Finite Group Databasebeta

← #27413710

Subgroups — #27413710

Order 13568.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810733C211yesmaximal, characteristic, complemented
2C2×#16810684C211yesmaximal, characteristic, complemented
3#20277408C211yesmaximal, characteristic, complemented
4#20276217C211yesmaximal, characteristic, complemented
5#20276151C211yesmaximal, characteristic, complemented
6#20276100C211yesmaximal, characteristic, complemented
7#20276089C211yesmaximal, characteristic, complemented
8#20276025C211yesmaximal, characteristic, complemented
9#20275904C211yesmaximal, characteristic, complemented
10#20275894C211yesmaximal, characteristic, complemented
11#20275711C211yesmaximal, characteristic
12#20274613C211yesmaximal, characteristic, complemented
13C4×#13133137C211yesmaximal, characteristic, complemented
14C4×#13133138C211yesmaximal, characteristic, complemented
15C53×#2324C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C2×#13133191C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19#16810733—24no—
20#16810684—24no—
21C2×#13133150C2211yescharacteristic
22C2×#13133148C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×C4⋊#88322C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810523—21no—
38#16810521C2211yescharacteristic
39#16810513—21no—
40#16810499—21no—
41#16810494—21no—
42#16810483C2211yescharacteristic
43C4×C4⋊Dic53C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C2×#121×C53C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C2×#117×C53C2211yescharacteristic
53C53×#390—21no—
54C53×#390C2211yescharacteristic
55C53×#389C2211yescharacteristic
56C53×#388—21no—
57C53×#386—21no—
58C53×#385—21no—
59C53×#380C2211yescharacteristic
60C4×C4⋊C4×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64C2×#11719922—22no—
65C2×#11719922—22no—
66C2×#11719922—22no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133191—22no—
72#13133191—22no—
73C4×D212—22no—
74C4×D212—22no—
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×#11719919—21no—
79C2×C22⋊Dic53—21no—
80C2×#11719921—21no—
81C2×#11719921—21no—
82C2×#11719921—21no—
83C2×#11719921—21no—
84C2×C4×Dic53—21no—
85#13133150—22no—
86#13133148—22no—
87#13133148—22no—
88C4⋊#88322—22no—
89C4⋊#88322—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—22no—
93#13133137—22no—
94#13133137—22no—
95#13133137—22no—
96C22⋊#88322—22no—
97C22⋊#88322—22no—
98#13133128D414yescomplemented
99C4×#88322—22no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103C22×D4×C53—21no—
104C22×D4×C53C2311yescharacteristic
105C23×C4×C53—21no—
106C23×C4×C53C2311yescharacteristic
107#121×C53—22no—
108#121×C53—22no—
109C4×D4×C53—22no—
110C4×D4×C53—22no—
111#117×C53—22no—
112#117×C53—22no—
113C2×C4⋊C4×C53—21no—
114C2×C4⋊C4×C53D411yescharacteristic
115C2×C4⋊C4×C53D411yescharacteristic
116C2×C4⋊C4×C53C2311yescharacteristic
117C2×C4⋊C4×C53C2311yescharacteristic
118C2×C4⋊C4×C53C2311yescharacteristic
119C2×C22⋊C4×C53—21no—
120C2×C22⋊C4×C53—21no—
121C2×C22⋊C4×C53—21no—
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53D411yescharacteristic
125C2×C22⋊C4×C53D411yescharacteristic
126C2×C42×C53—21no—
127C2×C42×C53C2311yescharacteristic
128C2×C42×C53C2311yescharacteristic
129#95×C53—21no—
130#95×C53—21no—
131#95×C53—21no—
132C24×C53—21no—
133C24×C53C2×D411yescharacteristic
134C23×D53—21no—
