Finite Group Databasebeta

← #27389363

Subgroups — #27389363

Order 13568.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811238C211yesmaximal, characteristic
2C2×#16810577C211yesmaximal, characteristic, complemented
3#20277320C211yesmaximal, characteristic, complemented
4#20275686C211yesmaximal, characteristic, complemented
5#20275674C211yesmaximal, characteristic, complemented
6#20275530C211yesmaximal, characteristic, complemented
7#20275525C211yesmaximal, characteristic, complemented
8#20275150C211yesmaximal, characteristic
9#20275147C211yesmaximal, characteristic, complemented
10#20275140C211yesmaximal, characteristic
11#20275137C211yesmaximal, characteristic, complemented
12#20274548C211yesmaximal, characteristic, complemented
13#20274540C211yesmaximal, characteristic, complemented
14C4×#13133142C211yesmaximal, characteristic, complemented
15C4×#102×C53C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811238—24no—
19#16811238C418yescomplemented
20C2×#13133216C2211yescharacteristic
21C2×#13133210—21no—
22C2×#13133204C2211yescharacteristic
23C2×#13133203—21no—
24C2×#13133200—21no—
25C2×#13133197C2211yescharacteristic
26C2×#13133196—21no—
27C2×#13133188C2211yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×#13133174C2211yescharacteristic
30C2×#13133142C2211yescharacteristic
31C2×#13133142C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×#13133140C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36#16810577—24no—
37C2×#13133128C2211yescharacteristic
38C2×#13133127C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40#16810514—21no—
41#16810512—21no—
42#16810507—21no—
43#16810505—21no—
44#16810492C2211yescharacteristic
45#16810488C2211yescharacteristic
46#16810480C2211yescharacteristic
47#16810480C2211yescharacteristic
48C4×C4⋊Dic53C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×C4×D4×C53C2211yescharacteristic
56C2×#102×C53C2211yescharacteristic
57C2×#102×C53C2211yescharacteristic
58C2×C4×C8×C53C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×Dic106—21no—
63C22×Dic106C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C4×D53C2311yescharacteristic
66C2×#11719912—22no—
67C2×#11719912—22no—
68C2×#11719912—22no—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C2×C8×D53—22no—
72C2×C8×D53—22no—
73C2×C8×D53—22no—
74#13133216—22no—
75#13133216C2×C414yes—
76#13133210—28no—
77#13133204—22no—
78#13133204C2×C414yes—
79#13133203—28no—
80#13133200—28no—
81#13133197—22no—
82#13133197C2×C414yes—
83#13133196—28no—
84#13133188—22no—
85#13133188C2×C414yes—
86C4×Dic106—22no—
87C4×Dic106C2×C414yes—
88#13133174C2×C414yes—
89#13133174D414yes—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×#11719919—21no—
95C2×#11719919—21no—
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919D411yescharacteristic
99C2×#11719919D411yescharacteristic
100C2×C22⋊Dic53—21no—
101C2×C22⋊Dic53—21no—
102C2×C22⋊Dic53—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C2×#11719921D411yescharacteristic
107C2×#11719921D411yescharacteristic
108C2×C4×Dic53—21no—
109C2×C4×Dic53—21no—
110C2×C4×Dic53C2311yescharacteristic
111#13133142—22no—
112#13133142—22no—
113#13133140—22no—
114#13133140—22no—
115#13133138—22no—
116#13133138—22no—
117#13133128—22no—
118#13133127—22no—
119C8×Dic53—22no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123#13133124—21no—
124#13133124—21no—
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C4×D4×C53—22no—
130C4×D4×C53C2×C414yes—
