Finite Group Databasebeta

← C2×#24207 #6448795

Subgroups — C2×#24207 #6448795

Order 512.

3470 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic
2C22×#464C211yesmaximal, characteristic
3C22×#441C211yesmaximal, characteristic, complemented
4C2×#2582C211yesmaximal, characteristic, complemented
5#24207C2116yesmaximal, direct product factor
6C2×#2043C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic
8C2×#2016C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic
10C2×#1985C211yesmaximal, characteristic, complemented
11C2×#1959C211yesmaximal, characteristic
12C2×#1878C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C2×#556—28no—
21C2×#556—28no—
22C2×#556—24no—
23C2×#556C2218yes—
24C22×C4⋊Q8C2211yescharacteristic
25C22×#126—21no—
26C22×#126—21no—
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×C22⋊Q8—21no—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117—21no—
36C2×#464—28no—
37C2×#464C2218yes—
38C2×#441—28no—
39C2×#441C2218yescomplemented
40C22×#106C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×#102C2211yescharacteristic
52C22×#97C2211yescharacteristic
53#2582—24no—
54#2582C2218yescomplemented
55C2×#398—21no—
56C2×#398—21no—
57C2×#391—21no—
58C2×#391C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#389—21no—
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2043C2218yescomplemented
65#2042C2218yes—
66#2016C2218yescomplemented
67#2015C2218yes—
68#1985C2218yescomplemented
69#1959C2218yes—
70#1878C2218yescomplemented
71#1877C2218yes—
72#1865C2218yescomplemented
73#1864C2218yes—
74#1803C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8D411yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×Q8C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C22×Q16—24no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—24no—
92C22×Q16—42no—
93C22×Q16C2314yes—
94C22×Q16C2314yes—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—42no—
98C22×SD16C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103#556—264no—
104#556—232no—
105#556—232no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—22no—
109C2×C4⋊Q8C2314yes—
110C2×#126—216no—
111C2×#126—216no—
112C2×#126—28no—
113C2×#126—28no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—22no—
117C2×#124—22no—
118C2×#124—24no—
119C2×#124D418yes—
120C2×#124C2314yes—
121C2×#124C2314yes—
122C2×C22⋊Q8—216no—
123C2×C22⋊Q8—28no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8—24no—
127C2×C4×Q8—22no—
128C2×C4×Q8—22no—
129C2×C4×Q8—24no—
130C2×C4×Q8—24no—
131C2×C4×Q8—22no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8D418yes—
135C2×C4×Q8D414yes—
136C2×C4×Q8C2314yes—
137C2×C4×Q8C2314yes—
138C2×C4×Q8C2314yes—
139C2×C4×Q8C2314yes—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—22no—
143C2×C4×D4C2314yes—
144C2×#117—216no—
145C2×#117—28no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4D411yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C42—21no—
168C22×C42—21no—
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#464—232no—
174#441—232no—
175C2×#106—24no—
176C2×#106C2314yes—
177C2×C4⋊C8—24no—
178C2×C4⋊C8C2314yes—
179C2×#103—24no—
180C2×#103—24no—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—42no—
184C2×#103—42no—
185C2×#103—42no—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#102—24no—
194C2×#102—24no—
195C2×#102—42no—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#97—24no—
200C2×#97C2314yes—
201#398—28no—
202#398—28no—
203#391—28no—
204#391—22no—
205#391—22no—
206#391C2314yes—
207#391C2314yes—
208#389—28no—
209#389—22no—
210#389—22no—
211#389C2314yes—
212#389C2314yes—
213#384—22no—
214#384C2314yes—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—21no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—42no—
249C22×Q8C2×D414yes—
250C22×Q8C2×D414yes—
251C22×Q8C2×D414yes—
252C22×Q8#4114yes—
253C22×Q8C2412yes—
254C22×Q8C2412yes—
255C22×Q8C2412yes—
256C22×D4—21no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4C2×D414yes—
263C22×D4C2412yes—
264C23×C4—28no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—24no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2411yescharacteristic
282C2×Q16—232no—
283C2×Q16—28no—
284C2×Q16—28no—
285C2×Q16—28no—
286C2×Q16—28no—
287C2×Q16—28no—
288C2×Q16—44no—
289C2×Q16—416no—
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—44no—
293C2×SD16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8#4114yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—216no—
311C4⋊Q8—28no—
312C4⋊Q8—28no—
313#126—264no—
314#126—264no—
315#124—216no—
316#124—28no—
317#124—28no—
318#124—216no—
319#124—28no—
320#124C2×D4116yes—
321C22⋊Q8—264no—
322C4×Q8—216no—
323C4×Q8—28no—
324C4×Q8—28no—
325C4×Q8—216no—
326C4×Q8—216no—
327C4×Q8—28no—
328C4×Q8—28no—
329C4×Q8—28no—
330C4×Q8—28no—
331C4×Q8—28no—
332C4×Q8—48no—
333C4×Q8C2×D4116yes—
334C4×D4—216no—
335C4×D4—28no—
336C4×D4—28no—
337#117—264no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—82no—
