Finite Group Databasebeta

← C2×#28568 #6459489

Subgroups — C2×#28568 #6459489

Order 512.

2630 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#470C211yesmaximal, characteristic, complemented
2C22×#436C211yesmaximal, characteristic
3C2×#2415C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic
5#28568C2116yesmaximal, direct product factor
6C2×#2088C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2056C211yesmaximal, characteristic, complemented
9C2×#2001C211yesmaximal, characteristic, complemented
10C2×#1933C211yesmaximal, characteristic, complemented
11C2×#1933C211yesmaximal, characteristic, complemented
12C2×#1894C211yesmaximal, characteristic, complemented
13C2×#1894C211yesmaximal, characteristic, complemented
14C2×#1873C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C2×#1736C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#470—28no—
28C2×#470C2218yescomplemented
29C2×#436—28no—
30C2×#436C2218yes—
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2417—24no—
43#2417C2218yes—
44#2415—24no—
45#2415C2218yes—
46C2×#398—21no—
47C2×#397—21no—
48C2×#396—21no—
49C2×#394—21no—
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#389—21no—
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#386—21no—
57C2×#380—21no—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60#2088C2218yescomplemented
61#2077C2218yescomplemented
62#2056C2218yescomplemented
63#2001C2218yescomplemented
64#1933C2218yescomplemented
65#1933C2218yescomplemented
66#1894C2218yescomplemented
67#1894C2218yescomplemented
68#1873C2218yescomplemented
69#1872C2218yescomplemented
70#1736C2218yescomplemented
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4D411yescharacteristic
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×Q16—24no—
86C22×Q16—42no—
87C22×Q16—42no—
88C22×Q16C2314yes—
89C22×M16—24no—
90C22×M16—42no—
91C22×M16—42no—
92C22×M16—42no—
93C22×M16—42no—
94C22×M16D418yes—
95C22×M16C2314yes—
96C22×M16C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C2×C22⋊Q8—22no—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8C2314yes—
114C2×C22⋊Q8C2314yes—
115C2×C22⋊Q8C2314yes—
116C2×C22⋊Q8C2314yes—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4D414yes—
120C2×C4×D4C2314yes—
121C2×#117—22no—
122C2×#117—24no—
123C2×#117—42no—
124C2×#117C2314yes—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—22no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4D411yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
151C22×C22⋊C4D411yescharacteristic
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154#470—232no—
155#436—232no—
156C2×#106—24no—
157C2×#106C2314yes—
158C2×C4⋊C8—24no—
159C2×C4⋊C8C2314yes—
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×C22⋊C8—24no—
173C2×C22⋊C8—24no—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176C2×C4×C8—24no—
177C2×C4×C8C2314yes—
178#398—28no—
179#397—28no—
180#396—28no—
181#394—28no—
182#391—22no—
183#391—22no—
184#391C2314yes—
185#391C2314yes—
186#389—28no—
187#389—22no—
188#389—22no—
189#389C2314yes—
190#389C2314yes—
191#388—28no—
192#386—28no—
193#380—22no—
194#380—22no—
195#380—28no—
196#380C2314yes—
197#380C2314yes—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206#340C2314yes—
207#340C2314yes—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214C25C2×D411yescharacteristic
215C25C2×D411yescharacteristic
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8C2412yes—
231C22×Q8C2412yes—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—42no—
235C22×D4C2×D414yes—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—24no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—82no—
258C23×C4C2×D412yes—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D412yes—
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D414yes—
264C23×C4C2×D411yescharacteristic
265C23×C4#4114yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C2×Q16—28no—
270C2×Q16—44no—
271C2×Q16—44no—
272C2×Q16—416no—
273C2×M16—28no—
274C2×M16—416no—
275C2×M16—44no—
276C2×M16—44no—
277C2×M16—44no—
278C2×M16—44no—
279C2×M16—416no—
280C2×M16C2×D4116yes—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8C2×D414yes—
292C22×C8C2×D414yes—
293C22×C8C2412yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22⋊Q8—28no—
298C22⋊Q8—28no—
299C22⋊Q8—28no—
300C22⋊Q8—28no—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—48no—
306C22⋊Q8—48no—
307C22⋊Q8—48no—
308C22⋊Q8—48no—
309C4×D4—216no—
310C4×D4—28no—
311C4×D4—28no—
312#117—28no—
313#117—44no—
314#117—48no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—48no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—82no—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4#4114yes—
