Finite Group Databasebeta

← #26217548

Subgroups — #26217548

Order 12032.

1842 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic
2C2×#15689603C211yesmaximal, characteristic, complemented
3C2×#15689124C211yesmaximal, characteristic, complemented
4C2×#15689089C211yesmaximal, characteristic, complemented
5#20243707C212yesmaximal, complemented
6#20243702C212yesmaximal, complemented
7#20243697C212yesmaximal, complemented
8#20243692C212yesmaximal, complemented
9#20243109C211yesmaximal, characteristic, complemented
10C2×#15688886C211yesmaximal, characteristic, complemented
11C2×C47×#416C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14#15689701—24no—
15#15689701C418yescomplemented
16C2×#13094003—21no—
17C2×#13094000C2212yes—
18C2×#13093998—21no—
19C2×#13093996—22no—
20C2×#13093995C2212yes—
21#15689603—24no—
22#15689603—24no—
23C2×C4×Dic94—21no—
24C2×C4×D188—21no—
25C2×(C22⋊D47)⋊C4—22no—
26C2×#13093982C2212yes—
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C2×C4⋊C4×D47C2212yes—
30#15689124—24no—
31C2×#13093948C2212yes—
32C2×#13093945C2212yes—
33#15689089—24no—
34C2×(C2×D47)⋊C8C2212yes—
35C2×(C2×D47)⋊C8C2212yes—
36#15688886C2212yes—
37#15688886C2212yes—
38#15688885C2212yes—
39#15688885C2212yes—
40C22×#41×C47C2211yescharacteristic
41C23×C8×C47C2211yescharacteristic
42C2×#117×C47C2211yescharacteristic
43C47×#416—24no—
44C2×#103×C47C2211yescharacteristic
45C2×#103×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#10625350—22no—
49C2×#10625350—22no—
50C2×#10625350—22no—
51C2×#10625350—22no—
52C2×#10625350C2×C414yes—
53C2×#10625350D414yes—
54C22×Dic94D411yescharacteristic
55C22×D188D411yescharacteristic
56C22×C22⋊D47—22no—
57C22×C22⋊D47D412yes—
58C23×Dic47—21no—
59C23×Dic47—21no—
60C22×C4×D47—22no—
61C22×C4×D47C2312yes—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C22×C47⋊C8C2312yes—
66#13094003—28no—
67#13094000—24no—
68#13094000C2×C418yescomplemented
69#13093998—28no—
70#13093996—216no—
71#13093995—24no—
72#13093995C2×C418yescomplemented
73C4×Dic94—28no—
74C4×D188—28no—
75(C22⋊D47)⋊C4—216no—
76#13093982—24no—
77#13093982—24no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—22no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47C2×C414yescomplemented
83C2×C4⋊Dic47D414yescomplemented
84C2×C4⋊Dic47C2312yes—
85C2×C4⋊Dic47C2312yes—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C4⋊C4×D47—24no—
89C4⋊C4×D47—24no—
90C2×C22⋊Dic47—22no—
91C2×(C2×D47)⋊C4—22no—
92C2×(C2×D47)⋊C4—22no—
93C2×C4×Dic47—22no—
94#13093948—24no—
95#13093945—24no—
96(C2×D47)⋊C8—24no—
97(C2×D47)⋊C8—24no—
98C2×#41×C47—22no—
99C2×#41×C47—22no—
100C2×#41×C47—22no—
101C2×#41×C47—22no—
102C2×#41×C47—22no—
103C2×#41×C47C2×C414yescomplemented
104C22×Q8×C47C2311yescharacteristic
105C22×D4×C47—21no—
106C22×D4×C47C2311yescharacteristic
107C23×C4×C47—21no—
108C23×C4×C47C2311yescharacteristic
109C22×C8×C47—22no—
110C22×C8×C47—22no—
111C22×C8×C47—22no—
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114#117×C47—22no—
115#117×C47D414yescomplemented
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C42×C47—21no—
120#103×C47—22no—
121#103×C47—22no—
122#102×C47—22no—
123#102×C47—22no—
124C24×C47—21no—
125C24×C47C2×D411yescharacteristic
126C23×D47C2×D412yes—
127#41×C47—28no—
128#41×C47—28no—
129#41×C47—44no—
130#41×C47—44no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47C22×C412yes—
137C2×D4×C47—24no—
138C2×D4×C47—21no—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—42no—
144C2×D4×C47—42no—
