Finite Group Databasebeta

← C4×#5751 #11659424

Subgroups — C4×#5751 #11659424

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5751C211yesmaximal, characteristic
2C4×#1009C211yesmaximal, characteristic, complemented
3C4×#1010C211yesmaximal, characteristic, complemented
4C3×C4×#131C211yesmaximal, characteristic, complemented
5#83806C211yesmaximal, characteristic, complemented
6#83797C211yesmaximal, characteristic, complemented
7#83784C211yesmaximal, characteristic, complemented
8#78574C213yesmaximal, complemented
9#78572C213yesmaximal, complemented
10#78571C213yesmaximal, complemented
11#78560C213yesmaximal, complemented
12C4×#909C213yesmaximal, complemented
13C4×#908C213yesmaximal, complemented
14C2×C4×#204C213yesmaximal, complemented
15C4×#904C213yesmaximal, complemented
16C4×#577—31nomaximal, Sylow
17C2×#1010C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C2×C3×#131C2211yescharacteristic
20C2×C3×#131C2211yescharacteristic
21C3×C4×#41C2211yescharacteristic
22#5827C2211yescharacteristic
23#5827C2211yescharacteristic
24#5751C4116yesdirect product factor
25C2×#909C2213yes—
26C2×#908C2213yes—
27C2×#904C2213yes—
28C22×#204C2213yes—
29#5574—21no—
30C4×#239—21no—
31#5572—21no—
32C4×D3×Q8—21no—
33#5546—23no—
34#5545—23no—
35C4×D3×D4—23no—
36C4×#237—23no—
37#5523C2213yes—
38#5523C2213yescomplemented
39#5521C2213yes—
40#5516C2213yescomplemented
41C4×#235C2213yes—
42C4×#235C2213yescomplemented
43C2×C4×D12C2213yes—
44C2×C4×Dic6C2213yescomplemented
45C3×#405C2213yescomplemented
46C3×#405C2213yescomplemented
47C3×C4×M16C2213yescomplemented
48C2×C3×C4×C8C2213yescomplemented
49#5133C2213yes—
50#5133C2213yescomplemented
51#5131C2213yes—
52#5121C2213yescomplemented
53#5121C2213yescomplemented
54#5120C2213yescomplemented
55#5113C2213yes—
56#5113C2213yescomplemented
57C2×#821C2213yes—
58#5106C2213yescomplemented
59C2×#817C2213yescomplemented
60C2×#816C2213yescomplemented
61#4716C2216yescomplemented
62#4711C2216yescomplemented
63#4710C2216yescomplemented
64#4710C2216yescomplemented
65C4×Dic12C2213yescomplemented
66C4×Dic12C2213yescomplemented
67C4×D24C2213yescomplemented
68C4×D24C2213yescomplemented
69C4×#204C2211yescharacteristic, complemented
70C4×#204C2213yescomplemented
71C4×#204C2213yescomplemented
72C4×#204C2213yescomplemented
73C4×#204C2216yescomplemented
74C4×#204C2216yescomplemented
75C4×#204C2216yescomplemented
76C2×#577—31no—
77C4×2−1+4—31no—
78C4×H(5,𝔽2)—31no—
79#2952—33no—
80#2949—33no—
81#2947—33no—
82#2946—33no—
83C4×#137—33no—
84C4×AGL(1,ℤ/8)—33no—
85C4×#135—33no—
86C2×C4×SD16—33no—
87#2912—31no—
88#2898—31no—
89#2897—31no—
90C4×#131D311yescharacteristic, complemented
91C2×C3×#41C2311yescharacteristic
