Finite Group Databasebeta

← #27401377

Subgroups — #27401377

Order 13568.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810624C211yesmaximal, characteristic
2#20277582C211yesmaximal, characteristic, complemented
3#20275408C211yesmaximal, characteristic, complemented
4#20275394C211yesmaximal, characteristic, complemented
5#20275353C211yesmaximal, characteristic, complemented
6#20275346C211yesmaximal, characteristic, complemented
7#20274976C211yesmaximal, characteristic, complemented
8#20274962C211yesmaximal, characteristic, complemented
9#20274803C211yesmaximal, characteristic, complemented
10#20274746C211yesmaximal, characteristic, complemented
11#20274655C211yesmaximal, characteristic
12#20274540C211yesmaximal, characteristic, complemented
13C4×#13133138C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2339C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×#13133173—21no—
18C22×C4⋊Dic53C2211yescharacteristic
19C2×#13133150C2211yescharacteristic
20C2×#13133148C2211yescharacteristic
21#16810624C418yescomplemented
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×#13133128C2211yescharacteristic
32C2×C4×#88322C2211yescharacteristic
33#16810521C2211yescharacteristic
34#16810521C2211yescharacteristic
35#16810508—21no—
36#16810508—21no—
37#16810484—21no—
38#16810483C2211yescharacteristic
39C4×C4⋊Dic53C2211yescharacteristic
40C4×C4⋊Dic53C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810378C2211yescharacteristic
49C22×#41×C53C2211yescharacteristic
50C2×C4×D4×C53C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C53×#391C2211yescharacteristic
53C53×#391C2211yescharacteristic
54C53×#386—21no—
55C53×#386—21no—
56C53×#381—21no—
57C53×#380C2211yescharacteristic
58C4×C22⋊C4×C53C2211yescharacteristic
59C2×#95×C53—21no—
60C23×Dic53—21no—
61C2×#11719917—41no—
62C2×#11719917—41no—
63C2×#11719917C2×C414yescomplemented
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68#13133173—44no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53C2×C414yescomplemented
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C4×Dic53—21no—
80C2×C4×Dic53—21no—
81#13133150—41no—
82#13133148—41no—
83#13133141—41no—
84#13133141—41no—
85#13133141C2×C414yescomplemented
86#13133141C2×C414yescomplemented
87#13133138—22no—
88#13133138—22no—
89#13133138C2×C414yes—
90#13133138C2×C414yes—
91C22⋊#88322—22no—
92#13133128—41no—
93C4×#88322—41no—
94#13133124—21no—
95#13133124—21no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99C2×#41×C53—22no—
100C2×#41×C53—22no—
101C2×#41×C53—22no—
102C2×#41×C53—41no—
103C2×#41×C53—41no—
104C2×#41×C53C2×C414yes—
105C22×Q8×C53C2311yescharacteristic
106C22×D4×C53—21no—
107C22×D4×C53C2311yescharacteristic
108C23×C4×C53—21no—
109C23×C4×C53—21no—
110C23×C4×C53—21no—
111C23×C4×C53C2311yescharacteristic
112C4×D4×C53—22no—
113C4×D4×C53—22no—
114C4×D4×C53—41no—
115C4×D4×C53—41no—
116C2×C4⋊C4×C53C2311yescharacteristic
117C2×C4⋊C4×C53C2311yescharacteristic
118C2×C22⋊C4×C53—21no—
119C2×C22⋊C4×C53—21no—
120C2×C22⋊C4×C53—21no—
121C2×C22⋊C4×C53D411yescharacteristic
122C2×C22⋊C4×C53D411yescharacteristic
123C2×C42×C53C2311yescharacteristic
124C2×C42×C53C2311yescharacteristic
125#95×C53—21no—
126#95×C53—21no—
127#95×C53—21no—
128#95×C53—21no—
129#95×C53—21no—
130#95×C53D411yescharacteristic
131#95×C53D411yescharacteristic
132C24×C53—21no—
133C24×C53C2×D411yescharacteristic
134#41×C53—28no—
