Finite Group Databasebeta

← C4×#3586 #10574169

Subgroups — C4×#3586 #10574169

Order 512.

10333 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3586C211yesmaximal, characteristic
2C4×#585C211yesmaximal, characteristic, complemented
3C2×C4×2−1+4C211yesmaximal, characteristic, complemented
4#60175C218yesmaximal, complemented
5#60174C218yesmaximal, complemented
6C4×#578C218yesmaximal, complemented
7C4×#577C218yesmaximal, complemented
8#60170C216yesmaximal, complemented
9#60169C216yesmaximal, complemented
10C4×#575C216yesmaximal, complemented
11C2×C4×#137C216yesmaximal, complemented
12#60109C211yesmaximal, characteristic, complemented
13#60089C211yesmaximal, characteristic, complemented
14#60088C211yesmaximal, characteristic, complemented
15C4×#568C211yesmaximal, characteristic, complemented
16C2×#585C2211yescharacteristic
17C22×2−1+4C2211yescharacteristic
18#3586C4132yesdirect product factor
19C2×#578C2218yes—
20C2×#577C2218yes—
21C2×#575C2216yes—
22C22×#137C2216yes—
23C2×#568C2211yescharacteristic
24C2×#568C2211yescharacteristic
25C4×2−1+4—24no—
26C4×2−1+4—24no—
27C4×2−1+4—21no—
28C4×2−1+4—21no—
29C4×2−1+4C2218yescomplemented
30C4×2−1+4C2214yescomplemented
31C4×2−1+4C2218yescomplemented
32C4×2−1+4C2214yescomplemented
33C4×H(5,𝔽2)—23no—
34C4×H(5,𝔽2)—23no—
35C4×H(5,𝔽2)C2214yescomplemented
36C4×H(5,𝔽2)C2214yescomplemented
37#3428—24no—
38#3428C2216yes—
39#3428C2211yescharacteristic
40C2×#520—23no—
41C2×#520C2211yescharacteristic
42C2×#520C2213yescomplemented
43C2×#519—21no—
44C2×#519C2213yescomplemented
45C2×C4×#41—24no—
46C2×C4×#41—23no—
47C2×C4×#41C2216yes—
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2213yescomplemented
50C22×C4×Q8—21no—
51C22×C4×Q8C2213yescomplemented
52#2952C22124yescomplemented
53#2951C22124yescomplemented
54#2950C22124yescomplemented
55#2949C22124yescomplemented
56#2947C22124yescomplemented
57#2947C22124yescomplemented
58#2947C22124yescomplemented
59#2946C22124yescomplemented
60C4×#137C22112yescomplemented
61C4×#137C22124yescomplemented
62C4×#137C22124yescomplemented
63C4×#137C22112yescomplemented
64C4×#137C22124yescomplemented
65C4×#137C22112yescomplemented
66C4×#137C22112yescomplemented
67C4×AGL(1,ℤ/8)C22112yescomplemented
68C4×AGL(1,ℤ/8)C22112yescomplemented
69C4×AGL(1,ℤ/8)C22112yescomplemented
70C4×AGL(1,ℤ/8)C2214yescomplemented
71#2943C22124yescomplemented
72C2×#441C22112yescomplemented
73C2×#440C22112yescomplemented
74C4×#135C22124yescomplemented
75C2×C4×Q16C22112yescomplemented
76C2×C4×SD16C22112yescomplemented
77#2913C2218yescomplemented
78#2912C2218yescomplemented
79#2911C2216yescomplemented
80C2×#428C2216yescomplemented
