Finite Group Databasebeta

← #6519831

Subgroups — #6519831

Order 512.

2168 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
1C2×#3246C211yesmaximal, characteristic, complemented
2C2×#2988C211yesmaximal, characteristic, complemented
3#35273C211yesmaximal, characteristic
4#34947C211yesmaximal, characteristic, complemented
5#28555C214yesmaximal, complemented
6#25470C212yesmaximal, complemented
7#25385C212yesmaximal, complemented
8#25339C212yesmaximal, complemented
9#25293C212yesmaximal, complemented
10#24838C212yesmaximal, complemented
11#24776C214yesmaximal, complemented
12#24753C212yesmaximal, complemented
13#24703C212yesmaximal, complemented
14#24653C212yesmaximal, complemented
15#21860C211yesmaximal, characteristic, complemented
16#21386C211yesmaximal, characteristic, complemented
17C2×#1948C211yesmaximal, characteristic, complemented
18C2×#537—21no—
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22#3246—28no—
23C2×#475C2212yes—
24C2×#476C2212yes—
25C2×#465C2214yes—
26C2×#465C2214yes—
27C2×#460C2212yes—
28C2×#461C2212yes—
29#2988—28no—
30C2×C8×Q8C2212yes—
31C2×C8×D4C2212yes—
32C2×C8×D4C2214yes—
33C2×#431C2212yes—
34C2×#431C2211yescharacteristic
35C22×#106C2212yes—
36C22×C4⋊C8C2212yes—
37C22×C4⋊C8C2211yescharacteristic
38#2857C2212yes—
39#2856C2212yes—
40#2620—22no—
41#2568C2211yescharacteristic
42#2567C2211yescharacteristic
43#2566—21no—
44#2565—21no—
45#2564—22no—
46#2563C2211yescharacteristic
47#2542C2211yescharacteristic
48#2538—21no—
49#2538C2212yes—
50#2537—21no—
51#2537C2212yes—
52#2417C2212yes—
53#2417C2212yes—
54#2416—22no—
55#2416C2214yes—
56#2396—22no—
57#2311—21no—
58C4×C22⋊Q8C2212yes—
59C4×C22⋊Q8C2212yes—
60#2297—21no—
61#2285—21no—
62C2×#384C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2088C2214yes—
65#2077C2214yes—
66#2066C2214yes—
67#2065C2214yes—
68#2055C2214yes—
69#2035C2214yes—
70#2034C2214yes—
71#2000C2214yes—
72#1990C2212yes—
73#1988C2211yescharacteristic
74#1988C2211yescharacteristic
75#1982C2211yescharacteristic
76#1982C2211yescharacteristic
77#1968C2214yes—
78#1956C2212yes—
79#1948C2212yes—
80#1948C2212yes—
81#1948C2212yes—
82#1948C2212yes—
83#1941C2214yes—
84#1934C2214yes—
85#1933C2214yes—
86#1893C2214yes—
87#1892C2214yes—
88#1874C2212yes—
89#1874C2212yes—
90#1872C2214yes—
91#1807C2214yes—
92#1803C2212yes—
93#1803C2212yes—
94C4×#102C2212yes—
95C4×#102C2212yes—
96C2×#340C2212yes—
97C22×#41—21no—
98C22×#41D411yescharacteristic
99C22×SD16C2314yes—
100C23×C8C2314yes—
101C23×C8C2312yes—
102#537—48no—
103#533—24no—
104#533—24no—
105#532—24no—
106#532—24no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#125—21no—
112C2×#124—21no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—24no—
120C2×#121—22no—
121C2×#121—22no—
122C2×#121—21no—
123C2×#121—22no—
124C2×#121C2312yes—
125C2×#121C2314yes—
126C4×#41—24no—
127C4×#41—24no—
128C2×C4×Q8—21no—
129C2×C4×Q8D411yescharacteristic
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2311yescharacteristic
132C2×C4×D4—21no—
133C2×C4×D4D412yes—
134C2×C4×D4D411yescharacteristic
135C2×C4×D4C2312yes—
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2312yes—
138C2×#117—21no—
139C2×#117D411yescharacteristic
140C2×#117D412yes—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C42—21no—
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149#476—28no—
150#475—28no—
151#465—216no—
152#465—48no—
153#461—28no—
154#460—28no—
155C8×Q8—28no—
156C8×D4—216no—
157C8×D4—28no—
158#431—24no—
159#431—28no—
160C2×#106—44no—
161C2×#106C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×C4⋊C8—28no—
165C2×C4⋊C8D418yescomplemented
166C2×C4⋊C8C2314yes—
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2312yes—
175C2×#102C2314yes—
176C2×#102C2312yes—
177C2×#102C2312yes—
