Finite Group Databasebeta

← #823420

Subgroups — #823420

Order 512.

3482 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2417C212yesmaximal, complemented
2C2×#2360C211yesmaximal, characteristic, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#16992C212yesmaximal, complemented
5#15786C214yesmaximal, complemented
6#15324C214yesmaximal, complemented
7#15195C211yesmaximal, characteristic, complemented
8#15185C211yesmaximal, characteristic, complemented
9#15181C212yesmaximal, complemented
10#15177C211yesmaximal, characteristic, complemented
11#15165C212yesmaximal, complemented
12#14175C212yesmaximal
13#13969C212yesmaximal, complemented
14#13933C211yesmaximal, characteristic, complemented
15#13907C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17C4×#392C211yesmaximal, characteristic
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26#2417—216no—
27C2×#398C2214yes—
28C2×#396C2214yes—
29C2×#392C2211yescharacteristic
30#2360—28no—
31D4×C4⋊C4—28no—
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#387C2212yes—
39C2×#386C2214yes—
40C2×#386C2214yes—
41C2×#385C2214yes—
42C2×#385C2212yes—
43C2×#384C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2214yes—
47C2×#380C2212yes—
48C2×#380C2214yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53#1445C2214yes—
54#1444C2211yescharacteristic
55#1444C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1439C2211yescharacteristic
66#1439C2212yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2212yes—
72#1438C2211yescharacteristic
73#1438C2212yes—
74#1438C2212yes—
75#1437C2214yes—
76#1436C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82#1434C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C4×#95C2211yescharacteristic
86C23×Q8C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2314yes—
92C24×C4C2312yes—
93C2×C22⋊Q8—28no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—44no—
98C2×C22⋊Q8D418yescomplemented
99C2×C4×Q8—24no—
100C2×C4×Q8—44no—
101C2×C4×D4—28no—
102C2×C4×D4—28no—
103C2×C4×D4—28no—
104C2×C4×D4—24no—
105C2×C4×D4—28no—
106C2×C4×D4—44no—
107C2×C4×D4—48no—
108C22×C4⋊C4—28no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—28no—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—44no—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2312yes—
145C22×C42C2312yes—
146#398—216no—
147#396—216no—
148#392Q818yescomplemented
149#391—28no—
150#391—24no—
151#389—24no—
152#389—28no—
153#389—28no—
154#389—28no—
155#387—28no—
156#386—216no—
157#386—48no—
158#385—216no—
159#385—28no—
160#384—24no—
161#380—28no—
162#380—28no—
163#380—216no—
164#380—48no—
165#380—44no—
166C4×C4⋊C4D418yescomplemented
167C4×C22⋊C4—24no—
168C4×C22⋊C4—28no—
169C4×C22⋊C4—44no—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2311yescharacteristic
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2311yescharacteristic
179C2×#95C2312yes—
180C2×#95C2311yescharacteristic
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C25C2411yescharacteristic
196C25C2412yes—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8C2×D414yes—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4C2×Q814yes—
213C22×D4C2×Q818yes—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—28no—
225C23×C4—24no—
226C23×C4—28no—
227C23×C4—24no—
228C23×C4—28no—
229C23×C4—28no—
230C23×C4—44no—
231C23×C4—44no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4—42no—
235C23×C4—44no—
236C23×C4C2×D414yes—
237C23×C4#4118yes—
238C23×C4C2411yescharacteristic
239C23×C4C2414yes—
240C23×C4C2412yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C22⋊Q8—232no—
254C22⋊Q8—432no—
255C4×Q8—416no—
256C4×D4—232no—
257C4×D4—432no—
258C4×D4—432no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—416no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—432no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4C2×D414yes—
297C2×C4⋊C4C2×D418yes—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4#4114yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4C2×D418yes—
335C2×C22⋊C4C2×Q814yes—
336C2×C22⋊C4C2×Q818yes—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—22no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—44no—
345C2×C42—44no—
346C2×C42C2×D414yes—
347C2×C42C2×D418yes—
348#95—22no—
349#95—24no—
350#95—22no—
351#95—24no—
352#95—28no—
353#95—28no—
354#95—28no—
355#95—24no—
356#95—28no—
357#95—28no—
358#95—22no—
359#95—24no—
360#95—42no—
361#95—44no—
362#95—44no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95C2×D418yes—
372#95C2×Q814yes—