81#2898C2218yescomplemented
82#2898C2218yescomplemented
83#2898C2218yescomplemented
84#2897C2218yescomplemented
85#2896C2216yes—
86#2896C2216yescomplemented
87C2×#417C2216yes—
88C2×#419C2216yescomplemented
89#2875C2218yescomplemented
90C4×#131C2218yescomplemented
91#2873C2216yescomplemented
92C2×C4×M16C2216yescomplemented
93#585—28no—
94#585C2×C4116yescomplemented
95C2×2−1+4—24no—
96C2×2−1+4—28no—
97C2×2−1+4—21no—
98C2×2−1+4C2×C4116yescomplemented
99C2×2−1+4C2318yes—
100C2×2−1+4C2314yes—
101C2×H(5,𝔽2)—23no—
102C2×H(5,𝔽2)C2314yes—
103C22×#41—24no—
104C22×#41—23no—
105C22×#41C2316yes—
106C22×#41C2313yes—
107C22×#41C2311yescharacteristic
108C23×Q8—21no—
109C23×Q8C2313yes—
110#578C2×C41128yescomplemented
111#577C2×C41128yescomplemented
112#575C2×C4196yescomplemented
113C2×#137C2×C4196yescomplemented
114C2×#137C23112yes—
115C2×#137C23124yes—
116C2×#137C23112yes—
117C2×AGL(1,ℤ/8)C2314yes—
118C2×AGL(1,ℤ/8)C23112yes—
119C2×#135C23124yes—
120C22×Q16C23112yes—
121C22×SD16C23112yes—
122#568—28no—
123#568C2×C4116yescomplemented
124C2×#131C2318yes—
125C2×#131C2318yes—
126C22×M16C2316yes—
127C22×M16C2316yes—
128#520—24no—
129#520—24no—
130#520—24no—
131#520—224no—
132#520—224no—
133#520—212no—
134#520—212no—
135#520—212no—
136#520—26no—
137#520—26no—
138#520C23124yes—
139#520C23112yes—
140#520C23112yes—
141#520C2318yes—
142#520C2314yes—
143#520C2314yes—
144#519—21no—
145#519—28no—
146#519—28no—
147#519—24no—
148#519—24no—
149#519—212no—
150#519C23124yes—
151#519C23112yes—
152#518—23no—
153#518—212no—
154#518—212no—
155#518—212no—
156#518C23112yes—
157C4×#41—24no—
158C4×#41—24no—
159C4×#41—24no—
160C4×#41—212no—
161C4×#41—212no—
162C4×#41—224no—
163C4×#41—224no—
164C4×#41—212no—
165C4×#41—26no—
166C4×#41—26no—
167C4×#41—26no—
168C4×#41—26no—
169C4×#41—26no—
170C4×#41—26no—
171C4×#41D414yes—
172C4×#41D414yes—
173C4×#41C2314yes—
174C4×#41C23112yes—
175C4×#41C23112yes—
176C4×#41C23112yes—
177C4×#41C23112yes—
178C4×#41C23112yes—
179C4×#41C2314yes—
180C4×#41C2314yes—
181C2×C4×Q8—21no—
182C2×C4×Q8—28no—
183C2×C4×Q8—28no—
184C2×C4×Q8—24no—
185C2×C4×Q8—24no—
186C2×C4×Q8—23no—
187C2×C4×Q8—23no—
188C2×C4×Q8—23no—
189C2×C4×Q8—23no—
190C2×C4×Q8—26no—
191C2×C4×Q8—26no—
192C2×C4×Q8D411yescharacteristic
193C2×C4×Q8D411yescharacteristic
194C2×C4×Q8C2313yes—
195C2×C4×Q8C2316yes—
196C2×C4×Q8C23112yes—
197C2×C4×Q8C23112yes—
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2313yes—
201C2×C4×D4—23no—
202C2×C4×D4—23no—
203C2×C4×D4—26no—
204C2×C4×D4—26no—
205C2×C4×D4—23no—
206C2×C4×D4—212no—
207C2×C4×D4—212no—
208C2×C4×D4—26no—
209C2×C4×D4D413yes—
210C2×C4×D4D413yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2313yes—
