Finite Group Databasebeta

← #10576120

Subgroups — #10576120

Order 512.

10430 conjugacy classes of subgroups.

The subgroup lattice has 1633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3585C211yesmaximal, characteristic, complemented
2C22×#577C211yesmaximal, characteristic, complemented
3#62859C211yesmaximal, characteristic, complemented
4#62842C211yesmaximal, characteristic, complemented
5#61094C218yesmaximal, complemented
6#61092C218yesmaximal, complemented
7#61073C218yesmaximal, complemented
8#61071C218yesmaximal, complemented
9#61060C214yesmaximal, complemented
10#61058C214yesmaximal, complemented
11#61051C214yesmaximal, complemented
12#61050C214yesmaximal, complemented
13#60645C211yesmaximal, characteristic, complemented
14#60455C211yesmaximal, characteristic, complemented
15#60453C211yesmaximal, characteristic, complemented
16#60422C211yesmaximal, characteristic, complemented
17C2×#3042C211yesmaximal, characteristic, complemented
18#60368C211yesmaximal, characteristic, complemented
19#60367C211yesmaximal, characteristic, complemented
20#60366C211yesmaximal, characteristic, complemented
21C2×#3009C211yesmaximal, characteristic, complemented
22#60168C211yesmaximal, characteristic, complemented
23#60142C211yesmaximal, characteristic, complemented
24C2×#585C2211yescharacteristic, complemented
25C22×2−1+4C2211yescharacteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C22×H(5,𝔽2)C2211yescharacteristic, complemented
28#3585—216no—
29C2×#577—216no—
30C2×#577C2218yescomplemented
31C2×#577C2214yescomplemented
32C2×#577C2218yescomplemented
33C2×#577C2214yescomplemented
34C2×#576C2214yescomplemented
35C2×#576C2214yescomplemented
36C2×#575C2211yescharacteristic, complemented
37C2×#575C2211yescharacteristic, complemented
38C2×#575C2211yescharacteristic, complemented
39C2×#575C2214yescomplemented
40C22×#137C2211yescharacteristic, complemented
41C22×#137C2211yescharacteristic, complemented
42C22×#137C2212yescomplemented
43C22×AGL(1,ℤ/8)C2211yescharacteristic
44C22×AGL(1,ℤ/8)C2211yescharacteristic
45C22×AGL(1,ℤ/8)C2212yescomplemented
46C22×AGL(1,ℤ/8)C2214yescomplemented
47C22×#135C2211yescharacteristic, complemented
48C22×#135C2212yescomplemented
49C23×SD16C2211yescharacteristic, complemented
50C23×SD16C2212yescomplemented
51C2×#568C2211yescharacteristic, complemented
52C22×#131C2211yescharacteristic, complemented
53#3500—22no—
54#3500C2214yescomplemented
55#3499—22no—
56#3499C2214yescomplemented
57#3496—24no—
58#3496C2218yescomplemented
59#3489—24no—
60#3489C2218yescomplemented
61#3486C2214yescomplemented
62#3485—22no—
63#3485—22no—
64#3485—24no—
65#3485C2214yescomplemented
66#3485C2214yescomplemented
67#3485C2214yescomplemented
68#3484—22no—
69#3484—22no—
70#3484C2214yescomplemented
71#3484C2214yescomplemented
72#3449—22no—
73#3449C2211yescharacteristic
74#3449C2211yescharacteristic
75#3449C2211yescharacteristic, complemented
76#3449C2211yescharacteristic, complemented
77#3449C2211yescharacteristic, complemented
78C2×#536—22no—
79C2×#536C2211yescharacteristic, complemented
80C2×#536C2211yescharacteristic, complemented
81C2×#534—24no—
82#3428C2211yescharacteristic, complemented
83C2×#518C2211yescharacteristic, complemented
84#3283C22116yescomplemented
85#3282C22116yescomplemented
86D4×SD16C22116yescomplemented
87#3280C22116yescomplemented
88#3276C22116yescomplemented
89#3275C22116yescomplemented
90#3273C22116yescomplemented
91#3272C22116yescomplemented
92#3269C22116yescomplemented
93#3267C22116yescomplemented
94#3267C22116yescomplemented
95#3267C22116yescomplemented
96#3266C22116yescomplemented
97#3266C22116yescomplemented
98#3265C22116yescomplemented
99#3264C22116yescomplemented
100#3156C2214yescomplemented
101#3156C2214yescomplemented
102#3154C2214yescomplemented
103#3154C2214yescomplemented
104#3153C2214yescomplemented
105#3152C2214yescomplemented
106#3063C2214yescomplemented
107#3063C2214yescomplemented
108#3063C2218yescomplemented
109#3062C2214yescomplemented
110#3062C2214yescomplemented
111#3059C2214yescomplemented
112#3057C2214yescomplemented
113#3056C2218yescomplemented
114#3054C2214yescomplemented
115#3050C2214yescomplemented
116#3046C2214yescomplemented
117#3045C2214yescomplemented
118#3044C2212yescomplemented
119#3043C2212yescomplemented
120#3042C2214yescomplemented
121#3042C2214yescomplemented
122#3042C2218yescomplemented
123#3042C2212yescomplemented
124#3041C2212yescomplemented
125#3035C2218yescomplemented
126C2×#463C2214yescomplemented
127C2×#461C2214yescomplemented
128#3013C2218yescomplemented
129#3013C2214yescomplemented
130#3012C2218yescomplemented
131#3012C2214yescomplemented
132#3011C2212yescomplemented
133#3011C2214yescomplemented
134#3010C2212yescomplemented
135#3010C2214yescomplemented
136#3009C2214yescomplemented
137#3009C2214yescomplemented
138#3009C2212yescomplemented
139#3009C2218yescomplemented
140#3009C2214yescomplemented
141#3008C2212yescomplemented
142#3008C2214yescomplemented
143#3005C2214yescomplemented
144#3005C2214yescomplemented
145#3004C2214yescomplemented
146#3003C2214yescomplemented
147#3002C2218yescomplemented
148C2×#452C2214yescomplemented