135#41×C53—44no—
136#41×C53—44no—
137#41×C53—44no—
138C2×Q8×C53—21no—
139C2×Q8×C53—21no—
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53C22×C412yes—
144C2×D4×C53—24no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—42no—
149C2×D4×C53—42no—
150C2×D4×C53C22×C412yes—
151C2×D4×C53#4112yes—
152C2×D4×C53#4112yes—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—24no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—42no—
162C22×C4×C53—42no—
163C22×C4×C53—42no—
164C22×C4×C53—42no—
165C22×C4×C53—42no—
166C22×C4×C53—42no—
167C22×C4×C53—81no—
168C22×C4×C53—81no—
169C22×C4×C53C22×C412yes—
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53#4112yes—
176C22×C4×C53C2411yescharacteristic
177C22×Dic53—24no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—42no—
183C22×Dic53—42no—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C22⋊C4×C53—22no—
189C22⋊C4×C53—41no—
190C22⋊C4×C53—42no—
191C22⋊C4×C53—42no—
192C22⋊C4×C53—81no—
193C42×C53—21no—
194C42×C53—21no—
195C42×C53—21no—
196C42×C53—21no—
197C22⋊Dic53—42no—
198C4⋊Dic53—24no—
199C4⋊Dic53—21no—
200C4⋊Dic53—21no—
201C4⋊Dic53—21no—
202C4⋊Dic53—21no—
203C4⋊Dic53—21no—
204C4⋊Dic53—21no—
205C4⋊Dic53C22×C412yes—
206C4⋊Dic53C22×C412yes—
207#11719919—42no—
208#11719919—42no—
209C4×Dic53—42no—
210C4×Dic53—42no—
211#11719917—44no—
212C2×#88322—21no—
213C2×#88322—21no—
214C2×#88322—21no—
215C2×#88322—21no—
216C2×#88322—21no—
217C2×#88322—21no—
218C2×#88322—21no—
219C2×#88322—21no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322C22×C412yes—
223C2×#88322C22×C412yes—
224C23×C53—22no—
225C23×C53—21no—
226C23×C53—21no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53C4×D412yes—
238C23×C53C22×D411yescharacteristic
239Q8×C53—22no—
240Q8×C53—22no—
241Q8×C53—41no—
242Q8×C53—41no—
243D4×C53—22no—
244D4×C53—22no—
245D4×C53—22no—
246D4×C53—48no—
247D4×C53#11714yescomplemented
248C2×C4×C53—21no—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—21no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—48no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—84no—
276C2×C4×C53—84no—
277C2×C4×C53C4×D412yes—
278C2×C4×C53AGL(1,ℤ/8)12yes—
279C2×C4×C53C23×C411yescharacteristic
280C2×C4×C53C2×#4111yescharacteristic
281C2×C4×C53C2×#4111yescharacteristic
282C2×C4×C53C2×#4111yescharacteristic
283C2×C4×C53H(5,𝔽2)11yescharacteristic
284C2×C4×C53H(5,𝔽2)11yescharacteristic
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—48no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298#88322—22no—
299#88322—22no—
300#88322—41no—
301#88322—41no—
302#22582—531nomaximal, Sylow
303C22×C53—22no—
304C22×C53—24no—
305C22×C53—22no—
306C22×C53—22no—
307C22×C53—41no—
308C22×C53—42no—
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—42no—
312C22×C53—41no—
313C22×C53—41no—
314C22×C53—42no—
315C22×C53—42no—
316C22×C53—41no—
317C22×C53C2×C4×D411yescharacteristic
318C22×C53#54611yescharacteristic
319C22×C53#54611yescharacteristic
320C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C53#57511yescharacteristic
322C22×C53#57711yescharacteristic
323C22×C53#57811yescharacteristic
324C4×C53—22no—
325C4×C53—22no—
326C4×C53—41no—
327C4×C53—42no—
328C4×C53—41no—
329C4×C53—41no—
330C4×C53—81no—
331C4×C53—81no—
332C4×C53C2×#11711yescharacteristic
333C4×C53#51811yescharacteristic
334C4×C53#55111yescharacteristic
335C4×C53#55111yescharacteristic
336Dic53—42no—
