Finite Group Databasebeta

← #27390706

Subgroups — #27390706

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810852C211yesmaximal, characteristic
2C2×#16810725C211yesmaximal, characteristic, complemented
3#20277408C211yesmaximal, characteristic
4#20277397C211yesmaximal, characteristic, complemented
5#20275596C211yesmaximal, characteristic, complemented
6#20275458C211yesmaximal, characteristic, complemented
7#20275398C211yesmaximal, characteristic, complemented
8#20275391C211yesmaximal, characteristic, complemented
9#20275153C211yesmaximal, characteristic
10#20275148C211yesmaximal, characteristic, complemented
11#20274744C211yesmaximal, characteristic, complemented
12#20274612C211yesmaximal, characteristic, complemented
13C4×#13133142C211yesmaximal, characteristic, complemented
14C4×#13133139C211yesmaximal, characteristic, complemented
15C2×C53×#405C211yesmaximal, characteristic, complemented
16C22×#11719913C2211yescharacteristic
17C2×#13133196C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×Dic106C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21#16810852C418yescomplemented
22#16810725—24no—
23C2×#13133151C2211yescharacteristic
24C2×#13133151C2211yescharacteristic
25C2×#13133149C2211yescharacteristic
26C2×#13133142C2211yescharacteristic
27C2×#13133142C2211yescharacteristic
28C2×#13133142C2211yescharacteristic
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133139C2211yescharacteristic
32#16810529C2211yescharacteristic
33#16810525C2211yescharacteristic
34#16810523—21no—
35#16810521C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810518—21no—
38#16810517—21no—
39#16810513—21no—
40#16810511—21no—
41#16810504—21no—
42#16810499—21no—
43#16810494—21no—
44#16810483C2211yescharacteristic
45#16810483C2211yescharacteristic
46C4×C4⋊Dic53C2211yescharacteristic
47C4×C4⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54C22×M16×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×#117×C53C2211yescharacteristic
57C53×#405—24no—
58C2×#97×C53C2211yescharacteristic
59C2×#97×C53C2211yescharacteristic
60C2×C4×C8×C53C2211yescharacteristic
61C2×C4×C8×C53C2211yescharacteristic
62C22×Dic106C2311yescharacteristic
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C4×D53—21no—
66C2×#11719913—22no—
67C2×#11719913—22no—
68C2×#11719913C2×C414yes—
69#13133196—22no—
70#13133196C2×C414yescomplemented
71#13133191—22no—
72#13133191C2×C414yes—
73C4×Dic106—22no—
74C4×Dic106—22no—
75C4×D212—22no—
76C4×D212—22no—
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×C4×Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97#13133151—22no—
98#13133151—22no—
99#13133149C2×C414yescomplemented
100#13133142—22no—
101#13133142—22no—
102#13133142C2×C414yescomplemented
103#13133139—22no—
104#13133139—22no—
105#13133139C2×C414yes—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114C23×C4×C53C2311yescharacteristic
115C2×M16×C53—22no—
116C2×M16×C53—22no—
117C2×M16×C53—22no—
118C22×C8×C53—22no—
119C22×C8×C53—22no—