149C2×#450C2214yescomplemented
150#2949C2214yescomplemented
151#2948C2214yescomplemented
152#2946C2218yescomplemented
153C4×AGL(1,ℤ/8)C2218yescomplemented
154#2935C2218yescomplemented
155#2933C2218yescomplemented
156#2930C2214yescomplemented
157#2929C2214yescomplemented
158#2911C2211yescharacteristic, complemented
159C2×#424C2211yescharacteristic, complemented
160#2896C2211yescharacteristic, complemented
161#2896C2211yescharacteristic, complemented
162C2×#419C2211yescharacteristic, complemented
163C2×#418C2211yescharacteristic, complemented
164C2×#416C2211yescharacteristic, complemented
165C2×#416C2211yescharacteristic, complemented
166#2879C2211yescharacteristic, complemented
167C2×#408C2211yescharacteristic, complemented
168#2873C2211yescharacteristic, complemented
169#585—28no—
170#585—44no—
171C2×2−1+4—22no—
172C2×2−1+4—22no—
173C2×2−1+4—21no—
174C2×2−1+4—28no—
175C2×2−1+4—44no—
176C2×2−1+4C2314yes—
177C2×2−1+4C2312yes—
178C2×2−1+4C2314yescomplemented
179C2×2−1+4C2312yescomplemented
180C2×H(5,𝔽2)—22no—
181C2×H(5,𝔽2)—22no—
182C2×H(5,𝔽2)—22no—
183C2×H(5,𝔽2)—22no—
184C2×H(5,𝔽2)—22no—
185C2×H(5,𝔽2)—21no—
186C2×H(5,𝔽2)—28no—
187C2×H(5,𝔽2)—28no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C2×H(5,𝔽2)C2314yes—
191C2×H(5,𝔽2)C2314yes—
192C2×H(5,𝔽2)C2314yes—
193C2×H(5,𝔽2)C2314yes—
194C2×H(5,𝔽2)C2312yes—
195C2×H(5,𝔽2)C2312yescomplemented
196C22×#41—22no—
197C22×#41—22no—
198C22×#41—21no—
199C22×#41—21no—
200C22×#41—21no—
201C22×#41—22no—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2312yes—
206C22×#41C2312yes—
207C22×#41C2311yescharacteristic
208C22×#41C2311yescharacteristic
209C22×#41C2311yescharacteristic
210C22×#41C2312yescomplemented
211C22×#41C2314yescomplemented
212C23×Q8—21no—
213C23×Q8C2311yescharacteristic
214C23×Q8C2312yescomplemented
215C23×D4—22no—
216C23×D4—21no—
217C23×D4—22no—
218C23×D4—21no—
219C23×D4C2312yes—
220C23×D4C2312yes—
221C23×D4C2311yescharacteristic
222#577—232no—
223#577—264no—
224#577—264no—
225#577—232no—
226#576—232no—
227#576—232no—
228#575—28no—
229#575—232no—
230#575—28no—
231#575—44no—
232C2×#137—216no—
233C2×#137—28no—
234C2×#137—44no—
235C2×#137C2314yes—
236C2×#137C2312yes—
237C2×#137C2314yes—
238C2×#137C2312yescomplemented
239C2×#137C2314yescomplemented
240C2×#137C2312yescomplemented
241C2×#137C2318yescomplemented
242C2×#137C23116yescomplemented
243C2×#137C2312yescomplemented
244C2×#137C2312yescomplemented
245C2×#137C2314yescomplemented
246C2×#137C2312yescomplemented
247C2×AGL(1,ℤ/8)—28no—
248C2×AGL(1,ℤ/8)—232no—
249C2×AGL(1,ℤ/8)—216no—
250C2×AGL(1,ℤ/8)D4116yescomplemented
251C2×AGL(1,ℤ/8)C2314yes—
252C2×AGL(1,ℤ/8)C2312yes—
253C2×AGL(1,ℤ/8)C2314yes—
254C2×AGL(1,ℤ/8)C2314yes—
255C2×AGL(1,ℤ/8)C2314yes—
256C2×AGL(1,ℤ/8)C2312yescomplemented
257C2×AGL(1,ℤ/8)C2312yescomplemented
258C2×AGL(1,ℤ/8)C23116yescomplemented
259C2×AGL(1,ℤ/8)C2318yescomplemented
260C2×AGL(1,ℤ/8)C2312yescomplemented
261C2×AGL(1,ℤ/8)C2318yescomplemented
262C2×AGL(1,ℤ/8)C2318yescomplemented
263C2×AGL(1,ℤ/8)C2312yescomplemented
264C2×AGL(1,ℤ/8)C2312yescomplemented
265C2×#135—28no—
266C2×#135—216no—
267C2×#135C2314yes—
268C2×#135C2314yes—
269C2×#135C2314yes—
270C2×#135C23116yescomplemented
271C2×#135C2318yescomplemented
272C2×#135C2314yescomplemented
273C2×#135C2314yescomplemented
274C2×#135C2318yescomplemented
275C22×Q16C2312yescomplemented
276C22×Q16C2311yescharacteristic, complemented
277C22×Q16C2312yescomplemented
278C22×SD16—28no—
279C22×SD16—216no—
280C22×SD16C2314yes—
281C22×SD16C2312yes—
282C22×SD16C2314yes—
283C22×SD16C2312yes—
284C22×SD16C2312yes—
285C22×SD16C2312yes—
286C22×SD16C2312yescomplemented
287C22×SD16C2311yescharacteristic, complemented
288C22×SD16C23116yescomplemented
289C22×SD16C2311yescharacteristic, complemented
290C22×SD16C2318yescomplemented
291C22×SD16C2312yescomplemented
292C22×D8C2312yes—
293C22×D8C2312yes—
294C22×D8C2311yescharacteristic, complemented
295C22×D8C2318yescomplemented
296#568—28no—
297C2×#131—28no—
298C2×#131C2314yes—
299C2×#131C2314yes—
300C2×#131C2314yescomplemented
301C2×#131C2314yescomplemented
302C22×M16C2311yescharacteristic
303C22×M16C2311yescharacteristic
304C22×M16C2311yescharacteristic
305C22×M16C2312yescomplemented
306C22×M16C2314yescomplemented
307C23×C8C2311yescharacteristic
308C23×C8C2312yescomplemented
309D4×Q8—28no—
310D4×Q8C23116yescomplemented
311#548—28no—
312#548C23116yescomplemented
313#547—28no—
314#547—216no—
315#547—28no—
316#547—28no—
317#547—28no—
318#547—216no—
319#547C23116yes—
320#547C23116yescomplemented
321#546—28no—
322#546—28no—
323#546—28no—
324#546—28no—
325#546—28no—
326#546—28no—
327#546—216no—
328#546—28no—
329#546—216no—
330#546C23116yes—
331#546C23116yes—
332#546C23116yescomplemented
333D42—28no—
334D42—28no—
335D42—28no—
336D42C23116yes—
337#537—28no—
338#537—22no—
339#537D414yes—
340#537C2314yes—
341#537C2314yes—
342#537C2314yes—
343#536—22no—
344#536—22no—
345#536—21no—
346#536—21no—
347#536—21no—
348#536—24no—
349#536—24no—
350#536—24no—
351#536—28no—
352#536—28no—
353#536—22no—
354#536—22no—
355#536D412yes—
356#536D412yes—
357#536C2312yes—
358#536C2312yes—
359#536C2314yes—
360#536C2312yes—
