—24no—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2318yescomplemented
207C2×#127—22no—
208C2×#127—21no—
209C2×#127—21no—
210C2×#127—24no—
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2312yes—
215C2×#127C2318yes—
216C2×#126—22no—
217C2×#126—22no—
218C2×#125—21no—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#124—22no—
222C2×#124—22no—
223C2×#124—22no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#123—22no—
232C2×#123—22no—
233C2×#123—22no—
234C2×#123—22no—
235C2×#123—22no—
236C2×#123—22no—
237C2×C22⋊Q8—22no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—22no—
244C2×C22⋊Q8—22no—
245C2×C22⋊Q8C2312yes—
246C2×#121—22no—
247C2×#121—22no—
248C2×#121—22no—
249C2×#121—21no—
250C2×#121—21no—
251C2×#121—21no—
252C2×#121—21no—
253C2×#121—21no—
254C2×#121—21no—
255C2×#121—21no—
256C2×#121—21no—
257C2×#121—21no—
258C2×#121—22no—
259C2×#121—22no—
260C2×#121—22no—
261C2×#121—22no—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#120—22no—
268C2×#120—22no—
269#520—216no—
270#518—216no—
271C4×#41D418yes—
272C4×#41C2318yes—
273C2×C4×Q8—21no—
274C2×C4×Q8—21no—
275C2×C4×Q8—21no—
276C2×C4×Q8—21no—
277C2×C4×Q8—21no—
278C2×C4×Q8D411yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×D4—22no—
282C2×C4×D4—22no—
283C2×C4×D4—22no—
284C2×C4×D4—22no—
285C2×C4×D4—21no—
286C2×C4×D4—21no—
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C2×C4×D4—21no—
290C2×C4×D4—21no—
291C2×C4×D4—21no—
292C2×C4×D4—21no—
293C2×C4×D4—21no—
294C2×C4×D4D411yescharacteristic
295C2×C4×D4D411yescharacteristic
296C2×C4×D4D411yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×#117—21no—
306C2×#117—22no—
307C2×#117D411yescharacteristic
308C2×#117D411yescharacteristic
309C2×#117D411yescharacteristic
310C2×#117C2312yes—
311C2×#117C2312yes—
312C22×C4⋊C4—21no—
313C22×C4⋊C4—22no—
314C22×C4⋊C4C2312yes—
315C22×C22⋊C4—22no—
316C22×C22⋊C4—22no—
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#500C2318yescomplemented
321#500C2318yescomplemented
322#498C2318yescomplemented
323#493C2318yes—
324#493C2318yes—
325#492C2318yescomplemented
326#490C23132yes—
327#489C23132yescomplemented
328#488C23132yescomplemented
329#487C2318yescomplemented
330#487C2318yescomplemented
331#487C2318yescomplemented
332#486C2318yes—
333#486C2318yes—
334#486C2318yes—
335#486C2318yes—
336#486C2318yes—
337#486C2318yes—
338#486C2318yescomplemented
339#485C23132yes—
340#482C23132yescomplemented
341#480C23132yescomplemented
342#479C23132yescomplemented
343#478C23132yescomplemented
344#474C23132yescomplemented
345#469C23132yescomplemented
346#468C23132yes—
347#466C23132yescomplemented
348#463C23132yescomplemented
349#463C23132yescomplemented
350#459C23132yes—
351#449C23132yescomplemented
352#449C23132yescomplemented
353#447C23132yes—
354#446C23116yescomplemented
355#442C23132yescomplemented
356#440C23132yescomplemented
357C4×D8C23132yescomplemented
358#436C23116yes—
359#435C23116yes—
360#435C23116yescomplemented
361#431C2318yes—
362#431C2318yescomplemented
363#431C2318yescomplemented
364C2×#107C2314yes—
365C2×#107C2314yes—
