Finite Group Databasebeta

← #7505046

Subgroups — #7505046

Order 512.

2184 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2#34745C211yesmaximal, characteristic, complemented
3#31540C214yesmaximal, complemented
4#31538C214yesmaximal, complemented
5#31520C214yesmaximal, complemented
6#31518C214yesmaximal, complemented
7#23734C211yesmaximal, characteristic, complemented
8#23658C211yesmaximal, characteristic, complemented
9#23618C211yesmaximal, characteristic, complemented
10#23552C211yesmaximal, characteristic, complemented
11#23454C211yesmaximal, characteristic, complemented
12#23452C211yesmaximal, characteristic, complemented
13#21322C211yesmaximal, characteristic, complemented
14#21236C211yesmaximal, characteristic
15#21023C211yesmaximal, characteristic, complemented
16#20928C211yesmaximal, characteristic
17#20925C211yesmaximal, characteristic
18#20873C211yesmaximal, characteristic, complemented
19#20648C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8—22no—
24C2×C4×#41C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#423C2211yescharacteristic
30C2×#417C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#418C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37#2542—22no—
38#2542—22no—
39#2542C2214yes—
40#2542C2214yes—
41#2454C2212yescomplemented
42#2453C2212yescomplemented
43#2452C2212yescomplemented
44#2451C2212yescomplemented
45#2450—22no—
46#2449—22no—
47#2396—22no—
48C2×#399—22no—
49C4×C22⋊Q8—22no—
50#2297C2211yescharacteristic
51#2297C2211yescharacteristic
52#2296C2211yescharacteristic
53#2296C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59#2096C2212yescomplemented
60#2095C2212yescomplemented
61#2094C2212yescomplemented
62#2093C2212yescomplemented
63#2084C2214yescomplemented
64#2083C2214yescomplemented
65#2067C2214yes—
66#2065C2214yes—
67#2058C2214yescomplemented
68#2057C2214yescomplemented
69#2025C2214yes—
70#2024C2214yescomplemented
71#2023C2214yes—
72#2023C2214yescomplemented
73#1992C2214yescomplemented
74#1990C2214yescomplemented
75#1973C2212yes—
76#1972C2212yes—
77#1970C2212yes—
78#1968C2212yes—
79#1917C2214yescomplemented
80#1916C2214yescomplemented
81#1880C2214yes—
82#1879C2214yes—
83#1879C2214yes—
84#1877C2214yes—
85#1864C2214yes—
86#1862C2214yes—
87#1803C2214yescomplemented
88#1802C2214yescomplemented
89#1736C2211yescharacteristic
90#1736C2211yescharacteristic
91#1736C2211yescharacteristic
92#1736C2211yescharacteristic
93#1736C2211yescharacteristic
94#1736C2211yescharacteristic
95#1728C2211yescharacteristic
96#1728C2211yescharacteristic
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41C2311yescharacteristic
100C23×Q8—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C2×AGL(1,ℤ/8)—42no—
104C2×AGL(1,ℤ/8)—42no—
105C2×AGL(1,ℤ/8)Q818yescomplemented
106C22×SD16C2312yes—
107C22×D8C2312yes—
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C22×M16C2311yescharacteristic
112#533—24no—
113#533—42no—
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2314yes—
119C2×#125C2312yes—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—416no—
127C4×#41—24no—
128C4×#41—42no—
129C2×C4×Q8—22no—
130C2×C4×Q8C2312yes—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—42no—
134C2×C4×D4—42no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2314yes—
137C2×#117—21no—
138C2×#117C2311yescharacteristic
139C2×#117C2311yescharacteristic
140C2×#117C2311yescharacteristic
141C22×C4⋊C4—21no—
142C22×C4⋊C4—22no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4D412yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—21no—
149C22×C22⋊C4—22no—
150C22×C22⋊C4—22no—
151C22×C42—21no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#428—42no—
156#428—42no—
157#428—42no—
158C2×#107C2312yes—
159C2×#107C2312yes—
160C2×#107C2312yes—
161C2×#106C2312yes—
162C2×#106C2312yes—
163C2×#106C2312yes—
164#423—42no—
165C2×C4⋊C8C2314yes—
166#418—24no—
167#418—42no—
168#418—42no—
169#417—42no—
170#417—42no—
171#417—42no—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#102C2314yes—
176C2×#102C2312yes—