361#536C2312yes—
362#536C2314yescomplemented
363#536C2314yescomplemented
364#536C2314yescomplemented
365#536C2312yescomplemented
366#535—21no—
367#535—21no—
368#535—21no—
369#535—24no—
370#535D412yes—
371#535D412yes—
372#535C2312yes—
373#535C2312yes—
374#535C2312yes—
375#535C2312yes—
376#535C2312yescomplemented
377#534—22no—
378#534—22no—
379#534—22no—
380#534—28no—
381#534—28no—
382#534—216no—
383#534—28no—
384#534—28no—
385#534—28no—
386#534—22no—
387#534D414yes—
388#532—22no—
389#532—22no—
390#532—22no—
391#532—24no—
392#532—24no—
393#532C2314yes—
394#532C2314yes—
395C2×C4⋊Q8—21no—
396C2×C4⋊Q8—24no—
397C2×C4⋊Q8C2312yescomplemented
398C2×#124—21no—
399C2×#124—24no—
400C2×#124C2312yescomplemented
401#525—22no—
402#525—22no—
403#525—22no—
404#525—28no—
405#525—28no—
406#525—22no—
407#525—22no—
408#525C2314yes—
409#525C2314yes—
410#525C2314yes—
411#525C2314yes—
412#525C2314yescomplemented
413C2×#123—22no—
414C2×#123—28no—
415C2×#123—28no—
416C2×#123—28no—
417C2×#123—22no—
418C2×C22⋊Q8—28no—
419C2×C22⋊Q8—22no—
420C2×C22⋊Q8C2314yescomplemented
421C2×#121—216no—
422C2×#120—28no—
423C2×#120—28no—
424#520—22no—
425#520C2314yescomplemented
426#519C2312yescomplemented
427#518—22no—
428#518—22no—
429#518—22no—
430#518C2314yes—
431#518C2314yes—
432#518C2312yescomplemented
433C4×#41—22no—
434C4×#41C2314yescomplemented
435C2×C4×D4—22no—
436C2×C4×D4C2314yes—
437C2×#117—22no—
438C2×#117C2311yescharacteristic
439C2×#117C2311yescharacteristic
440C2×#117C2311yescharacteristic
441C22×C22⋊C4—22no—
442#497C2318yescomplemented
443#497C2318yescomplemented
444#497C2318yescomplemented
445#496C2318yescomplemented
446#495C2318yescomplemented
447#495C2318yescomplemented
448#494C2318yescomplemented
449#492C2318yescomplemented
450#470C23116yescomplemented
451#470C2318yescomplemented
452#469C2318yescomplemented
453#468C23116yescomplemented
454#468C2318yescomplemented
455#468C2318yescomplemented
456#467C2318yescomplemented
457#467C23116yescomplemented
458#466C2318yescomplemented
459#465C23116yescomplemented
460#465C2318yescomplemented
461#465C2318yescomplemented
462#464C2318yescomplemented
463#464C2318yescomplemented
464#463C23116yescomplemented
465#463C23116yescomplemented
466#463C2318yescomplemented
467#463C2318yescomplemented
468#462C2318yescomplemented
469#461C23116yescomplemented
470#461C23116yescomplemented
471#461C2318yescomplemented
472#460C2318yescomplemented
473#459C2318yescomplemented
474#452C23116yescomplemented
475#452C23116yescomplemented
476#452C2318yescomplemented
477#452C2318yescomplemented
478#452C23116yescomplemented
479#452C23116yescomplemented
480#451C2318yescomplemented
481#451C23116yescomplemented
482#450C23116yescomplemented
483#450C23116yescomplemented
484#450C2318yescomplemented
485#450C23116yescomplemented
486#449C2318yescomplemented
487#449C2318yescomplemented
488#449C23116yescomplemented
489#449C23116yescomplemented
490#448C2318yescomplemented
491#448C23116yescomplemented
492#447C2318yescomplemented
493#447C23116yescomplemented
494#442C23116yescomplemented
495#440C23116yescomplemented
496C4×SD16C23116yescomplemented
497C4×D8C23116yescomplemented
498#436C23116yescomplemented
499#435C23116yescomplemented
500#435C23116yescomplemented
501C8×D4C23116yescomplemented
502#428C2314yescomplemented
503#428C2314yescomplemented
504#427C2314yescomplemented
505#424C2312yescomplemented
506#424C2312yescomplemented
507#424C2314yescomplemented
508C2×C4⋊C8C2314yescomplemented
509#419C2314yescomplemented
510#419C2314yescomplemented
511#419C2312yescomplemented
512#419C2312yescomplemented
513#418C2314yes—
514#418C2314yes—
515#418C2312yescomplemented
516#418C2312yescomplemented
517#417C2314yes—
518#417C2314yescomplemented
519#416C2312yes—
520#416C2312yes—
521#416C2314yescomplemented
522#416C2312yescomplemented
523#416C2314yescomplemented
524#416C2312yescomplemented
525#416C2314yescomplemented
526#416C2314yescomplemented
527C2×#103C2312yescomplemented
528C2×#103C2312yescomplemented
529C2×#103C2314yescomplemented
530C2×#102C2314yes—
531C2×#102C2312yescomplemented
532C2×#102C2312yescomplemented
533#408C2312yes—
534#408C2312yes—
535#408C2314yes—
536#408C2314yescomplemented
537#408C2314yescomplemented
538#407C2314yescomplemented
539C2×C22⋊C8C2314yescomplemented
540#405C2314yescomplemented
541#405C2314yescomplemented
542C4×M16C2314yescomplemented
543C25—21no—
544C25—22no—
545C25—22no—
5462−1+4—216no—
5472−1+4—216no—
5482−1+4—28no—
5492−1+4—28no—
5502−1+4—48no—
5512−1+4—48no—
5522−1+4—44no—
5532−1+4—44no—
5542−1+4—48no—
5552−1+4—416no—
5562−1+4—416no—
557H(5,𝔽2)—28no—
558H(5,𝔽2)—28no—
559H(5,𝔽2)—216no—
560H(5,𝔽2)—216no—
561H(5,𝔽2)—216no—
562H(5,𝔽2)—216no—
563H(5,𝔽2)—416no—
564H(5,𝔽2)—48no—
565H(5,𝔽2)—48no—
566H(5,𝔽2)—48no—
567H(5,𝔽2)—48no—
568H(5,𝔽2)—44no—
569H(5,𝔽2)—44no—
570H(5,𝔽2)—416no—
571H(5,𝔽2)—416no—
572H(5,𝔽2)—416no—
573H(5,𝔽2)—416no—
574H(5,𝔽2)—48no—
575C2×#41—22no—
576C2×#41—24no—
577C2×#41—24no—
578C2×#41—24no—
579C2×#41—24no—
580C2×#41—22no—
581C2×#41—24no—
582C2×#41—24no—
583C2×#41—24no—
584C2×#41—22no—
585C2×#41—28no—
586C2×#41—28no—
587C2×#41—24no—
588C2×#41—22no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—24no—