351C2×C4⋊C4#4114yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—44no—
380C2×C42C2×D412yes—
381C2×C42C2412yes—
382#106—28no—
383C4⋊C8—28no—
384#103—28no—
385#103—28no—
386#103—28no—
387#103—28no—
388#103—44no—
389#103—44no—
390C22⋊C8—28no—
391C22⋊C8—28no—
392C4×C8—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24#12114yes—
415C24C22×D412yes—
416C24C22×D412yes—
417C24C22×D411yescharacteristic
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—44no—
447C2×D4—416no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—48no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—48no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—84no—
516C22×C4—816no—
517C22×C4#12114yes—
518C22×C4#12118yes—
519C22×C4#13714yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D412yes—
527C22×C4C2×#4114yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4C2×#4112yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4C2511yescharacteristic
534Q16—416no—
535M16—416no—
536M16—416no—
537C2×C8—28no—
538C2×C8—28no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—44no—
550C2×C8—44no—
551C2×C8C22×D414yes—
552C2×C8C22×D414yes—
553C4⋊C4—28no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—48no—
576C4⋊C4—84no—
577C4⋊C4C2×#4114yes—
578C4⋊C4C2×#4114yes—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—84no—
588C42—24no—
589C42—22no—
590C42—22no—
591C42—48no—
592C23—22no—
593C23—22no—
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23C2×#12114yes—
620C23C2×#12112yes—
621C23#54612yes—
622C23#54612yes—
623C23C2×#13712yes—
624C23#57512yes—
625C23#57712yes—
626C23#57812yes—
627C23C23×D411yescharacteristic
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—42no—
632Q8—42no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—84no—
637Q8—84no—
638D4—416no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—216no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—48no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—48no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—816no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C2×#12114yes—
697C2×C4C2×#12112yes—
698C2×C4#53214yes—
699C2×C4#53414yes—
700C2×C4#54612yes—
701C2×C4#54612yes—
702C2×C4#55314yes—
703C2×C4#55314yes—
704C2×C4C2×#13714yes—
705C2×C4C23×D411yescharacteristic
706C2×C4C22×#4111yescharacteristic
707C2×C4C22×#4111yescharacteristic
708C2×C4C22×#4111yescharacteristic
709C2×C4C2×H(5,𝔽2)11yescharacteristic
710C2×C4C2×H(5,𝔽2)11yescharacteristic
711C8—24no—
712C8—24no—
713C8—42no—
714C8—42no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—416no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—88no—
731C22#254314yes—
732C22#305614yes—
733C22#306314yes—
734C22#332314yes—
735C22#332714yes—
736C22#332814yes—
737C22#333114yes—
738C22C22×#12111yescharacteristic
739C22C2×#54611yescharacteristic
740C22C2×#54611yescharacteristic
741C22C22×#13711yescharacteristic
742C22C2×#57511yescharacteristic
743C22C2×#57711yescharacteristic
744C22C2×#57811yescharacteristic
745C4—24no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—44no—
750C4—44no—
751C4—82no—
752C4—82no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4#254314yes—
758C4C2×#53211yescharacteristic
759C4C2×#53411yescharacteristic
760C4C2×#55311yescharacteristic
761C4C2×#55311yescharacteristic
762C2—44no—
763C2—82no—
764C2#2856818yesdirect product factor
765C2C2×#254311yescharacteristic
766C2C2×#305611yescharacteristic
767C2C2×#306311yescharacteristic
768C2C2×#332311yescharacteristic
769C2C2×#332711yescharacteristic
770C2C2×#332811yescharacteristic
771C2C2×#333111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
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×#470C2semidirect
5. #28568C2direct (N × H)
6. C2×#2088C2semidirect
7. C2×#2077C2semidirect
8. C2×#2056C2semidirect
9. C2×#2001C2semidirect
10. C2×#1933C2semidirect
11. C2×#1933C2semidirect
12. C2×#1894C2semidirect
13. C2×#1894C2semidirect
14. C2×#1873C2semidirect
15. C2×#1872C2semidirect
16. C2×#1736C2semidirect
28. C2×#470C22semidirect
60. #2088C22semidirect
61. #2077C22semidirect
62. #2056C22semidirect
63. #2001C22semidirect
64. #1933C22semidirect
65. #1933C22semidirect
66. #1894C22semidirect
67. #1894C22semidirect
68. #1873C22semidirect
69. #1872C22semidirect
70. #1736C22semidirect
764. C2#28568direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4702
C22×#4362
C2×#24152
C2×#24172
#285682
C2×#20882
C2×#20772
C2×#20562
C2×#20012
C2×#19332
C2×#18942
C2×#18732
C2×#18722
C2×#17362