Finite Group Databasebeta

← #378754

Subgroups — #378754

Order 512.

1030 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23609C211yesmaximal, characteristic
2C2×#1922C211yesmaximal, characteristic, complemented
3C2×#1866C211yesmaximal, characteristic
4#20435C211yesmaximal, characteristic, complemented
5#20383C211yesmaximal, characteristic
6#11233C211yesmaximal, characteristic, complemented
7#11226C211yesmaximal, characteristic, complemented
8#11075C211yesmaximal, characteristic
9#10934C211yesmaximal, characteristic
10#10934C211yesmaximal, characteristic
11#10910C211yesmaximal, characteristic, complemented
12#10909C211yesmaximal, characteristic, complemented
13#10834C211yesmaximal, characteristic, complemented
14#10809C211yesmaximal, characteristic, complemented
15#10791C211yesmaximal, characteristic
16C22×#131C2211yescharacteristic
17C22×#108C2211yescharacteristic
18C2×#427C2211yescharacteristic
19C2×#424C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C2×#416C2211yescharacteristic
24C2×#416C2211yescharacteristic
25C2×#408C2211yescharacteristic
26C2×#405C2211yescharacteristic
27C2×#405C2211yescharacteristic
28C2×#405C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30#2297C2211yescharacteristic
31#2296C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33#2068C411yescharacteristic, complemented
34#2068C411yescharacteristic, complemented
35#2067C411yescharacteristic, complemented
36#2067C411yescharacteristic, complemented
37#2066C411yescharacteristic, complemented
38#2066C411yescharacteristic, complemented
39#2065C411yescharacteristic, complemented
40#2065C411yescharacteristic, complemented
41#1922—24no—
42#1866—24no—
43#1771—21no—
44#1771—21no—
45C8×C4⋊C4—21no—
46C8×C4⋊C4—21no—
47#1753—21no—
48#1753—21no—
49C8×C22⋊C4—21no—
50C8×C22⋊C4—21no—
51C2×#341C2211yescharacteristic
52C2×#341C2211yescharacteristic
53C2×#341C2211yescharacteristic
54#1735C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1728C2211yescharacteristic
64#1728C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C22×#41C2311yescharacteristic
70C2×#131—22no—
71C2×#131—22no—
72C2×#131—22no—
73C2×#131—22no—
74C2×#131—41no—
75C2×#131—41no—
76C22×M16—21no—
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C23×C8—21no—
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C2×#117C2311yescharacteristic
87C2×#117C2311yescharacteristic
88C2×#117C2311yescharacteristic
89C22×C4⋊C4—21no—
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C2×#108—22no—
94C2×#108—22no—
95C2×#108—41no—
96#427—22no—
97#427—22no—
98C2×#107C2×C411yescharacteristic
99C2×#107C2×C411yescharacteristic
100C2×#106C2×C411yescharacteristic
101C2×#106C2×C411yescharacteristic
102#424—22no—
103#424D414yes—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—41no—
107C2×C4⋊C8—41no—
108C2×C4⋊C8C2×C411yescharacteristic
109C2×C4⋊C8C2×C411yescharacteristic
110C2×C4⋊C8C2×C411yescharacteristic
111C2×C4⋊C8C2×C411yescharacteristic
112C2×#104—22no—
113C2×#104—22no—
114C2×#104—22no—
115C2×#104—22no—
116C2×#104—41no—
117C2×#104—41no—
118#416—22no—
119#416—22no—
120#416—41no—
121#416—41no—
122C2×#103C2×C411yescharacteristic
123C2×#103C2×C411yescharacteristic
124C2×#103C2×C411yescharacteristic
125C2×#103C2×C411yescharacteristic
126C2×#102C2×C411yescharacteristic
127C2×#102C2×C411yescharacteristic
128C2×#102C2×C411yescharacteristic
129C2×#102C2×C411yescharacteristic
130#408—22no—
131#408Q814yes—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134#405—22no—
135#405—22no—
136#405—22no—
137#405—22no—
138#405—41no—
139#405—41no—
140C2×#97—21no—
141C2×#97—21no—
142C2×#97—21no—
143C2×C4×C8—21no—
144C2×C4×C8—21no—
145C2×C4×C8—21no—
146C2×C4×C8—41no—
147C2×C4×C8—41no—
148C2×C4×C8D411yescharacteristic
149C2×C4×C8D411yescharacteristic
150C2×C4×C8D411yescharacteristic