592C2×#41—24no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—24no—
600C2×#41—24no—
601C2×#41—24no—
602C2×#41—24no—
603C2×#41—24no—
604C2×#41—24no—
605C2×#41—24no—
606C2×#41—24no—
607C2×#41—216no—
608C2×#41—28no—
609C2×#41—28no—
610C2×#41—28no—
611C2×#41—24no—
612C2×#41—24no—
613C2×#41—24no—
614C2×#41—24no—
615C2×#41—24no—
616C2×#41—24no—
617C2×#41—44no—
618C2×#41—44no—
619C2×#41—44no—
620C2×#41—48no—
621C2×#41—48no—
622C2×#41—416no—
623C2×#41—416no—
624C2×#41—48no—
625C2×#41—48no—
626C2×#41—416no—
627C2×#41C2×D412yes—
628C2×#41C2×D412yes—
629C2×#41C2×D412yes—
630C2×#41C2×D412yes—
631C2×#41C2×D418yescomplemented
632C2×#41C2412yes—
633C2×#41C2412yes—
634C2×#41C2412yes—
635C2×#41C2412yes—
636C2×#41C2412yes—
637C2×#41C2412yes—
638C2×#41C2418yes—
639C2×#41C2418yes—
640C2×#41C2418yes—
641C2×#41C2414yes—
642C2×#41C2414yes—
643C2×#41C2412yes—
644C2×#41C2412yes—
645C2×#41C2412yes—
646C2×#41C2412yes—
647C2×#41C2412yes—
648C2×#41C2412yes—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—22no—
652C22×Q8—22no—
653C22×Q8—21no—
654C22×Q8—21no—
655C22×Q8—21no—
656C22×Q8—22no—
657C22×Q8—24no—
658C22×Q8—28no—
659C22×Q8—24no—
660C22×Q8—24no—
661C22×Q8—44no—
662C22×Q8—48no—
663C22×Q8C2×D411yescharacteristic
664C22×Q8C2×D411yescharacteristic
665C22×Q8C2412yes—
666C22×Q8C2412yes—
667C22×Q8C2411yescharacteristic
668C22×Q8C2411yescharacteristic
669C22×Q8C2411yescharacteristic
670C22×Q8C2412yes—
671C22×Q8C2418yes—
672C22×Q8C2414yes—
673C22×Q8C2411yescharacteristic
674C22×D4—21no—
675C22×D4—28no—
676C22×D4—28no—
677C22×D4—21no—
678C22×D4—21no—
679C22×D4—21no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4—24no—
684C22×D4—28no—
685C22×D4—28no—
686C22×D4—28no—
687C22×D4—28no—
688C22×D4—24no—
689C22×D4—22no—
690C22×D4—24no—
691C22×D4—24no—
692C22×D4—24no—
693C22×D4—24no—
694C22×D4—22no—
695C22×D4—24no—
696C22×D4—216no—
697C22×D4—21no—
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—22no—
701C22×D4—22no—
702C22×D4—24no—
703C22×D4—24no—
704C22×D4—24no—
705C22×D4—44no—
706C22×D4—44no—
707C22×D4—48no—
708C22×D4—48no—
709C22×D4—416no—
710C22×D4—416no—
711C22×D4C2×D412yes—
712C22×D4C2×D411yescharacteristic
713C22×D4C2×D412yes—
714C22×D4C2×D411yescharacteristic
715C22×D4C2×D418yes—
716C22×D4C2411yescharacteristic
717C22×D4C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2418yes—
720C22×D4C2418yes—
721C22×D4C2414yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2412yes—
725C22×D4C2411yescharacteristic
726C23×C4—21no—
727C23×C4—21no—
728C23×C4—22no—
729C23×C4—21no—
730C23×C4—24no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—22no—
734C23×C4—21no—
735C23×C4—21no—
736C23×C4—24no—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740#137—28no—
741#137—28no—
742#137—264no—
743#137—232no—
744#137—216no—
745#137—216no—
746#137—28no—
747#137—28no—
748#137—48no—
749#137—48no—
750#137—44no—
751#137—44no—
752AGL(1,ℤ/8)—28no—
753AGL(1,ℤ/8)—216no—
754AGL(1,ℤ/8)—216no—
755AGL(1,ℤ/8)—28no—
756AGL(1,ℤ/8)—232no—
757AGL(1,ℤ/8)—232no—
758AGL(1,ℤ/8)—264no—
759AGL(1,ℤ/8)—232no—
760AGL(1,ℤ/8)—28no—
761AGL(1,ℤ/8)—28no—
762AGL(1,ℤ/8)—44no—
763AGL(1,ℤ/8)—44no—
764AGL(1,ℤ/8)C2×D4132yescomplemented
765AGL(1,ℤ/8)C2×D4132yescomplemented
766#135—216no—
767#135—216no—
768#135—216no—
769#135—232no—
770#135—264no—
771#135—232no—
772#135—216no—
773#135—48no—
774C2×Q16—24no—
775C2×Q16—28no—
776C2×Q16—44no—
777C2×Q16C2414yes—
778C2×Q16C2418yes—
779C2×Q16C2414yes—
780C2×Q16C2414yes—
781C2×Q16C2418yes—
782C2×Q16C2414yes—
783C2×SD16—24no—
784C2×SD16—28no—
785C2×SD16—28no—
786C2×SD16—216no—
787C2×SD16—216no—
788C2×SD16—28no—
789C2×SD16—24no—
790C2×SD16—264no—
791C2×SD16—232no—
792C2×SD16—28no—
793C2×SD16—44no—
794C2×SD16C2×D4116yescomplemented
795C2×SD16C2418yes—
796C2×SD16C2418yes—
797C2×SD16C2418yes—
798C2×SD16C2414yes—
799C2×SD16C2418yes—
800C2×SD16C2414yes—
801C2×SD16C2414yes—
802C2×SD16C2414yes—
803C2×SD16C2414yes—
804C2×SD16C2414yes—
805C2×SD16C2418yes—
806C2×SD16C2414yes—
807C2×SD16C2414yes—
808C2×SD16C2418yes—
809C2×D8—28no—
810C2×D8—24no—
811C2×D8—232no—
812C2×D8C2×D4116yescomplemented
813C2×D8C2418yes—
814C2×D8C2414yes—
815C2×D8C2414yes—
816C2×D8C2414yes—
817C2×D8C2414yes—
818C2×D8C2418yes—
819#131—216no—
820#131—216no—
821#131—216no—
822#131—216no—
823C2×M16—24no—
824C2×M16—24no—
825C2×M16—216no—
826C2×M16—28no—
827C2×M16C2×D418yescomplemented
828C2×M16C2412yes—
829C2×M16C2412yes—
830C2×M16C2412yes—
831C2×M16C2412yes—
832C2×M16C2418yes—
833C2×M16C2418yes—
834C2×M16C2412yes—
835C2×M16C2412yes—
836C22×C8—24no—
837C22×C8—28no—
838C22×C8C2411yescharacteristic
839C22×C8C2411yescharacteristic
840C22×C8C2412yes—
841C22×C8C2412yes—
842C22×C8C2418yes—
843C22×C8C2412yes—
844C22×C8C2412yes—
845C22×C8C2418yes—
846C22×C8C2412yes—
847C4⋊Q8—24no—
848C4⋊Q8—22no—
849C4⋊Q8—24no—
850C4⋊Q8—22no—
851C4⋊Q8—22no—
852C4⋊Q8—216no—
853C4⋊Q8—24no—
854C4⋊Q8C2×D414yes—
855C4⋊Q8C2418yes—
856C4⋊Q8C2414yes—
857#127—22no—
858#127—22no—
859#127—22no—
860#127C2×D414yes—
861#127C2414yes—
862#124—22no—
863#124—22no—
864#124—22no—
865#124—24no—
866#124—24no—
867#124—22no—
868#124—22no—
869#124—22no—
870#124—216no—