145C2×D4×C47C22×C412yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—24no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×C4×C47C2411yescharacteristic
160C2×C22⋊D47—24no—
161C2×C22⋊D47—24no—
162C2×C22⋊D47—28no—
163C2×C22⋊D47—82no—
164C2×C22⋊D47—82no—
165C2×C22⋊D47C22⋊C418yes—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—24no—
169C22×Dic47—24no—
170C22×Dic47—81no—
171C22×Dic47—81no—
172C22×Dic47—81no—
173C22×Dic47—81no—
174C22×Dic47C2×D412yes—
175#10625350—28no—
176#10625350—28no—
177#10625350—28no—
178#10625350—28no—
179C2×D188—22no—
180C2×D188—22no—
181C2×D188C22⋊C414yes—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—28no—
187C2×C4×D47—82no—
188C2×C4×D47—82no—
189C2×C4×D47C22×C414yes—
190C2×C4×D47C2×D414yes—
191C2×Dic94—22no—
192C2×Dic94—22no—
193C2×Dic94C22⋊C414yes—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—44no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47C2×D412yes—
204C4⋊C4×C47C2×D412yes—
205C22⋊C4×C47—24no—
206C42×C47—24no—
207C22⋊Dic47—28no—
208(C2×D47)⋊C4—28no—
209(C2×D47)⋊C4—28no—
210C4⋊Dic47—24no—
211C4⋊Dic47—24no—
212C4⋊Dic47—22no—
213C4⋊Dic47—22no—
214C4⋊Dic47C22×C414yes—
215C4⋊Dic47C2×D414yes—
216Dic47⋊C4—28no—
217Dic47⋊C4—28no—
218C4×Dic47—28no—
219#10625329—44no—
220C2×C47⋊C8—22no—
221C2×C47⋊C8—22no—
222C2×C47⋊C8—22no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—22no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47C2×C22⋊C412yes—
235C23×C47#12012yes—
236C23×C47#12312yes—
237C23×C47C22×D411yescharacteristic
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47C2×C22⋊C414yes—
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47—48no—
252D4×C47—41no—
253D4×C47—41no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—48no—
264C2×C4×C47C2×C22⋊C412yes—
265C2×C4×C47C4×D414yes—
266C2×C4×C47C4×D414yes—
267C2×C4×C47#12012yes—
268C2×C4×C47#12114yes—
269C2×C4×C47#12114yes—
270C2×C4×C47#12312yes—
271C2×C4×C47C23×C411yescharacteristic
272C2×C4×C47C22×D411yescharacteristic
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C22⋊D47—216no—
278C22⋊D47—88no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—84no—
288C2×Dic47—84no—
289C2×Dic47C2×C22⋊C414yes—
290D188—28no—
291C4×D47—24no—
292C4×D47—24no—
293C4×D47—24no—
294C4×D47—24no—
295C4×D47—88no—
296Dic94—28no—
297C8×C47—41no—
298C8×C47—41no—
299C47⋊C8—42no—
300#20915—471nomaximal, Sylow
301C22×C47—22no—
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—42no—
308C22×C47—42no—
309C22×C47—42no—
310C22×C47—81no—
311C22×C47—81no—
312C22×C47—81no—
313C22×C47—81no—
314C22×C47#38614yes—
315C22×C47C22×C22⋊C411yescharacteristic
316C22×C47C2×#12011yescharacteristic
317C22×C47C2×#12311yescharacteristic
318C22×C47#57611yescharacteristic
319C22×C47#57711yescharacteristic
320C22×C47#57711yescharacteristic
321C22×C47#57811yescharacteristic
322C2×D47—24no—
323C2×D47—24no—
324C2×D47—24no—
325C2×D47—42no—
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47—42no—
332C4×C47#38614yes—
333C4×C47C2×C4×D411yescharacteristic
334C4×C47C2×C4×D411yescharacteristic
335C4×C47C2×#12111yescharacteristic
336C4×C47C2×#12111yescharacteristic
337Dic47—24no—
338Dic47—44no—
339Dic47—44no—
340C2×#537—471no—
341C2×#520—471no—
342C2×#417—471no—
343C2×#416D4711yescharacteristic, complemented
344C2×#408—471no—
345#1875—472no—
346#1874—472no—
347#1873—472no—
348#1872—472no—
349#1736—471no—
350C2×#340—471no—
351C2×C47—24no—
352C2×C47—82no—
353C2×C47C2×#38611yescharacteristic
354C2×C47#289711yescharacteristic
