Finite Group Databasebeta

← #416245

Subgroups — #416245

Order 512.

1108 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1949C211yesmaximal, characteristic
2C2×#1832C211yesmaximal, characteristic
3C2×#1805C211yesmaximal, characteristic
4C2×#1803C211yesmaximal, characteristic
5#14277C211yesmaximal, characteristic
6#13786C211yesmaximal, characteristic
7#11316C211yesmaximal, characteristic
8#11315C211yesmaximal, characteristic
9#11220C211yesmaximal, characteristic
10#11219C211yesmaximal, characteristic
11#11124C211yesmaximal, characteristic
12#11122C211yesmaximal, characteristic
13#11067C211yesmaximal, characteristic
14#11067C211yesmaximal, characteristic
15#10849C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C2×#391C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#384C2211yescharacteristic
30C2×#382C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×#376C2211yescharacteristic
33#1949—24no—
34#1832—24no—
35#1805—24no—
36#1803—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1444—21no—
52#1444—21no—
53#1442—21no—
54#1442—21no—
55#1436—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62#1434—21no—
63C23×Q8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4×Q8—22no—
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8Q814yes—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C42—21no—
87C22×C42—21no—
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C2×#107—22no—
92C2×#107—22no—
93C2×#107—41no—
94C2×#106—22no—
95C2×#106—22no—
96C2×#106—41no—
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8D414yes—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115#391—22no—
116#391—22no—
117#391—22no—
118#391—22no—
119#389—41no—
120#389—41no—
121#389—41no—
122#389—41no—
123#384—22no—
124#384—22no—
125#382—22no—
126#382D414yes—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129#376—22no—
130#376—22no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
150C2×#95D411yescharacteristic
151C2×#95D411yescharacteristic
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—41no—
161#340—41no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8C2×Q812yes—
178C22×Q8#4112yes—
179C22×Q8#4112yes—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2411yescharacteristic
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8C2×D412yes—
222C22×C8C2×D412yes—
223C4×Q8—28no—
224C4×Q8—28no—
225C4×Q8—44no—
226C4×Q8—44no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
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⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4—81no—
274C2×C4⋊C4—81no—
275C2×C4⋊C4—81no—
276C2×C4⋊C4—81no—
277C2×C4⋊C4—81no—
278C2×C4⋊C4—81no—
279C2×C4⋊C4C2×D412yes—
280C2×C4⋊C4C2×D412yes—
281C2×C4⋊C4C2×Q812yes—
282C2×C4⋊C4#4112yes—
283C2×C4⋊C4#4112yes—
284C2×C42—24no—
285C2×C42—21no—
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—21no—
296C2×C42—21no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—81no—
301C2×C42—81no—
302C2×C42C2×D412yes—
303C2×C42C2×D412yes—
304C2×C42C2×Q812yes—
305C2×C42#4112yes—
306C2×C42#4112yes—
307C2×C42#4112yes—
308#107—44no—
309#106—44no—
310C4⋊C8—28no—
311C4⋊C8—44no—
312#103—44no—
313#103—44no—
314#103—44no—
315#103—44no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95—42no—
327#95—42no—
328#95—42no—
329#95—81no—
330#95—81no—
331#95—81no—
332#95—81no—
333#95—81no—
334#95—81no—
335#95—81no—
336#95—81no—
337C24C22×D411yescharacteristic
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8#12514yes—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
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—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
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×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4#12112yes—
459C22×C4#12112yes—
460C22×C4#12112yes—
461C22×C4#12112yes—
462C22×C4C22⋊Q812yes—
463C22×C4C22⋊Q812yes—
464C22×C4C22×D411yescharacteristic
465C22×C4C22×D411yescharacteristic
466C22×C4C22×Q811yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4H(5,𝔽2)11yescharacteristic
475C22×C4H(5,𝔽2)11yescharacteristic
476C22×C42−1+411yescharacteristic
477C22×C42−1+411yescharacteristic
