Finite Group Databasebeta

← C4×#1513 #182626

Subgroups — C4×#1513 #182626

Order 512.

1632 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C4×#407C211yesmaximal, characteristic, complemented
3C2×#1513C212yesmaximal
4C4×#380C211yesmaximal, characteristic, complemented
5#8217C212yesmaximal, complemented
6#8216C212yesmaximal, complemented
7C4×#328C212yesmaximal, complemented
8C4×#327C212yesmaximal, complemented
9#8016C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C411yescharacteristic, complemented
12C23×C42C2211yescharacteristic
13C2×#407C2212yes—
14C2×C4×M16—21no—
15C4×C22⋊Q8C411yescharacteristic, complemented
16C4×C22⋊Q8C411yescharacteristic, complemented
17C4×C22⋊Q8C2211yescharacteristic
18C4×C22⋊Q8C2211yescharacteristic
19C4×#123—21no—
20C4×#123—21no—
21C4×#121C411yescharacteristic, complemented
22C4×#121C411yescharacteristic, complemented
23C4×#121C2211yescharacteristic
24C4×#121C2211yescharacteristic
25C4×#120—21no—
26C4×#120—21no—
27#2297C411yescharacteristic, complemented
28#2296C411yescharacteristic, complemented
29#2290—21no—
30#2290—21no—
31#2280C2211yescharacteristic
32C2×#380C2212yes—
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C411yescharacteristic, complemented
36C2×C4×C4⋊C4—21no—
37C2×C4×C22⋊C4—21no—
38#1749—21no—
39#1749C2212yes—
40C4×C22⋊C8—21no—
41C4×C22⋊C8C2212yes—
42#1728—21no—
43#1513C4116yesdirect product factor
44C2×#328C2214yes—
45C2×#327C2214yes—
46C4⋊#95—21no—
47#1434C2212yes—
48C22⋊#95—21no—
49C4×#95C2212yes—
50#1294C2214yes—
51#1294C2214yes—
52C22×#41C2×C411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4D411yescharacteristic
55C24×C4C2311yescharacteristic
56C22×M16—22no—
57#525—24no—
58#525C2×C418yes—
59C2×#123—21no—
60C2×C22⋊Q8C2×C411yescharacteristic
61C2×C22⋊Q8C2311yescharacteristic
62C2×#121C2×C411yescharacteristic
63C2×#121C2311yescharacteristic
64C2×#120—21no—
65C4×#41—44no—
66C2×C4×Q8C2×C411yescharacteristic
67C2×C4×Q8C2×C411yescharacteristic
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—21no—
75C2×C4×D4—21no—
76C2×C4×D4C2×C411yescharacteristic
77C2×C4×D4C2×C411yescharacteristic
78C2×#117—21no—
79C2×#117C2×C411yescharacteristic
80C2×#117C2×C411yescharacteristic
81C2×#117C2×C411yescharacteristic
82C22×C4⋊C4—22no—
83C22×C22⋊C4—22no—
84C22×C42—21no—
85C22×C42—22no—
86C22×C42—44no—
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#407—24no—
100#407C2×C418yescomplemented
101C2×C22⋊C8—22no—
102C2×C22⋊C8C2314yes—
103C4×M16—44no—
104C2×#97—22no—
105C2×C4×C8—22no—
106#391C2×C411yescharacteristic
107#391C2×C411yescharacteristic
108#390C2×C411yescharacteristic
109#390C2×C411yescharacteristic
110#389C2×C411yescharacteristic
111#389C2×C411yescharacteristic
112#389C2×C411yescharacteristic
113#389C2×C411yescharacteristic
114#388—21no—
115#388—21no—
116#388—21no—
117#388—21no—
118#387—21no—
119#387—21no—
120#387—21no—
121#387—21no—
122#386—21no—
123#386—21no—
124#386—21no—
125#386—21no—
126#386—21no—
127#386—21no—
128#385—21no—
129#385—21no—
130#385—21no—
131#385—21no—
132#385—21no—
133#385—21no—
134#381—21no—
135#380—24no—
136#380C2×C411yescharacteristic
137#380C2×C411yescharacteristic
138#380C2×C418yescomplemented
139#380C2311yescharacteristic
140#380C2311yescharacteristic
141#379—21no—
142C4×C4⋊C4—21no—
143C4×C4⋊C4—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—44no—
149C4×C4⋊C4C2×C411yescharacteristic
150C4×C4⋊C4C2×C411yescharacteristic
151C4×C4⋊C4C2×C411yescharacteristic
152C4×C4⋊C4C2×C411yescharacteristic
153C4×C22⋊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—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—44no—
168#376—21no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95C2314yes—
173C43—21no—
174#336—22no—
175#336—22no—
176#328C2×C4116yescomplemented
177#327C2×C4116yescomplemented
