Finite Group Databasebeta

← C2×#30617 #7501255

Subgroups — C2×#30617 #7501255

Order 512.

2612 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C22×#461C211yesmaximal, characteristic, complemented
3C2×#2429C211yesmaximal, characteristic, complemented
4C2×#2422C211yesmaximal, characteristic
5#30617C2116yesmaximal, direct product factor
6C2×#2095C211yesmaximal, characteristic, complemented
7C2×#2086C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2043C211yesmaximal, characteristic, complemented
10C2×#2036C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic
12C2×#1894C211yesmaximal, characteristic, complemented
13C2×#1880C211yesmaximal, characteristic, complemented
14C2×#1862C211yesmaximal, characteristic, complemented
15C2×#1851C211yesmaximal, characteristic, complemented
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#123—21no—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#468—28no—
28C2×#468C2218yes—
29C2×#461—28no—
30C2×#461C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#107C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2429—24no—
45#2429C2218yescomplemented
46#2422—24no—
47#2422C2218yes—
48C2×#398—21no—
49C2×#397—21no—
50C2×#396—21no—
51C2×#394—21no—
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389—21no—
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#385—21no—
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2095C2218yescomplemented
63#2086C2218yescomplemented
64#2055C2218yescomplemented
65#2043C2218yescomplemented
66#2036C2218yescomplemented
67#2000C2218yes—
68#1894C2218yescomplemented
69#1880C2218yescomplemented
70#1862C2218yescomplemented
71#1851C2218yescomplemented
72#1803C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4C2311yescharacteristic
85C22×SD16—24no—
86C22×SD16—42no—
87C22×SD16—42no—
88C22×SD16—42no—
89C22×SD16—42no—
90C22×SD16D418yes—
91C22×SD16C2314yes—
92C22×SD16C2314yes—
93C22×M16—24no—
94C22×M16—42no—
95C22×M16—42no—
96C22×M16C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—22no—
103C2×C4⋊Q8—42no—
104C2×C4⋊Q8C2314yes—
105C2×#123—28no—
106C2×#123—48no—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8C2314yes—
114C2×C22⋊Q8C2314yes—
115C2×#121—22no—
116C2×#121—24no—
117C2×#121—42no—
118C2×#121C2314yes—
119C2×C4×Q8—22no—
120C2×C4×Q8—24no—
121C2×C4×Q8—42no—
122C2×C4×Q8C2314yes—
123C2×C4×D4—24no—
124C2×C4×D4—22no—
125C2×C4×D4—42no—
126C2×C4×D4C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4D411yescharacteristic
149C22×C22⋊C4D411yescharacteristic
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#468—232no—
154#461—232no—
155C2×#107—24no—
156C2×#107—42no—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8—42no—
161C2×C4⋊C8C2314yes—
162C2×C4⋊C8C2314yes—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102—24no—
176C2×#102—24no—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181#398—28no—
182#397—28no—
183#396—28no—
184#394—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389—28no—
192#389C2314yes—
193#389C2314yes—
194#388—28no—
195#385—28no—
196#384—22no—
197#384C2314yes—
198#380—22no—
199#380C2314yes—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—21no—
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×Q8C2×D414yes—
231C22×Q8C2412yes—
232C22×Q8C2412yes—
233C22×D4—24no—
234C22×D4—21no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—82no—
243C22×D4C2×D414yes—
244C22×D4C2412yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—24no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—82no—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C2×SD16—28no—
271C2×SD16—416no—
272C2×SD16—44no—
273C2×SD16—44no—
274C2×SD16—44no—
275C2×SD16—44no—
276C2×SD16—416no—
277C2×SD16C2×D4116yes—
278C2×M16—28no—
279C2×M16—44no—
280C2×M16—44no—
281C2×M16—416no—
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×C8—22no—
292C22×C8—22no—
293C22×C8C2×D414yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C4⋊Q8—28no—
299C4⋊Q8—44no—
300C4⋊Q8—48no—
301#123—432no—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—48no—
307C22⋊Q8—48no—
308#121—28no—
309#121—44no—
310#121—48no—
311C4×Q8—28no—
312C4×Q8—44no—
313C4×Q8—48no—
314C4×D4—28no—
315C4×D4—44no—
316C4×D4—48no—
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—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
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⋊C4#4114yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
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—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4C2×D414yes—
372C2×C22⋊C4C2×D414yes—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—44no—
379C2×C42C2×D412yes—
380C2×C42C2×D412yes—
381C2×C42C2412yes—
382C2×C42C2412yes—
383#107—28no—
384#107—44no—
385C4⋊C8—28no—
386C4⋊C8—44no—
387#103—28no—
388#103—28no—
389#103—28no—
390#103—44no—
391#103—44no—
392#103—44no—
393#102—28no—