366C2×#106C2314yes—
367C2×C4⋊C8C2312yes—
368C2×C4⋊C8C2312yes—
369C2×C4⋊C8C2312yes—
370#418C23132yes—
371#417C23132yescomplemented
372#416C23132yescomplemented
373C2×#103C2314yes—
374C2×#103C2314yes—
375C2×#103C2314yes—
376C2×#102C2314yes—
377C2×#102C2314yes—
378C2×#102C2314yes—
379C2×#102C2314yes—
380C2×#102C2314yes—
381C2×#102C2314yes—
382C2×#102C2314yes—
383C2×C22⋊C8C2312yes—
384C2×C22⋊C8C2312yes—
385C2×C22⋊C8C2312yes—
386C4×M16C2318yes—
387C4×M16C2318yescomplemented
388C2×#97C2312yes—
389C2×#97C2312yes—
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2312yes—
393C2×C4×C8C2311yescharacteristic
394C2×C4×C8C2311yescharacteristic
395C2×C4×C8C2318yescomplemented
396C25—22no—
397C2×#41—28no—
398C2×#41—24no—
399C2×#41—24no—
400C2×#41—28no—
401C2×#41—28no—
402C2×#41—28no—
403C2×#41—28no—
404C2×#41—44no—
405C2×#41—48no—
406C2×#41—48no—
407C2×#41—48no—
408C2×#41—84no—
409C2×#41—84no—
410C2×#41—84no—
411C2×#41—84no—
412C2×#41C2×D418yes—
413C2×#41C2418yes—
414C2×#41C2418yes—
415C22×Q8—21no—
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8—21no—
419C22×Q8—22no—
420C22×Q8—28no—
421C22×Q8—84no—
422C22×Q8C2×D411yescharacteristic
423C22×Q8C2412yes—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—28no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—24no—
442C22×D4—28no—
443C22×D4—48no—
444C22×D4—48no—
445C22×D4—84no—
446C22×D4C2×D411yescharacteristic
447C22×D4C2×D411yescharacteristic
448C22×D4C2×D411yescharacteristic
449C22×D4C2412yes—
450C22×D4C2412yes—
451C22×D4C2412yes—
452C22×D4C2418yes—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4C2×D411yescharacteristic
462C23×C4C2×D411yescharacteristic
463C23×C4C2×D411yescharacteristic
464C23×C4C2×D411yescharacteristic
465C23×C4C2×D411yescharacteristic
466C23×C4C2×D411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C2×SD16—48no—
471C2×SD16C24116yes—
472C2×D8—48no—
473C2×D8—48no—
474C2×D8C24116yes—
475C2×D8C24116yes—
476C2×M16—44no—
477C2×M16—44no—
478C2×M16C2418yes—
479C2×M16C2418yes—
480C22×C8—44no—
481C22×C8C2412yes—
482C22×C8C2412yes—
483C22×C8C2412yes—
484C22×C8C2412yes—
485C22×C8C2418yes—
486C4⋊Q8—22no—
487C4⋊Q8—22no—
488C4⋊Q8—24no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—22no—
492C4⋊Q8—22no—
493C4⋊Q8—22no—
494C4⋊Q8C2414yes—
495C4⋊Q8C2414yes—
496C4⋊Q8C2414yes—
497C4⋊Q8C2418yes—
498C4⋊Q8C2414yes—
499C4⋊Q8C2414yes—
500#127—216no—
501#127—22no—
502#127—22no—
503#127—28no—
504#127—24no—
505#127—28no—
506#127—22no—
507#127C2414yes—
508#127C2414yes—
509#127C2418yes—
510#127C2414yes—
511#126—216no—
512#126—216no—
513#125—28no—
514#125—24no—
515#125—24no—
516#125C2418yes—
517#125C2418yes—
518#124—216no—
519#124—216no—
520#124—216no—
521#124—28no—
522#124—28no—
523#124—28no—
524#124—28no—
525#124—28no—
526#124—24no—
527#124—24no—
528#124C2418yes—
529#124C2418yes—
530#123—216no—
531#123—216no—
532#123—216no—
533#123—216no—
534#123—216no—
535#123—216no—
536C22⋊Q8—216no—
537C22⋊Q8—28no—
538C22⋊Q8—28no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—28no—
542C22⋊Q8—24no—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8C2418yes—