120C22×C8×C53C2×C414yescomplemented
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C22×C8×C53C2311yescharacteristic
125#117×C53—22no—
126#117×C53—22no—
127C2×C4⋊C4×C53D411yescharacteristic
128C2×C4⋊C4×C53D411yescharacteristic
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C2×C42×C53C2311yescharacteristic
133#97×C53—22no—
134#97×C53D414yescomplemented
135C4×C8×C53—22no—
136C4×C8×C53—22no—
137C24×C53C2×D411yescharacteristic
138C23×D53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C2×D411yescharacteristic
145C22×C4×C53C2×D411yescharacteristic
146C22×C4×C53C2×D411yescharacteristic
147C22×C4×C53C2×D411yescharacteristic
148C22×C4×C53C2×D411yescharacteristic
149C22×C4×C53#4112yes—
150C22×C4×C53C2411yescharacteristic
151C2×C22⋊D53—24no—
152C2×C22⋊D53—81no—
153C2×C22⋊D53—81no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C2×D212—21no—
162C2×D212—21no—
163C2×D212—21no—
164C2×D212—21no—
165C2×D212—21no—
166C2×D212C22×C412yes—
167C2×C4×D53—42no—
168C2×C4×D53—81no—
169C2×C4×D53—81no—
170C2×Dic106—21no—
171C2×Dic106—21no—
172C2×Dic106—21no—
173C2×Dic106—21no—
174C2×Dic106—21no—
175C2×Dic106C22×C412yes—
176M16×C53—28no—
177C2×C8×C53—21no—
178C2×C8×C53—21no—
179C2×C8×C53—21no—
180C2×C8×C53—21no—
181C2×C8×C53—21no—
182C2×C8×C53—21no—
183C2×C8×C53—28no—
184C2×C8×C53C22×C412yes—
185C2×C8×C53C22×C412yes—
186C2×C8×C53C2×D412yes—
187C2×C8×C53C2×D412yes—
188C2×C8×C53#4112yes—
189C2×C8×C53#4112yes—
190C4⋊C4×C53—22no—
191C4⋊C4×C53—22no—
192C22⋊C4×C53—22no—
193C22⋊C4×C53—22no—
194C42×C53—21no—
195C42×C53—21no—
196C42×C53C2×D412yes—
197C42×C53#4112yes—
198C22⋊Dic53—24no—
199C22⋊Dic53—81no—
200C22⋊Dic53—81no—
201#11719921—24no—
202#11719921—42no—
203#11719921—81no—
204#11719921—81no—
205C4⋊Dic53—21no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53C22×C412yes—
216C4⋊Dic53C22×C412yes—
217#11719919—24no—
218#11719919—42no—
219#11719919—81no—
220#11719919—81no—
221C4×Dic53—42no—
222C4×Dic53—81no—
223C4×Dic53—81no—
224#11719913—28no—
225C23×C53—21no—
226C23×C53—21no—
227C23×C53—21no—
228C23×C53—21no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53C4×D412yes—
232C23×C53C22×D411yescharacteristic
233C22×D53—22no—
234C22×D53—41no—
235C22×D53—41no—
236C22×D53—41no—
237C22×D53—41no—
238C22×D53—41no—
239C22×D53—41no—
240C2×C4×C53—21no—
241C2×C4×C53—21no—
242C2×C4×C53—21no—
243C2×C4×C53—21no—
244C2×C4×C53—21no—
245C2×C4×C53—21no—
246C2×C4×C53—22no—
247C2×C4×C53—22no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—21no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53C4×D412yes—
257C2×C4×C53#12112yes—
258C2×C4×C53#12112yes—
259C2×C4×C53C23×C411yescharacteristic
260C2×C4×C53C22×D411yescharacteristic
261C2×C4×C53C2×#4111yescharacteristic
262C2×C4×C53C2×#4111yescharacteristic
263C2×C4×C53C2×#4111yescharacteristic
264C2×C4×C53C2×#4111yescharacteristic
265C22⋊D53—84no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—41no—
270C2×Dic53—41no—
271C2×Dic53—41no—