178C2×#102C2312yes—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2312yes—
181C2×C4×C8C2314yes—
182C2×C4×C8C2312yes—
183#400—22no—
184#399—22no—
185#398—22no—
186#398—22no—
187#396—24no—
188#396—24no—
189#396—22no—
190#396—22no—
191#395—22no—
192#394—24no—
193#394—24no—
194#393—22no—
195#391—21no—
196#391—21no—
197#391—22no—
198#391C2312yes—
199#391C2312yes—
200#390—21no—
201#390—21no—
202#390—22no—
203#390—22no—
204#390C2314yes—
205#389—22no—
206#389C2312yes—
207#389C2312yes—
208#389C2314yes—
209#387—22no—
210#387—22no—
211#386—22no—
212#386—22no—
213#386—24no—
214#385—22no—
215#385—22no—
216#384—21no—
217#384—21no—
218#384—21no—
219#384—21no—
220#384C2312yes—
221#384C2312yes—
222#382—21no—
223#382—21no—
224#380—22no—
225#380—22no—
226#380—22no—
227#380—22no—
228#380—22no—
229#380C2312yes—
230#380C2312yes—
231#380C2314yes—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4C2311yescharacteristic
237C4×C4⋊C4C2311yescharacteristic
238C4×C4⋊C4C2311yescharacteristic
239C4×C4⋊C4C2311yescharacteristic
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C2×#95—21no—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2312yes—
247#340C2312yes—
248#340C2312yes—
249#340C2314yes—
250#340C2312yes—
251C2×#41—24no—
252C2×#41—24no—
253C2×#41—44no—
254C2×#41—44no—
255C2×#41—44no—
256C2×#41SD1618yescomplemented
257C22×Q8—21no—
258C22×Q8—21no—
259C22×Q8C2×D411yescharacteristic
260C22×Q8C2412yes—
261C22×D4—22no—
262C22×D4—24no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4C2×D412yes—
266C22×D4C2×D411yescharacteristic
267C22×D4C2412yes—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4C2×D412yes—
273C23×C4C2×D412yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C2×SD16—28no—
279C2×SD16—44no—
280C2×SD16—44no—
281C22×C8—28no—
282C22×C8—42no—
283C22×C8—42no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8C2×D418yes—
287C22×C8C2412yes—
288C22×C8C2412yes—
289C22×C8C2414yes—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296#127—22no—
297#127—22no—
298#125—44no—
299#124—44no—
300C22⋊Q8—24no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306C22⋊Q8—48no—
307C22⋊Q8—44no—
308C22⋊Q8—48no—
309#121—24no—
310#121—24no—
311#121—48no—
312#121—416no—
313#121—44no—
314#121—48no—
315#121—44no—
316#121—44no—
317#121—84no—
318C4×Q8—24no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8—44no—
324C4×D4—28no—
325C4×D4—24no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—22no—
329C4×D4—24no—
330C4×D4—22no—
331C4×D4—24no—
332C4×D4—44no—
333#117—24no—
334#117—28no—
335#117—44no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C4⋊C4C2×D412yes—
366C2×C4⋊C4C2414yes—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2411yescharacteristic
372C2×C4⋊C4C2411yescharacteristic
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4C2×D412yes—
385C2×C22⋊C4C2×D412yes—
386C2×C22⋊C4C2×D412yes—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—44no—
395C2×C42C2×D412yes—
396C2×C42C2×D412yes—
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D414yes—
400C2×C42#4114yes—
401C2×C42C2412yes—
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404#106—28no—
405#106—28no—
406#106—44no—
407C4⋊C8—28no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410C4⋊C8C2×D418yes—
411C4⋊C8C2×D418yes—
412#103—28no—
413#103—44no—
414#103—44no—
415#102—28no—
416#102—24no—
417#102—24no—
418#102—42no—
419#102—42no—
420C22⋊C8—24no—
421C22⋊C8—28no—
422C4×C8—28no—
423C4×C8—24no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—24no—
437#95—24no—
438C24—22no—
439C24C22×D412yes—
440C24C22×D411yescharacteristic
441#41—232no—
442#41—816no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×Q8C2×SD1614yes—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4C2×SD1618yes—
