Finite Group Databasebeta

← #719817

Subgroups — #719817

Order 512.

3550 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×#2536C211yesmaximal, characteristic, complemented
3C2×#2426C212yesmaximal, complemented
4C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#2326C211yesmaximal, characteristic, complemented
6#16514C214yesmaximal, complemented
7#15436C214yesmaximal, complemented
8#15316C214yesmaximal, complemented
9#15131C212yesmaximal, complemented
10#15126C212yesmaximal, complemented
11#14799C214yesmaximal, complemented
12#14276C211yesmaximal, characteristic, complemented
13#13969C212yesmaximal, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13847C211yesmaximal, characteristic, complemented
16C22×#124C2211yescharacteristic
17C22×C22⋊Q8C2212yes—
18C22×#121C2212yes—
19C22×#121C2212yes—
20C22×C4×Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24#2537—28no—
25#2536—28no—
26#2426—216no—
27C2×#398C2212yes—
28C2×#396C2214yes—
29C2×#396C2214yes—
30C2×#394C2212yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34Q8×C4⋊C4—28no—
35#2326—28no—
36C2×#391C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2212yes—
39C2×#390C2214yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2214yes—
43C2×#388C2214yes—
44C2×#388C2214yes—
45C2×#388C2214yes—
46C2×#385C2214yes—
47C2×#384C2211yescharacteristic
48C2×#384C2212yes—
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×#376C2211yescharacteristic
59#1445C2212yes—
60#1441C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2214yes—
73#1438C2214yes—
74#1438C2212yes—
75#1437C2214yes—
76#1436C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C22⋊#95C2214yes—
80C23×Q8C2311yescharacteristic
81C23×D4C2311yescharacteristic
82C23×D4C2311yescharacteristic
83C23×D4C2314yes—
84C24×C4C2312yes—
85C24×C4C2312yes—
86C2×#124—24no—
87C2×#124—24no—
88C2×#124D418yescomplemented
89C2×C22⋊Q8—28no—
90C2×C22⋊Q8—28no—
91C2×C22⋊Q8—28no—
92C2×#121—28no—
93C2×#121—28no—
94C2×#121—28no—
95C2×#121—48no—
96C2×#121—44no—
97C2×C4×Q8—28no—
98C2×C4×Q8—28no—
99C2×C4×Q8—24no—
100C2×C4×Q8—24no—
101C2×C4×Q8—44no—
102C2×C4×Q8D418yescomplemented
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C42C2312yes—
139C22×C42C2311yescharacteristic
140C22×C42C2314yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#398—28no—
145#396—216no—
146#396—48no—
147#394—28no—
148#394—216no—
149#394—216no—
150#394—48no—
151#391—24no—
152#390—28no—
153#390—24no—
154#390—216no—
155#389—216no—
156#389—28no—
157#389—28no—
158#388—216no—
159#388—216no—
160#388—216no—
161#385—216no—
162#384—24no—
163#384—28no—
164#384D418yes—
165#382—24no—
166#380—28no—
167#380—28no—
168#380—28no—
169C4×C4⋊C4—28no—
170C4×C4⋊C4—24no—
171C4×C22⋊C4—28no—
172C4×C22⋊C4—44no—
173#376—24no—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C25C2412yes—
193C25C2412yes—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8C2×D414yes—
199C22×Q8C2×D414yes—
200C22×Q8#4114yes—
201C22×D4—24no—
202C22×D4—28no—
203C22×D4—28no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—28no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—42no—
215C22×D4—44no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4C2×D414yes—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—44no—
231C23×C4—44no—
232C23×C4C2412yes—
233C23×C4C2414yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2414yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2411yescharacteristic
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245#124—232no—
246C22⋊Q8—432no—
247#121—432no—
248#121—432no—
249C4×Q8—232no—
250C4×Q8—432no—
251C4×D4—416no—
252C4×D4—416no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4C2×D418yes—
290C2×C4⋊C4C2×D414yes—
291C2×C4⋊C4C2×D418yes—
292C2×C4⋊C4C2×D418yes—
293C2×C4⋊C4C2×D418yes—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—28no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4C2×D4116yes—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42—28no—
342C2×C42—24no—
343C2×C42—28no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—44no—
349C2×C42C2×D418yes—
350C2×C42C2×D414yes—
351C2×C42C2×D414yes—
352C2×C42C2×D414yes—
353C2×C42#4114yes—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—28no—
359#95—24no—
360#95—28no—
361#95—28no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—28no—
366#95—44no—
367#95—44no—
368#95—42no—
369#95—42no—
370#95—44no—
371#95—44no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—22no—
384C24—22no—
385C24—24no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24C22×D414yes—