135C2×D4×C53—24no—
136C2×D4×C53—21no—
137C2×D4×C53—21no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—81no—
142C2×D4×C53—81no—
143C2×D4×C53#4112yes—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—42no—
154C22×C4×C53—81no—
155C22×C4×C53—81no—
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2411yescharacteristic
162C2×C22⋊D53—24no—
163C2×C22⋊D53—81no—
164C2×C22⋊D53—81no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C2×D212—21no—
169C2×D212—21no—
170C2×D212—21no—
171C2×D212—21no—
172C2×D212—21no—
173C2×D212#4112yes—
174C2×C4×D53—42no—
175C2×C4×D53—81no—
176C2×C4×D53—81no—
177C4⋊C4×C53—22no—
178C4⋊C4×C53—22no—
179C4⋊C4×C53—21no—
180C4⋊C4×C53—21no—
181C4⋊C4×C53—21no—
182C4⋊C4×C53—21no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—81no—
185C4⋊C4×C53#4112yes—
186C22⋊C4×C53—24no—
187C22⋊C4×C53—22no—
188C22⋊C4×C53—22no—
189C22⋊C4×C53—42no—
190C22⋊C4×C53—81no—
191C22⋊C4×C53—81no—
192C22⋊C4×C53—81no—
193C42×C53—21no—
194C42×C53—21no—
195C42×C53—81no—
196C42×C53C2×D412yes—
197C42×C53#4112yes—
198C22⋊Dic53—81no—
199#11719922—28no—
200#11719921—24no—
201#11719921—42no—
202#11719921—81no—
203#11719921—81no—
204C4⋊Dic53—21no—
205C4⋊Dic53—21no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53#4112yes—
210#11719919—81no—
211C4×Dic53—81no—
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×#88322C2×D412yes—
223C2×#88322C2×D412yes—
224C23×C53—21no—
225C23×C53—21no—
226C23×C53—21no—
227C23×C53—22no—
228C23×C53—21no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53C22×D411yescharacteristic
239C22×D53—22no—
240C22×D53—41no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53—41no—
245C22×D53—41no—
246D4×C53—22no—
247D4×C53—22no—
248D4×C53—41no—
249D4×C53—41no—
250D4×C53—84no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—22no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
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—41no—
276C2×C4×C53—41no—
277C2×C4×C53—84no—
278C2×C4×C53#12112yes—
279C2×C4×C53#12112yes—
280C2×C4×C53C22×D411yescharacteristic
281C2×C4×C53C2×#4111yescharacteristic
282C2×C4×C53C2×#4111yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C22⋊D53—84no—
287C2×Dic53—22no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296D212—22no—
297D212—22no—
298D212—41no—
299D212—41no—
300C4×D53—84no—
301#88322—22no—
302#88322—22no—
303#88322—41no—
304#88322—41no—
305#23712—531nomaximal, Sylow
306C22×C53—41no—
307C22×C53—41no—
308C22×C53—41no—
309C22×C53—42no—
310C22×C53—41no—
311C22×C53—42no—
312C22×C53—41no—
313C22×C53—42no—
314C22×C53—41no—
315C22×C53—41no—
316C22×C53—81no—
317C22×C53—81no—
318C22×C53—81no—
319C22×C53—81no—
320C22×C53C2×#12111yescharacteristic
321C22×C53#52511yescharacteristic
322C22×C53#52511yescharacteristic
323C22×C53#57611yescharacteristic
324C22×C53#57611yescharacteristic
325C22×C53#57711yescharacteristic
326C22×C53#57711yescharacteristic
327C2×D53—42no—
328C2×D53—42no—
329C2×D53—42no—
330C2×D53—81no—
331C2×D53—81no—
332C2×D53—81no—
333C2×D53—81no—
334C4×C53—22no—
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—41no—
338C4×C53—41no—
339C4×C53—41no—
340C4×C53—81no—
341C4×C53—81no—
342C4×C53#52511yescharacteristic
343C4×C53#52911yescharacteristic
344C4×C53#52911yescharacteristic
345C4×C53#53211yescharacteristic
346Dic53—42no—
347Dic53—81no—
348Dic53—81no—