337Dic53—42no—
338Dic53—81no—
339Dic53—81no—
340C2×#417—531no—
341#2344—531no—
342#2339D5311yescharacteristic
343#1935—531no—
344#1933—531no—
345#1928—531no—
346#1927—531no—
347#1864—531no—
348#1862—531no—
349#1824—531no—
350#1809—531no—
351#1788—531no—
352#1762—531no—
353C4×#102—531no—
354#1753—531no—
355C2×C53—42no—
356C2×C53—44no—
357C2×C53#234211yescharacteristic
358C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
359C2×C53#294711yescharacteristic
360C2×C53#330611yescharacteristic
361C2×C53#331511yescharacteristic
362C2×C53#332311yescharacteristic
363C2×C53#333011yescharacteristic
364C22×#41C2×D5311yescharacteristic
365C22×M16—531no—
366C2×C4×D4C2×D5311yescharacteristic
367C2×C4×D4C2×D5311yescharacteristic
368C2×#117—1061no—
369C22×C4⋊C4—531no—
370C2×#107—531no—
371C2×#106—531no—
372#417—538no—
373C2×#103—531no—
374C2×#103—531no—
375C2×#103—531no—
376C2×#103—531no—
377C2×#102—531no—
378C2×#102—531no—
379C2×#102—531no—
380C2×#102—531no—
381C2×C22⋊C8—531no—
382C2×#97—531no—
383C2×C4×C8—531no—
384#391C2×D5311yescharacteristic
385#391C2×D5311yescharacteristic
386#389—531no—
387#389—531no—
388#387—1061no—
389#387—1061no—
390#386—21no—
391#386—21no—
392#381—21no—
393#381—1061no—
394#380—531no—
395#380C2×D5311yescharacteristic
396C4×C4⋊C4—531no—
397C4×C4⋊C4—531no—
398C4×C22⋊C4C2×D5311yescharacteristic
399C2×#95—21no—
400#340—531no—
401#340—531no—
402#340—531no—
403#340—531no—
404#340—531no—
405#340—531no—
406#336—531no—
407#336—531no—
408C53#2258211yescharacteristic, complemented, Sylow
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—41no—
413C2×#41—41no—
414C2×#41C4×D5314yes—
415C22×Q8C22×D5311yescharacteristic
416C22×D4—21no—
417C22×D4C22×D5311yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—1061no—
422C23×C4C22×D5311yescharacteristic
423C2×M16—534no—
424C2×M16—2121no—
425C2×M16—2121no—
426C22×C8—531no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8—531no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—41no—
433C4×D4—41no—
434#117—2124no—
435C2×C4⋊C4—534no—
436C2×C4⋊C4—531no—
437C2×C4⋊C4—531no—
438C2×C4⋊C4—531no—
439C2×C4⋊C4—531no—
440C2×C4⋊C4—1062no—
441C2×C4⋊C4—1061no—
442C2×C4⋊C4—1061no—
443C2×C4⋊C4—1061no—
444C2×C4⋊C4C22×D5311yescharacteristic
445C2×C4⋊C4C22×D5311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—1061no—
450C2×C22⋊C4C22⋊D5311yescharacteristic
451C2×C22⋊C4C22⋊D5311yescharacteristic
452C2×C42—1061no—
453C2×C42—1061no—
454C2×C42C22×D5311yescharacteristic
455C2×C42C22×D5311yescharacteristic
456#107—2121no—
457#106—2121no—
458#103—534no—
459#103—534no—
460#103—2121no—
461#103—2121no—
462#102—534no—
463#102—534no—
464#102—1062no—
465#102—1062no—
466C22⋊C8—1062no—
467#97—2121no—
468C4×C8—2121no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—1061no—
475#95—1061no—
476#95—1061no—
477#95—1061no—
478#95—1061no—
479#95C22⋊D5311yescharacteristic
480#95C22⋊D5311yescharacteristic
481C24—21no—
482C24C2×C22⋊D5311yescharacteristic
483#41—28no—
484#41—44no—
485#41—44no—
486#41—44no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8C2×C4×D5312yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4C2×C4×D5312yes—
500C2×D4#1171994712yes—
501C2×D4#1171994712yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—1064no—
519C22×C4—1061no—
520C22×C4—1061no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—2122no—
524C22×C4—2122no—
525C22×C4C2×C4×D5312yes—