871#124—24no—
872#124C2×D414yes—
873#124C2×D414yes—
874#124C2418yes—
875#124C2414yes—
876#124C2414yes—
877#123—24no—
878#123—24no—
879#123—28no—
880#123—28no—
881#123—24no—
882#123—24no—
883#123—24no—
884#123—24no—
885#123—216no—
886#123—216no—
887#123—216no—
888#123—24no—
889#123—24no—
890#123—28no—
891#123—216no—
892#123—216no—
893#123—216no—
894#123—28no—
895#123—216no—
896#123C2×D418yes—
897#123C2×D418yes—
898C22⋊Q8—24no—
899C22⋊Q8—24no—
900C22⋊Q8—24no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—216no—
904C22⋊Q8—28no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—216no—
908C22⋊Q8—216no—
909C22⋊Q8C2×D418yes—
910C22⋊Q8C2×D418yes—
911C22⋊Q8C24116yes—
912C22⋊Q8C2418yes—
913C22⋊Q8C2418yes—
914C22⋊Q8C2418yes—
915#121—28no—
916#121—28no—
917#121—216no—
918#121—24no—
919#121—216no—
920#121—24no—
921#121—24no—
922#121—216no—
923#121—28no—
924#121—28no—
925#121—216no—
926#121—24no—
927#121—24no—
928#121—216no—
929#121—216no—
930#121—216no—
931#121C2×D4116yes—
932#121C2×D418yes—
933#121C2×D418yes—
934#121C2418yes—
935#121C2418yes—
936#121C2418yes—
937#120—24no—
938#120—24no—
939#120—24no—
940#120—24no—
941#120—24no—
942#120—216no—
943#120—216no—
944#120—216no—
945#120—24no—
946#120—24no—
947#120—24no—
948#120—216no—
949#120—216no—
950#120C2×D418yes—
951#120C2×D418yes—
952C4×Q8—24no—
953C4×Q8C2418yes—
954C4×D4—216no—
955C4×D4—28no—
956C4×D4—28no—
957C4×D4—28no—
958C4×D4—28no—
959C4×D4—28no—
960C4×D4—28no—
961C4×D4—24no—
962C4×D4—28no—
963C4×D4—216no—
964C4×D4—28no—
965C4×D4—28no—
966C4×D4C24116yes—
967C4×D4C2418yes—
968C4×D4C24116yes—
969#117—21no—
970#117—21no—
971#117—21no—
972#117—21no—
973#117—24no—
974#117—24no—
975#117—24no—
976#117C2×D412yes—
977#117C2×D412yes—
978#117C2412yes—
979#117C2412yes—
980#117C2412yes—
981#117C2412yes—
982#117C2412yes—
983#117C2412yes—
984C2×C4⋊C4—24no—
985C2×C4⋊C4—24no—
986C2×C4⋊C4—24no—
987C2×C4⋊C4—216no—
988C2×C4⋊C4—216no—
989C2×C4⋊C4C2×D412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C22⋊C4—21no—
993C2×C22⋊C4—21no—
994C2×C22⋊C4—24no—
995C2×C22⋊C4—24no—
996C2×C22⋊C4—24no—
997C2×C22⋊C4—28no—
998C2×C22⋊C4—28no—
999C2×C22⋊C4—24no—
1000C2×C22⋊C4—216no—
1001C2×C22⋊C4—216no—
1002C2×C22⋊C4—216no—
1003C2×C22⋊C4C2×D412yes—
1004C2×C42—21no—
1005C2×C42—21no—
1006C2×C42—24no—
1007C2×C42C2412yes—
1008#107C2418yes—
1009#106C2418yes—
1010C4⋊C8C2418yes—
1011C4⋊C8C2418yes—
1012#103C2414yes—
1013#103C2414yes—
1014#103C2414yes—
1015#103C2414yes—
1016#103C24116yes—
1017#103C2418yes—
1018#103C2418yes—
1019#102C24116yes—
1020#102C2414yes—
1021#102C2414yes—
1022#102C2414yes—
1023#102C2414yes—
1024#102C2418yes—
1025#102C2418yes—
1026C22⋊C8C2418yes—
1027C22⋊C8C2418yes—
1028C22⋊C8C24116yes—
1029#97C2418yes—
1030C4×C8C2418yes—
1031C24—21no—
1032C24—22no—
1033C24—22no—
1034C24—22no—
1035C24—28no—
1036C24—24no—
1037C24—21no—
1038C24—28no—
1039C24—28no—
1040C24—21no—
1041C24—21no—
1042C24—48no—
1043C24—48no—
1044C24—162no—
1045C24—164no—
1046C24—164no—
1047C24C22×D412yes—
1048C24C22×D412yes—
1049C24C22×D411yescharacteristic
1050#41—28no—
1051#41—28no—
1052#41—28no—
1053#41—28no—
1054#41—28no—
1055#41—28no—
1056#41—24no—
1057#41—24no—
1058#41—24no—
1059#41—24no—
1060#41—24no—
1061#41—24no—
1062#41—24no—
1063#41—24no—
1064#41—24no—
1065#41—24no—
1066#41—28no—
1067#41—28no—
1068#41—216no—
1069#41—216no—
1070#41—216no—
1071#41—24no—
1072#41—24no—
1073#41—24no—
1074#41—24no—
1075#41—24no—
1076#41—24no—
1077#41—24no—
1078#41—24no—
1079#41—24no—
1080#41—24no—
1081#41—24no—
1082#41—24no—
1083#41—416no—
1084#41—48no—
1085#41—48no—
1086#41—44no—
1087#41—44no—
1088#41—48no—
1089#41—416no—
1090#41—416no—
1091#41—416no—
1092#41—416no—
1093#41—416no—
1094#41—48no—
1095#41—416no—
1096#41—416no—
1097#41—48no—
1098#41—416no—
1099#41—432no—
1100#41—432no—
1101#41—416no—
1102#41—416no—
1103#41—416no—
1104#41—416no—
1105#41—48no—
1106#41—48no—
1107#41—44no—
1108#41—44no—
1109#41—44no—
1110#41—44no—
1111#41—44no—
1112#41—44no—
1113#41C22×D418yes—
1114#41C22×D418yes—
1115C2×Q8—24no—
1116C2×Q8—24no—
1117C2×Q8—21no—
1118C2×Q8—22no—
1119C2×Q8—28no—
1120C2×Q8—22no—
1121C2×Q8—21no—
1122C2×Q8—21no—
1123C2×Q8—24no—
1124C2×Q8—22no—
1125C2×Q8—21no—
1126C2×Q8—22no—
1127C2×Q8—216no—
1128C2×Q8—28no—
1129C2×Q8—24no—
1130C2×Q8—24no—
1131C2×Q8—24no—
1132C2×Q8—22no—
1133C2×Q8—22no—
1134C2×Q8—22no—
1135C2×Q8—24no—
1136C2×Q8—22no—
1137C2×Q8—24no—
1138C2×Q8—24no—
1139C2×Q8—22no—
1140C2×Q8—22no—
1141C2×Q8—48no—
1142C2×Q8—48no—
1143C2×Q8—44no—
1144C2×Q8—416no—
1145C2×Q8—416no—
1146C2×Q8—416no—
1147C2×Q8—48no—
1148C2×Q8—48no—
1149C2×Q8—44no—
1150C2×Q8—44no—
1151C2×Q8—44no—
1152C2×Q8C22×D414yes—
1153C2×Q8C22×D412yes—
1154C2×Q8C22×D412yes—
1155C2×Q8C22×D412yes—
1156C2×Q8C22×D412yes—
1157C2×Q8C2514yes—
1158C2×Q8C2512yes—
1159C2×Q8C2512yes—
1160C2×Q8C2512yes—
1161C2×Q8C2512yes—
1162C2×D4—28no—
1163C2×D4—28no—
1164C2×D4—28no—
1165C2×D4—22no—
1166C2×D4—22no—
1167C2×D4—28no—
1168C2×D4—216no—
1169C2×D4—216no—
1170C2×D4—22no—
1171C2×D4—22no—
1172C2×D4—28no—
1173C2×D4—28no—
1174C2×D4—28no—
1175C2×D4—22no—
1176C2×D4—22no—
1177C2×D4—22no—
1178C2×D4—24no—
1179C2×D4—22no—
1180C2×D4—24no—
1181C2×D4—28no—
1182C2×D4—28no—