546#121—216no—
547#121—216no—
548#121—216no—
549#121—28no—
550#121—28no—
551#121—28no—
552#121—28no—
553#121—28no—
554#121—28no—
555#121—28no—
556#121—28no—
557#121—28no—
558#121—24no—
559#121—24no—
560#121—24no—
561#121—24no—
562#121—24no—
563#121—216no—
564#121—216no—
565#121—216no—
566#121—216no—
567#121C2418yes—
568#121C2418yes—
569#121C2418yes—
570#121C2418yes—
571#121C2418yes—
572#120—216no—
573#120—216no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—24no—
580C4×Q8C2×D418yes—
581C4×Q8C2×D414yes—
582C4×Q8C2418yes—
583C4×Q8C2414yes—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4C2×D418yes—
603C4×D4C2×D418yes—
604C4×D4C2×D418yes—
605C4×D4C2×D414yes—
606C4×D4C2×D414yes—
607C4×D4C2×D414yes—
608C4×D4C2418yes—
609C4×D4C2418yes—
610C4×D4C2418yes—
611C4×D4C2418yes—
612C4×D4C2418yes—
613C4×D4C2414yes—
614C4×D4C2414yes—
615C4×D4C2414yes—
616#117—28no—
617#117—24no—
618#117—24no—
619#117—216no—
620#117C2×D418yes—
621#117C2×D418yes—
622#117C2×D418yes—
623#117C2418yes—
624#117C2418yes—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—216no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—216no—
671C2×C22⋊C4—216no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C42—22no—
679C2×C42—22no—
680C2×C42—22no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D414yes—
688C2×C42C2×D414yes—
689C2×C42C2×D414yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697#107C24116yes—
698#107C24116yes—
699#106C24116yes—
700C4⋊C8C2418yes—
701C4⋊C8C2418yes—
702C4⋊C8C2418yes—
703#103C24116yes—
704#103C24116yes—
705#103C24116yes—
706#102C24116yes—
707#102C24116yes—
708#102C24116yes—
709#102C24116yes—
710#102C24116yes—
711#102C24116yes—
712#102C24116yes—
713C22⋊C8C2418yes—
714C22⋊C8C2418yes—
715C22⋊C8C2418yes—
716#97C2418yes—
717#97C2418yes—
718C4×C8C2414yes—
719C4×C8C2414yes—
720C4×C8C2418yes—
721C4×C8C2414yes—
722C4×C8C2414yes—
723C24—22no—
724C24—22no—
725C24—22no—
726C24—28no—
727C24—48no—
728C24—84no—
729C24—84no—
730C24C22×D411yescharacteristic
731C24C22×D411yescharacteristic
732C24C22×D411yescharacteristic
733#41—416no—
734#41—432no—
735#41—416no—
736#41—416no—
737#41—88no—
738#41—88no—
739#41—816no—
740#41—816no—
741#41—816no—
742#41—816no—
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—28no—
750C2×Q8—42no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—84no—
756C2×Q8—816no—
757C2×Q8C22×D414yes—
758C2×Q8C2514yes—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—22no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—28no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—416no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—48no—
786C2×D4—432no—
787C2×D4—48no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—88no—
795C2×D4—816no—
796C2×D4—84no—
797C2×D4—84no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—84no—
802C2×D4—84no—
803C2×D4—84no—
804C2×D4C22×D414yes—
805C2×D4C22×D414yes—
806C2×D4C22×D414yes—
807C2×D4C2514yes—
808C2×D4C2514yes—
