Finite Group Databasebeta

← C2×#31028 #7503172

Subgroups — C2×#31028 #7503172

Order 512.

3702 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic, complemented
4C2×#2408C211yesmaximal, characteristic
5#31028C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic, complemented
14C2×#1934C211yesmaximal, characteristic, complemented
15C2×#1875C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic, complemented
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#120—21no—
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic, complemented
27C2×#482—28no—
28C2×#482C2218yescomplemented
29C2×#450—28no—
30C2×#450C2218yescomplemented
31C22×#107C2211yescharacteristic, complemented
32C22×#106C2211yescharacteristic, complemented
33C22×C4⋊C8C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C22×#103C2211yescharacteristic, complemented
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic, complemented
45C22×C22⋊C8C2211yescharacteristic, complemented
46C22×C4×C8C2211yescharacteristic, complemented
47#2415—24no—
48#2415C2218yescomplemented
49#2408—24no—
50#2408C2218yes—
51C2×#397—21no—
52C2×#394—21no—
53C2×#394—21no—
54C2×#392—21no—
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389—21no—
59C2×#389C2211yescharacteristic, complemented
60C2×#388—21no—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#379—21no—
64#2077C2218yescomplemented
65#2067C2218yescomplemented
66#2055C2218yescomplemented
67#2036C2218yescomplemented
68#2000C2218yescomplemented
69#2000C2218yescomplemented
70#1968C2218yescomplemented
71#1954C2218yescomplemented
72#1934C2218yescomplemented
73#1875C2218yescomplemented
74#1786C2218yescomplemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8C2311yescharacteristic
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—21no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4—22no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4D411yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2314yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16C2314yes—
104C22×SD16C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8C2314yes—
116C2×C22⋊Q8C2314yescomplemented
117C2×#121—22no—
118C2×#121—22no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—42no—
122C2×#121—42no—
123C2×#121C2314yes—
124C2×#121C2314yes—
125C2×#120—28no—
126C2×#120—48no—
127C2×C4×D4—42no—
128C2×C4×D4—42no—
129C2×C4×D4D414yes—
130C2×C4×D4C2314yes—
131C2×#117—22no—
132C2×#117—24no—
133C2×#117—42no—
134C2×#117C2314yescomplemented
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4D411yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4D411yescharacteristic
156C22×C22⋊C4D411yescharacteristic
157C22×C42—21no—
158C22×C42C2311yescharacteristic
159#482—232no—
160#450—232no—
161C2×#107—24no—
162C2×#107C2314yescomplemented
163C2×#106—24no—
164C2×#106C2314yescomplemented
165C2×C4⋊C8—42no—
166C2×C4⋊C8C2314yescomplemented
167C2×#103—42no—
168C2×#103—42no—
169C2×#103C2314yescomplemented
170C2×#103C2314yescomplemented
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102—42no—
176C2×#102D418yescomplemented
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8—24no—
184C2×C22⋊C8—24no—
185C2×C22⋊C8—42no—
186C2×C22⋊C8—42no—
187C2×C22⋊C8C2314yes—
188C2×C22⋊C8C2314yes—
189C2×C22⋊C8C2314yescomplemented
190C2×C22⋊C8C2314yescomplemented
191C2×C4×C8—42no—
192C2×C4×C8C2314yescomplemented
193#397—28no—
194#394—28no—
195#394—28no—
196#392—28no—
197#391—22no—
198#391C2314yescomplemented
199#390—22no—
200#390—22no—
201#390C2314yes—
202#390C2314yes—
203#389—28no—
204#389—22no—
205#389C2314yescomplemented
206#388—28no—
207#380—22no—
208#380—22no—
209#380C2314yes—
210#380C2314yes—
211#379—28no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217#340C2314yescomplemented
218#340C2314yescomplemented
219#340C2314yescomplemented
220#340C2314yescomplemented
221C25—21no—
222C25—21no—
223C25—24no—
224C25—44no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—44no—
229C25—82no—
230C25—82no—
231C25C2×D411yescharacteristic
232C25C2×D411yescharacteristic
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8C2412yes—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—24no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—48no—
265C22×D4—48no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—48no—
271C22×D4—416no—
272C22×D4—416no—
273C22×D4—416no—
274C22×D4—416no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4—44no—
279C22×D4—82no—
280C22×D4—82no—
281C22×D4C2×D414yes—
282C22×D4C2×D414yes—
283C22×D4#4114yes—
284C22×D4C2412yes—
285C22×D4C2412yes—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16—44no—
317C2×SD16—44no—
318C2×SD16—44no—
319C2×SD16—416no—
320C2×SD16—416no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8C2×D414yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C22×C8C2412yes—
337C22⋊Q8—28no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343#121—28no—
344#121—28no—
345#121—44no—
346#121—44no—
347#121—48no—
348#121—48no—
349#120—432no—
350C4×D4—48no—
351C4×D4—44no—
352C4×D4—44no—
353#117—28no—
354#117—44no—
355#117—48no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—82no—
407C2×C22⋊C4—82no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—44no—
414C2×C42C2×D412yes—
415C2×C42C2412yes—
416#107—28no—
417#106—28no—
418C4⋊C8—44no—
419#103—44no—
420#103—44no—
421#102—28no—
422#102—28no—
423#102—44no—
424#102—44no—
425#102—44no—
426#102C2×D4116yescomplemented
427C22⋊C8—28no—
428C22⋊C8—28no—
429C22⋊C8—44no—
430C22⋊C8—44no—
431C4×C8—44no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—432no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—48no—
472C24—84no—
473C24—84no—