151C2×C4×C8D411yescharacteristic
152#391C2×C411yescharacteristic
153#391C2×C411yescharacteristic
154#390C2×C411yescharacteristic
155#390C2×C411yescharacteristic
156#389C2×C411yescharacteristic
157#389C2×C411yescharacteristic
158#389C2×C411yescharacteristic
159#389C2×C411yescharacteristic
160#386—21no—
161#386—21no—
162#385—21no—
163#385—21no—
164C4×C4⋊C4—21no—
165C4×C4⋊C4—21no—
166C4×C4⋊C4—41no—
167C4×C4⋊C4—41no—
168C4×C22⋊C4—21no—
169C4×C22⋊C4—21no—
170C2×#95—21no—
171#341—22no—
172#341—22no—
173#341—41no—
174#340C2×C411yescharacteristic
175#340C2×C411yescharacteristic
176#340C2×C411yescharacteristic
177#340C2×C411yescharacteristic
178#339—22no—
179#339—22no—
180#339—22no—
181#339—22no—
182#339—41no—
183#339—41no—
184#336—22no—
185#336—22no—
186#336—21no—
187#336—21no—
188#336—21no—
189#336—21no—
190#336—22no—
191#336—22no—
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196C2×#41—21no—
197C2×#41—21no—
198C2×#41—21no—
199C2×#41—21no—
200C2×#41—21no—
201C2×#41—21no—
202C2×#41—21no—
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2×Q812yes—
207C2×#41#4112yes—
208C22×Q8C22×C411yescharacteristic
209C22×D4—21no—
210C22×D4C22×C411yescharacteristic
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4#4111yescharacteristic
215C23×C4#4111yescharacteristic
216C23×C4C2411yescharacteristic
217#131—44no—
218#131—44no—
219#131—44no—
220#131—44no—
221C2×M16—24no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—42no—
243C2×M16—42no—
244C2×M16C2×D412yes—
245C2×M16C2×Q812yes—
246C2×M16#4112yes—
247C2×M16#4112yes—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—24no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—42no—
274C22×C8—42no—
275C22×C8C22×C411yescharacteristic
276C22×C8C22×C411yescharacteristic
277C22×C8C22×C411yescharacteristic
278C22×C8C22×C411yescharacteristic
279C22×C8C2×D412yes—
280C22×C8C2×D411yescharacteristic
281C22×C8C2×D411yescharacteristic
282C22×C8C2×D411yescharacteristic
283C22×C8C2×D411yescharacteristic
284C22×C8C2×Q812yes—
285C22×C8#4112yes—
286C22×C8#4112yes—
287#117—21no—
288#117—21no—
289#117—21no—
290#117—21no—
291#117—21no—
292#117—21no—
293#117—21no—
294#117—21no—
295#117—21no—
296#117—21no—
297#117C2×D412yes—
298#117#4112yes—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C4⋊C4C22×C411yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42C22×C411yescharacteristic
339C2×C42C22×C411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342#108—44no—
343#107—22no—
344#107—22no—
345#106—22no—
346#106—22no—
347C4⋊C8—24no—
348C4⋊C8—24no—
349C4⋊C8—41no—
350C4⋊C8—41no—
351C4⋊C8—41no—
352C4⋊C8—41no—
353#104—44no—
354#104—44no—
355#103—22no—
356#103—22no—
357#103—41no—
358#103—41no—
359#102—22no—
360#102—22no—
361#102—41no—
362#102—41no—
363C22⋊C8—24no—
364C22⋊C8—24no—
365#97—24no—
366#97—42no—
367#97—42no—
368C4×C8—24no—
369C4×C8—41no—
370C4×C8—41no—
371C4×C8—41no—
372C4×C8—41no—
373C4×C8—42no—
374C4×C8—42no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—42no—
384C24—21no—
385C24C2×#4111yescharacteristic
386#41—22no—
387#41—22no—
388#41—22no—
389#41—22no—
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8C4×Q812yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4C4×Q812yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
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—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4C4×D411yescharacteristic
456C22×C4C4×D411yescharacteristic
457C22×C4C4×D411yescharacteristic
458C22×C4C4×D411yescharacteristic
459C22×C4C23×C411yescharacteristic
460C22×C4C22×D411yescharacteristic
461C22×C4C22×D411yescharacteristic
462C22×C4C22×Q811yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4H(5,𝔽2)11yescharacteristic
470C22×C4H(5,𝔽2)11yescharacteristic
471C22×C4H(5,𝔽2)11yescharacteristic
472C22×C42−1+411yescharacteristic