177C2×#102C2312yes—
178C2×#102C2312yes—
179C2×#102C2314yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C4×M16—42no—
183C2×#97C2312yes—
184C2×C4×C8C2312yes—
185#400—22no—
186#399—22no—
187#399—24no—
188#399—24no—
189#399—24no—
190#399—24no—
191#398—22no—
192#398—22no—
193#396—22no—
194#396—22no—
195#395—22no—
196#393—22no—
197#391—22no—
198#391C2311yescharacteristic
199#391C2311yescharacteristic
200#391C2312yes—
201#390—21no—
202#390—22no—
203#390—21no—
204#390C2314yes—
205#390C2311yescharacteristic
206#390C2311yescharacteristic
207#390C2312yes—
208#390C2312yes—
209#390C2312yes—
210#389—22no—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#387—22no—
216#387—22no—
217#386—21no—
218#386—22no—
219#386—21no—
220#385—21no—
221#385—22no—
222#385—21no—
223#385—22no—
224#385—22no—
225#384—21no—
226#384—22no—
227#384—21no—
228#384C2314yes—
229#384C2312yes—
230#384C2312yes—
231#380—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—22no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4D412yes—
236C4×C4⋊C4D412yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C2×#95D412yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#336C2314yes—
249#336C2314yes—
250#336C2312yes—
251#336C2312yes—
252#336C2314yes—
253C25—21no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41C2×Q814yes—
260C22×Q8—24no—
261C22×Q8—22no—
262C22×Q8—48no—
263C22×Q8—44no—
264C22×Q8C2411yescharacteristic
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4C2×Q814yes—
273C22×D4C2411yescharacteristic
274C22×D4C2412yes—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—44no—
282C23×C4—48no—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D412yes—
285C23×C4C2×D412yes—
286C23×C4C2×D411yescharacteristic
287C23×C4C2411yescharacteristic
288AGL(1,ℤ/8)—416no—
289C2×SD16—42no—
290C2×SD16—42no—
291C2×SD16C2×Q818yescomplemented
292C2×D8—42no—
293C2×D8—42no—
294C2×D8C2×Q818yescomplemented
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16C2×Q814yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C4⋊Q8—24no—
312C4⋊Q8—44no—
313C4⋊Q8—44no—
314C4⋊Q8—42no—
315C4⋊Q8—48no—
316#125—24no—
317#125—42no—
318C22⋊Q8—48no—
319C22⋊Q8—416no—
320C22⋊Q8—416no—
321C22⋊Q8—416no—
322C22⋊Q8—48no—
323C22⋊Q8—416no—
324C4×Q8—24no—
325C4×Q8—48no—
326C4×Q8—42no—
327C4×D4—24no—
328C4×D4—44no—
329C4×D4—44no—
330C4×D4—42no—
331C4×D4—48no—
332C4×D4—48no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—44no—
339#117#4114yes—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—48no—
364C2×C4⋊C4—48no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2×D412yes—
369C2×C4⋊C4C2×D412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2411yescharacteristic
375C2×C4⋊C4C2411yescharacteristic
376C2×C4⋊C4C2412yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—48no—
392C2×C22⋊C4—48no—
393C2×C42—21no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—22no—
403C2×C42—44no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D411yescharacteristic
408C2×C42C2412yes—
409C2×C42C2412yes—
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412#107—42no—
413#107—42no—
414#107—42no—
415#106—42no—
416#106—42no—
417#106—42no—
418C4⋊C8—44no—
419#103—42no—
420#103—42no—
421#103—42no—
422#102—28no—
423#102—42no—
424#102—42no—
425#102—42no—
426#102—42no—
427#102—42no—
428#102—44no—
429#97—42no—
430C4×C8—42no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95C2×D412yes—
440#95C2×D412yes—
441#95C2×D412yes—
442#95C2×D412yes—
443C24—24no—
444C24—21no—
445C24—22no—
446C24—44no—
447C24—44no—
448C24—42no—
449C24—42no—
450C24C22×D411yescharacteristic
451#41—28no—
452#41—28no—
453#41—44no—
454#41—44no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—44no—
461C2×Q8—48no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—44no—
465C2×Q8—82no—
466C2×Q8—816no—
467C2×Q8C22×Q812yes—
468C2×D4—24no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—28no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—44no—
486C2×D4—42no—
487C2×D4—44no—
488C2×D4C22×Q812yes—
