Finite Group Databasebeta

← #6617317

Subgroups — #6617317

Order 512.

3143 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic
2C2×#3369C212yesmaximal, complemented
3Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
4#32956C211yesmaximal, characteristic
5#32954C212yesmaximal, complemented
6#25864C212yesmaximal
7#25856C211yesmaximal, characteristic, complemented
8#25662C214yesmaximal, complemented
9#25646C212yesmaximal, complemented
10#24217C212yesmaximal
11#24212C211yesmaximal, characteristic, complemented
12#24207C214yesmaximal, complemented
13#24189C212yesmaximal, complemented
14#22544C212yesmaximal, complemented
15#22510C211yesmaximal, characteristic, complemented
16#21455C212yesmaximal, complemented
17C4×#450C211yesmaximal, characteristic
18C2×Q82C2211yescharacteristic, complemented
19C2×#556—216no—
20C2×#556—21no—
21C2×#556—22no—
22C2×#556—21no—
23C2×#556C2212yes—
24C2×#556C2214yes—
25C2×#556C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×#126—22no—
28C22×#124C2212yes—
29C22×C22⋊Q8—21no—
30C22×C4×Q8C2212yes—
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×#117—21no—
34#3369—216no—
35C2×#489C2214yes—
36C2×#487C2212yescomplemented
37C2×#475C2214yescomplemented
38C2×#476C2212yes—
39C2×#464C2214yes—
40C2×#462C2212yescomplemented
41C2×#451C2212yes—
42C2×#450C2211yescharacteristic
43C2×#446C2212yescomplemented
44C2×#441C2214yescomplemented
45C2×C4×SD16C2212yes—
46#2857C2211yescharacteristic
47#2857C2212yes—
48#2582C2211yescharacteristic, complemented
49#2582C2212yescomplemented
50#2567C2211yescharacteristic, complemented
51#2567C2212yescomplemented
52#2451—21no—
53#2451—22no—
54#2440—21no—
55#2440—22no—
56Q8×C4⋊C4—21no—
57Q8×C4⋊C4C2211yescharacteristic, complemented
58Q8×C22⋊C4—21no—
59C4×C22⋊Q8C2211yescharacteristic
60C4×C22⋊Q8C2212yes—
61#2043C2214yescomplemented
62#2043C2212yescomplemented
63#2042C2214yes—
64#2042C2214yes—
65#2042C2214yes—
66#2016C2212yescomplemented
67#2015C2214yes—
68#1985C2214yescomplemented
69#1984C2212yescomplemented
70#1983C2214yes—
71#1981C2212yescomplemented
72#1959C2214yes—
73#1956C2212yescomplemented
74#1878C2214yescomplemented
75#1877C2212yes—
76#1872C2211yescharacteristic
77#1865C2214yescomplemented
78#1865C2214yescomplemented
79#1865C2214yescomplemented
80#1864C2212yes—
81#1864C2214yes—
82#1853C2211yescharacteristic
83#1853C2212yes—
84#1803C2214yescomplemented
85#1802C2212yes—
86#1797C2211yescharacteristic
87#1797C2212yes—
88#1787C2212yes—
89#1787C2212yes—
90#1787C2212yes—
91#1786C2211yescharacteristic
92#1786C2212yes—
93#1763C2214yescomplemented
94C4×#102C2212yes—
95#1749C2212yes—
96C4×C22⋊C8C2211yescharacteristic
97C23×Q8D411yescharacteristic
98C23×Q8C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C22×Q16C2314yes—
102C22×SD16C2312yes—
103Q82—28no—
104#556—216no—
105#556—232no—
106#556—216no—
107#556—28no—
108#556—216no—
109#556—216no—
110#556—28no—
111#556—28no—
112#556D4116yes—
113C2×C4⋊Q8—28no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2312yes—
120C2×C4⋊Q8C2312yes—
121C2×C4⋊Q8C2311yescharacteristic
122C2×#126—232no—
123C2×#126—24no—
124C2×#126—24no—
125C2×#126—24no—
126C2×#126—24no—
127C2×#124—216no—
128C2×#124—22no—
129C2×#124—22no—
130C2×#124C2314yes—
131C2×#124C2314yes—
132C2×C22⋊Q8—216no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—22no—
138C2×C22⋊Q8C2311yescharacteristic
139C2×C4×Q8—216no—
140C2×C4×Q8—28no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—22no—
144C2×C4×Q8—22no—
145C2×C4×Q8D411yescharacteristic
146C2×C4×Q8D411yescharacteristic
147C2×C4×Q8D412yes—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2314yes—
151C2×C4×Q8C2314yes—
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—28no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×#117—216no—
161C2×#117—22no—
162C2×#117—24no—
163C2×#117—22no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4D411yescharacteristic
168C22×C4⋊C4D412yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C22⋊C4—22no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—22no—
173C22×C42—22no—
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176#489—216no—
177#487—28no—
178#476—28no—
179#475—216no—
180#464—216no—
181#462—28no—
182#451—28no—
183#450—24no—
184#446—28no—
185#441—216no—