355C2×C47#289811yescharacteristic
356C2×C47#301211yescharacteristic
357C2×C47#301311yescharacteristic
358C2×C47#309811yescharacteristic
359C2×C47#309911yescharacteristic
360D47—44no—
361C22×#41—471no—
362C22×#41C2×D4711yescharacteristic
363C22×M16—471no—
364C23×C8C2×D4711yescharacteristic
365#537—478no—
366#537—944no—
367C2×C22⋊Q8—472no—
368C2×C22⋊Q8—941no—
369C2×#121—472no—
370C2×#121—941no—
371C2×#121—942no—
372#520—944no—
373#520—944no—
374C2×C4×Q8—941no—
375C2×C4×D4—941no—
376C2×C4×D4—942no—
377C2×#117—472no—
378C2×#117C2×D4711yescharacteristic
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—472no—
382#417—944no—
383#416—24no—
384C2×#103—472no—
385C2×#103C2×D4711yescharacteristic
386C2×#103C2×D4711yescharacteristic
387C2×#102—472no—
388C2×#102C2×D4711yescharacteristic
389C2×#102C2×D4711yescharacteristic
390#408—944no—
391C2×C22⋊C8—472no—
392C2×C22⋊C8—472no—
393#340—472no—
394#340—472no—
395#340—472no—
396#340—472no—
397C47#2091511yescharacteristic, complemented, Sylow
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—474no—
404C2×#41—474no—
405C2×#41—942no—
406C2×#41—942no—
407C2×#41—942no—
408C2×#41—942no—
409C2×#41C4×D4714yescomplemented
410C22×Q8—471no—
411C22×Q8C22×D4711yescharacteristic
412C22×D4—21no—
413C22×D4—472no—
414C22×D4—471no—
415C22×D4—942no—
416C22×D4C22×D4711yescharacteristic
417C23×C4—21no—
418C23×C4—472no—
419C23×C4—942no—
420C23×C4—941no—
421C23×C4—941no—
422C23×C4C22×D4711yescharacteristic
423C2×M16—942no—
424C2×M16—942no—
425C2×M16—942no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—472no—
430C22×C8C22×D4711yescharacteristic
431C22×C8C22×D4711yescharacteristic
432C22⋊Q8—478no—
433C22⋊Q8—948no—
434C22⋊Q8—944no—
435#121—478no—
436#121—948no—
437#121—944no—
438#121—9416no—
439C4×Q8—948no—
440C4×D4—948no—
441C4×D4—9416no—
442#117—22no—
443#117—944no—
444#117—944no—
445#117C22⋊D4714yescomplemented
446C2×C4⋊C4—474no—
447C2×C4⋊C4—474no—
448C2×C4⋊C4—472no—
449C2×C4⋊C4—472no—
450C2×C4⋊C4—944no—
451C2×C4⋊C4—942no—
452C2×C4⋊C4—942no—
453C2×C4⋊C4—941no—
454C2×C4⋊C4—941no—
455C2×C4⋊C4—942no—
456C2×C4⋊C4—942no—
457C2×C4⋊C4—944no—
458C2×C4⋊C4C22×D4711yescharacteristic
459C2×C4⋊C4C22×D4711yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—942no—
462C2×C22⋊C4—942no—
463C2×C22⋊C4—942no—
464C2×C42—21no—
465C2×C42—942no—
466#103—22no—
467#103—22no—
468#103—944no—
469#102—22no—
470#102—22no—
471#102—944no—
472C22⋊C8—944no—
473C22⋊C8—944no—
474C24—21no—
475C24—472no—
476C24D4×D4711yescharacteristic
477#41—28no—
478#41—28no—
479#41—44no—
480#41—44no—
481#41—948no—
482#41—948no—
483#41—948no—
484#41—948no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—474no—
491C2×Q8—942no—
492C2×Q8—942no—
493C2×Q8C2×C4×D4712yes—
494C2×D4—24no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—478no—
503C2×D4—474no—
504C2×D4—944no—
505C2×D4—944no—
506C2×D4—948no—
507C2×D4—942no—
508C2×D4—942no—
509C2×D4—3762no—
510C2×D4—3762no—
511C2×D4C2×C4×D4712yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—472no—
519C22×C4—474no—
520C22×C4—474no—
521C22×C4—948no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—944no—
527C22×C4—944no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—3762no—
531C22×C4—3762no—
532C22×C4—3761no—
533C22×C4—3761no—
534C22×C4—3761no—
535C22×C4—3761no—
536C22×C4C2×C4×D4712yes—
537C22×C4#1062535012yes—
538C22×C4D4×D4711yescharacteristic
539C22×C4D4×D4712yes—
540C22×C4D4×D4712yes—
541C22×C4#1062535212yes—
542C22×C4C2×C22⋊D4712yes—
543C22×C4C23×D4711yescharacteristic