349C2×#442—531no—
350C2×#433—531no—
351#2324—531no—
352#2324D5311yescharacteristic, complemented
353#2088—531no—
354#2077—531no—
355#2067—531no—
356#2065—531no—
357#2054—531no—
358#2034—531no—
359#2033—531no—
360#1999—531no—
361#1776—531no—
362C4×#102—531no—
363C4×#102—531no—
364C2×C53—81no—
365C2×C53—82no—
366C2×C53#239211yescharacteristic
367C2×C53#306211yescharacteristic
368C2×C53#306211yescharacteristic
369C2×C53#311811yescharacteristic
370C2×C53#311911yescharacteristic
371C2×C53#312211yescharacteristic
372C2×C53#312511yescharacteristic
373D53—82no—
374C22×D8—531no—
375C2×#121—531no—
376C2×#121C2×D5311yescharacteristic
377C2×C4×D4—531no—
378C2×C4×D4C2×D5311yescharacteristic
379C2×#117C2×D5311yescharacteristic
380#442—1064no—
381#433—1064no—
382C2×#107—531no—
383C2×#106—531no—
384C2×#106—531no—
385C2×C4⋊C8—531no—
386C2×C4⋊C8—531no—
387C2×#102—531no—
388C2×#102—531no—
389C2×#102—531no—
390C2×#102—531no—
391C2×#102—531no—
392C2×#102—531no—
393C2×C22⋊C8—531no—
394C2×C22⋊C8—531no—
395C2×#97—531no—
396C2×C4×C8—531no—
397#390—21no—
398#390—531no—
399#390—1061no—
400#390C2×D5311yescharacteristic
401#389—531no—
402#389C2×D5311yescharacteristic
403#388—21no—
404#388—1061no—
405#386—21no—
406#386—1061no—
407#385—21no—
408#385—1061no—
409#380—531no—
410#380C2×D5311yescharacteristic
411C4×C4⋊C4—531no—
412C4×C4⋊C4C2×D5311yescharacteristic
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419C53#2371211yescharacteristic, complemented, Sylow
420C22×D4—21no—
421C22×D4—531no—
422C22×D4—1061no—
423C22×D4C22×D5311yescharacteristic
424C23×C4—21no—
425C23×C4—1061no—
426C23×C4C22×D5311yescharacteristic
427C2×D8—1062no—
428C2×D8—1062no—
429C2×D8—1062no—
430C22×C8—531no—
431C22×C8—531no—
432C22×C8—531no—
433C22×C8—531no—
434#121—22no—
435#121—22no—
436#121—1062no—
437#121—1062no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—1062no—
441C4×D4—1062no—
442#117—22no—
443#117—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—531no—
446C2×C4⋊C4—531no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—1061no—
449C2×C4⋊C4C22⋊D5311yescharacteristic
450C2×C4⋊C4C22⋊D5311yescharacteristic
451C2×C4⋊C4C22×D5311yescharacteristic
452C2×C4⋊C4C22×D5311yescharacteristic
453C2×C4⋊C4C22×D5311yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C22⋊C4C22⋊D5311yescharacteristic
465C2×C22⋊C4C22⋊D5311yescharacteristic
466C2×C42—21no—
467C2×C42—1061no—
468C2×C42C22×D5311yescharacteristic
469C2×C42C22×D5311yescharacteristic
470#107—1062no—
471#106—1062no—
472#106—1062no—
473C4⋊C8—1062no—
474C4⋊C8—1062no—
475#102—1062no—
476#102—1062no—
477#102—1062no—
478#102—1062no—
479#102—1062no—
480#102—1062no—
481C22⋊C8—1062no—
482C22⋊C8—1062no—
483#97—534no—
484C4×C8—1062no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491C24—21no—
492C24—1061no—
493C24C2×C22⋊D5311yescharacteristic
494C2×D4—24no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—532no—
503C2×D4—1064no—
504C2×D4—1061no—
505C2×D4—1061no—
506C2×D4—1061no—
507C2×D4—1061no—
508C2×D4—1061no—
509C2×D4—4241no—
510C2×D4—4241no—
511C2×D4#1171994512yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—4241no—
528C22×C4—4241no—
529C22×C4—2122no—
530C22×C4C2×C22⋊D5311yescharacteristic
531C22×C4C2×C22⋊D5311yescharacteristic
532C22×C4C2×C22⋊D5311yescharacteristic
533C22×C4C2×C22⋊D5311yescharacteristic