474C24—816no—
475C24—816no—
476C24—816no—
477C24—816no—
478C24—816no—
479C24—816no—
480C24#13514yes—
481C24C22×D412yes—
482C24C22×D412yes—
483C24C22×D411yescharacteristic
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—24no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—24no—
504C2×D4—28no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—44no—
516C2×D4—416no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—416no—
521C2×D4—416no—
522C2×D4—416no—
523C2×D4—432no—
524C2×D4—464no—
525C2×D4—416no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—84no—
539C2×D4—84no—
540C2×D4—816no—
541C2×D4—816no—
542C2×D4C22×D414yes—
543C2×D4C2×#4114yes—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4AGL(1,ℤ/8)14yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C2×#4112yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4C2511yescharacteristic
618SD16—416no—
619SD16—416no—
620C2×C8—28no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—44no—
633C2×C8—44no—
634C2×C8—44no—
635C2×C8C22×D414yes—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—44no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—48no—
654C4⋊C4C22×D414yes—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—84no—
667C22⋊C4—84no—
668C42—24no—
669C42—22no—
670C42—22no—
671C42—48no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—28no—
677C23—28no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—432no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—48no—
700C23—48no—
701C23—44no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—48no—
706C23—44no—
707C23—48no—
708C23—44no—
709C23—48no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—44no—
715C23—48no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—816no—
721C23—816no—
722C23—816no—
723C23—816no—
724C23—816no—
725C23—8128no—
726C23—816no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23#53412yes—
736C23D4212yes—
737C23#54612yes—
738C23C2×#13514yes—
739C23C2×#13512yes—
740C23C2×AGL(1,ℤ/8)12yes—
741C23#57712yes—
742C23#57712yes—
743C23C23×D411yescharacteristic
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—84no—
749D4—24no—
750D4—24no—
751D4—24no—
752D4—24no—
753D4—416no—
754D4—432no—
755D4—48no—
756D4—48no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—816no—
762D4—816no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—48no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4#53412yes—
813C2×C4#53514yes—
814C2×C4#53814yes—
815C2×C4D4212yes—
816C2×C4#54612yes—
817C2×C4#54614yes—
818C2×C4#56014yes—
819C2×C4C2×AGL(1,ℤ/8)14yes—
820C2×C4C23×D411yescharacteristic
821C2×C4C22×#4111yescharacteristic
822C2×C4C2×H(5,𝔽2)11yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×H(5,𝔽2)11yescharacteristic
826C8—24no—
827C8—42no—
828C8—42no—
829C8—42no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—416no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—44no—
851C22—864no—
852C22—88no—
853C22—816no—
854C22—816no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22#267814yes—
864C22#318814yes—
865C22#320014yes—
866C22#327214yes—
867C22#328214yes—
868C22#329614yes—
869C22#332414yes—
870C22C2×#53411yescharacteristic
871C22C2×D4211yescharacteristic
872C22C2×#54611yescharacteristic
873C22C22×#13511yescharacteristic
874C22C22×AGL(1,ℤ/8)11yescharacteristic
875C22C2×#57711yescharacteristic
876C22C2×#57711yescharacteristic
877C4—24no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4#267814yes—
888C4C2×#53511yescharacteristic
889C4C2×#53811yescharacteristic
890C4C2×#54611yescharacteristic
891C4C2×#56011yescharacteristic
892C2—44no—
893C2—82no—
894C2—84no—
895C2—84no—
896C2#3102818yesdirect product factor
897C2C2×#267811yescharacteristic
898C2C2×#318811yescharacteristic
899C2C2×#320011yescharacteristic
900C2C2×#327211yescharacteristic
901C2C2×#328211yescharacteristic
902C2C2×#329611yescharacteristic
903C2C2×#332411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#482C2semidirect
2. C22×#450C2semidirect
3. C2×#2415C2semidirect
5. #31028C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2067C2semidirect
8. C2×#2055C2semidirect
9. C2×#2036C2semidirect
10. C2×#2000C2semidirect
11. C2×#2000C2semidirect
12. C2×#1968C2semidirect
13. C2×#1954C2semidirect
14. C2×#1934C2semidirect
15. C2×#1875C2semidirect
16. C2×#1786C2semidirect
21. C22×C22⋊Q8C22semidirect
26. C22×#117C22semidirect
28. C2×#482C22semidirect
30. C2×#450C22semidirect
31. C22×#107C22semidirect
32. C22×#106C22semidirect
33. C22×C4⋊C8C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×C22⋊C8C22semidirect
45. C22×C22⋊C8C22semidirect
46. C22×C4×C8C22semidirect
48. #2415C22semidirect
55. C2×#391C22semidirect
59. C2×#389C22semidirect
64. #2077C22semidirect
65. #2067C22semidirect
66. #2055C22semidirect
67. #2036C22semidirect
68. #2000C22semidirect
69. #2000C22semidirect
70. #1968C22semidirect
71. #1954C22semidirect
72. #1934C22semidirect
73. #1875C22semidirect
74. #1786C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
116. C2×C22⋊Q8C23semidirect
134. C2×#117C23semidirect
162. C2×#107C23semidirect
164. C2×#106C23semidirect
166. C2×C4⋊C8C23semidirect
169. C2×#103C23semidirect
170. C2×#103C23semidirect
176. C2×#102D4semidirect
189. C2×C22⋊C8C23semidirect
190. C2×C22⋊C8C23semidirect
192. C2×C4×C8C23semidirect
198. #391C23semidirect
205. #389C23semidirect
217. #340C23semidirect
218. #340C23semidirect
219. #340C23semidirect
220. #340C23semidirect
426. #102C2×D4semidirect
896. C2#31028direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4822
C22×#4502
C2×#24152
C2×#24082
#310282
C2×#20772
C2×#20672
C2×#20552
C2×#20362
C2×#20002
C2×#19682
C2×#19542
C2×#19342
C2×#18752
C2×#17862