397C24H(5,𝔽2)14yes—
398C24C2511yescharacteristic
399C2×Q8—28no—
400C2×Q8—28no—
401C2×Q8—28no—
402C2×Q8—28no—
403C2×Q8—28no—
404C2×Q8—28no—
405C2×Q8#121116yescomplemented
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—44no—
413C2×D4—416no—
414C2×D4—416no—
415C2×D4—416no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—88no—
422C2×D4—88no—
423C2×D4—88no—
424C2×D4—88no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—88no—
499C22×C4—88no—
500C22×C4C22×D414yes—
501C22×C4C22×D418yes—
502C22×C4C22×D414yes—
503C22×C4C22×D412yes—
504C22×C4C22×D412yes—
505C22×C4C22×D414yes—
506C22×C4C22×D412yes—
507C22×C4C22×D412yes—
508C22×C4C22×D414yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D412yes—
512C22×C4C2×#4112yes—
513C22×C4C2×#4112yes—
514C22×C4C2×#4114yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4112yes—
517C22×C4H(5,𝔽2)12yes—
518C22×C42−1+414yes—
519C22×C42−1+412yes—
520C4⋊C4—28no—
521C4⋊C4—216no—
522C4⋊C4—28no—
523C4⋊C4—216no—
524C4⋊C4—48no—
525C4⋊C4—48no—
526C4⋊C4—416no—
527C4⋊C4—44no—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C4⋊C4—48no—
531C4⋊C4—416no—
532C4⋊C4—88no—
533C4⋊C4—88no—
534C4⋊C4—88no—
535C22⋊C4—232no—
536C22⋊C4—48no—
537C22⋊C4—416no—
538C22⋊C4—48no—
539C22⋊C4—416no—
540C22⋊C4—416no—
541C22⋊C4—416no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—416no—
547C22⋊C4—88no—
548C22⋊C4—88no—
549C42—216no—
550C42—28no—
551C42—416no—
552C42—44no—
553C42—48no—
554C42#121116yes—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—28no—
562C23—28no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—44no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—44no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—44no—
594C23—42no—
595C23—42no—
596C23—44no—
597C23—42no—
598C23—42no—
599C23—44no—
600C23—42no—
601C23—42no—
602C23—44no—
603C23—42no—
604C23—42no—
605C23—44no—
606C23—44no—
607C23—42no—
608C23—44no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23C23×D411yescharacteristic
614C23C23×D411yescharacteristic
615C23C23×D411yescharacteristic
616C23C22×#4111yescharacteristic
617C23C22×#4111yescharacteristic
618C23C2×H(5,𝔽2)11yescharacteristic
619C23C2×H(5,𝔽2)12yes—
620C23C2×2−1+411yescharacteristic
621C23C2×2−1+412yes—
622C23#58512yes—
623C23#58512yes—
624Q8—232no—
625D4—416no—
626D4—416no—
627D4—832no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—816no—
702C2×C4—816no—
703C2×C4C2×#12114yes—
704C2×C4C2×#12114yes—
705C2×C4C2×#12118yes—
706C2×C4C2×#12114yes—
707C2×C4C2×#12114yes—
708C2×C4#53714yes—
709C2×C4D4214yes—
710C2×C4#54714yes—
711C2×C4#54814yes—
712C2×C4#55314yes—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—48no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—48no—
724C22—44no—
725C22—82no—
726C22—84no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—84no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C22×#12111yescharacteristic
740C22C22×#12111yescharacteristic
741C22C2×#53711yescharacteristic
742C22#346112yes—
743C22C2×D4211yescharacteristic
744C22C2×#54711yescharacteristic
745C22C2×#54811yescharacteristic
746C22C2×#55311yescharacteristic
747C22#348411yescharacteristic
748C22#348511yescharacteristic
749C22#348611yescharacteristic
750C22#348711yescharacteristic
751C22#348812yes—
752C22#348812yes—
753C22#348912yes—
754C22#349412yes—
755C22#349712yes—
756C22#352212yes—
757C22#352412yes—
758C22#354112yes—
759C22#354212yes—
760C22#354412yes—
761C22#356512yes—
762C4—24no—
763C4—28no—
764C4—24no—
765C4—48no—
766C4—44no—
767C4—44no—
768C4—44no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—84no—
774C4#241618yes—
775C2—84no—
776C2—84no—
777C2C2×#241611yescharacteristic
778C2#3515311yescharacteristic
779C2#3556311yescharacteristic
780C2#3583112yes—
781C2#3776612yes—
782C2#3926112yes—
783C2#4279812yes—
784C2#4493211yescharacteristic
785C2#4493711yescharacteristic
786C2#4526711yescharacteristic
787C2#4527011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2536C2semidirect
3. C2×#2426C2semidirect
4. C2×Q8×C4⋊C4C2semidirect
5. C2×#2326C2semidirect
6. #16514C2semidirect
7. #15436C2semidirect
8. #15316C2semidirect
9. #15131C2semidirect
10. #15126C2semidirect
11. #14799C2semidirect
12. #14276C2semidirect
13. #13969C2semidirect
14. #13941C2semidirect
15. #13847C2semidirect
88. C2×#124D4semidirect
102. C2×C4×Q8D4semidirect
405. C2×Q8#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#25362
C2×#24262
C2×Q8×C4⋊C42
C2×#23262
#165142
#154362
#153162
#151312
#151262
#147992
#142762
#139692
#139412
#138472