809C2×D4C2514yes—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—48no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4C22×D412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D414yes—
844C22×C4C22×D414yes—
845C22×C4C22×D414yes—
846C22×C4C22×D414yes—
847C22×C4C22×D414yes—
848C22×C4C22×D414yes—
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864SD16—416no—
865D8—416no—
866D8—416no—
867M16—48no—
868M16—48no—
869C2×C8—24no—
870C2×C8—24no—
871C2×C8—24no—
872C2×C8—24no—
873C2×C8—48no—
874C2×C8C2514yes—
875C2×C8C2514yes—
876C2×C8C2514yes—
877C2×C8C2514yes—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4C22×D414yes—
897C4⋊C4C22×D414yes—
898C4⋊C4C22×D414yes—
899C4⋊C4C22×D414yes—
900C4⋊C4C22×D414yes—
901C4⋊C4C22×D414yes—
902C4⋊C4C2514yes—
903C4⋊C4C2514yes—
904C4⋊C4C2514yes—
905C4⋊C4C2514yes—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4C22×D414yes—
924C22⋊C4C22×D414yes—
925C22⋊C4C22×D414yes—
926C22⋊C4C22×D414yes—
927C22⋊C4C22×D414yes—
928C22⋊C4C22×D414yes—
929C42—28no—
930C42—28no—
931C42—28no—
932C42C22×D412yes—
933C42C22×D414yes—
934C42C22×D414yes—
935C42C22×D414yes—
936C42C22×D412yes—
937C42C22×D414yes—
938C42C22×D412yes—
939C42C22×D414yes—
940C42C22×D412yes—
941C42C22×D414yes—
942C42C2512yes—
943C42C2512yes—
944C42C2512yes—
945C42C2512yes—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—416no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23—88no—
969C23—88no—
970C23—1616no—
971C23C23×D412yes—
972C23C23×D412yes—
973C23C23×D412yes—
974C23C23×D411yescharacteristic
975Q8—28no—
976Q8—44no—
977Q8—44no—
978Q8—48no—
979Q8—48no—
980Q8—48no—
981Q8—48no—
982Q8—88no—
983D4—28no—
984D4—28no—
985D4—28no—
986D4—44no—
987D4—44no—
988D4—44no—
989D4—416no—
990D4—416no—
991D4—44no—
992D4—44no—
993D4—44no—
994D4—48no—
995D4—48no—
996D4—48no—
997D4—48no—
998D4—48no—
999D4—48no—
1000D4—88no—
1001D4—88no—
1002D4—88no—
1003D4—88no—
1004D4—88no—
1005D4—88no—
1006D4—88no—
1007D4—88no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—416no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—88no—
1041C2×C4—88no—
1042C2×C4—88no—
1043C2×C4—88no—
1044C2×C4—88no—
1045C2×C4—88no—
1046C2×C4—88no—
1047C2×C4#57514yes—
1048C2×C4#57614yes—
1049C2×C4C23×D412yes—
1050C2×C4C23×D412yes—
1051C2×C4C23×D412yes—
1052C2×C4C23×D412yes—
1053C2×C4C23×D412yes—
1054C2×C4C23×D412yes—
1055C2×C4C23×D412yes—
1056C2×C4C23×D412yes—
1057C2×C4C23×D412yes—
1058C2×C4C23×D411yescharacteristic
1059C2×C4C23×D412yes—
1060C2×C4C23×D412yes—
1061C2×C4#58514yes—
1062C2×C4C2611yescharacteristic
1063C8—24no—
1064C8—24no—
1065C8—24no—
1066C8—24no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—88no—
1089C22—88no—
1090C22—88no—
1091C22—1616no—
1092C22#350012yes—
1093C22C2×#57512yes—
1094C22C2×#57612yes—
1095C22C24×D411yescharacteristic
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4#350012yes—
1111C4C2×#57514yes—
1112C4C2×#57614yes—
1113C4C2×#58512yes—
1114C2—42no—
1115C2—42no—
1116C2—42no—
1117C2—84no—
1118C2—84no—
1119C2—84no—
1120C2#6254614yesdirect product factor
1121C2C2×#350011yescharacteristic
1122C2C22×#57511yescharacteristic
1123C2C22×#57611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3511C2semidirect
