Finite Group Databasebeta

← #642340

Subgroups — #642340

Order 512.

3056 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic
2C2×#2618C211yesmaximal, characteristic
3C22×#387C211yesmaximal, characteristic, complemented
4C2×#2283C211yesmaximal, characteristic, complemented
5#16685C214yesmaximal, complemented
6#16677C212yesmaximal, complemented
7#16664C212yesmaximal, complemented
8#15069C212yesmaximal, complemented
9#14912C212yesmaximal, complemented
10#14903C212yesmaximal, complemented
11#14898C212yesmaximal, complemented
12#14864C214yesmaximal, complemented
13#14339C211yesmaximal, characteristic, complemented
14#14275C211yesmaximal, characteristic, complemented
15#14271C211yesmaximal, characteristic
16#14020C212yesmaximal, complemented
17#13996C212yesmaximal, complemented
18C22×#123C2212yes—
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2854—28no—
25#2618—28no—
26C2×#398C2212yes—
27C2×#396C2214yes—
28C2×#394C2212yes—
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#387—28no—
36C2×#387C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#387C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#385C2212yes—
45#2283—28no—
46C2×#383C2212yes—
47C2×#382C2212yes—
48C2×#381C2212yes—
49C2×#381C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×#376C2212yes—
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1445C2214yes—
61#1445C2212yes—
62#1444C2214yes—
63#1444C2212yes—
64#1444C2214yes—
65#1443C2214yes—
66#1442C2214yes—
67#1442C2212yes—
68#1441C2214yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2212yes—
81#1437C2214yes—
82#1437C2214yes—
83C4⋊#95C2214yes—
84#1434C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C2×#123—28no—
97C2×#123—28no—
98C2×#123—28no—
99C2×#123—44no—
100C2×#123—44no—
101C2×#123—44no—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42D418yes—
139C22×C42C2314yes—
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#398—28no—
145#396—216no—
146#394—28no—
147#390—24no—
148#390—24no—
149#389—24no—
150#389—24no—
151#388—28no—
152#388—28no—
153#387—28no—
154#387—28no—
155#387—28no—
156#387—28no—
157#386—28no—
158#386—28no—
159#386—28no—
160#386—44no—
161#385—44no—
162#383—28no—
163#382—28no—
164#381—28no—
165#381—44no—
166#380—24no—
167#380—24no—
168#380D418yes—
169C4×C4⋊C4—28no—
170C4×C22⋊C4—28no—
171#376—28no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C25C2412yes—
203C25C2411yescharacteristic
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—42no—
215C22×D4—42no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4C2×D414yes—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4#4114yes—
253C23×C4#4114yes—
254C23×C4#4114yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2414yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2414yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270#123—432no—
271#123—432no—
272#121—416no—
273C2×C4⋊C4—232no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4C2×D418yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4C2×D418yes—
346C2×C42—232no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—28no—
356C2×C42—28no—
357C2×C42—44no—
358C2×C42C2×D414yes—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361C2×C42C2×D414yes—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—28no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D418yes—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24C22×D412yes—
404C24C22×D412yes—
405C24C2×#4112yes—
406C24C2×#4112yes—
407C24C2×#4112yes—
408C24H(5,𝔽2)12yes—
409C24H(5,𝔽2)12yes—
410C24C2511yescharacteristic
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—44no—
421C2×D4—84no—
422C2×D4—84no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—48no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4#121116yes—
535C22×C4C22×D412yes—
536C22×C4C22×D418yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C2×#4114yes—
545C22×C4C2×#4114yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C42−1+414yes—
549C4⋊C4—216no—
550C4⋊C4—216no—
551C4⋊C4—48no—
552C4⋊C4—416no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—44no—
561C4⋊C4—88no—
562C22⋊C4—216no—
563C22⋊C4—416no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—88no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C42—28no—
575C42—28no—
576C42—28no—
577C42—28no—
578C42—416no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—44no—
603C23—44no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23C2×#12114yes—
619C23#52514yes—
620C23#53514yes—
621C23#54614yes—
622C23#55014yes—
623C23#55314yes—
624C23#55514yes—
625C23C23×D411yescharacteristic
626C23C23×D411yescharacteristic
627C23C22×#4111yescharacteristic
628C23C22×#4111yescharacteristic
629C23C22×#4111yescharacteristic
630C23C2×H(5,𝔽2)11yescharacteristic
631C23C2×H(5,𝔽2)11yescharacteristic
632C23C2×2−1+412yes—
633C23#58512yes—
634C23#58512yes—
635C23#58512yes—
636D4—88no—
637D4—816no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—28no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—416no—
668C2×C4—416no—
669C2×C4—416no—
670C2×C4—42no—
671C2×C4—416no—
672C2×C4—416no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—88no—
728C2×C4—88no—
729C2×C4C2×#12114yes—
730C2×C4C2×#12114yes—
731C2×C4#53614yes—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—28no—
737C22—28no—
738C22—28no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—84no—
746C22—84no—
747C22—84no—
748C22—84no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22#241418yes—
754C22C22×#12111yescharacteristic
755C22C2×#52511yescharacteristic
756C22C2×#53511yescharacteristic
757C22C2×#53611yescharacteristic
758C22#344911yescharacteristic
759C22#344911yescharacteristic
760C22#344911yescharacteristic
761C22#346112yes—
762C22#346112yes—
763C22C2×#54611yescharacteristic
764C22C2×#55011yescharacteristic
765C22C2×#55311yescharacteristic
766C22C2×#55511yescharacteristic
767C22#348512yes—
768C22#348912yes—
769C22#349112yes—
770C22#349112yes—
771C22#349312yes—
772C22#349512yes—
773C22#355912yes—
774C22#355912yes—
775C22#356012yes—
776C22#356012yes—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—44no—
781C4—48no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—42no—
786C4—82no—
787C4—84no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C2—28no—
793C2—162no—
794C2#3460211yescharacteristic
795C2C2×#241411yescharacteristic
796C2#3508911yescharacteristic
797C2#3511811yescharacteristic
798C2#3530611yescharacteristic
799C2#3753911yescharacteristic
800C2#3754711yescharacteristic
801C2#3774712yes—
802C2#3777112yes—
803C2#3794312yes—
804C2#3795112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#387C2semidirect
4. C2×#2283C2semidirect
5. #16685C2semidirect
6. #16677C2semidirect
7. #16664C2semidirect
8. #15069C2semidirect
9. #14912C2semidirect
10. #14903C2semidirect
11. #14898C2semidirect
12. #14864C2semidirect
13. #14339C2semidirect
14. #14275C2semidirect
16. #14020C2semidirect
17. #13996C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#26182
C22×#3872
C2×#22832
#166852
#166772
#166642
#150692
#149122
#149032
#148982
#148642
#143392
#142752
#142712
#140202
#139962