215C2×#117—212no—
216C2×#117—23no—
217C2×#117—26no—
218C2×#117—26no—
219C2×#117—23no—
220C2×#117C2316yes—
221C2×#117C2313yes—
222C2×#117C2313yes—
223C22×C4⋊C4—23no—
224C22×C4⋊C4—23no—
225C22×C4⋊C4C2313yes—
226C22×C42—23no—
227C22×C42—23no—
228C22×C42—26no—
229C22×C42C2313yes—
230#442C2318yes—
231#442C23124yes—
232#441C23124yes—
233#441C23148yes—
234#441C23124yes—
235#440C23124yes—
236#440C23148yes—
237#440C2318yes—
238#440C23124yes—
239#440C23124yes—
240C4×Q16C23124yes—
241C4×Q16C23148yes—
242C4×Q16C23124yes—
243C4×SD16C23124yes—
244C4×SD16C23148yes—
245C4×SD16C2318yes—
246C4×SD16C23124yes—
247C4×SD16C23124yes—
248C4×D8C2318yes—
249C4×D8C23124yes—
250#428C23112yes—
251#428C23124yes—
252#428C2314yes—
253#428C23112yes—
254#428C23112yes—
255#427C23124yes—
256C2×#107C23112yes—
257C2×#106C23112yes—
258#419C23112yes—
259#419C23124yes—
260#419C23112yes—
261#418C23112yes—
262#418C2314yes—
263#417C23112yes—
264#417C23124yes—
265#417C2314yes—
266#417C23112yes—
267#417C23112yes—
268#416C23124yes—
269#416C23124yes—
270C2×#103C23112yes—
271C2×#103C23112yes—
272C2×#103C23112yes—
273C2×#102C23112yes—
274#405C23124yes—
275#405C23124yes—
276C4×M16C2314yes—
277C4×M16C23112yes—
278C4×M16C23112yes—
279C4×M16C23112yes—
280C2×#97C23112yes—
281C2×C4×C8C23112yes—
2822−1+4—264no—
2832−1+4—232no—
2842−1+4—216no—
2852−1+4—216no—
2862−1+4C22×C4164yescomplemented
2872−1+4C22×C4132yescomplemented
288H(5,𝔽2)—216no—
289H(5,𝔽2)—248no—
290H(5,𝔽2)C22×C4132yescomplemented
291C2×#41—264no—
292C2×#41—24no—
293C2×#41—248no—
294C2×#41—212no—
295C2×#41—224no—
296C2×#41—26no—
297C2×#41—26no—
298C2×#41—26no—
299C2×#41—212no—
300C2×#41—224no—
301C2×#41C22×C4148yes—
302C2×#41C22×C418yes—
303C2×#41C22×C4124yescomplemented
304C2×#41C2×D414yes—
305C2×#41#4118yes—
306C2×#41C2414yes—
307C2×#41C24112yes—
308C2×#41C24112yes—
309C2×#41C2414yes—
310C22×Q8—216no—
311C22×Q8—28no—
312C22×Q8—24no—
313C22×Q8—23no—
314C22×Q8—26no—
315C22×Q8—212no—
316C22×Q8C22×C4124yescomplemented
317C22×Q8C2×D411yescharacteristic
318C22×Q8C2413yes—
319C22×Q8C24112yes—
320C22×Q8C2416yes—
321C22×D4—23no—
322C22×D4—26no—
323C22×D4—212no—
324C22×D4C2×D413yes—
325C22×D4C2411yescharacteristic
326C22×D4C2416yes—
327C23×C4—23no—
328C23×C4—23no—
329C23×C4—26no—
330C23×C4—23no—
331C23×C4—21no—
332C23×C4—23no—
333C23×C4—26no—
334C23×C4—26no—
335C23×C4C2×D413yes—
336C23×C4C2×D413yes—
337C23×C4C2413yes—
338#137C22×C4196yescomplemented
339#137C22×C41192yescomplemented
340#137C22×C4196yescomplemented
341AGL(1,ℤ/8)C22×C4132yescomplemented
342AGL(1,ℤ/8)C22×C4196yescomplemented
343#135C22×C41192yescomplemented
344C2×Q16C22×C4196yescomplemented
345C2×Q16C24124yes—