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C22⋊C4×C53—21no—
135C2×C42×C53—21no—
136C2×C42×C53C2311yescharacteristic
137#102×C53—22no—
138#102×C53—22no—
139C4×C8×C53—22no—
140#95×C53—21no—
141C24×C53—21no—
142C23×D53C2×D411yescharacteristic
143C2×D4×C53—21no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53C22×C412yes—
149C22×C4×C53—21no—
150C22×C4×C53—24no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—81no—
154C22×C4×C53—81no—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2411yescharacteristic
158C2×C22⋊D53—24no—
159C2×C22⋊D53—81no—
160C2×C22⋊D53—81no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53C2×D411yescharacteristic
166C22×Dic53C2×D411yescharacteristic
167C22×Dic53C2×D411yescharacteristic
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53C22×C412yes—
173C2×C4×D53C2×D412yes—
174C2×Dic106—21no—
175C2×Dic106—21no—
176C2×Dic106—21no—
177C2×Dic106—21no—
178C2×Dic106—21no—
179C2×Dic106—24no—
180C2×Dic106—81no—
181C2×Dic106—81no—
182C2×Dic106C22×C412yes—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53#4112yes—
188C2×C8×C53#4112yes—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53C22×C412yes—
195C22⋊C4×C53—24no—
196C42×C53—81no—
197C42×C53C22×C412yes—
198C42×C53C2×D412yes—
199C22⋊Dic53—24no—
200C22⋊Dic53—24no—
201C22⋊Dic53—24no—
202#11719921—24no—
203#11719921—81no—
204#11719921—81no—
205#11719921C22⋊C414yes—
206#11719921C22⋊C414yes—
207C4⋊Dic53—21no—
208C4⋊Dic53—24no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53C22×C412yes—
214#11719919—24no—
215#11719919—24no—
216#11719919—81no—
217#11719919—81no—
218#11719919C22⋊C414yes—
219#11719919C22⋊C414yes—
220C4×Dic53—24no—
221C4×Dic53—81no—
222C4×Dic53C22×C412yes—
223C4×Dic53C2×D412yes—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322#4112yes—
229C2×#88322#4112yes—
230#11719912—28no—
231C8×D53—28no—
232C23×C53—22no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53C22×D411yescharacteristic
240C22×D53—21no—
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53C2×C22⋊C412yes—
247D4×C53—22no—
248D4×C53—22no—
249D4×C53—41no—
250D4×C53—41no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—22no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—84no—
265C2×C4×C53C2×C22⋊C412yes—
266C2×C4×C53C2×C22⋊C412yes—
267C2×C4×C53C23×C411yescharacteristic
268C2×C4×C53C22×D411yescharacteristic
269C2×C4×C53C2×#4111yescharacteristic
270C2×C4×C53C2×#4111yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C22⋊D53—84no—
274C2×Dic53—21no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53C2×C22⋊C412yes—
293C2×Dic53C2×C22⋊C412yes—
294C2×Dic53C2×C22⋊C412yes—
295C4×D53—22no—
296C4×D53—22no—
297C4×D53—22no—
298C4×D53—22no—
299Dic106—22no—
300Dic106—22no—
301Dic106—41no—
302Dic106—41no—
303Dic106—84no—
304C8×C53—22no—
305C8×C53—22no—
306#88322—22no—
307#88322—22no—
308#21412—531nomaximal, Sylow
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—42no—
312C22×C53—81no—
313C22×C53—81no—
314C22×C53—81no—
315C22×C53—81no—
316C22×C53C22×C22⋊C411yescharacteristic
317C22×C53#53211yescharacteristic
318C22×C53#53211yescharacteristic
319C22×C53#57611yescharacteristic
320C22×C53#57711yescharacteristic
321C22×C53#57711yescharacteristic
322C22×C53#57811yescharacteristic
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—41no—
327C2×D53—41no—
328C2×D53—41no—
329C2×D53—41no—
330C4×C53—22no—
331C4×C53—22no—
332C4×C53—42no—
333C4×C53—81no—
334C4×C53—81no—
335C4×C53C4×#4111yescharacteristic