92#1010—24no—
93#1010C2×C418yescomplemented
94#1009—24no—
95#1009C2×C418yescomplemented
96C2×#239—21no—
97C2×D3×Q8—21no—
98C2×#237—23no—
99C2×D3×D4—23no—
100C2×#235C2313yes—
101C2×#235C2313yes—
102C22×D12C2313yes—
103C22×C4×D3—23no—
104C22×Dic6C2313yes—
105C3×#131—24no—
106C3×#131C2×C418yescomplemented
107C2×C3×M16C2313yes—
108C2×C3×M16C2313yes—
109C22×C3×C8C2313yes—
110C22×C3×C8C2313yes—
111C3×C4×Q8D411yescharacteristic
112C3×C4×Q8D411yescharacteristic
113C3×C4×D4D413yes—
114C3×C4×D4D413yes—
115C3×#117C2313yes—
116C2×C3×C42C2313yes—
117Q8×Dic3—21no—
118Q8×Dic3—21no—
119D4×Dic3—23no—
120D4×Dic3—23no—
121C4×#67—23no—
122C4×#67—23no—
123C4×#67—23no—
124C4×#67—23no—
125C2×(C2×D3)⋊C4—23no—
126#926C2313yes—
127#926C2313yes—
128C2×C4⋊Dic3C2313yes—
129C2×C4⋊Dic3C2313yes—
130C2×Dic3⋊C4—23no—
131C2×C4×Dic3—23no—
132#909C2×C4124yescomplemented
133#908C2×C4124yescomplemented
134C2×Dic12C2313yes—
135#904C2×C4124yescomplemented
136C2×D24C2313yes—
137C2×#204C2×C4124yescomplemented
138C2×#204C2313yes—
139C2×#204C2311yescharacteristic
140C2×#204C2316yes—
141#893—23no—
142#893—23no—
143#892—23no—
144#892—23no—
145D3×C4⋊C4—23no—
146D3×C4⋊C4—23no—
147#887—23no—
148#887—23no—
149#67⋊C4—26no—
150#67⋊C4—26no—
151D3×C22⋊C4—26no—
152#877—26no—
153C4×D12—23no—
154C4×D12—23no—
155C4×D12C2313yes—
156C4×D12C2316yes—
157C4×D12C2311yescharacteristic
158C4×D12C2313yes—
159C4×D12C2313yes—
160#872—23no—
161#872—23no—
162C42×D3—23no—
163C42×D3—23no—
164C4×Dic6—23no—
165C4×Dic6—23no—
166C4×Dic6C2313yes—
167C4×Dic6C2316yes—
168C4×Dic6C2311yescharacteristic
169C4×Dic6C2313yes—
170C4×Dic6C2313yes—
171C3×#97C2316yes—
172C3×C4×C8C2311yescharacteristic
173C3×C4×C8C2313yes—
174C3×C4×C8C2313yes—
175C3×C4×C8C2313yes—
176#821C2313yes—
177#821C2316yes—
178#821C2313yes—
179#821C2313yes—
180#821C2311yescharacteristic
181#818C2313yes—
182#818C2313yes—
183#817C2316yes—
184#817C2313yes—
185#817C2311yescharacteristic
186#816C2313yes—
187#816C2316yes—
188#816C2313yes—
189#816C2313yes—
190#816C2311yescharacteristic
191C2×2−1+4—31no—
192C2×H(5,𝔽2)—31no—
193#577—316no—
194C2×#137—33no—
195C2×AGL(1,ℤ/8)—33no—
196C2×#135—33no—
197C22×SD16—33no—
198C2×#131C2×D311yescharacteristic
199C2×#131C2×D311yescharacteristic
200#520—31no—
201#520—31no—
202#520—33no—
203#520—33no—
204#520—61no—
205#520—63no—
206#519—33no—
207#519—61no—
208#518—33no—
209#518—63no—
210C4×#41—33no—
211C4×#41—33no—
212C4×#41—61no—
213C4×#41—63no—
214C4×#41C2×D311yescharacteristic
215C2×C4×Q8—33no—
216C2×C4×Q8—61no—
217C2×C4×D4—33no—
218C2×C4×D4—63no—
219#442—36no—
220#441—36no—
221#440—36no—
222#440—36no—
223C4×Q16—33no—
224C4×Q16—33no—
225C4×SD16—33no—
226C4×SD16—36no—
227C4×SD16—36no—