272C2×Dic53—41no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—41no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—41no—
280C2×Dic53—41no—
281C2×Dic53—41no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287D212—22no—
288D212—22no—
289D212—41no—
290D212—41no—
291C4×D53—84no—
292Dic106—22no—
293Dic106—22no—
294Dic106—41no—
295Dic106—41no—
296C8×C53—22no—
297C8×C53—22no—
298C8×C53—22no—
299C8×C53C4×D414yes—
300#21531—531nomaximal, Sylow
301C22×C53—22no—
302C22×C53—22no—
303C22×C53—22no—
304C22×C53—41no—
305C22×C53—41no—
306C22×C53—41no—
307C22×C53—41no—
308C22×C53C2×C4×D411yescharacteristic
309C22×C53C2×#12111yescharacteristic
310C22×C53#53211yescharacteristic
311C22×C53#57611yescharacteristic
312C22×C53#57711yescharacteristic
313C22×C53#57711yescharacteristic
314C22×C53#57811yescharacteristic
315C2×D53—42no—
316C2×D53—42no—
317C2×D53—42no—
318C2×D53—81no—
319C2×D53—81no—
320C2×D53—81no—
321C2×D53—81no—
322C4×C53—22no—
323C4×C53—22no—
324C4×C53—22no—
325C4×C53—41no—
326C4×C53—41no—
327C4×C53C2×C4×D411yescharacteristic
328C4×C53C4×#4111yescharacteristic
329C4×C53#52511yescharacteristic
330C4×C53#52911yescharacteristic
331Dic53—42no—
332Dic53—42no—
333Dic53—42no—
334Dic53—81no—
335Dic53—81no—
336Dic53—81no—
337Dic53—81no—
338C2×#465—531no—
339C2×#440—531no—
340C2×#405D5311yescharacteristic, complemented
341#2324—531no—
342#2323—531no—
343#1973—531no—
344#1944—531no—
345#1934—531no—
346#1933—531no—
347#1895—531no—
348#1894—531no—
349#1808—531no—
350#1776—531no—
351C4×#103—531no—
352C4×#102—531no—
353C2×C53—42no—
354C2×C53C4×#12111yescharacteristic
355C2×C53#294911yescharacteristic
356C2×C53#295111yescharacteristic
357C2×C53#306211yescharacteristic
358C2×C53#306311yescharacteristic
359C2×C53#317811yescharacteristic
360C2×C53#317911yescharacteristic
361D53—82no—
362C22×SD16—531no—
363C22×M16C2×D5311yescharacteristic
364C23×C8C2×D5311yescharacteristic
365C2×C22⋊Q8—531no—
366C2×#121—531no—
367C2×C4×Q8—531no—
368C2×C4×D4—531no—
369C2×#117C2×D5311yescharacteristic
370#465—538no—
371#440—1064no—
372C2×#107—531no—
373C2×#107—531no—
374C2×#106—531no—
375C2×#103—531no—
376C2×#103—531no—
377C2×#103—531no—
378C2×#102—531no—
379C2×#102—531no—
380C2×#102—531no—
381#405—24no—
382C2×#97C2×D5311yescharacteristic
383C2×#97C2×D5311yescharacteristic
384C2×C4×C8C2×D5311yescharacteristic
385C2×C4×C8C2×D5311yescharacteristic
386#391—531no—
387#390—531no—
388#390—1061no—
389#389—531no—
390#389—531no—
391#389—1061no—
392#388—1061no—
393#388—1061no—
394#388—1061no—
395#387—1061no—
396#386—1061no—
397#385—1061no—
398#380—531no—
399#380—531no—
400C4×C4⋊C4—531no—
401C4×C4⋊C4—531no—
402#340—531no—
403#340—531no—
404#340—531no—
405#340—531no—
406#340—531no—
407#340—531no—
408C53#2153111yescharacteristic, complemented, Sylow
409C22×Q8—531no—
410C22×D4—531no—
411C22×D4—1061no—
412C23×C4—1061no—
413C23×C4C22×D5311yescharacteristic
414C2×SD16—534no—
415C2×SD16—1062no—
416C2×SD16—1062no—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16—22no—
420C22×C8—22no—
421C22×C8—22no—