186C4×SD16—28no—
187C2×#106C2312yes—
188C2×#106C2314yes—
189C2×C4⋊C8C2314yes—
190C2×C4⋊C8C2312yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2312yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#102C2312yes—
200C2×#102C2314yes—
201C2×#102C2312yes—
202C2×#102C2314yes—
203C2×#102C2312yes—
204C2×C22⋊C8C2311yescharacteristic
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2311yescharacteristic
207C2×#97C2314yes—
208C2×C4×C8C2312yes—
209#398—22no—
210#398—22no—
211#398—22no—
212#395—22no—
213#395—22no—
214#395—22no—
215#391—21no—
216#391—22no—
217#391—21no—
218#391—22no—
219#391—21no—
220#391—22no—
221#391C2311yescharacteristic
222#391C2312yes—
223#389—21no—
224#389—22no—
225#389—21no—
226#389—22no—
227#389—21no—
228#389—22no—
229#389C2311yescharacteristic
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#387—21no—
235#387—22no—
236#385—21no—
237#385—22no—
238#384—21no—
239#384—22no—
240#384C2311yescharacteristic
241#384C2312yes—
242#380—22no—
243#380—21no—
244#380C2312yes—
245#380C2311yescharacteristic
246C4×C4⋊C4—21no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4C2311yescharacteristic
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—21no—
252#340C2314yes—
253#340C2312yes—
254#340C2312yes—
255#336C2312yes—
256#336C2314yes—
257#336C2312yes—
258#336C2314yes—
259C25—21no—
260C22×Q8—24no—
261C22×Q8—28no—
262C22×Q8—24no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—21no—
266C22×Q8—24no—
267C22×Q8—24no—
268C22×Q8—42no—
269C22×Q8—44no—
270C22×Q8C2×D411yescharacteristic
271C22×Q8C2×D412yes—
272C22×Q8C2×D411yescharacteristic
273C22×Q8C2414yes—
274C22×Q8C2411yescharacteristic
275C22×D4—24no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—42no—
280C22×D4C2412yes—
281C23×C4—28no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×Q16—28no—
294C2×Q16—28no—
295C2×Q16—44no—
296C2×SD16—24no—
297C2×SD16—24no—
298C2×SD16—42no—
299C22×C8C2412yes—
300C22×C8C2414yes—
301C22×C8C2412yes—
302C4⋊Q8—28no—
303C4⋊Q8—28no—
304C4⋊Q8—28no—
305C4⋊Q8—24no—
306C4⋊Q8—28no—
307C4⋊Q8—24no—
308C4⋊Q8—44no—
309C4⋊Q8—48no—
310C4⋊Q8C2×D418yes—
311#126—232no—
312#126—232no—
313#126—232no—
314#126—232no—
315#124—216no—
316#124—216no—
317#124—28no—
318#124—28no—
319#124—28no—
320#124C2×D4116yes—
321C22⋊Q8—216no—
322C22⋊Q8—232no—
323C22⋊Q8—216no—
324C22⋊Q8—22no—
325C22⋊Q8—82no—
326C22⋊Q8—84no—
327C22⋊Q8#4114yes—
328C4×Q8—216no—
329C4×Q8—216no—
330C4×Q8—24no—
331C4×Q8—28no—
332C4×Q8—28no—
333C4×Q8—24no—
334C4×Q8—28no—
335C4×Q8—28no—
336C4×Q8—28no—
337C4×Q8—24no—
338C4×Q8—24no—
339C4×Q8—28no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×Q8C2×D4116yes—
343C4×Q8C2×D418yes—
344C4×D4—28no—
345C4×D4—28no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4C2×D418yes—
350#117—216no—
351#117—232no—
352#117—216no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—216no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C22⋊C4—216no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—216no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C42—216no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—28no—
410C2×C42—22no—
411C2×C42—21no—
412C2×C42—22no—
413C2×C42—21no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D412yes—
417C2×C42C2×D412yes—
418C2×C42C2411yescharacteristic
419C2×C42C2412yes—
420C2×C42C2411yescharacteristic
421C2×C42C2412yes—
422#106—24no—
423#106—28no—
424C4⋊C8—24no—
425C4⋊C8—28no—
426#103—28no—
427#103—28no—
428#103—28no—
429#103—24no—
430#103—28no—
431#103—44no—
432#103—44no—
433#103—44no—
434#102—24no—
435#102—28no—
436#102—24no—
437#102—42no—
438#102—44no—
439C22⋊C8—22no—
440C22⋊C8—24no—
441C22⋊C8—22no—
442#97—28no—
443C4×C8—24no—
444#95—22no—
445#95—21no—
446#95—22no—
447#95—21no—
448#95—21no—
449#95—22no—
450#95—22no—
451#95—21no—
452#95—22no—
453#95—21no—
454#95—22no—
455#95—22no—
456#95—22no—
457C24—24no—
458C24—22no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24C22×D411yescharacteristic
466C2×Q8—28no—
467C2×Q8—24no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—21no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—42no—
483C2×Q8—416no—
484C2×Q8—416no—
485C2×Q8—416no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—42no—
489C2×Q8—44no—
490C2×Q8—82no—
491C2×Q8—81no—