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—48no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—41no—
488M16—41no—
489M16—41no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—48no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8#12112yes—
540C2×C8#12112yes—
541C2×C8C22⋊Q812yes—
542C2×C8C22⋊Q812yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—48no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4C4×D412yes—
559C4⋊C4C4×D412yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—22no—
575C42—22no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C2×C4×D411yescharacteristic
604C23#52911yescharacteristic
605C23#52911yescharacteristic
606C23#53211yescharacteristic
607C23#53311yescharacteristic
608C23#53811yescharacteristic
609C23#53911yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614D4—22no—
615D4—22no—
616D4—42no—
617D4—42no—
618D4—42no—
619D4—42no—
620D4—41no—
621D4—41no—
622C2×C4—24no—
623C2×C4—24no—
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—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4#44312yes—
676C2×C4#44412yes—
677C2×C4C2×C4×D411yescharacteristic
678C2×C4C2×C4×Q811yescharacteristic
679C2×C4C4×#4111yescharacteristic
680C2×C4C4×#4111yescharacteristic
681C2×C4#51811yescharacteristic
682C2×C4#52011yescharacteristic
683C2×C4C2×#12111yescharacteristic
684C2×C4C2×C22⋊Q811yescharacteristic
685C2×C4#52511yescharacteristic
686C2×C4#52511yescharacteristic
687C2×C4#53411yescharacteristic
688C2×C4#53711yescharacteristic
689C2×C4#54611yescharacteristic
690C2×C4#54611yescharacteristic
691C2×C4D4×Q811yescharacteristic
692C2×C4#55011yescharacteristic
693C2×C4#55111yescharacteristic
694C2×C4#55111yescharacteristic
695C2×C4#55111yescharacteristic
696C2×C4#55211yescharacteristic
697C2×C4#55211yescharacteristic
698C2×C4#55311yescharacteristic
699C2×C4#55311yescharacteristic
700C2×C4#55411yescharacteristic
701C2×C4#55411yescharacteristic
702C2×C4#55411yescharacteristic
703C2×C4#55511yescharacteristic
704C2×C4#55611yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8—22no—
709C8—42no—
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—42no—
715C8—42no—
716C8—42no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C4×#12111yescharacteristic
737C22C4×C22⋊Q811yescharacteristic
738C22#232511yescharacteristic
739C22#255411yescharacteristic
740C22#255611yescharacteristic
741C22#257311yescharacteristic
742C22#257411yescharacteristic
743C22C2×#44311yescharacteristic
744C22C2×#44411yescharacteristic
745C22#295511yescharacteristic
746C22#295511yescharacteristic
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—41no—
754C4—82no—
755C4—82no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4#236011yescharacteristic
761C4#236311yescharacteristic
762C4#236811yescharacteristic
763C4#237311yescharacteristic
764C4#253411yescharacteristic
765C4#253811yescharacteristic
766C4#257911yescharacteristic
767C4#260911yescharacteristic
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—82no—
773C2#1422211yescharacteristic
774C2#2151711yescharacteristic
775C2#2151811yescharacteristic
776C2#2162711yescharacteristic
777C2#2162811yescharacteristic
778C2#2220411yescharacteristic
779C2#2220511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1922C2semidirect
4. #20435C2semidirect
6. #11233C2semidirect
7. #11226C2semidirect
11. #10910C2semidirect
12. #10909C2semidirect
13. #10834C2semidirect
14. #10809C2semidirect
33. #2068C4semidirect
34. #2068C4semidirect
35. #2067C4semidirect
36. #2067C4semidirect
37. #2066C4semidirect
38. #2066C4semidirect
39. #2065C4semidirect
40. #2065C4semidirect

Maximal subgroups

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

subgroupindex
#236092
C2×#19222
C2×#18662
#204352
#203832
#112332
#112262
#110752
#109342
#109102
#109092
#108342
#108092
#107912