368C2×C4⋊C4—82no—
369C2×C4⋊C4—82no—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C42—28no—
389C2×C42—28no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—44no—
398C2×C42C2×D412yes—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42C2×D414yes—
402C2×C42C2×D414yes—
403C2×C42C2412yes—
404C2×C42C2412yes—
405C2×C42C2412yes—
406#106—28no—
407C4⋊C8—28no—
408#103—28no—
409#103—28no—
410#103—28no—
411#103—28no—
412#103—44no—
413#103—44no—
414#103—44no—
415#102—28no—
416#102—28no—
417#102—44no—
418#97—28no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425C24—24no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24C22×D411yescharacteristic
434C2×Q8—28no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—28no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—44no—
461C2×Q8—416no—
462C2×Q8—42no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8C22×D414yes—
475C2×Q8C22×D414yes—
476C2×Q8C2×#4114yes—
477C2×D4—24no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4C22×D414yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—216no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—432no—
518C22×C4—48no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—48no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4#12014yes—
538C22×C4#12014yes—
539C22×C4#13714yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C42−1+412yes—
553C22×C4C2511yescharacteristic
554Q16—232no—
555Q16—416no—
556SD16—416no—
557C2×C8—28no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—44no—
570C2×C8—44no—
571C2×C8—44no—
572C2×C8C2×#4114yes—
573C4⋊C4—216no—
574C4⋊C4—216no—
575C4⋊C4—216no—
576C4⋊C4—216no—
577C4⋊C4—28no—
578C4⋊C4—24no—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—48no—
589C4⋊C4—42no—
590C4⋊C4—48no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—84no—
594C4⋊C4—84no—
595C4⋊C4—84no—
596C4⋊C4C22×D414yes—
597C22⋊C4—216no—
598C22⋊C4—216no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—216no—
602C42—216no—
603C42—216no—
604C42—24no—
605C42—24no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—48no—
611C42#12018yes—
612C42C22×D414yes—
613C42C22×D414yes—
614C23—24no—
615C23—48no—
616C23—42no—
617C23—42no—
618C23—48no—
619C23—48no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23C2×#12012yes—
629C23#54812yes—
630C23#55012yes—
631C23C2×#13712yes—
632C23#57512yes—
633C23#57712yes—
634C23#57812yes—
635C23C23×D411yescharacteristic
636Q8—24no—
637Q8—24no—
638Q8—24no—
639Q8—24no—
640Q8—24no—
641Q8—24no—
642Q8—416no—
643Q8—48no—
644Q8—48no—
645Q8—48no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—42no—
651Q8—42no—
652D4—24no—
653D4—24no—
654D4—48no—
655D4—42no—
656D4—42no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—432no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4C2×#12014yes—
708C2×C4C2×#12014yes—
709C2×C4C2×#12012yes—
710C2×C4#52514yes—
711C2×C4#53714yes—
712C2×C4#54614yes—
713C2×C4#54714yes—
714C2×C4#54812yes—
715C2×C4#55012yes—
716C2×C4C2×#13714yes—
717C2×C4C23×D411yescharacteristic
718C2×C4C23×D411yescharacteristic
719C2×C4C22×#4111yescharacteristic
720C2×C4C22×#4111yescharacteristic
721C2×C4C2×H(5,𝔽2)11yescharacteristic
722C2×C4C2×2−1+411yescharacteristic
723C8—24no—
724C8—42no—
725C8—42no—
726C8—42no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22—816no—
733C22—82no—
734C22—82no—
735C22#240714yes—
736C22#300714yes—
737C22#301314yes—
738C22#336914yes—
739C22#337714yes—
740C22#339814yes—
741C22#340114yes—
742C22C22×#12011yescharacteristic
743C22C2×#54811yescharacteristic
744C22C2×#55011yescharacteristic
745C22C22×#13711yescharacteristic
746C22C2×#57511yescharacteristic
747C22C2×#57711yescharacteristic
748C22C2×#57811yescharacteristic
749C4—24no—
750C4—24no—
751C4—24no—
752C4—44no—
753C4—44no—
754C4—44no—
755C4—42no—
756C4—44no—
757C4—42no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—82no—
762C4#240714yes—
763C4C2×#52511yescharacteristic
764C4C2×#53711yescharacteristic
765C4C2×#54611yescharacteristic
766C4C2×#54711yescharacteristic
767C2—84no—
768C2#2420718yesdirect product factor
769C2C2×#240711yescharacteristic
770C2C2×#300711yescharacteristic
771C2C2×#301311yescharacteristic
772C2C2×#336911yescharacteristic
773C2C2×#337711yescharacteristic
774C2C2×#339811yescharacteristic
775C2C2×#340111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#441C2semidirect
4. C2×#2582C2semidirect
5. #24207C2direct (N × H)
6. C2×#2043C2semidirect
8. C2×#2016C2semidirect
10. C2×#1985C2semidirect
12. C2×#1878C2semidirect
14. C2×#1865C2semidirect
16. C2×#1803C2semidirect
39. C2×#441C22semidirect
54. #2582C22semidirect
64. #2043C22semidirect
66. #2016C22semidirect
68. #1985C22semidirect
70. #1878C22semidirect
72. #1865C22semidirect
74. #1803C22semidirect
768. C2#24207direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5562
C22×#4642
C22×#4412
C2×#25822
#242072
C2×#20432
C2×#20422
C2×#20162
C2×#20152
C2×#19852
C2×#19592
C2×#18782
C2×#18772
C2×#18652
C2×#18642
C2×#18032