Finite Group Databasebeta

← #688345

Subgroups — #688345

Order 512.

4030 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#544C211yesmaximal, characteristic, complemented
2C2×#2440C212yesmaximal, complemented
3C2×#2352C211yesmaximal, characteristic
4#16605C212yesmaximal, complemented
5#16603C212yesmaximal, complemented
6#15951C214yesmaximal
7#15279C214yesmaximal, complemented
8#15228C212yesmaximal, complemented
9#15216C212yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#14916C212yesmaximal, complemented
12#14264C211yesmaximal, characteristic, complemented
13#14053C212yesmaximal, complemented
14#13951C211yesmaximal, characteristic, complemented
15#13880C211yesmaximal, characteristic, complemented
16#13872C211yesmaximal, characteristic
17#13839C211yesmaximal, characteristic
18C2×#544—216no—
19C2×#544—28no—
20C22×C4⋊Q8C2212yes—
21C22×C4⋊Q8C2212yes—
22C22×#125C2212yes—
23C22×#125C2212yes—
24C22×C22⋊Q8C2214yes—
25C22×C22⋊Q8C2214yes—
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2440—216no—
32C2×#398C2214yes—
33C2×#395C2214yes—
34#2352—28no—
35C2×#391C2214yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#388C2212yes—
39C2×#387C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#384C2212yes—
45C2×#382C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54#1446C2214yes—
55#1444C2212yes—
56#1444C2212yes—
57#1444C2214yes—
58#1444C2212yes—
59#1444C2214yes—
60#1442C2212yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2211yescharacteristic
64#1441C2211yescharacteristic
65#1441C2212yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1440C2212yes—
70#1439C2211yescharacteristic
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2212yes—
78#1436C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2314yes—
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93#544—2128no—
94C2×C4⋊Q8—216no—
95C2×C4⋊Q8—28no—
96C2×C4⋊Q8—28no—
97C2×C4⋊Q8—28no—
98C2×C4⋊Q8D4116yescomplemented
99C2×#125—216no—
100C2×#125—28no—
101C2×#125—28no—
102C2×#125—28no—
103C2×#125—28no—
104C2×C22⋊Q8—216no—
105C2×C22⋊Q8—216no—
106C2×C22⋊Q8—216no—
107C2×C22⋊Q8—216no—
108C2×C22⋊Q8—48no—
109C2×C22⋊Q8—48no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4Q818yescomplemented
113C2×#117—24no—
114C2×#117—28no—
115C2×#117—28no—
116C2×#117D418yes—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#398—216no—
156#395—216no—
157#391—48no—
158#389—28no—
159#389—28no—
160#388—28no—
161#387—28no—
162#386—28no—
163#386—44no—
164#385—216no—
165#385—48no—
166#384—28no—
167#382—24no—
168#380—24no—
169#380—24no—
170#380—24no—
171#380—28no—
172C4×C4⋊C4—24no—
173C4×C22⋊C4—24no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—28no—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2311yescharacteristic
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2311yescharacteristic
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C25C2411yescharacteristic
202C25C2411yescharacteristic
203C22×Q8—28no—
204C22×Q8—28no—
205C22×Q8—44no—
206C22×Q8—44no—
207C22×Q8—44no—
208C22×Q8—44no—
209C22×Q8C2×D4116yes—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—41no—
215C22×D4—41no—
216C22×D4C2×Q814yes—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—28no—
225C23×C4—24no—
226C23×C4—28no—
227C23×C4—24no—
228C23×C4—44no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—44no—
232C23×C4—42no—
233C23×C4C2×D414yes—
234C23×C4C2×Q814yes—
235C23×C4C2×Q814yes—
236C23×C4#4114yes—
237C23×C4C2414yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2414yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C4⋊Q8—264no—
253C4⋊Q8—264no—
254#125—264no—
255#125—264no—
256C22⋊Q8—2128no—
257C22⋊Q8—464no—
258C4×D4—232no—
259#117—232no—
260#117—232no—
261C2×C4⋊C4—232no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4C2×D418yes—
304C2×C4⋊C4C2×D414yes—
305C2×C4⋊C4C2×D4116yes—
306C2×C4⋊C4C2×D418yes—
307C2×C4⋊C4C2×D414yes—
308C2×C4⋊C4C2×Q814yes—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4C2×D418yes—
338C2×C22⋊C4C2×Q814yes—
339C2×C22⋊C4C2×Q814yes—
340C2×C42—28no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—44no—
350C2×C42C2×D418yes—
351C2×C42C2×D418yes—
352C2×C42C2×Q814yes—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—28no—
360#95—24no—
361#95—28no—
362#95—28no—
363#95—22no—
364#95—22no—
365#95—24no—
366#95—28no—
367#95—24no—
368#95—24no—
369#95—28no—
370#95—42no—
371#95—44no—
372#95—44no—