228C4×SD16—36no—
229C4×SD16—31no—
230C4×SD16—33no—
231C4×SD16—33no—
232C4×D8—33no—
233C4×D8—33no—
234#428—33no—
235#428—33no—
236#427—33no—
237C2×#106—33no—
238#419—33no—
239#418—33no—
240#417—33no—
241#417—33no—
242#416—33no—
243#416—33no—
244C2×#103—33no—
245C2×#102—33no—
246#405C2×D313yescomplemented
247#405C2×D313yescomplemented
248C4×M16C2×D313yescomplemented
249C2×C4×C8C2×D313yescomplemented
250C23×D3—23no—
251C3×#41C22×C414yes—
252C3×#41#4114yes—
253C2×C3×Q8C2×D411yescharacteristic
254C2×C3×D4C2×D413yes—
255C22×C3×C4C2×D413yes—
256C22×C3×C4C2×D413yes—
257C22×C3×C4C2413yes—
258C2×#67—23no—
259C2×#67—23no—
260C22×Dic3—23no—
261C22×Dic3—23no—
262C22×Dic3—23no—
263#239—28no—
264D3×Q8—28no—
265#237—224no—
266D3×D4—224no—
267#235—26no—
268#235—26no—
269#235C22×C4112yes—
270#235C22×C4112yescomplemented
271C2×D12—23no—
272C2×D12—26no—
273C2×D12C22×C4112yes—
274C2×D12C2413yes—
275C2×D12C2411yescharacteristic
276C2×C4×D3—23no—
277C2×C4×D3—23no—
278C2×C4×D3—21no—
279C2×C4×D3—23no—
280C2×C4×D3—23no—
281C2×C4×D3—23no—
282C2×C4×D3—26no—
283C2×C4×D3—86no—
284C2×Dic6—23no—
285C2×Dic6—26no—
286C2×Dic6C22×C4112yescomplemented
287C2×Dic6C2413yes—
288C2×Dic6C2411yescharacteristic
289C3×M16—26no—
290C3×M16C22×C4112yescomplemented
291C2×C3×C8—26no—
292C2×C3×C8C22×C4112yescomplemented
293C2×C3×C8C2411yescharacteristic
294C2×C3×C8C2413yes—
295C2×C3×C8C2411yescharacteristic
296C2×C3×C8C2413yes—
297C3×C4⋊C4C2×D413yes—
298C3×C4⋊C4C2×D413yes—
299C3×C22⋊C4C2×D416yes—
300C3×C42C2×D413yes—
301C3×C42C2×D413yes—
302C3×C42C2411yescharacteristic
303C3×C42C2413yes—
304#217—23no—
305#217—23no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—23no—
308(C2×D3)⋊C4—23no—
309(C2×D3)⋊C4—23no—
310(C2×D3)⋊C4—26no—
311C4⋊Dic3—23no—
312C4⋊Dic3—23no—
313C4⋊Dic3C2413yes—
314C4⋊Dic3C2411yescharacteristic
315C4⋊Dic3C2413yes—
316C4⋊Dic3C2411yescharacteristic
317Dic3⋊C4—23no—
318Dic3⋊C4—26no—
319Dic3⋊C4—21no—
320Dic3⋊C4—23no—
321Dic3⋊C4—23no—
322C4×Dic3—23no—
323C4×Dic3—26no—
324C4×Dic3—21no—
325C4×Dic3—23no—
326C4×Dic3—23no—
327C4×Dic3—23no—
328C4×Dic3—23no—
329Dic12C22×C4112yescomplemented
330D24C22×C4112yescomplemented
331#204C22×C4112yescomplemented
332#204C22×C4124yescomplemented
333#204C22×C414yescomplemented
3342−1+4—38no—
3352−1+4—64no—
336H(5,𝔽2)—38no—
337H(5,𝔽2)—64no—
338C2×#41—33no—
339C2×#41—33no—
340C2×#41—61no—
341C2×#41—63no—
342C2×#41C22×D311yescharacteristic
343C22×Q8—33no—
344C22×Q8—61no—
345C22×D4—33no—
346C22×D4—63no—
347C23×C4—63no—
348#137—324no—
349AGL(1,ℤ/8)—324no—
350#135—324no—
351C2×Q16—33no—
352C2×SD16—324no—
353C2×SD16—33no—
354C2×SD16—36no—
355C2×SD16—31no—
356C2×D8—33no—
357#131—24no—
358#131C4×D318yescomplemented
