Finite Group Databasebeta

← #492994

Subgroups — #492994

Order 512.

1457 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34264C211yesmaximal, characteristic
2C2×#2121C212yesmaximal
3#20398C211yesmaximal, characteristic, complemented
4#20392C211yesmaximal, characteristic, complemented
5#12622C212yesmaximal, complemented
6#12621C212yesmaximal, complemented
7C4×#352C212yesmaximal, complemented
8C4×AΣL(1,𝔽16)C212yesmaximal, complemented
9C2×#1390C212yesmaximal, complemented
10C2×#534C2211yescharacteristic
11C2×#518C2211yescharacteristic
12C22×C4×D4C411yescharacteristic, complemented
13C22×#100C2212yes—
14C22×#99C2212yes—
15#2873—21no—
16#2364—21no—
17#2364—21no—
18#2361—21no—
19#2361—21no—
20#2359—21no—
21#2359—21no—
22#2358—21no—
23#2358—21no—
24#2322C411yescharacteristic, complemented
25#2322C2211yescharacteristic
26#2321C411yescharacteristic, complemented
27#2321C2211yescharacteristic
28#2308C411yescharacteristic, complemented
29C4×#123C411yescharacteristic, complemented
30C4×#123C2211yescharacteristic
31C4×#120C411yescharacteristic, complemented
32C4×#120C2211yescharacteristic
33C2×#386C2211yescharacteristic
34C2×#385C411yescharacteristic, complemented
35#2273—21no—
36#2273C411yescharacteristic, complemented
37#2121C4116yescomplemented
38C2×#352C2214yes—
39C2×AΣL(1,𝔽16)C2214yes—
40C4×#100—21no—
41C4×#100—21no—
42C4×#100C2212yes—
43C4×#100C2212yes—
44C4×#99—21no—
45C4×#99—21no—
46C4×#99C2212yes—
47C4×#99C2212yes—
48#1742—21no—
49C2×#342—21no—
50#1390C2214yes—
51#1390C2214yes—
52C23×D4C2×C411yescharacteristic
53C23×D4C2311yescharacteristic
54C24×C4C2×C411yescharacteristic
55C24×C4C2×C411yescharacteristic, complemented
56C22×M16—22no—
57#534—24no—
58#534C2×C418yes—
59C2×#123—21no—
60C2×#123C2×C411yescharacteristic
61C2×#123C2311yescharacteristic
62C2×#121—21no—
63C2×#121—21no—
64C2×#120—21no—
65C2×#120C2×C411yescharacteristic
66C2×#120C2311yescharacteristic
67#518—44no—
68C2×C4×D4—21no—
69C2×C4×D4—21no—
70C2×C4×D4—21no—
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—44no—
75C2×C4×D4C2×C411yescharacteristic
76C2×C4×D4C2×C411yescharacteristic
77C2×C4×D4D411yescharacteristic
78C2×C4×D4D411yescharacteristic
79C2×C4×D4D411yescharacteristic
80C2×C4×D4D411yescharacteristic
81C2×C4×D4C2311yescharacteristic
82C2×C4×D4C2311yescharacteristic
83C2×#117D411yescharacteristic
84C2×#117D411yescharacteristic
85C22×C4⋊C4—21no—
86C22×C4⋊C4C2×C411yescharacteristic, complemented
87C22×C22⋊C4—22no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic, complemented
94C22×C22⋊C4D411yescharacteristic
95C22×C22⋊C4D411yescharacteristic
96C22×C42C2×C411yescharacteristic, complemented
97C2×#100—22no—
98C2×#100—24no—
99C2×#100C2×C418yescomplemented
100C2×#100C2314yes—
101C2×#99—22no—
102C2×#99—24no—
103C2×#99C2×C418yescomplemented
104C2×#99C2314yes—
105#405—44no—
106C4×M16—22no—
107C4×M16—22no—
108#390—21no—
109#390—21no—
110#389—21no—
111#389—21no—
112#388—21no—
113#388—21no—
114#388—21no—
115#388—21no—
116#388—21no—
117#388—21no—
118#388—21no—
119#388—21no—
120#387—21no—
121#387—21no—
122#387—21no—
123#387—21no—
124#386—21no—
125#386—21no—
126#386—21no—
127#386—21no—
128#386—21no—
129#386—21no—
130#386—21no—
131#386—21no—
132#386—21no—
133#386—21no—
134#386C2×C411yescharacteristic
135#386C2×C411yescharacteristic
136#386C2311yescharacteristic
137#386C2311yescharacteristic
138#385—21no—
139#385—21no—
140#385—21no—
141#385—21no—
142#385—21no—
143#385—21no—
144#385C2×C411yescharacteristic, complemented
145#385C2×C411yescharacteristic, complemented
146#385C2×C411yescharacteristic, complemented
147#385C2×C411yescharacteristic, complemented
148#381C2×C411yescharacteristic, complemented
149#381C2×C411yescharacteristic, complemented
150#379C2×C411yescharacteristic, complemented
151#379C2×C411yescharacteristic, complemented
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154C4×C22⋊C4—21no—
155C4×C22⋊C4—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—22no—
163C4×C22⋊C4—22no—
