Finite Group Databasebeta

← #25118880

Subgroups — #25118880

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583117C211yesmaximal, characteristic
2C2×#14582984C211yesmaximal, characteristic, complemented
3C2×C4×D344C211yesmaximal, characteristic
4#19137671C211yesmaximal, characteristic, complemented
5#19137504C211yesmaximal, characteristic, complemented
6#19135403C211yesmaximal, characteristic, complemented
7#19135366C211yesmaximal, characteristic, complemented
8#19135279C211yesmaximal, characteristic, complemented
9#19134944C211yesmaximal, characteristic
10#19134932C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134851C211yesmaximal, characteristic, complemented
13C8×Dic43⋊C4C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583117C418yescomplemented
25#14582984—24no—
26C4×D344—24no—
27C2×#13063259C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582791—21no—
41#14582788—21no—
42#14582773—21no—
43#14582773—21no—
44#14582770—21no—
45#14582764C2211yescharacteristic
46#14582756—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48C4×Dic43⋊C4C2211yescharacteristic
49#14582746—21no—
50#95×D43—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yescomplemented
71C2×D344—22no—
72C2×D344—22no—
73C2×D344C2×C414yes—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063314—22no—
77#13063314C2×C414yescomplemented
78Q8×Dic43—22no—
79Q8×Dic43—41no—
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—41no—
83C4×D172—41no—
84#13063287—22no—
85#13063287—22no—
86#13063287—41no—
87#13063287C2×C414yescomplemented
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C2×Dic43⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106#13063259—22no—
107#13063256—22no—
108Dic43⋊C8C2×C414yescomplemented
109#13063249—41no—
110#13063247—22no—
111#13063247D414yes—
112#13063245—22no—
113#13063245—41no—
114#13063245C2×C414yescomplemented
115C8×Dic43—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95D411yescharacteristic
122C43⋊#95D411yescharacteristic
123C22×Q8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#103×C43—22no—
132#103×C43C2×C414yescomplemented
133C4×C8×C43—22no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172C22×C412yes—
167C2×D172C22×C412yes—
168C2×D172C2×D412yes—
169C2×D172#4112yes—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×C4×D43—81no—
180C2×C4×D43—81no—
181C2×C4×D43—81no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C22×C412yes—
187C2×C8×C43C2×D412yes—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—81no—
194C4⋊C4×C43C22×C412yes—
195C42×C43—21no—
196C42×C43—21no—
197#10621884—28no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—24no—
200(C2×D43)⋊C4—24no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—81no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—42no—
210C4⋊Dic43—81no—
211C4⋊Dic43C2×D412yes—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—42no—
217C4×Dic43—81no—
218C4×Dic43C22×C412yes—
219C4×Dic43#4112yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C22×C412yes—
226D344—28no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242Q8×C43—22no—
243Q8×C43—22no—
244Q8×C43—41no—
245Q8×C43—41no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43#13512yes—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C2×C4×C432−1+411yescharacteristic
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43C4×D412yes—
286C2×Dic43C4×D412yes—
287C2×Dic43#13512yes—
288D172—22no—
289D172—22no—
290D172—22no—
291D172—22no—
292D172—22no—
293D172—41no—
294D172—41no—
295D172C4×D414yes—
296C4×D43—84no—
297C4×D43—84no—
298C4×D43—84no—
299C4×D43—84no—
300C8×C43—22no—
301C8×C43—22no—
302C43⋊C8—22no—
303C43⋊C8—41no—
304#22999—431nomaximal, Sylow
305C22×C43C2×C4×D411yescharacteristic
306C22×C43D4211yescharacteristic
307C22×C43#54811yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C22×C43#57611yescharacteristic
311C22×C43#57711yescharacteristic
312C2×D43—24no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—22no—
327C4×C43—42no—
328C4×C43—42no—
329C4×C43—41no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43C2×C4×D411yescharacteristic
333C4×C43#52011yescharacteristic
334C4×C43#54711yescharacteristic