359C2×M16C22×D313yes—
360C2×M16C22×D313yes—
361C22×C8C22×D313yes—
362C22×C8C22×D313yes—
363C4×Q8—33no—
364C4×Q8—36no—
365C4×Q8—31no—
366C4×Q8—33no—
367C4×Q8—33no—
368C4×Q8—61no—
369C4×Q8—61no—
370C4×Q8—63no—
371C4×Q8—63no—
372C4×Q8—63no—
373C4×Q8—63no—
374C4×Q8D1211yescharacteristic
375C4×Q8D1211yescharacteristic
376C4×D4—33no—
377C4×D4—36no—
378C4×D4—31no—
379C4×D4—33no—
380C4×D4—33no—
381C4×D4—63no—
382C4×D4—63no—
383C4×D4—63no—
384C4×D4—63no—
385C4×D4—63no—
386C4×D4—63no—
387C4×D4—63no—
388C4×D4—63no—
389C4×D4—66no—
390C4×D4—66no—
391C4×D4—63no—
392C4×D4—63no—
393C4×D4D1213yes—
394C4×D4D1213yes—
395#117—33no—
396#117—33no—
397#117—63no—
398#117—63no—
399#117—66no—
400#117—63no—
401#117—63no—
402#117C22×D313yes—
403C2×C4⋊C4—33no—
404C2×C4⋊C4—33no—
405C2×C4⋊C4—63no—
406C2×C4⋊C4—63no—
407C2×C4⋊C4—63no—
408C2×C22⋊C4—63no—
409C2×C22⋊C4—66no—
410C2×C42—63no—
411C2×C42—63no—
412C2×C42—63no—
413C2×C42C22×D313yes—
414#107—33no—
415#107—33no—
416#106—33no—
417#106—36no—
418#106—31no—
419#103—33no—
420#103—36no—
421#103—31no—
422#103—33no—
423#103—33no—
424#102—33no—
425#102—36no—
426#102—31no—
427#102—33no—
428#102—33no—
429#97C22×D316yes—
430C4×C8C22×D311yescharacteristic
431C4×C8C22×D313yes—
432C4×C8C22×D313yes—
433C4×C8C22×D313yes—
434C23×C3C22×D413yes—
435C22×D3—21no—
436C22×D3—23no—
437C22×D3—212no—
438C22×D3—83no—
439C22×D3—83no—
440C3×Q8C4×D414yes—
441C3×D4C4×D4112yes—
442C2×C3×C4—26no—
443C2×C3×C4—43no—
444C2×C3×C4C23×C416yes—
445C2×C3×C4C22×D413yes—
446C2×C3×C4C22×D413yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D413yes—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C2×#4116yes—
451C2×C3×C4C2511yescharacteristic
452#67—212no—
453#67—212no—
454C2×Dic3—212no—
455C2×Dic3—23no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—23no—
459C2×Dic3—21no—
460C2×Dic3—23no—
461C2×Dic3—83no—
462C2×Dic3—83no—
463D12—212no—
464D12—23no—
465D12—21no—
466D12C23×C416yes—
467D12C23×C412yes—
468C4×D3—212no—
469C4×D3—212no—
470C4×D3—42no—
471C4×D3—46no—
472C4×D3—83no—
473C4×D3—83no—
474C4×D3—86no—
475Dic6—212no—
476Dic6—23no—
477Dic6—21no—
478Dic6C23×C416yes—
479Dic6C23×C412yes—
480C3×C8—21no—
481C3×C8—23no—
482C3×C8C23×C412yes—
483C3×C8C23×C416yes—
484C24—63no—
485#41—312no—
486#41—312no—
487#41—68no—
488#41—624no—
489#41—66no—
490#41—66no—
491#41C2×C4×D314yes—
492#41#23514yes—
493C2×Q8—312no—
494C2×Q8—33no—
495C2×Q8—31no—
496C2×Q8—68no—
497C2×Q8—63no—
498C2×Q8—66no—
499C2×Q8C2×D1211yescharacteristic
500C2×D4—312no—
501C2×D4—31no—
502C2×D4—33no—
503C2×D4—63no—
504C2×D4—63no—
505C2×D4—624no—
506C2×D4—63no—
507C2×D4—66no—
508C2×D4C2×D1213yes—
509C22×C4—63no—
510C22×C4—63no—
511C22×C4—63no—