489C2×D4C22×Q814yes—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—82no—
523C22×C4—816no—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D411yescharacteristic
531C22×C4C22×Q812yes—
532C22×C4C2×#4112yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C4H(5,𝔽2)12yes—
535C22×C4H(5,𝔽2)12yes—
536C22×C42−1+412yes—
537C22×C4C2511yescharacteristic
538SD16—48no—
539D8—48no—
540M16—28no—
541M16—44no—
542M16—44no—
543M16—44no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8C22×Q814yes—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4AGL(1,ℤ/8)18yescomplemented
589C4⋊C4C2×#4114yes—
590C22⋊C4—24no—
591C22⋊C4—44no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C42—24no—
604C42—22no—
605C42—22no—
606C42—24no—
607C42—24no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—44no—
617C42—42no—
618C42—42no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—416no—
624C23—42no—
625C23—44no—
626C23—42no—
627C23—41no—
628C23—48no—
629C23—41no—
630C23—42no—
631C23—44no—
632C23—42no—
633C23—84no—
634C23—84no—
635C23—88no—
636C23#53512yes—
637C23#54612yes—
638C23D4×Q812yes—
639C23C23×D411yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644Q8—88no—
645Q8—816no—
646D4—22no—
647D4—24no—
648D4—24no—
649D4—22no—
650D4—48no—
651D4—42no—
652D4—41no—
653D4—48no—
654D4—42no—
655D4—41no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—48no—
675C2×C4—48no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—48no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—88no—
696C2×C4—816no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4#53512yes—
701C2×C4#54214yes—
702C2×C4#54314yes—
703C2×C4#54612yes—
704C2×C4D4×Q812yes—
705C2×C4#55414yes—
706C2×C4#56214yes—
707C2×C4C2×AGL(1,ℤ/8)14yes—
708C2×C4C2×AGL(1,ℤ/8)14yes—
709C2×C4C2×AGL(1,ℤ/8)14yes—
710C2×C4C23×Q811yescharacteristic
711C2×C4C22×#4111yescharacteristic
712C2×C4C2×H(5,𝔽2)11yescharacteristic
713C2×C4C2×H(5,𝔽2)11yescharacteristic
714C2×C4C2×H(5,𝔽2)11yescharacteristic
715C2×C4C2×2−1+411yescharacteristic
716C8—24no—
717C8—42no—
718C8—42no—
719C8—42no—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—44no—
726C22—44no—
727C22—48no—
728C22—816no—
729C22—82no—
730C22—81no—
731C22—81no—
732C22—82no—
733C22—82no—
734C22—84no—
735C22#269214yes—
736C22C2×#53511yescharacteristic
737C22C2×#54611yescharacteristic
738C22C2×D4×Q811yescharacteristic
739C22C22×AGL(1,ℤ/8)12yes—
740C22#358612yes—
741C4—24no—
742C4—24no—
743C4—24no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—44no—
749C4—81no—
750C4—82no—
751C4—82no—
752C4—82no—
753C4—81no—
754C4—82no—
755C4#269214yes—
756C4C2×#54211yescharacteristic
757C4C2×#54311yescharacteristic
758C4C2×#55411yescharacteristic
759C4C2×#56211yescharacteristic
760C2—24no—
761C2—82no—
762C2—84no—
763C2C2×#269211yescharacteristic
764C2#6079811yescharacteristic
765C2#6080711yescharacteristic
766C2#6116112yes—
767C2Q8×AGL(1,ℤ/8)12yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2542C2semidirect
2. #34745C2semidirect
3. #31540C2semidirect
4. #31538C2semidirect
5. #31520C2semidirect
6. #31518C2semidirect
7. #23734C2semidirect
8. #23658C2semidirect
9. #23618C2semidirect
10. #23552C2semidirect
11. #23454C2semidirect
12. #23452C2semidirect
13. #21322C2semidirect
15. #21023C2semidirect
18. #20873C2semidirect
19. #20648C2semidirect
41. #2454C22semidirect
42. #2453C22semidirect
43. #2452C22semidirect
44. #2451C22semidirect
59. #2096C22semidirect
60. #2095C22semidirect
61. #2094C22semidirect
62. #2093C22semidirect
63. #2084C22semidirect
64. #2083C22semidirect
67. #2058C22semidirect
68. #2057C22semidirect
70. #2024C22semidirect
72. #2023C22semidirect
73. #1992C22semidirect
74. #1990C22semidirect
79. #1917C22semidirect
80. #1916C22semidirect
87. #1803C22semidirect
88. #1802C22semidirect
105. C2×AGL(1,ℤ/8)Q8semidirect
291. C2×SD16C2×Q8semidirect
294. C2×D8C2×Q8semidirect
588. C4⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
#347452
#315402
#315382
#315202
#315182
#237342
#236582
#236182
#235522
#234542
#234522
#213222
#212362
#210232
#209282
#209252
#208732
#206482