336C4×C53C4×#4111yescharacteristic
337C4×C53#52511yescharacteristic
338C4×C53#52511yescharacteristic
339Dic53—22no—
340Dic53—22no—
341Dic53—22no—
342Dic53—42no—
343Dic53—42no—
344Dic53—81no—
345Dic53—81no—
346C2×#542—531no—
347C2×#405—531no—
348#2314—531no—
349#1993—531no—
350#1990—531no—
351#1959—531no—
352#1958—531no—
353#1895—531no—
354#1894—531no—
355#1893—531no—
356#1892—531no—
357#1763—531no—
358#1762—531no—
359C4×#103—531no—
360C4×#102D5311yescharacteristic, complemented
361C2×C53—82no—
362C2×C53#229711yescharacteristic
363C2×C53#289711yescharacteristic
364C2×C53#289811yescharacteristic
365C2×C53#317311yescharacteristic
366C2×C53#317511yescharacteristic
367C2×C53#317811yescharacteristic
368C2×C53#317911yescharacteristic
369D53—42no—
370C22×M16—531no—
371C23×C8—531no—
372#542—538no—
373#542—1064no—
374C2×C4⋊Q8—531no—
375C2×#126—1061no—
376C2×#124—531no—
377C2×#124—1061no—
378C2×#123—1061no—
379C2×C22⋊Q8—531no—
380C2×C22⋊Q8—1061no—
381C2×#121—531no—
382C2×C4×Q8—531no—
383C2×C4×D4C2×D5311yescharacteristic
384C2×#117—531no—
385C2×#103—531no—
386C2×#103—531no—
387C2×#103—531no—
388C2×#103—531no—
389C2×#102—531no—
390C2×#102—531no—
391C2×#102C2×D5311yescharacteristic
392C2×#102C2×D5311yescharacteristic
393#405—1064no—
394C2×#97—531no—
395C2×#97—531no—
396C2×C4×C8—531no—
397C2×C4×C8C2×D5311yescharacteristic
398#388—1061no—
399#388—1061no—
400#387—1061no—
401#387—1061no—
402#384—531no—
403#382—531no—
404#380—531no—
405#380—531no—
406C4×C4⋊C4—531no—
407C4×C4⋊C4C2×D5311yescharacteristic
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340C2×D5311yescharacteristic
415#340C2×D5311yescharacteristic
416C53#2141211yescharacteristic, complemented, Sylow
417C22×Q8—531no—
418C22×Q8—1061no—
419C22×D4—1061no—
420C22×D4C22×D5311yescharacteristic
421C23×C4—21no—
422C23×C4—531no—
423C2×M16—1062no—
424C2×M16—1062no—
425C2×M16—1062no—
426C22×C8—531no—
427C22×C8—531no—
428C22×C8—1062no—
429C22×C8—1062no—
430C22×C8—1062no—
431C22×C8C22×D5311yescharacteristic
432C22×C8C22×D5311yescharacteristic
433C4⋊Q8—534no—
434C4⋊Q8—1062no—
435#126—1068no—
436#124—534no—
437#124—1062no—
438#124—1068no—
439#123—1068no—
440C22⋊Q8—534no—
441C22⋊Q8—1062no—
442C22⋊Q8—1068no—
443#121—534no—
444#121—1062no—
445C4×Q8—534no—
446C4×Q8—1062no—
447C4×D4—22no—
448C4×D4C4×D5314yes—
449#117—534no—
450#117—534no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—531no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—1061no—
457C2×C4⋊C4—1061no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4—1061no—
460C2×C4⋊C4—1061no—
461C2×C4⋊C4C22×D5311yescharacteristic
462C2×C4⋊C4C22×D5311yescharacteristic
463C2×C4⋊C4C22×D5311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—531no—
466C2×C22⋊C4—531no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C42—21no—
474C2×C42—531no—
475C2×C42—1061no—
476C2×C42—1061no—
477C2×C42C22×D5311yescharacteristic
478#103—1062no—
479#103—1062no—
480#103—1062no—
481#103—1062no—
482#102—22no—
483#102—22no—
484#102—1062no—
485#102—1062no—
486#97—1062no—
487#97—1062no—
488C4×C8—22no—
489C4×C8—1062no—
490#95—21no—
491#95—1061no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496C24—21no—
497C24—531no—
498C2×Q8—532no—
499C2×Q8—1064no—
500C2×Q8—1061no—
501C2×Q8—1061no—
502C2×Q8—1061no—
503C2×Q8—1061no—
504C2×Q8—1061no—
505C2×Q8—4241no—
506C2×Q8—4241no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—1064no—
513C2×D4—4241no—
514C2×D4—4241no—
515C2×D4C2×C4×D5312yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4D4×D5311yescharacteristic