481C2×D4C2×SD1614yes—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—82no—
518C22×C4—82no—
519C22×C4#12114yes—
520C22×C4#12114yes—
521C22×C4C2×SD1618yes—
522C22×C4C2×SD1614yes—
523C22×C4#13514yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C2×#4112yes—
534C22×C4C2511yescharacteristic
535SD16—88no—
536C2×C8—24no—
537C2×C8—24no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—48no—
545C2×C8—88no—
546C2×C8C22×D418yes—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—24no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—48no—
577C4⋊C4—82no—
578C4⋊C4—82no—
579C4⋊C4—82no—
580C4⋊C4—82no—
581C4⋊C4H(5,𝔽2)12yes—
582C4⋊C42−1+412yes—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—48no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—48no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C22⋊C4—82no—
596C22⋊C4—82no—
597C42—24no—
598C42—24no—
599C42—22no—
600C42—22no—
601C42—44no—
602C42—42no—
603C42—42no—
604C42—42no—
605C42—42no—
606C42#12114yes—
607C42#12114yes—
608C42C22×D412yes—
609C42C22×D412yes—
610C42C2×#4112yes—
611C42C2×#4112yes—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23C2×#12112yes—
630C23C22×SD1614yes—
631C23C22×SD1612yes—
632C23C2×#13512yes—
633C23C23×D411yescharacteristic
634Q8—28no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—84no—
640Q8—84no—
641D4—216no—
642D4—28no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—84no—
648D4—88no—
649D4—84no—
650D4—168no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—216no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—44no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—88no—
703C2×C4—164no—
704C2×C4#465116yescomplemented
705C2×C4C2×#12112yes—
706C2×C4C2×#12112yes—
707C2×C4C2×#12112yes—
708C2×C4C2×#12112yes—
709C2×C4C2×#12112yes—
710C2×C4C22×SD1614yes—
711C2×C4C22×SD1612yes—
712C2×C4C22×SD1612yes—
713C2×C4C2×#13512yes—
714C2×C4C2×#13512yes—
715C2×C4C23×D411yescharacteristic
716C2×C4C22×#4111yescharacteristic
717C2×C4C2×H(5,𝔽2)11yescharacteristic
718C2×C4C2×2−1+411yescharacteristic
719C2×C4#58511yescharacteristic
720C2×C4#58511yescharacteristic
721C8—28no—
722C8—42no—
723C8—42no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22C2×#46514yes—
745C22C22×#12111yescharacteristic
746C22#348811yescharacteristic
747C22#348911yescharacteristic
748C22C23×SD1611yescharacteristic
749C22C22×#13511yescharacteristic
750C22#358511yescharacteristic
751C22#358611yescharacteristic
752C4—24no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—82no—
761C4—82no—
762C4—81no—
763C4—82no—
764C4—81no—
765C4—84no—
766C4C2×#46514yes—
767C4C2×#46514yes—
768C4#349611yescharacteristic
769C4#349711yescharacteristic
770C4#351111yescharacteristic
771C4#351211yescharacteristic
772C2—24no—
773C2—44no—
774C2—162no—
775C2#3556411yescharacteristic
776C2C22×#46511yescharacteristic
777C2#6045611yescharacteristic
778C2#6195011yescharacteristic
779C2#6195111yescharacteristic
780C2#6209811yescharacteristic
781C2#6209911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35273C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3246C2semidirect
2. C2×#2988C2semidirect
4. #34947C2semidirect
5. #28555C2semidirect
6. #25470C2semidirect
7. #25385C2semidirect
8. #25339C2semidirect
9. #25293C2semidirect
10. #24838C2semidirect
11. #24776C2semidirect
12. #24753C2semidirect
13. #24703C2semidirect
14. #24653C2semidirect
15. #21860C2semidirect
16. #21386C2semidirect
17. C2×#1948C2semidirect
165. C2×C4⋊C8D4semidirect
256. C2×#41SD16semidirect
704. C2×C4#465semidirect

Maximal subgroups

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

subgroupindex
C2×#32462
C2×#29882
#352732
#349472
#285552
#254702
#253852
#253392
#252932
#248382
#247762
#247532
#247032
#246532
#218602
#213862
C2×#19482