346C2×SD16C22×C4196yescomplemented
347C2×SD16C24124yes—
348C2×SD16C2418yes—
349C2×D8C2418yes—
350#131—232no—
351#131C22×C4164yescomplemented
352C2×M16—224no—
353C2×M16C22×C4148yescomplemented
354C2×M16C2414yes—
355C2×M16C24112yes—
356C2×M16C2414yes—
357C2×M16C24112yes—
358C22×C8C24112yes—
359C22×C8C24112yes—
360C4×Q8—28no—
361C4×Q8—24no—
362C4×Q8—24no—
363C4×Q8—224no—
364C4×Q8—224no—
365C4×Q8—212no—
366C4×Q8—212no—
367C4×Q8—212no—
368C4×Q8—23no—
369C4×Q8—23no—
370C4×Q8—212no—
371C4×Q8—26no—
372C4×Q8—26no—
373C4×Q8—212no—
374C4×Q8—212no—
375C4×Q8—212no—
376C4×Q8—26no—
377C4×Q8—26no—
378C4×Q8—26no—
379C4×Q8C2×D414yes—
380C4×Q8C2×D414yes—
381C4×Q8C2×D414yes—
382C4×Q8C2×D414yes—
383C4×Q8C2416yes—
384C4×Q8C2416yes—
385C4×Q8C2414yes—
386C4×Q8C2414yes—
387C4×Q8C24124yes—
388C4×Q8C24112yes—
389C4×Q8C24112yes—
390C4×Q8C24112yes—
391C4×D4—212no—
392C4×D4—212no—
393C4×D4—224no—
394C4×D4—212no—
395C4×D4—24no—
396C4×D4—24no—
397C4×D4—212no—
398C4×D4—212no—
399C4×D4—212no—
400C4×D4—212no—
401C4×D4—212no—
402C4×D4—212no—
403C4×D4—212no—
404C4×D4—212no—
405C4×D4—212no—
406C4×D4—212no—
407C4×D4—212no—
408C4×D4—224no—
409C4×D4—224no—
410C4×D4—248no—
411C4×D4—26no—
412C4×D4—26no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—26no—
416C4×D4—26no—
417C4×D4—26no—
418C4×D4C2×D4112yes—
419C4×D4C2×D4112yes—
420C4×D4C2×D4112yes—
421C4×D4C2×D4112yes—
422C4×D4C2414yes—
423C4×D4C2414yes—
424C4×D4C2412yes—
425C4×D4C2412yes—
426C4×D4C24112yes—
427C4×D4C24112yes—
428C4×D4C24112yes—
429#117—26no—
430#117—26no—
431#117—26no—
432#117—212no—
433#117—212no—
434#117—224no—
435#117—224no—
436#117—248no—
437#117—212no—
438#117—24no—
439#117—212no—
440#117—212no—
441#117—212no—
442#117—212no—
443#117C2×D4112yes—
444#117C2414yes—
445#117C24112yes—
446#117C24112yes—
447#117C24112yes—
448C2×C4⋊C4—26no—
449C2×C4⋊C4—23no—
450C2×C4⋊C4—23no—
451C2×C4⋊C4—212no—
452C2×C4⋊C4—212no—
453C2×C4⋊C4—26no—
454C2×C4⋊C4—23no—
455C2×C4⋊C4—26no—
456C2×C4⋊C4—26no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—212no—
459C2×C4⋊C4—212no—
460C2×C4⋊C4C2×D413yes—
461C2×C4⋊C4C2×D413yes—
462C2×C4⋊C4C2413yes—
463C2×C4⋊C4C24112yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2416yes—
467C2×C22⋊C4—23no—
468C2×C22⋊C4—26no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—23no—
471C2×C22⋊C4—26no—
472C2×C22⋊C4—26no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4C2×D416yes—
475C2×C42—23no—
476C2×C42—26no—
477C2×C42—23no—
478C2×C42—26no—
479C2×C42—23no—
480C2×C42—26no—
481C2×C42—26no—
482C2×C42—212no—
483C2×C42—212no—
484C2×C42—212no—
485C2×C42—212no—
486C2×C42—212no—
487C2×C42—212no—
488C2×C42—212no—
489C2×C42—24no—
490C2×C42C2×D413yes—