536C22×C4D4×D5311yescharacteristic
537C22×C4C23×D5311yescharacteristic
538M16—1068no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—532no—
544C2×C8—532no—
545C2×C8—1068no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8#1171994512yes—
551C2×C8#1171994512yes—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—534no—
558C4⋊C4—534no—
559C4⋊C4—532no—
560C4⋊C4—1064no—
561C4⋊C4—1064no—
562C4⋊C4—1064no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—4241no—
569C4⋊C4—4241no—
570C4⋊C4C2×C4×D5312yes—
571C22⋊C4—24no—
572C22⋊C4—534no—
573C22⋊C4—534no—
574C22⋊C4—1064no—
575C22⋊C4—1064no—
576C22⋊C4—1064no—
577C22⋊C4—1064no—
578C22⋊C4—4241no—
579C22⋊C4—4241no—
580C42—81no—
581C42—532no—
582C42—532no—
583C42—1064no—
584C42—4241no—
585C42C2×C4×D5312yes—
586C42D4×D5312yes—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—532no—
595C23—1061no—
596C23—1061no—
597C23—1061no—
598C23—1061no—
599C23—1061no—
600C23—1061no—
601C23C2×D4×D5311yescharacteristic
602Q8—1062no—
603Q8—1062no—
604Q8—4244no—
605Q8—2121no—
606Q8—2121no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—4244no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—532no—
627C2×C4—532no—
628C2×C4—532no—
629C2×C4—1061no—
630C2×C4—1061no—
631C2×C4—1061no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4C22⋊C4×D5312yes—
652C2×C4C22⋊C4×D5312yes—
653C2×C4C22×C4×D5311yescharacteristic
654C2×C4C2×D4×D5311yescharacteristic
655C2×C4#41×D5311yescharacteristic
656C2×C4#41×D5311yescharacteristic
657C2×C4C2×#1171994511yescharacteristic
658C2×C4C2×#1171994511yescharacteristic
659C8—22no—
660C8—22no—
661C8—1062no—
662C8—1062no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—1062no—
671C22—1062no—
672C22—1062no—
673C22—2121no—
674C22—2121no—
675C22—2121no—
676C22—2121no—
677C22C2×C22⋊C4×D5311yescharacteristic
678C22#1681117011yescharacteristic
679C22#1681117011yescharacteristic
680C22#1681142411yescharacteristic
681C22#1681142911yescharacteristic
682C22#1681143011yescharacteristic
683C22#1681143711yescharacteristic
684C4—22no—
685C4—22no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—1062no—
690C4—1062no—
691C4—1062no—
692C4—4241no—
693C4—4241no—
694C4—2122no—
695C4—2122no—
696C4#1681109111yescharacteristic
697C4C4×#1171994511yescharacteristic
698C4#1681113211yescharacteristic
699C4#1681113211yescharacteristic
700C2—82no—
701C2—2122no—
702C2#2027720111yescharacteristic
703C2#2028323611yescharacteristic
704C2#2028324411yescharacteristic
705C2#2028532811yescharacteristic
706C2#2028535011yescharacteristic
707C2#2028537911yescharacteristic
708C2#2028540211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC4×#102×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
cosocleC22×C4×C53C24
hypercenterC4×#102D53
hypocenterC53#21412
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16810577C2semidirect
3. #20277320C2semidirect
4. #20275686C2semidirect
5. #20275674C2semidirect
6. #20275530C2semidirect
7. #20275525C2semidirect
9. #20275147C2semidirect
11. #20275137C2semidirect
12. #20274548C2semidirect
13. #20274540C2semidirect
14. C4×#13133142C2semidirect
15. C4×#102×C53C2semidirect
19. #16811238C4semidirect
360. C4×#102D53semidirect
416. C53#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#168112382
C2×#168105772
#202773202
#202756862
#202756742
#202755302
#202755252
#202751502
#202751472
#202751402
#202751372
#202745482
#202745402
C4×#131331422
C4×#102×C532
#2141253