512C22×C4—63no—
513C22×C4—63no—
514C22×C4—61no—
515C22×C4—63no—
516C22×C4—63no—
517C22×C4—63no—
518C22×C4—66no—
519C22×C4—246no—
520C22×C4C2×D1213yes—
521C22×C4C2×D1213yes—
522C22×C4C23×D313yes—
523Q16—312no—
524SD16—312no—
525SD16—324no—
526SD16—34no—
527D8—312no—
528M16—26no—
529M16C2×C4×D3112yescomplemented
530C2×C8—26no—
531C2×C8C2×C4×D3112yescomplemented
532C2×C8C23×D311yescharacteristic
533C2×C8C23×D313yes—
534C2×C8C23×D311yescharacteristic
535C2×C8C23×D313yes—
536C4⋊C4—33no—
537C4⋊C4—31no—
538C4⋊C4—33no—
539C4⋊C4—31no—
540C4⋊C4—63no—
541C4⋊C4—63no—
542C4⋊C4—63no—
543C4⋊C4—66no—
544C4⋊C4—63no—
545C4⋊C4—61no—
546C4⋊C4—63no—
547C4⋊C4C2×D1213yes—
548C4⋊C4C2×D1213yes—
549C22⋊C4—63no—
550C22⋊C4—63no—
551C22⋊C4—63no—
552C22⋊C4—66no—
553C22⋊C4—63no—
554C22⋊C4—61no—
555C22⋊C4—63no—
556C22⋊C4C2×D1216yes—
557C42—63no—
558C42—63no—
559C42—63no—
560C42—63no—
561C42—66no—
562C42—61no—
563C42—63no—
564C42C2×D1213yes—
565C42C2×D1213yes—
566C42C23×D313yes—
567C42C23×D311yescharacteristic
568C22×C3—23no—
569C22×C3—23no—
570C22×C3C2×C4×D416yes—
571C22×C3C23×D411yescharacteristic
572C2×D3—22no—
573C2×D3—26no—
574C2×D3—41no—
575C2×D3—43no—
576C2×D3—43no—
577C2×D3—41no—
578C2×D3—812no—
579C3×C4—23no—
580C3×C4—21no—
581C3×C4—23no—
582C3×C4C2×C4×D416yes—
583C3×C4#57712yescomplemented
584C3×C4C24×C411yescharacteristic
585C3×C4C22×#4111yescharacteristic
586Dic3—26no—
587Dic3—22no—
588Dic3—41no—
589Dic3—43no—
590Dic3—43no—
591Dic3—41no—
592C23—61no—
593C23—63no—
594C23—612no—
595C23—243no—
596C23—243no—
597C23C22×D1213yes—
598Q8—36no—
599Q8—32no—
600Q8—63no—
601Q8—61no—
602Q8—612no—
603Q8C4×D1214yes—
604D4—32no—
605D4—36no—
606D4—612no—
607D4—612no—
608D4—63no—
609D4—61no—
610D4—612no—
611D4C4×D12112yes—
612C2×C4—26no—
613C2×C4—43no—
614C2×C4—61no—
615C2×C4—63no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—63no—
622C2×C4—63no—
623C2×C4—126no—
624C2×C4—122no—
625C2×C4—246no—
626C2×C4—243no—
627C2×C4—243no—
628C2×C4—243no—
629C2×C4—243no—
630C2×C4C22×C4×D316yes—
631C2×C4C22×D1213yes—
632C2×C4C22×D1213yes—
633C2×C4C22×D1211yescharacteristic
634C2×C4C22×D1213yes—
635C2×C4C22×D1211yescharacteristic
636C2×C4C2×#23516yes—
637C2×C4C24×D311yescharacteristic
638C8—21no—
639C8—23no—
640C8C22×C4×D312yes—
641C8C22×C4×D316yes—
642C2×C3—26no—
643C2×C3C22×C4×D411yescharacteristic
644C2×C3C2×#57711yescharacteristic
645C2×C3#358411yescharacteristic
646D3—42no—
647D3—46no—
648C22—23no—
649C22—23no—
650C22—62no—
651C22—66no—
652C22—123no—
653C22—121no—
654C22—121no—
655C22—123no—
656C22—2412no—
657C22C2×C4×D1216yes—
658C22C23×D1211yescharacteristic
659C4—23no—
660C4—21no—
661C4—23no—
662C4—62no—
663C4—66no—
664C4—123no—
665C4—121no—