491C2×C42C2×D416yes—
492C2×C42C2×D413yes—
493C2×C42C2×D416yes—
494C2×C42C2413yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C2411yescharacteristic
498#107C24124yes—
499#107C2418yes—
500#106C24124yes—
501#106C2418yes—
502#103C24124yes—
503#103C24124yes—
504#103C24124yes—
505#103C2418yes—
506#102C24124yes—
507#102C2418yes—
508#102C2418yes—
509#102C2418yes—
510#97C2418yes—
511#97C24124yes—
512C4×C8C2418yes—
513C4×C8C24124yes—
514C24—21no—
515C24—26no—
516C24C22×D413yes—
517#41—232no—
518#41—296no—
519#41—2192no—
520#41—248no—
521#41—248no—
522#41—248no—
523#41—28no—
524#41—224no—
525#41—224no—
526#41C4×D4132yes—
527#41C23×C4148yes—
528#41C23×C4148yes—
529#41C23×C4116yes—
530#41C23×C4116yes—
531#41C2×#41116yes—
532C2×Q8—264no—
533C2×Q8—232no—
534C2×Q8—224no—
535C2×Q8—248no—
536C2×Q8—23no—
537C2×Q8—212no—
538C2×Q8—26no—
539C2×Q8—26no—
540C2×Q8—224no—
541C2×Q8—212no—
542C2×Q8C4×D418yes—
543C2×Q8C23×C4148yes—
544C2×Q8C23×C4124yes—
545C2×Q8C23×C4112yes—
546C2×Q8C22×D414yes—
547C2×Q8C2516yes—
548C2×Q8C2514yes—
549C2×D4—224no—
550C2×D4—248no—
551C2×D4—212no—
552C2×D4—24no—
553C2×D4—212no—
554C2×D4—296no—
555C2×D4—26no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—212no—
559C2×D4C4×D4124yes—
560C2×D4C23×C4124yes—
561C2×D4C23×C414yes—
562C2×D4C22×D4112yes—
563C2×D4C2512yes—
564C2×D4C2514yes—
565C22×C4—224no—
566C22×C4—23no—
567C22×C4—26no—
568C22×C4—212no—
569C22×C4—224no—
570C22×C4—248no—
571C22×C4—24no—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—21no—
575C22×C4—23no—
576C22×C4—26no—
577C22×C4—26no—
578C22×C4—212no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—212no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—46no—
587C22×C4—44no—
588C22×C4—812no—
589C22×C4—83no—
590C22×C4—812no—
591C22×C4—86no—
592C22×C4—86no—
593C22×C4C23×C4112yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D416yes—
596C22×C4C22×D413yes—
597C22×C4C22×D416yes—
598C22×C4C22×D413yes—
599C22×C4C22×D416yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D416yes—
602C22×C4C22×D413yes—
603C22×C4C22×D416yes—
604C22×C4C2×#41112yes—
605C22×C4C2511yescharacteristic
606C22×C4C2516yes—
607Q16C23×C4196yes—
608SD16C23×C4196yes—
609SD16C23×C4132yes—
610D8C23×C4132yes—
611M16—28no—
612M16—224no—
613M16C23×C4116yes—
614M16C23×C4148yes—
615C2×C8—224no—
616C2×C8C23×C4148yes—
617C2×C8C2518yes—
618C2×C8C2518yes—
619C4⋊C4—26no—
620C4⋊C4—224no—
621C4⋊C4—26no—
622C4⋊C4—23no—
623C4⋊C4—212no—
624C4⋊C4—24no—
625C4⋊C4—212no—
626C4⋊C4—212no—
627C4⋊C4—24no—
628C4⋊C4—26no—
629C4⋊C4—26no—
630C4⋊C4—212no—
631C4⋊C4—21no—
632C4⋊C4C22×D4112yes—
633C4⋊C4C22×D4112yes—
634C4⋊C4C2516yes—
635C4⋊C4C2512yes—