422C22×C8C4×D5314yescomplemented
423C22×C8C22×D5311yescharacteristic
424C22×C8C22×D5311yescharacteristic
425C22×C8C22×D5311yescharacteristic
426C22×C8C22×D5311yescharacteristic
427C22⋊Q8—534no—
428C22⋊Q8—1062no—
429#121—534no—
430#121—1062no—
431C4×Q8—1062no—
432C4×Q8—1062no—
433C4×D4—1062no—
434C4×D4—1062no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—531no—
438C2×C4⋊C4—531no—
439C2×C4⋊C4—531no—
440C2×C4⋊C4—531no—
441C2×C4⋊C4—531no—
442C2×C4⋊C4—531no—
443C2×C4⋊C4—1061no—
444C2×C4⋊C4—1061no—
445C2×C4⋊C4—1061no—
446C2×C4⋊C4—1061no—
447C2×C4⋊C4D21211yescharacteristic
448C2×C4⋊C4D21211yescharacteristic
449C2×C22⋊C4—1061no—
450C2×C22⋊C4—1061no—
451C2×C22⋊C4—1061no—
452C2×C22⋊C4—1061no—
453C2×C22⋊C4—1061no—
454C2×C22⋊C4—1061no—
455C2×C22⋊C4—1061no—
456C2×C22⋊C4D21211yescharacteristic
457C2×C22⋊C4D21211yescharacteristic
458C2×C42—1061no—
459C2×C42—1061no—
460C2×C42—1061no—
461C2×C42C22×D5311yescharacteristic
462C2×C42C22×D5311yescharacteristic
463#107—1062no—
464#107—1062no—
465#106—534no—
466#103—534no—
467#103—1062no—
468#103—1062no—
469#102—534no—
470#102—1062no—
471#102—1062no—
472#97—22no—
473#97C22⋊D5314yescomplemented
474C4×C8—22no—
475C4×C8—22no—
476#95—1061no—
477#95—1061no—
478#95—1061no—
479#95—1061no—
480#95—1061no—
481#95—1061no—
482#95—1061no—
483#95—1061no—
484C24—1061no—
485C24C2×D21211yescharacteristic
486C2×Q8—532no—
487C2×Q8—1061no—
488C2×Q8—1061no—
489C2×Q8—1061no—
490C2×Q8—1061no—
491C2×Q8—1061no—
492C2×D4—532no—
493C2×D4—1064no—
494C2×D4—1061no—
495C2×D4—1061no—
496C2×D4—1061no—
497C2×D4—1061no—
498C2×D4—1061no—
499C2×D4—4241no—
500C2×D4—4241no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—1061no—
506C22×C4—1061no—
507C22×C4—1061no—
508C22×C4—1061no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1061no—
512C22×C4—4241no—
513C22×C4—4241no—
514C22×C4—2122no—
515C22×C4C2×C4×D5312yes—
516C22×C4C2×D21211yescharacteristic
517C22×C4C2×D21211yescharacteristic
518C22×C4C2×D21211yescharacteristic
519C22×C4C2×D21211yescharacteristic
520C22×C4C2×D21211yescharacteristic
521C22×C4#1171994512yes—
522C22×C4C23×D5311yescharacteristic
523SD16—1068no—
524M16—28no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—28no—
532C2×C8C2×C4×D5312yes—
533C2×C8C2×C4×D5312yes—
534C2×C8#1171994512yes—
535C2×C8#1171994512yes—
536C2×C8C2×C22⋊D5312yes—
537C2×C8C2×C22⋊D5312yes—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—532no—
541C4⋊C4—532no—
542C4⋊C4—1064no—
543C4⋊C4—1061no—
544C4⋊C4—1061no—
545C4⋊C4—1061no—
546C4⋊C4—1061no—
547C4⋊C4—1061no—
548C4⋊C4—1061no—
549C4⋊C4—1061no—
550C4⋊C4—1061no—
551C4⋊C4—1061no—
552C4⋊C4—1061no—
553C4⋊C4—4241no—
554C4⋊C4—4241no—
555C4⋊C4—2122no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—1064no—
559C22⋊C4—1064no—
560C22⋊C4—4241no—
561C22⋊C4—4241no—
562C22⋊C4—4241no—
563C22⋊C4—4241no—
564C22⋊C4—2122no—
565C42—21no—
566C42—21no—
567C42—4241no—
568C42—4241no—
569C42—2122no—
570C42#1171994512yes—
571C42C2×C22⋊D5312yes—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—1062no—