666C4—121no—
667C4—123no—
668C4C2×C4×D1216yes—
669C4#575112yesdirect product factor
670C4C23×C4×D311yescharacteristic
671C4C22×#23511yescharacteristic
672C3C4×#57711yescharacteristic, complemented, Sylow
673C2—26no—
674C2—126no—
675C2—122no—
676C2C22×C4×D1211yescharacteristic
677C2C2×#575111yescharacteristic
678C2#8716311yescharacteristic
subgroupG/H
centerC2×C4C22×D12
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×C4×#131C2
socleC22×C3C23×D4
prime radicalC2×#5751C2
cosocleC2×C3×C4C25
hypercenterC4×#131D3
hypocenterC3C4×#577
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. C4×#1009C2semidirect
3. C4×#1010C2semidirect
4. C3×C4×#131C2semidirect
5. #83806C2semidirect
6. #83797C2semidirect
7. #83784C2semidirect
8. #78574C2semidirect
9. #78572C2semidirect
10. #78571C2semidirect
11. #78560C2semidirect
12. C4×#909C2semidirect
13. C4×#908C2semidirect
14. C2×C4×#204C2semidirect
15. C4×#904C2semidirect
24. #5751C4direct (N × H)
38. #5523C22semidirect
40. #5516C22semidirect
42. C4×#235C22semidirect
44. C2×C4×Dic6C22semidirect
45. C3×#405C22semidirect
46. C3×#405C22semidirect
47. C3×C4×M16C22semidirect
48. C2×C3×C4×C8C22semidirect
50. #5133C22semidirect
52. #5121C22semidirect
53. #5121C22semidirect
54. #5120C22semidirect
56. #5113C22semidirect
58. #5106C22semidirect
59. C2×#817C22semidirect
60. C2×#816C22semidirect
61. #4716C22semidirect
62. #4711C22semidirect
63. #4710C22semidirect
64. #4710C22semidirect
65. C4×Dic12C22semidirect
66. C4×Dic12C22semidirect
67. C4×D24C22semidirect
68. C4×D24C22semidirect
69. C4×#204C22semidirect
70. C4×#204C22semidirect
71. C4×#204C22semidirect
72. C4×#204C22semidirect
73. C4×#204C22semidirect
74. C4×#204C22semidirect
75. C4×#204C22semidirect
90. C4×#131D3semidirect
93. #1010C2×C4semidirect
95. #1009C2×C4semidirect
106. C3×#131C2×C4semidirect
132. #909C2×C4semidirect
133. #908C2×C4semidirect
135. #904C2×C4semidirect
137. C2×#204C2×C4semidirect
246. #405C2×D3semidirect
247. #405C2×D3semidirect
248. C4×M16C2×D3semidirect
249. C2×C4×C8C2×D3semidirect
270. #235C22×C4semidirect
286. C2×Dic6C22×C4semidirect
290. C3×M16C22×C4semidirect
292. C2×C3×C8C22×C4semidirect
329. Dic12C22×C4semidirect
330. D24C22×C4semidirect
331. #204C22×C4semidirect
332. #204C22×C4semidirect
333. #204C22×C4semidirect
358. #131C4×D3semidirect
529. M16C2×C4×D3semidirect
531. C2×C8C2×C4×D3semidirect
583. C3×C4#577semidirect
669. C4#5751direct (N × H)
672. C3C4×#577semidirect

Maximal subgroups

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

subgroupindex
C2×#57512
C4×#10092
C4×#10102
C3×C4×#1312
#838062
#837972
#837842
#785742
#785722
#785712
#785602
C4×#9092
C4×#9082
C2×C4×#2042
C4×#9042
C4×#5773