1183C2×D4—28no—
1184C2×D4—28no—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—24no—
1188C2×D4—24no—
1189C2×D4—22no—
1190C2×D4—22no—
1191C2×D4—22no—
1192C2×D4—21no—
1193C2×D4—22no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—28no—
1197C2×D4—28no—
1198C2×D4—24no—
1199C2×D4—21no—
1200C2×D4—21no—
1201C2×D4—21no—
1202C2×D4—28no—
1203C2×D4—24no—
1204C2×D4—24no—
1205C2×D4—24no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—48no—
1211C2×D4—48no—
1212C2×D4—44no—
1213C2×D4—416no—
1214C2×D4—416no—
1215C2×D4—48no—
1216C2×D4—48no—
1217C2×D4—48no—
1218C2×D4—416no—
1219C2×D4—416no—
1220C2×D4—416no—
1221C2×D4—416no—
1222C2×D4—416no—
1223C2×D4—48no—
1224C2×D4—432no—
1225C2×D4—432no—
1226C2×D4—432no—
1227C2×D4—432no—
1228C2×D4—416no—
1229C2×D4—416no—
1230C2×D4—48no—
1231C2×D4—48no—
1232C2×D4—48no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—44no—
1236C2×D4—1616no—
1237C2×D4C22×D414yes—
1238C2×D4C22×D414yes—
1239C2×D4C22×D414yes—
1240C2×D4C22×D414yes—
1241C2×D4C22×D412yes—
1242C2×D4C22×D412yes—
1243C2×D4C22×D412yes—
1244C2×D4C22×D412yes—
1245C2×D4C22×D414yes—
1246C2×D4C22×D418yes—
1247C2×D4C22×D418yes—
1248C2×D4C22×D418yes—
1249C2×D4C22×D4116yes—
1250C2×D4C2512yes—
1251C2×D4C2512yes—
1252C2×D4C2512yes—
1253C2×D4C2512yes—
1254C2×D4C2514yes—
1255C22×C4—21no—
1256C22×C4—28no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—24no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—21no—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—21no—
1269C22×C4—21no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—28no—
1274C22×C4—28no—
1275C22×C4—28no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—28no—
1285C22×C4—216no—
1286C22×C4—416no—
1287C22×C4—48no—
1288C22×C4—48no—
1289C22×C4—48no—
1290C22×C4—48no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—164no—
1296C22×C4C22×D412yes—
1297C22×C4C22×D414yes—
1298C22×C4C22×D414yes—
1299C22×C4C22×D412yes—
1300C22×C4C22×D414yes—
1301C22×C4C22×D411yescharacteristic
1302C22×C4C22×D411yescharacteristic
1303C22×C4C22×D411yescharacteristic
1304C22×C4C22×D414yes—
1305C22×C4H(5,𝔽2)14yes—
1306C22×C4C2514yes—
1307C22×C4C2514yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311Q16—28no—
1312Q16—28no—
1313Q16—216no—
1314Q16—28no—
1315Q16—48no—
1316Q16—44no—
1317SD16—28no—
1318SD16—28no—
1319SD16—216no—
1320SD16—216no—
1321SD16—216no—
1322SD16—28no—
1323SD16—28no—
1324SD16—216no—
1325SD16—28no—
1326SD16—28no—
1327SD16—48no—
1328SD16—44no—
1329SD16—44no—
1330SD16C22×D4132yes—
1331D8—216no—
1332D8—28no—
1333D8—28no—
1334D8—28no—
1335D8—44no—
1336D8C22×D4132yes—
1337M16—24no—
1338M16—24no—
1339M16—24no—
1340M16—24no—
1341M16—216no—
1342M16—216no—
1343M16C22×D418yes—
1344M16C22×D418yes—
1345C2×C8—22no—
1346C2×C8—22no—
1347C2×C8—24no—
1348C2×C8—24no—
1349C2×C8—24no—
1350C2×C8—24no—
1351C2×C8—216no—
1352C2×C8—216no—
1353C2×C8C22×D418yes—
1354C2×C8C2514yes—
1355C2×C8C2512yes—
1356C2×C8C2512yes—
1357C2×C8C2514yes—
1358C2×C8C2514yes—
1359C4⋊C4—22no—
1360C4⋊C4—28no—
1361C4⋊C4—28no—
1362C4⋊C4—28no—
1363C4⋊C4—216no—
1364C4⋊C4—216no—
1365C4⋊C4—28no—
1366C4⋊C4—28no—
1367C4⋊C4—22no—
1368C4⋊C4C22×D4116yes—
1369C4⋊C4C22×D414yes—
1370C4⋊C4C22×D414yes—
1371C4⋊C4C2514yes—
1372C4⋊C4C2514yes—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—28no—
1377C22⋊C4—28no—
1378C22⋊C4—216no—
1379C22⋊C4—22no—
1380C22⋊C4—28no—
1381C22⋊C4—216no—
1382C22⋊C4—28no—
1383C22⋊C4—28no—
1384C22⋊C4—28no—
1385C22⋊C4—28no—
1386C22⋊C4—216no—
1387C22⋊C4—28no—
1388C22⋊C4—28no—
1389C22⋊C4C22×D414yes—
1390C22⋊C4C22×D414yes—
1391C22⋊C4C22×D4116yes—
1392C22⋊C4C22×D4116yes—
1393C42—22no—
1394C42—28no—
1395C42—22no—
1396C42—22no—
1397C42—22no—
1398C42C22×D414yes—
1399C42C2514yes—
1400C23—22no—
1401C23—24no—
1402C23—24no—
1403C23—24no—
1404C23—24no—
1405C23—28no—
1406C23—28no—
1407C23—28no—
1408C23—22no—
1409C23—22no—
1410C23—22no—
1411C23—42no—
1412C23—44no—
1413C23—44no—
1414C23—48no—
1415C23—416no—
1416C23—416no—
1417C23—42no—
1418C23—42no—
1419C23—42no—
1420C23—84no—
1421C23—82no—
1422C23—84no—
1423C23—82no—
1424C23—84no—
1425C23—82no—
1426C23—816no—
1427C23—816no—
1428C23—82no—
1429C23—88no—
1430C23—168no—
1431C23—1616no—
1432C23—1616no—
1433C23D4214yes—
1434C23C23×D414yes—
1435C23C23×D414yes—
1436C23C23×D411yescharacteristic
1437C23C23×D411yescharacteristic
1438C23C23×D411yescharacteristic
1439Q8—22no—
1440Q8—24no—
1441Q8—24no—
1442Q8—24no—
1443Q8—24no—
1444Q8—24no—
1445Q8—24no—
1446Q8—22no—
1447Q8—22no—
1448Q8—22no—
1449Q8—24no—
1450Q8—22no—
1451Q8—22no—
1452Q8—22no—
1453Q8—416no—
1454Q8—48no—
1455Q8—44no—
1456Q8—44no—
1457Q8—44no—
1458Q8—42no—
1459Q8—42no—
1460Q8—42no—
1461Q8C23×D414yes—
1462D4—28no—
1463D4—28no—
1464D4—28no—
1465D4—28no—
1466D4—28no—
1467D4—28no—
1468D4—22no—
1469D4—22no—
1470D4—22no—
1471D4—24no—
1472D4—22no—
1473D4—22no—
1474D4—22no—
1475D4—22no—
1476D4—28no—
1477D4—28no—
1478D4—28no—
1479D4—24no—
1480D4—24no—
1481D4—24no—
1482D4—24no—
1483D4—24no—
1484D4—416no—
1485D4—416no—
1486D4—416no—
1487D4—48no—
1488D4—48no—
1489D4—416no—
1490D4—416no—
1491D4—48no—
1492D4—416no—
1493D4—44no—
1494D4—44no—
1495D4—44no—
1496D4—44no—
1497D4—44no—
1498D4—44no—
1499D4—42no—