2. C2×#3508C2semidirect
3. #62546C2direct (N × H)
4. C2×#3370C2semidirect
5. C2×#3322C2semidirect
6. C2×#3309C2semidirect
7. C2×#3319C2semidirect
8. C2×#3231C2semidirect
9. C2×#3228C2semidirect
10. C2×#3226C2semidirect
11. C2×#3207C2semidirect
12. C2×#3207C2semidirect
13. C2×#3205C2semidirect
14. C2×#3184C2semidirect
15. C2×#3182C2semidirect
16. C2×#3169C2semidirect
17. C2×#3141C2semidirect
18. C2×#3138C2semidirect
19. C2×#3131C2semidirect
20. C2×#2965C2semidirect
22. #3511C22semidirect
24. #3508C22semidirect
29. C2×#554C22semidirect
31. C2×#553C22semidirect
49. C2×#533C22semidirect
55. C2×#532C22semidirect
56. C2×#532C22semidirect
57. C22×C4⋊Q8C22semidirect
62. #3370C22semidirect
63. #3322C22semidirect
64. #3319C22semidirect
65. #3309C22semidirect
66. #3231C22semidirect
67. #3228C22semidirect
68. #3226C22semidirect
69. #3207C22semidirect
70. #3207C22semidirect
71. #3205C22semidirect
72. #3184C22semidirect
73. #3182C22semidirect
74. #3169C22semidirect
75. C2×#500C22semidirect
76. C2×#500C22semidirect
77. C2×#498C22semidirect
80. C2×#492C22semidirect
81. #3141C22semidirect
82. #3138C22semidirect
84. C2×#489C22semidirect
85. #3131C22semidirect
86. C2×#488C22semidirect
87. C2×#487C22semidirect
88. C2×#487C22semidirect
89. C2×#487C22semidirect
96. C2×#486C22semidirect
98. C2×#482C22semidirect
99. C2×#480C22semidirect
100. C2×#479C22semidirect
101. C2×#478C22semidirect
102. C2×#474C22semidirect
103. C2×#469C22semidirect
105. C2×#466C22semidirect
106. C2×#463C22semidirect
107. C2×#463C22semidirect
109. C2×#449C22semidirect
110. C2×#449C22semidirect
112. #2965C22semidirect
113. C2×#446C22semidirect
114. C2×#442C22semidirect
115. C2×#440C22semidirect
116. C2×C4×D8C22semidirect
119. C2×#435C22semidirect
121. C2×#431C22semidirect
122. C2×#431C22semidirect
123. C2×#417C22semidirect
125. C2×#416C22semidirect
127. C2×C4×M16C22semidirect
128. C22×C4×C8C22semidirect
154. #554C23semidirect
158. #553C23semidirect
182. #533C23semidirect
195. #532C23semidirect
196. #532C23semidirect
206. C2×C4⋊Q8C23semidirect
320. #500C23semidirect
321. #500C23semidirect
322. #498C23semidirect
325. #492C23semidirect
327. #489C23semidirect
328. #488C23semidirect
329. #487C23semidirect
330. #487C23semidirect
331. #487C23semidirect
338. #486C23semidirect
340. #482C23semidirect
341. #480C23semidirect
342. #479C23semidirect
343. #478C23semidirect
344. #474C23semidirect
345. #469C23semidirect
347. #466C23semidirect
348. #463C23semidirect
349. #463C23semidirect
351. #449C23semidirect
352. #449C23semidirect
354. #446C23semidirect
355. #442C23semidirect
356. #440C23semidirect
357. C4×D8C23semidirect
360. #435C23semidirect
362. #431C23semidirect
363. #431C23semidirect
371. #417C23semidirect
372. #416C23semidirect
387. C4×M16C23semidirect
395. C2×C4×C8C23semidirect
1120. C2#62546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#35082
#625462
C2×#33702
C2×#33222
C2×#33092
C2×#33192
C2×#32312
C2×#32282
C2×#32262
C2×#32072
C2×#32052
C2×#31842
C2×#31822
C2×#31692
C2×#31412
C2×#31382
C2×#31312
C2×#29652