394#102—28no—
395C22⋊C8—44no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95C2×D414yes—
402#95C2×D414yes—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24C22×D412yes—
419C24C22×D411yescharacteristic
420C2×Q8—24no—
421C2×Q8—22no—
422C2×Q8—28no—
423C2×Q8—28no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—44no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8C22×D414yes—
446C2×D4—28no—
447C2×D4—24no—
448C2×D4—28no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—42no—
457C2×D4—44no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—84no—
461C2×D4—816no—
462C2×D4C22×D414yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—48no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
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—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—48no—
519C22×C4—84no—
520C22×C4—816no—
521C22×C4AGL(1,ℤ/8)14yes—
522C22×C4#13714yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C2×#4112yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C42−1+412yes—
535C22×C4C2511yescharacteristic
536SD16—416no—
537SD16—416no—
538M16—416no—
539C2×C8—28no—
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—22no—
550C2×C8—22no—
551C2×C8—44no—
552C2×C8—44no—
553C2×C8—44no—
554C2×C8C22×D414yes—
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—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—84no—
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—48no—
588C42—24no—
589C42—24no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—48no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—48no—
606C23—42no—
607C23—42no—
608C23—44no—
609C23—44no—
610C23—48no—
611C23—44no—
612C23—44no—
613C23—48no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—84no—
620C23—84no—
621C23—84no—
622C23—84no—
623C23#53712yes—
624C23D4212yes—
625C23#54612yes—
626C23C2×AGL(1,ℤ/8)12yes—
627C23C2×#13712yes—
628C23#57712yes—
629C23#57812yes—
630C23C23×D411yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—48no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—84no—
641D4—24no—
642D4—24no—
643D4—48no—
644D4—42no—
645D4—42no—
646D4—816no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—48no—
666C2×C4—44no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—48no—
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—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—816no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4#53414yes—
700C2×C4#53712yes—
701C2×C4#54014yes—
702C2×C4D4212yes—
703C2×C4#54612yes—
704C2×C4#54714yes—
705C2×C4#56214yes—
706C2×C4C2×AGL(1,ℤ/8)14yes—
707C2×C4C2×#13714yes—
708C2×C4C23×D411yescharacteristic
709C2×C4C22×#4111yescharacteristic
710C2×C4C2×H(5,𝔽2)11yescharacteristic
711C2×C4C2×H(5,𝔽2)11yescharacteristic
712C2×C4C2×H(5,𝔽2)11yescharacteristic
713C2×C4C2×2−1+411yescharacteristic
714C8—24no—
715C8—42no—
716C8—42no—
717C8—42no—
718C22—44no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—42no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—816no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22#267114yes—
735C22#325414yes—
736C22#325814yes—
737C22#326514yes—
738C22#327614yes—
739C22#332014yes—
740C22#333014yes—
741C22C2×#53711yescharacteristic
742C22C2×D4211yescharacteristic
743C22C2×#54611yescharacteristic
744C22C22×AGL(1,ℤ/8)11yescharacteristic
745C22C22×#13711yescharacteristic
746C22C2×#57711yescharacteristic
747C22C2×#57811yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—44no—
753C4—42no—
754C4—44no—
755C4—82no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4—82no—
760C4#267114yes—
761C4C2×#53411yescharacteristic
762C4C2×#54011yescharacteristic
763C4C2×#54711yescharacteristic
764C4C2×#56211yescharacteristic
765C2—82no—
766C2—84no—
767C2#3061718yesdirect product factor
768C2C2×#267111yescharacteristic
769C2C2×#325411yescharacteristic
770C2C2×#325811yescharacteristic
771C2C2×#326511yescharacteristic
772C2C2×#327611yescharacteristic
773C2C2×#332011yescharacteristic
774C2C2×#333011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#461C2semidirect
3. C2×#2429C2semidirect
5. #30617C2direct (N × H)
6. C2×#2095C2semidirect
7. C2×#2086C2semidirect
8. C2×#2055C2semidirect
9. C2×#2043C2semidirect
10. C2×#2036C2semidirect
12. C2×#1894C2semidirect
13. C2×#1880C2semidirect
14. C2×#1862C2semidirect
15. C2×#1851C2semidirect
16. C2×#1803C2semidirect
30. C2×#461C22semidirect
45. #2429C22semidirect
62. #2095C22semidirect
63. #2086C22semidirect
64. #2055C22semidirect
65. #2043C22semidirect
66. #2036C22semidirect
68. #1894C22semidirect
69. #1880C22semidirect
70. #1862C22semidirect
71. #1851C22semidirect
72. #1803C22semidirect
767. C2#30617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4612
C2×#24292
C2×#24222
#306172
C2×#20952
C2×#20862
C2×#20552
C2×#20432
C2×#20362
C2×#20002
C2×#18942
C2×#18802
C2×#18622
C2×#18512
C2×#18032