492C2×Q8—82no—
493C2×Q8—81no—
494C2×Q8#12014yes—
495C2×Q8C22×D418yes—
496C2×Q8C2×#4112yes—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×D414yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—432no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4#13714yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C2×#4112yes—
553C22×C42−1+412yes—
554C22×C4C2511yescharacteristic
555Q16—416no—
556SD16—48no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—24no—
560C2×C8—22no—
561C2×C8—24no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—24no—
565C2×C8—22no—
566C4⋊C4—28no—
567C4⋊C4—24no—
568C4⋊C4—216no—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—216no—
572C4⋊C4—28no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—82no—
592C4⋊C4—81no—
593C4⋊C4—82no—
594C4⋊C4—81no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4#12014yes—
599C4⋊C4#12018yes—
600C4⋊C4C22×D414yes—
601C4⋊C4C2×#4112yes—
602C22⋊C4—216no—
603C22⋊C4—28no—
604C22⋊C4—216no—
605C22⋊C4—24no—
606C22⋊C4—216no—
607C22⋊C4—28no—
608C22⋊C4—216no—
609C22⋊C4—44no—
610C22⋊C4—42no—
611C42—216no—
612C42—216no—
613C42—22no—
614C42—22no—
615C42—24no—
616C42—24no—
617C42—22no—
618C42—24no—
619C42—44no—
620C42—44no—
621C42—42no—
622C42—42no—
623C42C22×D414yes—
624C42C22×D418yes—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—24no—
630C23—48no—
631C23—48no—
632C23—48no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23#54812yes—
644C23C2×#13712yes—
645C23#57712yes—
646C23C23×D411yescharacteristic
647Q8—28no—
648Q8—24no—
649Q8—28no—
650Q8—28no—
651Q8—48no—
652Q8—416no—
653Q8—44no—
654Q8—42no—
655Q8—44no—
656Q8—44no—
657Q8—164no—
658Q8—162no—
659D4—24no—
660D4—24no—
661D4—48no—
662D4—42no—
663D4—42no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—28no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—48no—
693C2×C4—416no—
694C2×C4—48no—
695C2×C4—416no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—416no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4C2×#12014yes—
718C2×C4C2×#12014yes—
719C2×C4C2×#12012yes—
720C2×C4C2×#12012yes—
721C2×C4#54812yes—
722C2×C4C2×#13712yes—
723C2×C4C2×#13712yes—
724C2×C4#57512yes—
725C2×C4C23×D412yes—
726C2×C4C22×#4111yescharacteristic
727C2×C4C2×2−1+411yescharacteristic
728C2×C4#58512yes—
729C8—42no—
730C8—44no—
731C8—42no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—816no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22#336914yescomplemented
747C22C22×#12011yescharacteristic
748C22C2×#54811yescharacteristic
749C22#348711yescharacteristic
750C22C22×#13711yescharacteristic
751C22C2×#57511yescharacteristic
752C22C2×#57711yescharacteristic
753C22#358611yescharacteristic
754C4—22no—
755C4—22no—
756C4—24no—
757C4—24no—
758C4—22no—
759C4—48no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4—42no—
765C4—41no—
766C4—82no—
767C4—81no—
768C4—82no—
769C4—81no—
770C4#300714yes—
771C4D4×#4112yes—
772C4#348912yes—
773C2—24no—
774C2—84no—
775C2#3642811yescharacteristic
776C2C2×#300711yescharacteristic
777C2#6037411yescharacteristic
778C2C2×#336911yescharacteristic
779C2#6132311yescharacteristic
780C2#6188911yescharacteristic
781C2#6189911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3369C2semidirect
3. Q8×C22⋊Q8C2semidirect
5. #32954C2semidirect
7. #25856C2semidirect
8. #25662C2semidirect
9. #25646C2semidirect
11. #24212C2semidirect
12. #24207C2semidirect
13. #24189C2semidirect
14. #22544C2semidirect
15. #22510C2semidirect
16. #21455C2semidirect
18. C2×Q82C22semidirect
36. C2×#487C22semidirect
37. C2×#475C22semidirect
40. C2×#462C22semidirect
43. C2×#446C22semidirect
44. C2×#441C22semidirect
48. #2582C22semidirect
49. #2582C22semidirect
50. #2567C22semidirect
51. #2567C22semidirect
57. Q8×C4⋊C4C22semidirect
61. #2043C22semidirect
62. #2043C22semidirect
66. #2016C22semidirect
68. #1985C22semidirect
69. #1984C22semidirect
71. #1981C22semidirect
73. #1956C22semidirect
74. #1878C22semidirect
77. #1865C22semidirect
78. #1865C22semidirect
79. #1865C22semidirect
84. #1803C22semidirect
93. #1763C22semidirect
746. C22#3369semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#33692
Q8×C22⋊Q82
#329562
#329542
#258642
#258562
#256622
#256462
#242172
#242122
#242072
#241892
#225442
#225102
#214552
C4×#4502