579C23—2121no—
580C23—2121no—
581C23—2121no—
582C23—2121no—
583C23—2121no—
584C23—2121no—
585C23C4×D21212yes—
586C23C22×D21211yescharacteristic
587Q8—1062no—
588Q8—1062no—
589Q8—2121no—
590Q8—2121no—
591D4—1062no—
592D4—1062no—
593D4—4244no—
594D4—2121no—
595D4—2121no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—4244no—
616C2×C4—2121no—
617C2×C4—2121no—
618C2×C4—2121no—
619C2×C4—2121no—
620C2×C4—2121no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4—2121no—
624C2×C4—2121no—
625C2×C4—2121no—
626C2×C4—2121no—
627C2×C4—2121no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4—2121no—
632C2×C4—2121no—
633C2×C4—2121no—
634C2×C4C4×D21212yes—
635C2×C4#1313319112yes—
636C2×C4#1313319112yes—
637C2×C4C22×C4×D5311yescharacteristic
638C2×C4C22×C22⋊D5311yescharacteristic
639C2×C4C2×#1171994511yescharacteristic
640C2×C4C2×#1171994511yescharacteristic
641C2×C4C2×#1171994511yescharacteristic
642C2×C4C2×#1171994511yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8C4×C22⋊D5314yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—4241no—
655C22—4241no—
656C22—4241no—
657C22—4241no—
658C22—2122no—
659C22—2122no—
660C22—2122no—
661C22C2×C4×D21211yescharacteristic
662C22C2×#1313319111yescharacteristic
663C22#1681117311yescharacteristic
664C22#1681142811yescharacteristic
665C22#1681143511yescharacteristic
666C22#1681143511yescharacteristic
667C22#1681144011yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—41no—
673C4—4241no—
674C4—4241no—
675C4—4241no—
676C4—4241no—
677C4—2122no—
678C4—2122no—
679C4—2122no—
680C4C2×C4×C22⋊D5311yescharacteristic
681C4C4×#1171994511yescharacteristic
682C4#1681113411yescharacteristic
683C4#1681115711yescharacteristic
684C2—42no—
685C2—4242no—
686C2C4×#1313319111yescharacteristic
687C2#2028357611yescharacteristic
688C2#2028359211yescharacteristic
689C2#2028439511yescharacteristic
690C2#2028440611yescharacteristic
691C2#2028538311yescharacteristic
692C2#2028539811yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#405C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenterC2×#405D53
hypocenterC53#21531
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#16810725C2semidirect
4. #20277397C2semidirect
5. #20275596C2semidirect
6. #20275458C2semidirect
7. #20275398C2semidirect
8. #20275391C2semidirect
10. #20275148C2semidirect
11. #20274744C2semidirect
12. #20274612C2semidirect
13. C4×#13133142C2semidirect
14. C4×#13133139C2semidirect
15. C2×C53×#405C2semidirect
21. #16810852C4semidirect
70. #13133196C2×C4semidirect
99. #13133149C2×C4semidirect
102. #13133142C2×C4semidirect
120. C22×C8×C53C2×C4semidirect
134. #97×C53D4semidirect
340. C2×#405D53semidirect
408. C53#21531semidirect
422. C22×C8C4×D53semidirect
473. #97C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168108522
C2×#168107252
#202774082
#202773972
#202755962
#202754582
#202753982
#202753912
#202751532
#202751482
#202747442
#202746122
C4×#131331422
C4×#131331392
C2×C53×#4052
#2153153