526C22×C4#1171994512yes—
527C22×C4C2×C22⋊D5311yescharacteristic
528C22×C4C2×C22⋊D5311yescharacteristic
529C22×C4C2×C22⋊D5311yescharacteristic
530C22×C4C2×C22⋊D5311yescharacteristic
531C22×C4C2×C22⋊D5311yescharacteristic
532C22×C4C23×D5311yescharacteristic
533M16—2124no—
534C2×C8—532no—
535C2×C8—532no—
536C2×C8—1061no—
537C2×C8—1061no—
538C2×C8—1061no—
539C2×C8—1061no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—532no—
551C4⋊C4—532no—
552C4⋊C4—1064no—
553C4⋊C4—1061no—
554C4⋊C4—1061no—
555C4⋊C4—1061no—
556C4⋊C4—1061no—
557C4⋊C4—1061no—
558C4⋊C4—1061no—
559C4⋊C4—2122no—
560C4⋊C4—2122no—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—2122no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—2122no—
572C42—2122no—
573C23—22no—
574C23—22no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23C4×C22⋊D5312yes—
587C23C22×C22⋊D5311yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4—48no—
596D4#1313317314yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4—2121no—
632C2×C4—2121no—
633C2×C4—2121no—
634C2×C4—2128no—
635C2×C4—2121no—
636C2×C4—2121no—
637C2×C4—2121no—
638C2×C4—2121no—
639C2×C4C4×C22⋊D5312yes—
640C2×C4#1313324212yes—
641C2×C4C22×C4×D5311yescharacteristic
642C2×C4C2×#1171994711yescharacteristic
643C2×C4C2×#1171994711yescharacteristic
644C2×C4C2×#1171994511yescharacteristic
645C2×C4#1313326211yescharacteristic
646C2×C4#1313326211yescharacteristic
647C8—1062no—
648C8—1062no—
649C8—2121no—
650C8—2121no—
651C22—22no—
652C22—24no—
653C22—22no—
654C22—22no—
655C22—41no—
656C22—42no—
657C22—41no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—41no—
665C22C2×C4×C22⋊D5311yescharacteristic
666C22#1681126711yescharacteristic
667C22#1681126711yescharacteristic
668C22C2×#1313324211yescharacteristic
669C22#1681142111yescharacteristic
670C22#1681143411yescharacteristic
671C22#1681143811yescharacteristic
672C4—22no—
673C4—22no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—4241no—
681C4—4241no—
682C4—2122no—
683C4—2122no—
684C4C2×#1313317311yescharacteristic
685C4#1681109611yescharacteristic
686C4#1681129911yescharacteristic
687C4#1681129911yescharacteristic
688C2—42no—
689C2—44no—
690C2#2027756011yescharacteristic
691C2C4×#1313324211yescharacteristic
692C2#2028355411yescharacteristic
693C2#2028667611yescharacteristic
694C2#2028681111yescharacteristic
695C2#2028693111yescharacteristic
696C2#2028702011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2339C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#2339D53
hypocenterC53#22582
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #20277582C2semidirect
3. #20275408C2semidirect
4. #20275394C2semidirect
5. #20275353C2semidirect
6. #20275346C2semidirect
7. #20274976C2semidirect
8. #20274962C2semidirect
9. #20274803C2semidirect
10. #20274746C2semidirect
12. #20274540C2semidirect
13. C4×#13133138C2semidirect
14. #20274499C2semidirect
21. #16810624C4semidirect
63. C2×#11719917C2×C4semidirect
71. C2×C4⋊Dic53C2×C4semidirect
85. #13133141C2×C4semidirect
86. #13133141C2×C4semidirect
247. D4×C53#117semidirect
408. C53#22582semidirect
596. D4#13133173semidirect

Maximal subgroups

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

subgroupindex
C2×#168106242
#202775822
#202754082
#202753942
#202753532
#202753462
#202749762
#202749622
#202748032
#202747462
#202746552
#202745402
C4×#131331382
#202744992
C53×#23392
#2258253