Finite Group Databasebeta

← C4×#1516 #182636

Subgroups — C4×#1516 #182636

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#1516C212yesmaximal
4C4×#381C211yesmaximal, characteristic, complemented
5#8221C212yesmaximal, complemented
6#8220C212yesmaximal, complemented
7C4×#328C212yesmaximal, complemented
8C4×#327C212yesmaximal, complemented
9#8024C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C411yescharacteristic, complemented
12C23×C42C2211yescharacteristic
13C22×C22⋊C8C2212yes—
14C22×C4×C8—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×#381C2212yes—
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C411yescharacteristic, complemented
36C2×C4×C22⋊C4—21no—
37C4×C22⋊C8—21no—
38C4×C22⋊C8—21no—
39C4×C22⋊C8C2212yes—
40C4×C22⋊C8C2212yes—
41C2×#336—21no—
42#1516C4116yesdirect product factor
43C2×#328C2214yes—
44C2×#327C2214yes—
45#1434—21no—
46#1434C2212yes—
47C22⋊#95—21no—
48C4×#95—21no—
49C4×#95C2212yes—
50#1294C2214yes—
51#1294C2214yes—
52C22×#41C2×C411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4D411yescharacteristic
55C24×C4C2311yescharacteristic
56C23×C8—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×C22⋊C4—22no—
83C22×C42—21no—
84C22×C42—22no—
85C22×C42—44no—
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42D411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×C22⋊C8—22no—
99C2×C22⋊C8—24no—
100C2×C22⋊C8C2×C418yescomplemented
101C2×C22⋊C8C2314yes—
102C2×C4×C8—22no—
103C2×C4×C8—22no—
104C2×C4×C8—44no—
105#391C2×C411yescharacteristic
106#391C2×C411yescharacteristic
107#390C2×C411yescharacteristic
108#390C2×C411yescharacteristic
109#389C2×C411yescharacteristic
110#389C2×C411yescharacteristic
111#389C2×C411yescharacteristic
112#389C2×C411yescharacteristic
113#388—21no—
114#388—21no—
115#388—21no—
116#388—21no—
117#387—21no—
118#387—21no—
119#387—21no—
120#387—21no—
121#386—21no—
122#386—21no—
123#386—21no—
124#386—21no—
125#386—21no—
126#386—21no—
127#385—21no—
128#385—21no—
129#385—21no—
130#385—21no—
131#385—21no—
132#385—21no—
133#381—21no—
134#381—24no—
135#381C2×C418yescomplemented
136#380C2×C411yescharacteristic
137#380C2×C411yescharacteristic
138#380C2311yescharacteristic
139#380C2311yescharacteristic
140#379—21no—
141C4×C4⋊C4—21no—
142C4×C4⋊C4—21no—
143C4×C4⋊C4—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4C2×C411yescharacteristic
148C4×C4⋊C4C2×C411yescharacteristic
149C4×C4⋊C4C2×C411yescharacteristic
150C4×C4⋊C4C2×C411yescharacteristic
151C4×C22⋊C4—21no—
152C4×C22⋊C4—21no—
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—44no—
166#376—21no—
167C2×#95—22no—
168C2×#95—22no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95C2314yes—
172C43—21no—
173#336—22no—
174#336—22no—
175#328C2×C4116yescomplemented
176#327C2×C4116yescomplemented
177C25C2×D411yescharacteristic
178C2×#41—22no—
179C2×#41—42no—
180C2×#41—42no—
181C2×#41C4214yescomplemented
182C22×Q8C22×C411yescharacteristic
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4C22×C411yescharacteristic
187C23×C4—24no—
188C23×C4—21no—
189C23×C4—24no—
190C23×C4—24no—
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×C4C22⋊C411yescharacteristic
200C23×C4C22⋊C411yescharacteristic
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×C414yes—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4#4114yes—
218C23×C4C2411yescharacteristic
219C22×C8—28no—
220C22×C8—24no—
221C22×C8—44no—
222C22×C8—44no—
223#123—28no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8C4214yescomplemented
227C22⋊Q8C22×C414yes—
228#121—22no—
229#121—22no—
230#121C4214yescomplemented
231#121C22×C414yes—
232#120—28no—
233C4×Q8—42no—
234C4×Q8—42no—
235C4×D4—28no—
236C4×D4—28no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4—44no—
240C4×D4—44no—
241C4×D4—44no—
242C4×D4—44no—
243C4×D4—44no—
244C4×D4—44no—
245#117—22no—
246#117—44no—
247#117—42no—
248#117—42no—
249#117C4214yescomplemented
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
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⋊C4C22×C411yescharacteristic
259C2×C4⋊C4C22×C411yescharacteristic
260C2×C4⋊C4C22×C411yescharacteristic
261C2×C4⋊C4C22×C411yescharacteristic
262C2×C4⋊C4C22×C411yescharacteristic
263C2×C4⋊C4C22×C411yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—28no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
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—44no—
283C2×C22⋊C4—44no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—42no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42—44no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—44no—
307C2×C42—44no—
308C2×C42—44no—
309C2×C42C22⋊C411yescharacteristic
310C2×C42C22⋊C411yescharacteristic
311C2×C42C22⋊C411yescharacteristic
312C2×C42C22⋊C411yescharacteristic
313C2×C42C22⋊C411yescharacteristic
314C2×C42C22⋊C411yescharacteristic
315C2×C42C22⋊C411yescharacteristic
316C2×C42C22⋊C411yescharacteristic
317C2×C42C22×C411yescharacteristic
318C2×C42C22×C411yescharacteristic
319C2×C42C22×C411yescharacteristic
320C2×C42C22×C411yescharacteristic