1500D4—42no—
1501D4—42no—
1502D4—88no—
1503D4—88no—
1504D4—88no—
1505D4—88no—
1506D4C23×D414yes—
1507D4C23×D418yes—
1508C2×C4—22no—
1509C2×C4—24no—
1510C2×C4—24no—
1511C2×C4—24no—
1512C2×C4—24no—
1513C2×C4—24no—
1514C2×C4—24no—
1515C2×C4—24no—
1516C2×C4—28no—
1517C2×C4—28no—
1518C2×C4—28no—
1519C2×C4—28no—
1520C2×C4—24no—
1521C2×C4—24no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—24no—
1525C2×C4—22no—
1526C2×C4—44no—
1527C2×C4—48no—
1528C2×C4—416no—
1529C2×C4—416no—
1530C2×C4—48no—
1531C2×C4—48no—
1532C2×C4—416no—
1533C2×C4—416no—
1534C2×C4—42no—
1535C2×C4—42no—
1536C2×C4—44no—
1537C2×C4—42no—
1538C2×C4—44no—
1539C2×C4—44no—
1540C2×C4—44no—
1541C2×C4—44no—
1542C2×C4—44no—
1543C2×C4—44no—
1544C2×C4—44no—
1545C2×C4—44no—
1546C2×C4—88no—
1547C2×C4—816no—
1548C2×C4—82no—
1549C2×C4—82no—
1550C2×C4D4214yes—
1551C2×C4D4214yes—
1552C2×C4D4214yes—
1553C2×C4C23×D418yes—
1554C2×C4C23×D414yes—
1555C2×C4C23×D414yes—
1556C2×C4C23×D412yes—
1557C2×C4C23×D412yes—
1558C2×C4C23×D412yes—
1559C2×C4C23×D411yescharacteristic
1560C2×C4C23×D411yescharacteristic
1561C2×C4C23×D411yescharacteristic
1562C2×C4C2×H(5,𝔽2)12yes—
1563C2×C4C2×H(5,𝔽2)12yes—
1564C2×C4C2×H(5,𝔽2)12yes—
1565C2×C4C2611yescharacteristic
1566C8—22no—
1567C8—24no—
1568C8—22no—
1569C8—24no—
1570C8C23×D418yes—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—28no—
1575C22—28no—
1576C22—24no—
1577C22—24no—
1578C22—24no—
1579C22—28no—
1580C22—44no—
1581C22—48no—
1582C22—44no—
1583C22—48no—
1584C22—44no—
1585C22—44no—
1586C22—44no—
1587C22—42no—
1588C22—42no—
1589C22—42no—
1590C22—84no—
1591C22—84no—
1592C22—88no—
1593C22—88no—
1594C22—88no—
1595C22—84no—
1596C22—84no—
1597C22—162no—
1598C22—168no—
1599C22—1616no—
1600C22—1616no—
1601C22C2×D4212yes—
1602C22C2×D4212yes—
1603C22C2×D4212yes—
1604C22C24×D411yescharacteristic
1605C4—28no—
1606C4—24no—
1607C4—24no—
1608C4—24no—
1609C4—44no—
1610C4—44no—
1611C4—42no—
1612C4—42no—
1613C4—42no—
1614C4—44no—
1615C4C2×D4212yes—
1616C4C2×D4212yes—
1617C4C2×D4212yes—
1618C4C24×D411yescharacteristic
1619C4C22×H(5,𝔽2)11yescharacteristic
1620C2—22no—
1621C2—22no—
1622C2—22no—
1623C2—44no—
1624C2—44no—
1625C2—48no—
1626C2—44no—
1627C2—82no—
1628C2—82no—
1629C2—82no—
1630C2C22×D4211yescharacteristic
1631C2#6309212yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3449 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3585C2semidirect
2. C22×#577C2semidirect
3. #62859C2semidirect
4. #62842C2semidirect
5. #61094C2semidirect
6. #61092C2semidirect
7. #61073C2semidirect
8. #61071C2semidirect
9. #61060C2semidirect
10. #61058C2semidirect
11. #61051C2semidirect
12. #61050C2semidirect
13. #60645C2semidirect
14. #60455C2semidirect
15. #60453C2semidirect
16. #60422C2semidirect
17. C2×#3042C2semidirect
18. #60368C2semidirect
19. #60367C2semidirect
20. #60366C2semidirect
21. C2×#3009C2semidirect
22. #60168C2semidirect
23. #60142C2semidirect
24. C2×#585C22semidirect
25. C22×2−1+4C22semidirect
27. C22×H(5,𝔽2)C22semidirect
30. C2×#577C22semidirect
31. C2×#577C22semidirect
32. C2×#577C22semidirect
33. C2×#577C22semidirect
34. C2×#576C22semidirect
35. C2×#576C22semidirect
36. C2×#575C22semidirect
37. C2×#575C22semidirect
38. C2×#575C22semidirect
39. C2×#575C22semidirect
40. C22×#137C22semidirect
41. C22×#137C22semidirect
42. C22×#137C22semidirect
45. C22×AGL(1,ℤ/8)C22semidirect
46. C22×AGL(1,ℤ/8)C22semidirect
47. C22×#135C22semidirect
48. C22×#135C22semidirect
49. C23×SD16C22semidirect
50. C23×SD16C22semidirect
51. C2×#568C22semidirect
52. C22×#131C22semidirect
54. #3500C22semidirect
56. #3499C22semidirect
58. #3496C22semidirect
60. #3489C22semidirect
61. #3486C22semidirect
65. #3485C22semidirect
66. #3485C22semidirect
67. #3485C22semidirect
70. #3484C22semidirect
71. #3484C22semidirect
75. #3449C22semidirect
76. #3449C22semidirect
77. #3449C22semidirect
79. C2×#536C22semidirect
80. C2×#536C22semidirect
82. #3428C22semidirect
83. C2×#518C22semidirect
84. #3283C22semidirect
85. #3282C22semidirect
86. D4×SD16C22semidirect
87. #3280C22semidirect
88. #3276C22semidirect
89. #3275C22semidirect
90. #3273C22semidirect
91. #3272C22semidirect
92. #3269C22semidirect
93. #3267C22semidirect
94. #3267C22semidirect
95. #3267C22semidirect
96. #3266C22semidirect
97. #3266C22semidirect
98. #3265C22semidirect
99. #3264C22semidirect
100. #3156C22semidirect
101. #3156C22semidirect
102. #3154C22semidirect
103. #3154C22semidirect
104. #3153C22semidirect
105. #3152C22semidirect
106. #3063C22semidirect
107. #3063C22semidirect
108. #3063C22semidirect
109. #3062C22semidirect
110. #3062C22semidirect
111. #3059C22semidirect
112. #3057C22semidirect
113. #3056C22semidirect
114. #3054C22semidirect
115. #3050C22semidirect
116. #3046C22semidirect
117. #3045C22semidirect
118. #3044C22semidirect
119. #3043C22semidirect
120. #3042C22semidirect
121. #3042C22semidirect
122. #3042C22semidirect
123. #3042C22semidirect
124. #3041C22semidirect
125. #3035C22semidirect
126. C2×#463C22semidirect
127. C2×#461C22semidirect
128. #3013C22semidirect
129. #3013C22semidirect
130. #3012C22semidirect
131. #3012C22semidirect
132. #3011C22semidirect
133. #3011C22semidirect