534C22×C4C2×C22⋊D5311yescharacteristic
535C22×C4C23×D5311yescharacteristic
536D8—1068no—
537C2×C8—532no—
538C2×C8—532no—
539C2×C8—1061no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—81no—
557C4⋊C4—532no—
558C4⋊C4—1061no—
559C4⋊C4—1061no—
560C4⋊C4—1061no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—4241no—
564C4⋊C4#1171994512yes—
565C22⋊C4—24no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—1064no—
573C22⋊C4—4241no—
574C22⋊C4—4241no—
575C22⋊C4—4241no—
576C22⋊C4—2122no—
577C42—21no—
578C42—21no—
579C42—81no—
580C42—4241no—
581C42D4×D5312yes—
582C42#1171994712yes—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—1062no—
598C23—2121no—
599C23—2121no—
600C23—2121no—
601C23—2121no—
602C23—2121no—
603C23—2121no—
604C23C22×C22⋊D5311yescharacteristic
605D4—22no—
606D4—22no—
607D4—41no—
608D4—41no—
609D4—84no—
610D4—1062no—
611D4—1062no—
612D4—4244no—
613D4—2121no—
614D4—2121no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
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—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—84no—
642C2×C4—1062no—
643C2×C4—4244no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4#1313318912yes—
653C2×C4#1313318912yes—
654C2×C4C2×D4×D5311yescharacteristic
655C2×C4#41×D5311yescharacteristic
656C2×C4#41×D5311yescharacteristic
657C2×C4C2×#1171994711yescharacteristic
658C2×C4C2×#1171994511yescharacteristic
659C2×C4C2×#1171994511yescharacteristic
660C8—1062no—
661C8—1062no—
662C8—2121no—
663C8—2121no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—4241no—
679C22—4241no—
680C22—4241no—
681C22—4241no—
682C22—2122no—
683C22—2122no—
684C22—2122no—
685C22C2×#1313318911yescharacteristic
686C22#1681113011yescharacteristic
687C22#1681113411yescharacteristic
688C22#1681142611yescharacteristic
689C22#1681142611yescharacteristic
690C22#1681143111yescharacteristic
691C22#1681143411yescharacteristic
692C4—22no—
693C4—22no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—4241no—
701C4—4241no—
702C4—2122no—
703C4#1681113211yescharacteristic
704C4#1681115311yescharacteristic
705C4#1681115511yescharacteristic
706C4#1681117011yescharacteristic
707C2—81no—
708C2—82no—
709C2—4242no—
710C2#2027795711yescharacteristic
711C2#2028439111yescharacteristic
712C2#2028439711yescharacteristic
713C2#2028489311yescharacteristic
714C2#2028490811yescharacteristic
715C2#2028495811yescharacteristic
716C2#2028499211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2324C2
socleC23×C53C22×D4
prime radical#20275711C2
hypercenter#2324D53
hypocenterC53#23712
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#16810733C2semidirect
2. C2×#16810684C2semidirect
3. #20277408C2semidirect
4. #20276217C2semidirect
5. #20276151C2semidirect
6. #20276100C2semidirect
7. #20276089C2semidirect
8. #20276025C2semidirect
9. #20275904C2semidirect
10. #20275894C2semidirect
12. #20274613C2semidirect
13. C4×#13133137C2semidirect
14. C4×#13133138C2semidirect
15. C53×#2324C2semidirect
98. #13133128D4semidirect
352. #2324D53semidirect
419. C53#23712semidirect

Maximal subgroups

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

subgroupindex
C2×#168107332
C2×#168106842
#202774082
#202762172
#202761512
#202761002
#202760892
#202760252
#202759042
#202758942
#202757112
#202746132
C4×#131331372
C4×#131331382
C53×#23242
#2371253