373C24—21no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—22no—
392C24—22no—
393C24C22×D412yes—
394C24C22×Q812yes—
395C24C22×Q814yes—
396C24C2×#4114yes—
397C24H(5,𝔽2)14yes—
398C242−1+412yes—
399C24C2511yescharacteristic
400C2×Q8—28no—
401C2×Q8—216no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—48no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—216no—
408C2×D4—216no—
409C2×D4—216no—
410C2×D4—216no—
411C2×D4—28no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—216no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—416no—
490C22×C4—416no—
491C22×C4—416no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—416no—
502C22×C4—88no—
503C22×C4—88no—
504C22×C4—88no—
505C22×C4—84no—
506C22×C4—88no—
507C22×C4—88no—
508C22×C4C22×D414yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D414yes—
512C22×C4C22×D414yes—
513C22×C4C22×D414yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×Q814yes—
518C22×C4C22×Q812yes—
519C22×C4C22×Q812yes—
520C22×C4C2×#4114yes—
521C22×C4C2×#4114yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4114yes—
524C22×C4H(5,𝔽2)14yes—
525C22×C42−1+412yes—
526C4⋊C4—28no—
527C4⋊C4—216no—
528C4⋊C4—28no—
529C4⋊C4—48no—
530C4⋊C4—416no—
531C4⋊C4—48no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—416no—
535C4⋊C4—48no—
536C4⋊C4—44no—
537C4⋊C4—48no—
538C4⋊C4—84no—
539C4⋊C4—88no—
540C4⋊C4—84no—
541C4⋊C4#121116yes—
542C22⋊C4—216no—
543C22⋊C4—216no—
544C22⋊C4—28no—
545C22⋊C4—48no—
546C22⋊C4—44no—
547C22⋊C4—48no—
548C22⋊C4—48no—
549C22⋊C4—416no—
550C22⋊C4—416no—
551C22⋊C4—48no—
552C22⋊C4—88no—
553C22⋊C4—88no—
554C42—28no—
555C42—48no—
556C42—48no—
557C42—44no—
558C42—48no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—22no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—42no—
590C23—41no—
591C23—41no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23D4×Q814yes—
616C23#55418yes—
617C23C23×D411yescharacteristic
618C23C23×D411yescharacteristic
619C23C23×Q811yescharacteristic
620C23C22×#4111yescharacteristic
621C23C22×#4112yes—
622C23C2×H(5,𝔽2)12yes—
623C23C2×H(5,𝔽2)12yes—
624C23C2×2−1+411yescharacteristic
625C23C2×2−1+411yescharacteristic
626C23#58511yescharacteristic
627C23#58512yes—
628Q8—416no—
629D4—232no—
630D4—432no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—28no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—416no—
679C2×C4—432no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—832no—
712C2×C4—816no—
713C2×C4C2×#12118yes—
714C2×C4C2×#12114yes—
715C2×C4#52514yes—
716C2×C4#53514yes—
717C2×C4#54618yes—
718C2×C4D4×Q814yes—
719C2×C4#55318yes—
720C22—28no—
721C22—28no—
722C22—24no—
723C22—28no—
724C22—28no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—42no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22C22×#12111yescharacteristic
747C22C2×#52511yescharacteristic
748C22C2×#53511yescharacteristic
749C22C2×#54612yes—
750C22C2×D4×Q811yescharacteristic
751C22C2×D4×Q811yescharacteristic
752C22C2×#55312yes—
753C22C2×#55412yes—
754C22Q8×#4111yescharacteristic
755C22#348411yescharacteristic
756C22#348812yes—
757C22#348911yescharacteristic
758C22#349212yes—
759C22#349512yes—
760C22#349711yescharacteristic
761C22#350011yescharacteristic
762C22#350112yes—
763C22#351212yes—
764C22#351312yes—
765C22#352311yescharacteristic
766C22#353612yes—
767C22#354212yes—
768C22#354712yes—
769C4—28no—
770C4—24no—
771C4—42no—
772C4—44no—
773C4—44no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—42no—
778C4—82no—
779C4—84no—
780C4—84no—
781C4—81no—
782C4—82no—
783C4#253518yes—
784C2—44no—
785C2—48no—
786C2C2×#253511yescharacteristic
787C2#3572811yescharacteristic
788C2#3608011yescharacteristic
789C2Q8×#12111yescharacteristic
790C2#3654611yescharacteristic
791C2#3961811yescharacteristic
792C2#4247811yescharacteristic
793C2#4491312yes—
794C2#4537112yes—
795C2#5901612yes—
796C2#5985612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2417C2semidirect
2. C2×#2360C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. #16992C2semidirect
5. #15786C2semidirect
6. #15324C2semidirect
7. #15195C2semidirect
8. #15185C2semidirect
9. #15181C2semidirect
10. #15177C2semidirect
11. #15165C2semidirect
13. #13969C2semidirect
14. #13933C2semidirect
15. #13907C2semidirect
16. #13872C2semidirect
98. C2×C22⋊Q8D4semidirect
148. #392Q8semidirect
166. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24172
C2×#23602
C2×D4×C4⋊C42
#169922
#157862
#153242
#151952
#151852
#151812
#151772
#151652
#141752
#139692
#139332
#139072
#138722
C4×#3922