178C25C2×D411yescharacteristic
179C2×#41—22no—
180C2×#41—42no—
181C2×#41—42no—
182C2×#41C4214yescomplemented
183C22×Q8C22×C411yescharacteristic
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4C22×C411yescharacteristic
188C23×C4—21no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—24no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4C22⋊C411yescharacteristic
202C23×C4C22⋊C411yescharacteristic
203C23×C4C22⋊C411yescharacteristic
204C23×C4C22⋊C411yescharacteristic
205C23×C4C22⋊C411yescharacteristic
206C23×C4C22⋊C411yescharacteristic
207C23×C4C22⋊C411yescharacteristic
208C23×C4C22⋊C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C414yes—
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4#4114yes—
220C23×C4C2411yescharacteristic
221C2×M16—28no—
222C2×M16—44no—
223C2×M16—44no—
224C22×C8—24no—
225#123—28no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8C4214yescomplemented
229C22⋊Q8C22×C414yes—
230#121—22no—
231#121—22no—
232#121C4214yescomplemented
233#121C22×C414yes—
234#120—28no—
235C4×Q8—42no—
236C4×Q8—42no—
237C4×D4—28no—
238C4×D4—28no—
239C4×D4—42no—
240C4×D4—42no—
241C4×D4—44no—
242C4×D4—44no—
243C4×D4—44no—
244C4×D4—44no—
245C4×D4—44no—
246C4×D4—42no—
247C4×D4—42no—
248#117—22no—
249#117—44no—
250#117—42no—
251#117—42no—
252#117C4214yescomplemented
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—21no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4C22×C411yescharacteristic
265C2×C4⋊C4C22×C411yescharacteristic
266C2×C4⋊C4C22×C411yescharacteristic
267C2×C4⋊C4C22×C411yescharacteristic
268C2×C4⋊C4C22×C411yescharacteristic
269C2×C4⋊C4C22×C411yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—28no—
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—21no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—44no—
290C2×C42—21no—
291C2×C42—24no—
292C2×C42—24no—
293C2×C42—24no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—42no—
303C2×C42—42no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—42no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—44no—
312C2×C42—44no—
313C2×C42—44no—
314C2×C42—44no—
315C2×C42C22⋊C411yescharacteristic
316C2×C42C22⋊C411yescharacteristic
317C2×C42C22⋊C411yescharacteristic
318C2×C42C22⋊C411yescharacteristic
319C2×C42C22⋊C411yescharacteristic
320C2×C42C22⋊C411yescharacteristic
321C2×C42C22⋊C411yescharacteristic
322C2×C42C22⋊C411yescharacteristic
323C2×C42C22×C411yescharacteristic
324C2×C42C22×C411yescharacteristic
325C2×C42C22×C411yescharacteristic
326C2×C42C22×C411yescharacteristic
327C2×C42C2×D411yescharacteristic
328C2×C42C2×D411yescharacteristic
329C2×C42C2×D411yescharacteristic
330C2×C42C2×D411yescharacteristic
331C22⋊C8—28no—
332C22⋊C8—24no—
333C22⋊C8C22×C418yes—
334#97—44no—
335C4×C8—44no—
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—21no—
351#95—21no—
352#95—24no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95C22×C418yes—
357C24—21no—
358C24—21no—
359C24—22no—
360C24—21no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24C2×C22⋊C411yescharacteristic
366C24C2×C22⋊C411yescharacteristic
367C24C4×D414yes—
368C24C22×D411yescharacteristic
369#41—48no—
370#41—48no—
371C2×Q8—21no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8C2×C4212yes—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—24no—
378C2×D4—21no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—42no—
388C2×D4C2×C4212yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—28no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—48no—
449C22×C4—48no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—416no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4C2×C4212yes—
466C22×C4C2×C4212yes—
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×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4#11712yes—
478C22×C4#11712yes—