373#95—42no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24C22×D412yes—
395C24C22×Q812yes—
396C24C22×Q812yes—
397C24C2×#4112yes—
398C24H(5,𝔽2)12yes—
399C242−1+412yes—
400C24C2511yescharacteristic
401C2×Q8—232no—
402C2×Q8—416no—
403C2×Q8—416no—
404C2×Q8—88no—
405C2×Q8—88no—
406C2×Q8—88no—
407C2×Q8—88no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—216no—
423C22×C4—216no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—216no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—416no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—88no—
499C22×C4—84no—
500C22×C4—88no—
501C22×C4—88no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4C22⋊Q8116yescomplemented
505C22×C4C22×D414yes—
506C22×C4C22×D414yes—
507C22×C4C22×D414yes—
508C22×C4C22×D418yes—
509C22×C4C22×D414yes—
510C22×C4C22×D418yes—
511C22×C4C22×D412yes—
512C22×C4C22×D412yes—
513C22×C4C22×D414yes—
514C22×C4C22×Q812yes—
515C22×C4C22×Q812yes—
516C22×C4C22×Q812yes—
517C22×C4C22×Q812yes—
518C22×C4C22×Q812yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4H(5,𝔽2)14yes—
522C22×C42−1+414yes—
523C22×C42−1+414yes—
524C4⋊C4—216no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—232no—
528C4⋊C4—232no—
529C4⋊C4—216no—
530C4⋊C4—28no—
531C4⋊C4—232no—
532C4⋊C4—28no—
533C4⋊C4—416no—
534C4⋊C4—416no—
535C4⋊C4—416no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—48no—
540C4⋊C4—88no—
541C4⋊C4#120116yes—
542C22⋊C4—216no—
543C22⋊C4—216no—
544C22⋊C4—216no—
545C22⋊C4—216no—
546C22⋊C4—28no—
547C22⋊C4—216no—
548C22⋊C4—28no—
549C22⋊C4—48no—
550C22⋊C4—416no—
551C22⋊C4—84no—
552C22⋊C4—84no—
553C42—216no—
554C42—216no—
555C42—28no—
556C42—48no—
557C42—84no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23C2×C22⋊Q814yes—
603C23#54414yescomplemented
604C23C23×D411yescharacteristic
605C23C23×D412yes—
606C23C23×Q811yescharacteristic
607C23C22×#4111yescharacteristic
608C23C2×H(5,𝔽2)11yescharacteristic
609C23C2×H(5,𝔽2)12yes—
610C23C2×2−1+412yes—
611C23C2×2−1+411yescharacteristic
612C23C2×2−1+412yes—
613C23#58511yescharacteristic
614C23#58511yescharacteristic
615Q8—832no—
616D4—416no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—28no—
622C2×C4—24no—
623C2×C4—28no—
624C2×C4—24no—
625C2×C4—232no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—28no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—416no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—816no—
702C2×C4—816no—
703C2×C4C2×#12018yes—
704C2×C4C2×#12014yes—
705C2×C4C2×C22⋊Q814yes—
706C2×C4C2×C22⋊Q814yes—
707C2×C4#53614yes—
708C2×C4#54818yes—
709C2×C4D4×Q818yes—
710C22—28no—
711C22—24no—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22C22×#12011yescharacteristic
733C22C22×C22⋊Q811yescharacteristic
734C22C2×#53611yescharacteristic
735C22C2×#54411yescharacteristic
736C22#345811yescharacteristic
737C22C2×#54812yes—
738C22C2×D4×Q812yes—
739C22#348412yes—
740C22#348612yes—
741C22#348811yescharacteristic
742C22#348911yescharacteristic
743C22#349212yes—
744C22#349411yescharacteristic
745C22#349511yescharacteristic
746C22#349612yes—
747C22#349712yes—
748C22#349811yescharacteristic
749C22#349911yescharacteristic
750C22#350312yes—
751C22#354412yes—
752C22#355212yes—
753C22#355912yes—
754C22#356312yes—
755C4—28no—
756C4—24no—
757C4—44no—
758C4—44no—
759C4—48no—
760C4—44no—
761C4—44no—
762C4—44no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—84no—
767C4—82no—
768C4—82no—
769C4#240918yes—
770C2—44no—
771C2—44no—
772C2C2×#240911yescharacteristic
773C2#3525311yescharacteristic
774C2#3553211yescharacteristic
775C2#3568011yescharacteristic
776C2#3568711yescharacteristic
777C2#3768612yes—
778C2#3936512yes—
779C2#4291411yescharacteristic
780C2#4296411yescharacteristic
781C2#4487812yes—
782C2#4510912yes—
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
1. C22×#544C2semidirect
2. C2×#2440C2semidirect
4. #16605C2semidirect
5. #16603C2semidirect
7. #15279C2semidirect
8. #15228C2semidirect
9. #15216C2semidirect
10. #15178C2semidirect
11. #14916C2semidirect
12. #14264C2semidirect
13. #14053C2semidirect
14. #13951C2semidirect
15. #13880C2semidirect
98. C2×C4⋊Q8D4semidirect
112. C2×C4×D4Q8semidirect
504. C22×C4C22⋊Q8semidirect
603. C23#544semidirect

Maximal subgroups

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

subgroupindex
C22×#5442
C2×#24402
C2×#23522
#166052
#166032
#159512
#152792
#152282
#152162
#151782
#149162
#142642
#140532
#139512
#138802
#138722
#138392