164C4×C22⋊C4—44no—
165C4×C22⋊C4C2×C411yescharacteristic, complemented
166C4×C22⋊C4C2×C411yescharacteristic, complemented
167C4×C22⋊C4C2×C411yescharacteristic, complemented
168C4×C22⋊C4C2×C411yescharacteristic, complemented
169C2×#95—21no—
170C2×#95—21no—
171#352C2×C4116yescomplemented
172AΣL(1,𝔽16)C2×C4116yescomplemented
173#343—22no—
174#343—22no—
175#342—22no—
176#342—22no—
177C25C22×C411yescharacteristic
178C25C22×C411yescharacteristic
179C25C2×D411yescharacteristic
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—22no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—42no—
186C22×D4—42no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4C4214yescomplemented
190C22×D4C22×C411yescharacteristic
191C22×D4C22×C414yes—
192C22×D4C2×D411yescharacteristic
193C22×D4C2×D411yescharacteristic
194C22×D4#4114yes—
195C22×D4C2411yescharacteristic
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—82no—
206C23×C4—82no—
207C23×C4C22⋊C411yescharacteristic
208C23×C4C22⋊C411yescharacteristic
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22⋊C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C2×M16—28no—
220C2×M16—24no—
221C2×M16—44no—
222C2×M16—42no—
223C22×C8—42no—
224#123—22no—
225#123—22no—
226#123—28no—
227#123C4214yescomplemented
228#123C22×C414yes—
229#121—28no—
230#121—28no—
231#120—28no—
232#120—22no—
233#120—22no—
234#120C4214yescomplemented
235#120C22×C414yes—
236C4×D4—42no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4—42no—
241C4×D4—42no—
242C4×D4—42no—
243C4×D4—42no—
244C4×D4—44no—
245C4×D4—44no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4—82no—
249C4×D4—82no—
250#117—24no—
251#117—42no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—82no—
262C2×C4⋊C4C22⋊C411yescharacteristic
263C2×C4⋊C4C22⋊C411yescharacteristic
264C2×C4⋊C4C2×D411yescharacteristic
265C2×C4⋊C4C2×D411yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—28no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—82no—
294C2×C22⋊C4C4214yescomplemented
295C2×C22⋊C4C22⋊C411yescharacteristic
296C2×C22⋊C4C22⋊C411yescharacteristic
297C2×C22⋊C4C22⋊C411yescharacteristic
298C2×C22⋊C4C22⋊C411yescharacteristic
299C2×C22⋊C4C22⋊C411yescharacteristic
300C2×C22⋊C4C22⋊C411yescharacteristic
301C2×C22⋊C4C22⋊C411yescharacteristic
302C2×C22⋊C4C22⋊C411yescharacteristic
303C2×C22⋊C4C22×C411yescharacteristic
304C2×C22⋊C4C22×C411yescharacteristic
305C2×C22⋊C4C22×C411yescharacteristic
306C2×C22⋊C4C22×C411yescharacteristic
307C2×C22⋊C4C22×C411yescharacteristic
308C2×C22⋊C4C22×C411yescharacteristic
309C2×C22⋊C4C2×D411yescharacteristic
310C2×C22⋊C4C2×D411yescharacteristic
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42C22⋊C411yescharacteristic
321C2×C42C22⋊C411yescharacteristic
322C2×C42C2×D411yescharacteristic
323C2×C42C2×D411yescharacteristic
324#100—28no—
325#100—24no—
326#100C22×C418yes—
327#99—28no—
328#99—24no—
329#99C22×C418yes—
330#97—42no—
331#97—42no—
332C4×C8—42no—
333C4×C8—42no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—42no—
351#95—42no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—21no—
357C24—21no—
358C24—41no—
359C24—41no—
360C24—81no—
361C24—81no—
362C24—81no—
363C24—81no—
364C24—81no—
365C24—81no—
366C24C2×C4212yes—
367C24C2×C4212yes—
368C24C2×C22⋊C411yescharacteristic
369C24C2×C22⋊C411yescharacteristic
370C24C2×C22⋊C411yescharacteristic
371C24#11712yes—
372C24C4×D414yes—
373C24C23×C411yescharacteristic
374C24C22×D411yescharacteristic
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—24no—
378C2×D4—24no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4—48no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—48no—
397C2×D4—81no—
398C2×D4—81no—
399C2×D4—81no—
400C2×D4—81no—
401C2×D4C2×C4212yes—
402C2×D4#11712yes—
403C2×D4C4×D414yes—
404C2×D4C4×D414yes—
405C2×D4C23×C412yes—
406C2×D4C2×#4112yes—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—48no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—41no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4—81no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4—84no—