321C2×C42C2×D411yescharacteristic
322C2×C42C2×D411yescharacteristic
323C2×C42C2×D411yescharacteristic
324C2×C42C2×D411yescharacteristic
325C22⋊C8—28no—
326C22⋊C8—24no—
327C22⋊C8C22×C418yes—
328C4×C8—44no—
329C4×C8—44no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
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—28no—
345#95—21no—
346#95—21no—
347#95—24no—
348#95—44no—
349#95—44no—
350#95—44no—
351#95C22×C418yes—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—21no—
357C24—41no—
358C24—41no—
359C24C2×C22⋊C411yescharacteristic
360C24C2×C22⋊C411yescharacteristic
361C24C4×D414yes—
362C24C22×D411yescharacteristic
363#41—48no—
364#41—48no—
365C2×Q8—21no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8C2×C4212yes—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4C2×C4212yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
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—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—28no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—48no—
437C22×C4—41no—
438C22×C4—416no—
439C22×C4—42no—
440C22×C4—416no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4#9914yes—
455C22×C4C2×C4212yes—
456C22×C4C2×C4212yes—
457C22×C4C2×C22⋊C411yescharacteristic
458C22×C4C2×C22⋊C411yescharacteristic
459C22×C4C2×C22⋊C411yescharacteristic
460C22×C4C2×C22⋊C411yescharacteristic
461C22×C4C2×C22⋊C411yescharacteristic
462C22×C4C2×C22⋊C411yescharacteristic
463C22×C4C2×C22⋊C411yescharacteristic
464C22×C4C2×C22⋊C411yescharacteristic
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4#11712yes—
468C22×C4#11712yes—
469C22×C4C4×D414yes—
470C22×C4C4×D414yes—
471C22×C4C4×D414yes—
472C22×C4#13514yes—
473C22×C4#13514yes—
474C22×C4C23×C411yescharacteristic
475C22×C4C23×C412yes—
476C22×C4C22×D411yescharacteristic
477C22×C4C2×#4112yes—
478C2×C8—28no—
479C2×C8—44no—
480C2×C8—44no—
481C2×C8—416no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4C2×C4212yes—
497C4⋊C4C2×C4212yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—416no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C42—24no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—41no—
530C42—41no—
531C42—41no—
532C42—41no—
533C42—42no—
534C42—42no—
535C42—42no—
536C42—42no—
537C42—42no—
538C42—42no—
539C42—42no—
540C42—42no—
541C42—88no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—28no—
557C23—28no—
558C23—22no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—44no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23C4×C22⋊C412yes—
571C23C4×C22⋊C412yes—
572C23C2×#9912yes—
573C23#41012yes—
574C23C22×C22⋊C411yescharacteristic
575C23C2×C4×D412yes—
576C23C2×#13512yes—
577C23C2×#13512yes—
578Q8—42no—
579Q8—42no—
580D4—42no—
581D4—42no—
582D4—48no—
583D4—48no—
584D4—48no—
585C2×C4—28no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—28no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—28no—
608C2×C4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—48no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—44no—
640C2×C4—48no—
641C2×C4—48no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—48no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4C4×C22⋊C412yes—
662C2×C4C4×C22⋊C412yes—
663C2×C4C2×#9912yes—
664C2×C4C2×#9912yes—
665C2×C4#41612yes—
666C2×C4#41612yes—
667C2×C4#41612yes—
668C2×C4#41612yes—
669C2×C4#42112yes—
670C2×C4#42112yes—
671C2×C4C22×C4211yescharacteristic
672C2×C4C2×#11711yescharacteristic
673C2×C4C2×C4×D412yes—
674C8—48no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—416no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C4×#9914yes—
703C22C2×C4×C22⋊C411yescharacteristic
704C22C22×#9911yescharacteristic
705C22C2×#41011yescharacteristic
706C22C2×#41611yescharacteristic
707C22C2×#41611yescharacteristic
708C22C2×#42111yescharacteristic
709C22C2×#42111yescharacteristic
710C22C4×#13514yes—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—21no—
719C4—22no—
720C4—21no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—88no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4#151614yesdirect product factor
732C2—24no—
733C2—24no—
734C2—42no—
735C2—82no—
736C2C2×#151611yescharacteristic
737C2#1757111yescharacteristic
738C2#1757211yescharacteristic
739C2#1757611yescharacteristic
740C2C2×C4×#9911yescharacteristic
741C2C4×#42111yescharacteristic
742C2C4×#41611yescharacteristic
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. C2×C4×C22⋊C8C2semidirect
4. C4×#381C2semidirect
5. #8221C2semidirect
6. #8220C2semidirect
7. C4×#328C2semidirect
8. C4×#327C2semidirect
9. #8024C2semidirect
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
42. #1516C4direct (N × H)
100. C2×C22⋊C8C2×C4semidirect
135. #381C2×C4semidirect
175. #328C2×C4semidirect
176. #327C2×C4semidirect
181. C2×#41C42semidirect
226. C22⋊Q8C42semidirect
230. #121C42semidirect
249. #117C42semidirect
731. C4#1516direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#5252
C2×C4×C22⋊C82
C2×#15162
C4×#3812
#82212
#82202
C4×#3282
C4×#3272
#80242