134. #3010C22semidirect
135. #3010C22semidirect
136. #3009C22semidirect
137. #3009C22semidirect
138. #3009C22semidirect
139. #3009C22semidirect
140. #3009C22semidirect
141. #3008C22semidirect
142. #3008C22semidirect
143. #3005C22semidirect
144. #3005C22semidirect
145. #3004C22semidirect
146. #3003C22semidirect
147. #3002C22semidirect
148. C2×#452C22semidirect
149. C2×#450C22semidirect
150. #2949C22semidirect
151. #2948C22semidirect
152. #2946C22semidirect
153. C4×AGL(1,ℤ/8)C22semidirect
154. #2935C22semidirect
155. #2933C22semidirect
156. #2930C22semidirect
157. #2929C22semidirect
158. #2911C22semidirect
159. C2×#424C22semidirect
160. #2896C22semidirect
161. #2896C22semidirect
162. C2×#419C22semidirect
163. C2×#418C22semidirect
164. C2×#416C22semidirect
165. C2×#416C22semidirect
166. #2879C22semidirect
167. C2×#408C22semidirect
168. #2873C22semidirect
178. C2×2−1+4C23semidirect
179. C2×2−1+4C23semidirect
195. C2×H(5,𝔽2)C23semidirect
210. C22×#41C23semidirect
211. C22×#41C23semidirect
214. C23×Q8C23semidirect
238. C2×#137C23semidirect
239. C2×#137C23semidirect
240. C2×#137C23semidirect
241. C2×#137C23semidirect
242. C2×#137C23semidirect
243. C2×#137C23semidirect
244. C2×#137C23semidirect
245. C2×#137C23semidirect
246. C2×#137C23semidirect
250. C2×AGL(1,ℤ/8)D4semidirect
256. C2×AGL(1,ℤ/8)C23semidirect
257. C2×AGL(1,ℤ/8)C23semidirect
258. C2×AGL(1,ℤ/8)C23semidirect
259. C2×AGL(1,ℤ/8)C23semidirect
260. C2×AGL(1,ℤ/8)C23semidirect
261. C2×AGL(1,ℤ/8)C23semidirect
262. C2×AGL(1,ℤ/8)C23semidirect
263. C2×AGL(1,ℤ/8)C23semidirect
264. C2×AGL(1,ℤ/8)C23semidirect
270. C2×#135C23semidirect
271. C2×#135C23semidirect
272. C2×#135C23semidirect
273. C2×#135C23semidirect
274. C2×#135C23semidirect
275. C22×Q16C23semidirect
276. C22×Q16C23semidirect
277. C22×Q16C23semidirect
286. C22×SD16C23semidirect
287. C22×SD16C23semidirect
288. C22×SD16C23semidirect
289. C22×SD16C23semidirect
290. C22×SD16C23semidirect
291. C22×SD16C23semidirect
294. C22×D8C23semidirect
295. C22×D8C23semidirect
300. C2×#131C23semidirect
301. C2×#131C23semidirect
305. C22×M16C23semidirect
306. C22×M16C23semidirect
308. C23×C8C23semidirect
310. D4×Q8C23semidirect
312. #548C23semidirect
320. #547C23semidirect
332. #546C23semidirect
362. #536C23semidirect
363. #536C23semidirect
364. #536C23semidirect
365. #536C23semidirect
376. #535C23semidirect
397. C2×C4⋊Q8C23semidirect
400. C2×#124C23semidirect
412. #525C23semidirect
420. C2×C22⋊Q8C23semidirect
425. #520C23semidirect
426. #519C23semidirect
432. #518C23semidirect
434. C4×#41C23semidirect
442. #497C23semidirect
443. #497C23semidirect
444. #497C23semidirect
445. #496C23semidirect
446. #495C23semidirect
447. #495C23semidirect
448. #494C23semidirect
449. #492C23semidirect
450. #470C23semidirect
451. #470C23semidirect
452. #469C23semidirect
453. #468C23semidirect
454. #468C23semidirect
455. #468C23semidirect
456. #467C23semidirect
457. #467C23semidirect
458. #466C23semidirect
459. #465C23semidirect
460. #465C23semidirect
461. #465C23semidirect
462. #464C23semidirect
463. #464C23semidirect
464. #463C23semidirect
465. #463C23semidirect
466. #463C23semidirect
467. #463C23semidirect
468. #462C23semidirect
469. #461C23semidirect
470. #461C23semidirect
471. #461C23semidirect
472. #460C23semidirect
473. #459C23semidirect
474. #452C23semidirect
475. #452C23semidirect
476. #452C23semidirect
477. #452C23semidirect
478. #452C23semidirect
479. #452C23semidirect
480. #451C23semidirect
481. #451C23semidirect
482. #450C23semidirect
483. #450C23semidirect
484. #450C23semidirect
485. #450C23semidirect
486. #449C23semidirect
487. #449C23semidirect
488. #449C23semidirect
489. #449C23semidirect
490. #448C23semidirect
491. #448C23semidirect
492. #447C23semidirect
493. #447C23semidirect
494. #442C23semidirect
495. #440C23semidirect
496. C4×SD16C23semidirect
497. C4×D8C23semidirect
498. #436C23semidirect
499. #435C23semidirect
500. #435C23semidirect
501. C8×D4C23semidirect
502. #428C23semidirect
503. #428C23semidirect
504. #427C23semidirect
505. #424C23semidirect
506. #424C23semidirect
507. #424C23semidirect
508. C2×C4⋊C8C23semidirect
509. #419C23semidirect
510. #419C23semidirect
511. #419C23semidirect
512. #419C23semidirect
515. #418C23semidirect
516. #418C23semidirect
518. #417C23semidirect
521. #416C23semidirect
522. #416C23semidirect
523. #416C23semidirect
524. #416C23semidirect
525. #416C23semidirect
526. #416C23semidirect
527. C2×#103C23semidirect
528. C2×#103C23semidirect
529. C2×#103C23semidirect
531. C2×#102C23semidirect
532. C2×#102C23semidirect
536. #408C23semidirect
537. #408C23semidirect
538. #407C23semidirect
539. C2×C22⋊C8C23semidirect
540. #405C23semidirect
541. #405C23semidirect
542. C4×M16C23semidirect
631. C2×#41C2×D4semidirect
764. AGL(1,ℤ/8)C2×D4semidirect
765. AGL(1,ℤ/8)C2×D4semidirect
794. C2×SD16C2×D4semidirect
812. C2×D8C2×D4semidirect
827. C2×M16C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35852
C22×#5772
#628592
#628422
#610942
#610922
#610732
#610712
#610602
#610582
#610512
#610502
#606452
#604552
#604532
#604222
C2×#30422
#603682
#603672
#603662
C2×#30092
#601682
#601422