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—48no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—84no—
536C4⋊C4—84no—
537C4⋊C4—84no—
538C4⋊C4—84no—
539C42—41no—
540C42—41no—
541C42—41no—
542C42—41no—
543C42—41no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—48no—
548C42—84no—
549C42#12114yes—
550C42C22⋊Q814yes—
551C42C22⋊Q814yes—
552C42#12614yes—
553C23C2×#12111yescharacteristic
554C23C2×#12111yescharacteristic
555C23C2×C22⋊Q811yescharacteristic
556C23#52511yescharacteristic
557C23#52511yescharacteristic
558C23#53511yescharacteristic
559C23#53611yescharacteristic
560C23#57611yescharacteristic
561C23#57711yescharacteristic
562C23#57711yescharacteristic
563C23#57711yescharacteristic
564C23#57711yescharacteristic
565C23#57811yescharacteristic
566C23#57811yescharacteristic
567C23#57811yescharacteristic
568Q8—24no—
569Q8—24no—
570Q8—42no—
571Q8—42no—
572Q8—42no—
573Q8—42no—
574Q8—42no—
575Q8—42no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4#39614yes—
673C2×C4#39614yes—
674C2×C4C2×#12111yescharacteristic
675C2×C4C2×C22⋊Q811yescharacteristic
676C2×C4C2×C22⋊Q811yescharacteristic
677C2×C4C2×#12511yescharacteristic
678C2×C4C2×#12611yescharacteristic
679C2×C4#52911yescharacteristic
680C2×C4#52911yescharacteristic
681C2×C4#53311yescharacteristic
682C2×C4#54211yescharacteristic
683C2×C4#54211yescharacteristic
684C2×C4#54411yescharacteristic
685C2×C4#54411yescharacteristic
686C2×C4#54611yescharacteristic
687C2×C4#54611yescharacteristic
688C2×C4#54611yescharacteristic
689C2×C4#54711yescharacteristic
690C2×C4#54811yescharacteristic
691C2×C4#54811yescharacteristic
692C2×C4#54811yescharacteristic
693C2×C4#55011yescharacteristic
694C2×C4#55211yescharacteristic
695C2×C4#55211yescharacteristic
696C2×C4#55211yescharacteristic
697C2×C4#55311yescharacteristic
698C2×C4#55311yescharacteristic
699C2×C4#55311yescharacteristic
700C2×C4#55511yescharacteristic
701C2×C4#55611yescharacteristic
702C8—42no—
703C8—42no—
704C8—81no—
705C8—81no—
706C22C2×#39611yescharacteristic
707C22#241411yescharacteristic
708C22#241511yescharacteristic
709C22#253511yescharacteristic
710C22#253611yescharacteristic
711C22#262811yescharacteristic
712C22#285111yescharacteristic
713C22#304511yescharacteristic
714C22#304611yescharacteristic
715C22#304611yescharacteristic
716C22#304611yescharacteristic
717C22#305711yescharacteristic
718C22#305911yescharacteristic
719C22#306211yescharacteristic
720C22#306311yescharacteristic
721C22#308211yescharacteristic
722C22#308211yescharacteristic
723C22#308311yescharacteristic
724C22#308411yescharacteristic
725C22#311911yescharacteristic
726C22#312011yescharacteristic
727C22#312111yescharacteristic
728C22#312111yescharacteristic
729C22#312411yescharacteristic
730C22#312511yescharacteristic
731C22#312611yescharacteristic
732C22#312711yescharacteristic
733C22#322211yescharacteristic
734C22#322311yescharacteristic
735C22#322411yescharacteristic
736C22#322511yescharacteristic
737C22#324211yescharacteristic
738C22#324211yescharacteristic
739C22#324311yescharacteristic
740C22#324411yescharacteristic
741C4—24no—
742C4—24no—
743C4—44no—
744C4—82no—
745C4—82no—
746C4—82no—
747C4—82no—
748C4—82no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—161no—
754C4—161no—
755C4#242611yescharacteristic
756C4#242711yescharacteristic
757C4#243911yescharacteristic
758C4#244111yescharacteristic
759C4#244211yescharacteristic
760C4#244211yescharacteristic
761C4#249411yescharacteristic
762C4#249511yescharacteristic
763C2#1522011yescharacteristic
764C2#2361311yescharacteristic
765C2#2361611yescharacteristic
766C2#2466411yescharacteristic
767C2#2466811yescharacteristic
768C2#2471411yescharacteristic
769C2#2471811yescharacteristic
770C2#2817211yescharacteristic
771C2#2817311yescharacteristic
772C2#2821511yescharacteristic
773C2#2821611yescharacteristic
774C2#2999211yescharacteristic
775C2#2999311yescharacteristic
776C2#3307511yescharacteristic
777C2#3307711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19492
C2×#18322
C2×#18052
C2×#18032
#142772
#137862
#113162
#113152
#112202
#112192
#111242
#111222
#110672
#108492