460C22×C4—84no—
461C22×C4—84no—
462C22×C4—84no—
463C22×C4—162no—
464C22×C4—162no—
465C22×C4C2×C4212yes—
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C4×D414yes—
476C22×C4C22×D411yescharacteristic
477M16—28no—
478M16—44no—
479M16—48no—
480C2×C8—44no—
481C2×C8—48no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—24no—
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—28no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—44no—
517C22⋊C4—48no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—81no—
528C22⋊C4#9914yes—
529C22⋊C4C2×C4212yes—
530C22⋊C4C2×C4212yes—
531C42—22no—
532C42—22no—
533C42—41no—
534C42—41no—
535C42—42no—
536C42—42no—
537C42—81no—
538C42—81no—
539C42—81no—
540C42—81no—
541C42—162no—
542C42—162no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—42no—
571C23—42no—
572C23—41no—
573C23—41no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—82no—
579C23—82no—
580C23—82no—
581C23—84no—
582C23—84no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23—84no—
587C23—162no—
588C23C4×C22⋊C412yes—
589C23C4×C22⋊C412yes—
590C23C4×C22⋊C412yes—
591C23C2×#9912yes—
592C23#41012yes—
593C23C22×C4211yescharacteristic
594C23C22×C22⋊C411yescharacteristic
595C23C2×#11711yescharacteristic
596C23C2×C4×D412yes—
597D4—42no—
598D4—42no—
599D4—44no—
600D4—44no—
601D4—42no—
602D4—42no—
603D4—48no—
604D4—48no—
605D4—84no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—82no—
654C2×C4—82no—
655C2×C4—82no—
656C2×C4—82no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—82no—
665C2×C4—161no—
666C2×C4—161no—
667C2×C4—161no—
668C2×C4—161no—
669C2×C4—162no—
670C2×C4—168no—
671C2×C4C4×C22⋊C412yes—
672C2×C4C2×#9912yes—
673C2×C4C2×#9912yes—
674C2×C4C2×C4×D412yes—
675C8—48no—
676C22—21no—
677C22—22no—
678C22—21no—
679C22—22no—
680C22—22no—
681C22—21no—
682C22—21no—
683C22—22no—
684C22—22no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—84no—
706C22—81no—
707C22—81no—
708C22—84no—
709C22—84no—
710C22—84no—
711C22—81no—
712C22—81no—
713C22—84no—
714C22—84no—
715C22—81no—
716C22—81no—
717C22C4×#9914yes—
718C22C2×C4×C22⋊C411yescharacteristic
719C22C22×#9911yescharacteristic
720C22C2×#41011yescharacteristic
721C4—22no—
722C4—22no—
723C4—22no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—88no—
738C4—81no—
739C2—21no—
740C2—21no—
741C2—24no—
742C2—42no—
743C2—42no—
744C2—41no—
745C2—41no—
746C2—42no—
747C2—82no—
748C2C2×C4×#9911yescharacteristic
749C2#3334811yescharacteristic
750C2#3335011yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC23C22×C42
Frattini, cosocleC22×D4C24
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#518 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #20398C2semidirect
4. #20392C2semidirect
5. #12622C2semidirect
6. #12621C2semidirect
7. C4×#352C2semidirect
8. C4×AΣL(1,𝔽16)C2semidirect
9. C2×#1390C2semidirect
12. C22×C4×D4C4semidirect
24. #2322C4semidirect
26. #2321C4semidirect
28. #2308C4semidirect
29. C4×#123C4semidirect
31. C4×#120C4semidirect
34. C2×#385C4semidirect
36. #2273C4semidirect
37. #2121C4semidirect
55. C24×C4C2×C4semidirect
86. C22×C4⋊C4C2×C4semidirect
93. C22×C22⋊C4C2×C4semidirect
96. C22×C42C2×C4semidirect
99. C2×#100C2×C4semidirect
103. C2×#99C2×C4semidirect
144. #385C2×C4semidirect
145. #385C2×C4semidirect
146. #385C2×C4semidirect
147. #385C2×C4semidirect
148. #381C2×C4semidirect
149. #381C2×C4semidirect
150. #379C2×C4semidirect
151. #379C2×C4semidirect
165. C4×C22⋊C4C2×C4semidirect
166. C4×C22⋊C4C2×C4semidirect
167. C4×C22⋊C4C2×C4semidirect
168. C4×C22⋊C4C2×C4semidirect
171. #352C2×C4semidirect
172. AΣL(1,𝔽16)C2×C4semidirect
189. C22×D4C42semidirect
227. #123C42semidirect
234. #120C42semidirect
294. C2×C22⋊C4C42semidirect

Maximal subgroups

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

subgroupindex
#342642
C2×#21212
#203982
#203922
#126222
#126212
C4×#3522
C4×AΣL(1,𝔽16)2
C2×#13902