636C4⋊C4C2514yes—
637C4⋊C4C2514yes—
638C22⋊C4—212no—
639C22⋊C4—24no—
640C22⋊C4—212no—
641C22⋊C4—24no—
642C22⋊C4—212no—
643C22⋊C4—212no—
644C22⋊C4—24no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—212no—
648C22⋊C4C22×D4124yes—
649C42—24no—
650C42—24no—
651C42—26no—
652C42—212no—
653C42—212no—
654C42—212no—
655C42—224no—
656C42—212no—
657C42—212no—
658C42—24no—
659C42—26no—
660C42C22×D416yes—
661C42C22×D416yes—
662C42C22×D416yes—
663C42C22×D411yescharacteristic
664C42C22×D416yes—
665C42C22×D411yescharacteristic
666C42C22×D416yes—
667C42C2516yes—
668C42C2511yescharacteristic
669C42C2511yescharacteristic
670C23—22no—
671C23—24no—
672C23—24no—
673C23—224no—
674C23—43no—
675C23—43no—
676C23—42no—
677C23—42no—
678C23—86no—
679C23—86no—
680C23C2×C4×D4112yes—
681C23C23×D416yes—
682C23C23×D411yescharacteristic
683Q8—26no—
684Q8—24no—
685Q8—212no—
686Q8—248no—
687Q8—224no—
688Q8C2×C4×D4116yes—
689Q8C24×C4112yes—
690Q8C24×C418yes—
691D4—216no—
692D4—248no—
693D4—248no—
694D4—24no—
695D4—22no—
696D4—224no—
697D4—24no—
698D4C2×C4×D4148yes—
699D4C24×C414yes—
700D4C24×C418yes—
701C2×C4—24no—
702C2×C4—26no—
703C2×C4—212no—
704C2×C4—224no—
705C2×C4—248no—
706C2×C4—22no—
707C2×C4—212no—
708C2×C4—216no—
709C2×C4—248no—
710C2×C4—248no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—26no—
715C2×C4—46no—
716C2×C4—43no—
717C2×C4—41no—
718C2×C4—46no—
719C2×C4—43no—
720C2×C4—46no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—42no—
724C2×C4—46no—
725C2×C4—44no—
726C2×C4—48no—
727C2×C4—812no—
728C2×C4—812no—
729C2×C4—812no—
730C2×C4—86no—
731C2×C4—86no—
732C2×C4—812no—
733C2×C4C2×C4×D4112yes—
734C2×C4C2×C4×D4124yes—
735C2×C4C24×C4112yes—
736C2×C4C24×C412yes—
737C2×C4C23×D411yescharacteristic
738C2×C4C23×D416yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C23×D416yes—
741C2×C4C23×D411yescharacteristic
742C2×C4C23×D411yescharacteristic
743C2×C4C23×D416yes—
744C2×C4C23×D411yescharacteristic
745C2×C4C22×#41112yes—
746C2×C4C22×#4112yes—
747C2×C4C2611yescharacteristic
748C8—28no—
749C8C24×C4116yes—
750C22—21no—
751C22—26no—
752C22—21no—
753C22—26no—
754C22—24no—
755C22—28no—
756C22—412no—
757C22—48no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—42no—
762C22—824no—
763C22C22×C4×D412yes—
764C22C22×C4×D4112yes—
765C22C24×D411yescharacteristic
766C4—21no—
767C4—26no—
768C4—21no—
769C4—21no—
770C4—26no—
771C4—28no—
772C4—212no—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—46no—
777C4C22×C4×D412yes—
778C4C22×C4×D4112yes—
779C4#358612yesdirect product factor
780C4C25×C411yescharacteristic
781C4C23×#4111yescharacteristic
782C2—22no—
783C2—212no—
784C2—44no—
785C2—48no—