544M16—1884no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8—942no—
553C2×C8—942no—
554C2×C8—942no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—474no—
558C4⋊C4—474no—
559C4⋊C4—948no—
560C4⋊C4—948no—
561C4⋊C4—944no—
562C4⋊C4—944no—
563C4⋊C4—942no—
564C4⋊C4—942no—
565C4⋊C4C2×C22⋊D4712yes—
566C4⋊C4C2×C22⋊D4712yes—
567C22⋊C4—24no—
568C22⋊C4—948no—
569C22⋊C4—948no—
570C22⋊C4—948no—
571C42—24no—
572C42—948no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—474no—
585C23—942no—
586C23—942no—
587C23—942no—
588C23—942no—
589C23—942no—
590C23—942no—
591C23C22⋊C4×D4712yes—
592C23#1309399212yes—
593C23#1309400612yes—
594C23C2×D4×D4711yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599Q8—948no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4—41no—
604D4—41no—
605D4—9416no—
606D4—948no—
607D4—3768no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—48no—
618C2×C4—474no—
619C2×C4—942no—
620C2×C4—942no—
621C2×C4—944no—
622C2×C4—944no—
623C2×C4—944no—
624C2×C4—944no—
625C2×C4—944no—
626C2×C4—944no—
627C2×C4—3768no—
628C2×C4—3764no—
629C2×C4—3764no—
630C2×C4—1882no—
631C2×C4—1882no—
632C2×C4—1882no—
633C2×C4—1882no—
634C2×C4C22⋊C4×D4712yes—
635C2×C4(C22⋊D47)⋊C414yes—
636C2×C4C4×C22⋊D4714yes—
637C2×C4#1309399212yes—
638C2×C4#1309399514yes—
639C2×C4#1309399714yes—
640C2×C4#1309400612yes—
641C2×C4C22×C4×D4711yescharacteristic
642C2×C4C2×D4×D4711yescharacteristic
643C2×C4C2×D4×D4711yescharacteristic
644C2×C4C22×C22⋊D4711yescharacteristic
645C2×C4C2×#1062535211yescharacteristic
646C2×C4C2×#1062535011yescharacteristic
647C8—41no—
648C8—41no—
649C8—1882no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—944no—
664C22—944no—
665C22—944no—
666C22—1882no—
667C22—1882no—
668C22—1882no—
669C22—1882no—
670C22#1568899914yes—
671C22C2×C22⋊C4×D4711yescharacteristic
672C22C2×#1309399211yescharacteristic
673C22C2×#1309400611yescharacteristic
674C22#1568992511yescharacteristic
675C22#1568993011yescharacteristic
676C22#1568993011yescharacteristic
677C22#1568993711yescharacteristic
678C4—42no—
679C4—42no—
680C4—42no—
681C4—944no—
682C4—1884no—
683C4—1884no—
684C4#1568899914yes—
685C4C2×(C22⋊D47)⋊C411yescharacteristic
686C4C2×C4×C22⋊D4711yescharacteristic
687C4C2×#1309399511yescharacteristic
688C4C2×#1309399711yescharacteristic
689C2—24no—
690C2—82no—
691C2—1884no—
692C2C2×#1568899911yescharacteristic
693C2#2025191011yescharacteristic
694C2#2025191711yescharacteristic
695C2#2025268811yescharacteristic
696C2#2025269911yescharacteristic
697C2#2025336411yescharacteristic
698C2#2025337511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC2×#15689701C2
cosocleC22×C4×C47C24
hypercenterC2×#416D47
hypocenterC47#20915
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#15689603C2semidirect
3. C2×#15689124C2semidirect
4. C2×#15689089C2semidirect
5. #20243707C2semidirect
6. #20243702C2semidirect
7. #20243697C2semidirect
8. #20243692C2semidirect
9. #20243109C2semidirect
10. C2×#15688886C2semidirect
11. C2×C47×#416C2semidirect
15. #15689701C4semidirect
68. #13094000C2×C4semidirect
72. #13093995C2×C4semidirect
82. C2×C4⋊Dic47C2×C4semidirect
83. C2×C4⋊Dic47D4semidirect
103. C2×#41×C47C2×C4semidirect
115. #117×C47D4semidirect
343. C2×#416D47semidirect
397. C47#20915semidirect
409. C2×#41C4×D47semidirect
445. #117C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156897012
C2×#156896032
C2×#156891242
C2×#156890892
#202437072
#202437022
#202436972
#202436922
#202431092
C2×#156888862
C2×C47×#4162
#2091547