479C22×C4C4×D414yes—
480C22×C4C4×D414yes—
481C22×C4C4×D414yes—
482C22×C4AGL(1,ℤ/8)12yes—
483C22×C4#13712yes—
484C22×C4C23×C411yescharacteristic
485C22×C4C23×C412yes—
486C22×C4C22×D411yescharacteristic
487C22×C4C2×#4112yes—
488M16—416no—
489C2×C8—28no—
490C2×C8—44no—
491C2×C8—44no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—416no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4C2×C4212yes—
508C4⋊C4C2×C4212yes—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—416no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C42—24no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—41no—
539C42—41no—
540C42—41no—
541C42—41no—
542C42—41no—
543C42—41no—
544C42—42no—
545C42—42no—
546C42—42no—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—42no—
551C42—42no—
552C42—88no—
553C42#9914yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—24no—
571C23—24no—
572C23—22no—
573C23—44no—
574C23—44no—
575C23—42no—
576C23—42no—
577C23—44no—
578C23—44no—
579C23—42no—
580C23—42no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C4×C22⋊C412yes—
588C23C4×C22⋊C412yes—
589C23C22×C22⋊C411yescharacteristic
590C23C2×C4×D412yes—
591C23C2×AGL(1,ℤ/8)11yescharacteristic
592C23C2×#13711yescharacteristic
593C23#57512yes—
594Q8—42no—
595Q8—42no—
596D4—42no—
597D4—42no—
598D4—48no—
599D4—48no—
600D4—44no—
601D4—44no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—28no—
615C2×C4—28no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—44no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—48no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—48no—
660C2×C4—48no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—48no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4C4×C22⋊C412yes—
681C2×C4C4×C22⋊C412yes—
682C2×C4C2×#9912yes—
683C2×C4C2×#9912yes—
684C2×C4C2×#9912yes—
685C2×C4#41012yes—
686C2×C4#41712yes—
687C2×C4#41712yes—
688C2×C4#42112yes—
689C2×C4#42112yes—
690C2×C4C22×C4211yescharacteristic
691C2×C4C2×#11711yescharacteristic
692C2×C4C2×C4×D412yes—
693C8—48no—
694C22—21no—
695C22—21no—
696C22—22no—
697C22—22no—
698C22—21no—
699C22—21no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—48no—
709C22—48no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×C4×C22⋊C411yescharacteristic
726C22C22×#9911yescharacteristic
727C22C2×#41011yescharacteristic
728C22C2×#41711yescharacteristic
729C22#289611yescharacteristic
730C22C2×#42111yescharacteristic
731C22C2×#42111yescharacteristic
732C22C4×AGL(1,ℤ/8)12yes—
733C22C4×#13712yes—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—21no—
739C4—22no—
740C4—21no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—88no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4#151314yesdirect product factor
754C4C4×#9914yes—
755C2—22no—
756C2—22no—
757C2—42no—
758C2—42no—
759C2—82no—
760C2C2×#151311yescharacteristic
761C2#1755811yescharacteristic
762C2#1755911yescharacteristic
763C2#1756311yescharacteristic
764C2C2×C4×#9911yescharacteristic
765C2C4×#42111yescharacteristic
766C2C4×#41711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#407C2semidirect
4. C4×#380C2semidirect
5. #8217C2semidirect
6. #8216C2semidirect
7. C4×#328C2semidirect
8. C4×#327C2semidirect
9. #8016C2semidirect
11. C2×C4×#41C4semidirect
15. C4×C22⋊Q8C4semidirect
16. C4×C22⋊Q8C4semidirect
21. C4×#121C4semidirect
22. C4×#121C4semidirect
27. #2297C4semidirect
28. #2296C4semidirect
35. C4×#117C4semidirect
43. #1513C4direct (N × H)
100. #407C2×C4semidirect
138. #380C2×C4semidirect
176. #328C2×C4semidirect
177. #327C2×C4semidirect
182. C2×#41C42semidirect
228. C22⋊Q8C42semidirect
232. #121C42semidirect
252. #117C42semidirect
753. C4#1513direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#5252
C4×#4072
C2×#15132
C4×#3802
#82172
#82162
C4×#3282
C4×#3272
#80162