786C2C23×C4×D411yescharacteristic
787C2C2×#358611yescharacteristic
788C2#6309011yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC4C25×C4
Frattini, cosocleC2×C4C26
socleC22C24×D4
prime radicalC2×#3586C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#585C2semidirect
3. C2×C4×2−1+4C2semidirect
4. #60175C2semidirect
5. #60174C2semidirect
6. C4×#578C2semidirect
7. C4×#577C2semidirect
8. #60170C2semidirect
9. #60169C2semidirect
10. C4×#575C2semidirect
11. C2×C4×#137C2semidirect
12. #60109C2semidirect
13. #60089C2semidirect
14. #60088C2semidirect
15. C4×#568C2semidirect
18. #3586C4direct (N × H)
29. C4×2−1+4C22semidirect
30. C4×2−1+4C22semidirect
31. C4×2−1+4C22semidirect
32. C4×2−1+4C22semidirect
35. C4×H(5,𝔽2)C22semidirect
36. C4×H(5,𝔽2)C22semidirect
42. C2×#520C22semidirect
44. C2×#519C22semidirect
49. C2×C4×#41C22semidirect
51. C22×C4×Q8C22semidirect
52. #2952C22semidirect
53. #2951C22semidirect
54. #2950C22semidirect
55. #2949C22semidirect
56. #2947C22semidirect
57. #2947C22semidirect
58. #2947C22semidirect
59. #2946C22semidirect
60. C4×#137C22semidirect
61. C4×#137C22semidirect
62. C4×#137C22semidirect
63. C4×#137C22semidirect
64. C4×#137C22semidirect
65. C4×#137C22semidirect
66. C4×#137C22semidirect
67. C4×AGL(1,ℤ/8)C22semidirect
68. C4×AGL(1,ℤ/8)C22semidirect
69. C4×AGL(1,ℤ/8)C22semidirect
70. C4×AGL(1,ℤ/8)C22semidirect
71. #2943C22semidirect
72. C2×#441C22semidirect
73. C2×#440C22semidirect
74. C4×#135C22semidirect
75. C2×C4×Q16C22semidirect
76. C2×C4×SD16C22semidirect
77. #2913C22semidirect
78. #2912C22semidirect
79. #2911C22semidirect
80. C2×#428C22semidirect
81. #2898C22semidirect
82. #2898C22semidirect
83. #2898C22semidirect
84. #2897C22semidirect
86. #2896C22semidirect
88. C2×#419C22semidirect
89. #2875C22semidirect
90. C4×#131C22semidirect
91. #2873C22semidirect
92. C2×C4×M16C22semidirect
94. #585C2×C4semidirect
98. C2×2−1+4C2×C4semidirect
110. #578C2×C4semidirect
111. #577C2×C4semidirect
112. #575C2×C4semidirect
113. C2×#137C2×C4semidirect
123. #568C2×C4semidirect
286. 2−1+4C22×C4semidirect
287. 2−1+4C22×C4semidirect
290. H(5,𝔽2)C22×C4semidirect
303. C2×#41C22×C4semidirect
316. C22×Q8C22×C4semidirect
338. #137C22×C4semidirect
339. #137C22×C4semidirect
340. #137C22×C4semidirect
341. AGL(1,ℤ/8)C22×C4semidirect
342. AGL(1,ℤ/8)C22×C4semidirect
343. #135C22×C4semidirect
344. C2×Q16C22×C4semidirect
346. C2×SD16C22×C4semidirect
351. #131C22×C4semidirect
353. C2×M16C22×C4semidirect
779. C4#3586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35862
C4×#5852
C2×C4×2−1+42
#601752
#601742
C4×#5782
C4×#5772
#601702
#601692
C4×#5752
C2×C4×#1372
#601092
#600892
#600882
C4×#5682