Finite Group Databasebeta

← #732511

Subgroups — #732511

Order 512.

2682 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic
2C2×#2566C211yesmaximal, characteristic
3C2×#2642C211yesmaximal, characteristic, complemented
4C2×#2365C211yesmaximal, characteristic, complemented
5#16595C214yesmaximal, complemented
6#15796C214yesmaximal, complemented
7#15787C214yesmaximal, complemented
8#15241C211yesmaximal, characteristic, complemented
9#15217C211yesmaximal, characteristic
10#15217C211yesmaximal, characteristic
11#15185C211yesmaximal, characteristic, complemented
12#14853C214yesmaximal, complemented
13#14160C211yesmaximal, characteristic, complemented
14#14026C211yesmaximal, characteristic
15#14026C211yesmaximal, characteristic
16#13942C211yesmaximal, characteristic, complemented
17#13926C211yesmaximal, characteristic, complemented
18#13848C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#2642—28no—
28#2566—28no—
29#2547—28no—
30C2×#400C2214yes—
31C2×#400C2214yes—
32C2×#397C2214yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35#2365—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2212yes—
49C2×#387C2212yes—
50C2×#387C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2214yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×#376C2211yescharacteristic
63#1445C2214yes—
64#1444C2212yes—
65#1443C2214yes—
66#1443C2214yes—
67#1442C2214yes—
68#1442C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1437C2214yes—
81#1437C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8D418yes—
102C2×#125—24no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—42no—
110C2×#124—42no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—42no—
116C2×C4×Q8—42no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157#400—216no—
158#400—216no—
159#397—216no—
160#396—28no—
161#396—28no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—24no—
169#391—24no—
170#390—24no—
171#390—24no—
172#390—24no—
173#390—24no—
174#389—28no—
175#387—28no—
176#387—28no—
177#385—28no—
178#385—28no—
179#384—24no—
180#382—24no—
181#380—216no—
182C4×C4⋊C4—28no—
183C4×C4⋊C4—24no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—42no—
186C4×C4⋊C4—42no—
187C4×C4⋊C4D418yes—
188#376—24no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C25C2412yes—
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×Q8—22no—
231C22×Q8—22no—
232C22×Q8C2×D414yes—
233C22×Q8C2×D414yes—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4#4114yes—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C4⋊Q8—232no—
265#125—416no—
266#124—416no—
267#124—416no—
268C4×Q8—416no—
269C4×Q8—416no—
270C4×D4—416no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C2×D418yes—
317C2×C4⋊C4C2×D418yes—
318C2×C4⋊C4C2×D414yes—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4#4114yes—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—44no—
368C2×C42C2×D414yes—
369C2×C42C2×D414yes—
370C2×C42C2×D414yes—
371C2×C42C2×D414yes—
372C2×C42#4114yes—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—28no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—24no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—42no—
400#95—42no—
401#95C2×D414yes—
402#95C2×D414yes—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24—22no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24C2×#4114yes—
414C24C2511yescharacteristic
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
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—22no—
473C22×C4—22no—
474C22×C4—22no—
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—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—416no—
520C22×C4—48no—
521C22×C4—84no—
522C22×C4—84no—
523C22×C4—88no—
524C22×C4C22×D414yes—
525C22×C4C22×D414yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C42−1+414yes—
544C22×C42−1+412yes—
545C4⋊C4—216no—
546C4⋊C4—216no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—84no—
562C4⋊C4—84no—
563C22⋊C4—416no—
564C22⋊C4—416no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—84no—
569C22⋊C4—84no—
570C22⋊C4—88no—
571C22⋊C4—88no—
572C42—28no—
573C42—28no—
574C42—48no—
575C42—48no—
576C42—48no—
577C42—44no—
578C42—44no—
579C42—44no—
580C42—44no—
581C42#121116yes—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—28no—
586C23—28no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—44no—
594C23—44no—
595C23—42no—
596C23—42no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23C23×D411yescharacteristic
606C23C23×D411yescharacteristic
607C23C22×#4111yescharacteristic
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C2×H(5,𝔽2)11yescharacteristic
611C23C2×2−1+412yes—
612C23C2×2−1+411yescharacteristic
613C23#58512yes—
614C23#58512yes—
615C23#58512yes—
616Q8—416no—
617Q8—416no—
618D4—416no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—44no—
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—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—816no—
714C2×C4C2×#12114yes—
715C2×C4C2×#12114yes—
716C2×C4C2×#12114yes—
717C2×C4#52914yes—
718C2×C4#53614yes—
719C2×C4#54214yes—
720C2×C4#54614yes—
721C2×C4#54614yes—
722C2×C4#54714yes—
723C2×C4#54814yes—
724C22—44no—
725C22—48no—
726C22—44no—
727C22—48no—
728C22—44no—
729C22—82no—
730C22—82no—
731C22—84no—
732C22—82no—
733C22—84no—
734C22—82no—
735C22C22×#12111yescharacteristic
736C22C2×#52911yescharacteristic
737C22C2×#53611yescharacteristic
738C22#344911yescharacteristic
739C22C2×#54211yescharacteristic
740C22C2×#54611yescharacteristic
741C22C2×#54611yescharacteristic
742C22C2×#54711yescharacteristic
743C22C2×#54811yescharacteristic
744C22#348712yes—
745C22#349712yes—
746C22#350011yescharacteristic
747C22#350011yescharacteristic
748C22#350712yes—
749C22#351012yes—
750C22#351512yes—
751C22#351612yes—
752C22#352112yes—
753C22#352112yes—
754C22#353912yes—
755C22#354112yes—
756C22#355512yes—
757C22#355712yes—
758C4—24no—
759C4—24no—
760C4—24no—
761C4—44no—
762C4—44no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—44no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4#242718yes—
776C2—84no—
777C2C2×#242711yescharacteristic
778C2#3517811yescharacteristic
779C2#3567711yescharacteristic
780C2#3597312yes—
781C2#3808511yescharacteristic
782C2#3809211yescharacteristic
783C2#3916311yescharacteristic
784C2#3917311yescharacteristic
785C2#4269812yes—
786C2#4524212yes—
787C2#4524312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2642C2semidirect
4. C2×#2365C2semidirect
5. #16595C2semidirect
6. #15796C2semidirect
7. #15787C2semidirect
8. #15241C2semidirect
11. #15185C2semidirect
12. #14853C2semidirect
13. #14160C2semidirect
16. #13942C2semidirect
17. #13926C2semidirect
18. #13848C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#25662
C2×#26422
C2×#23652
#165952
#157962
#157872
#152412
#152172
#151852
#148532
#141602
#140262
#139422
#139262
#138482
#137852