335C4×C43#55311yescharacteristic
336Dic43—22no—
337Dic43—22no—
338Dic43—22no—
339Dic43—42no—
340Dic43—41no—
341Dic43—81no—
342C2×#463—431no—
343C2×C4×SD16—431no—
344C2×C4×D8—431no—
345#2367—431no—
346#2349—431no—
347#1958—431no—
348#1949—431no—
349#1934—431no—
350#1933D4311yescharacteristic, complemented
351#1879—431no—
352#1877—431no—
353#1864—431no—
354#1863—431no—
355C8×C4⋊C4—431no—
356C4×#102—431no—
357C2×C43#236111yescharacteristic
358C2×C43C4×#13511yescharacteristic
359C2×C43#294611yescharacteristic
360C2×C43#328011yescharacteristic
361C2×C43#328211yescharacteristic
362C2×C43#336011yescharacteristic
363C2×C43#336111yescharacteristic
364D43—44no—
365D43—82no—
366C22×SD16—431no—
367C22×D8—431no—
368C2×#124—431no—
369C2×C4×Q8—431no—
370C2×C4×D4—431no—
371C2×C4×D4—431no—
372C2×C4×D4—431no—
373C2×C4×D4—431no—
374#463—438no—
375C4×SD16—864no—
376C4×D8—864no—
377C2×#107—431no—
378C2×#106—431no—
379C2×C4⋊C8—431no—
380C2×#103—431no—
381C2×#103C2×D4311yescharacteristic
382C2×#103C2×D4311yescharacteristic
383C2×#102—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×#102—431no—
388C2×C4×C8—431no—
389C2×C4×C8—431no—
390C2×C4×C8C2×D4311yescharacteristic
391#391C2×D4311yescharacteristic
392#390—431no—
393#389—431no—
394#389C2×D4311yescharacteristic
395#388—861no—
396#388—861no—
397#385—861no—
398#385—861no—
399#385—861no—
400#382—431no—
401#380—861no—
402C4×C4⋊C4—431no—
403C4×C4⋊C4—431no—
404C4×C22⋊C4—861no—
405C2×#95—861no—
406#340—431no—
407#340—431no—
408#340C2×D4311yescharacteristic
409#340C2×D4311yescharacteristic
410#336—431no—
411#336—431no—
412C43#2299911yescharacteristic, complemented, Sylow
413C22×Q8C22×D4311yescharacteristic
414C22×D4—431no—
415C22×D4—431no—
416C23×C4—861no—
417C23×C4—861no—
418C23×C4—861no—
419C23×C4—861no—
420C2×SD16—434no—
421C2×SD16—862no—
422C2×SD16—862no—
423C2×D8—434no—
424C2×D8—862no—
425C2×D8—862no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430#124—434no—
431#124—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×D4—434no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4—1721no—
440C4×D4—1721no—
441C4×D4—1721no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42C22×D4311yescharacteristic
465#107—862no—
466#106—862no—
467C4⋊C8—434no—
468#103—22no—
469#103—1721no—
470#103C4×D4314yescomplemented
471#102—434no—
472#102—434no—
473#102—862no—
474#102—862no—
475#102—1721no—
476C4×C8—22no—
477C4×C8—862no—
478C4×C8—862no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—431no—
483#95—431no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488C24—861no—
489C24—861no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×C4×D4312yes—
496C2×D4—432no—
497C2×D4—432no—
498C2×D4—432no—
499C2×D4—432no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—864no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—3441no—
520C22×C4—3441no—
521C22×C4—3441no—
522C22×C4—3441no—
523C22×C4—3441no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533SD16—868no—
534D8—868no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—432no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8C2×C4×D4312yes—
546C2×C8D4×D4312yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—81no—
553C4⋊C4—432no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—3441no—
560C4⋊C4—1722no—
561C4⋊C4C2×C4×D4312yes—
562C22⋊C4—864no—
563C22⋊C4—864no—
564C22⋊C4—864no—
565C22⋊C4—3441no—
566C22⋊C4—1722no—
567C22⋊C4—1722no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C42—21no—
571C42—21no—
572C42—432no—
573C42—432no—
574C42—861no—
575C42—861no—
576C42—3441no—
577C42—1722no—
578C23—862no—
579C23—862no—
580C23—862no—
581C23—862no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—434no—
598D4—862no—
599D4—862no—
600D4—862no—
601D4—862no—
602D4—862no—
603D4—1721no—
604D4—1721no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—432no—
623C2×C4—432no—
624C2×C4—432no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—862no—
635C2×C4—3444no—
636C2×C4—3444no—
637C2×C4—3444no—
638C2×C4—3444no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4#1306334812yes—
645C2×C4C22×C4×D4311yescharacteristic
646C2×C4C2×D4×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#41×D4311yescharacteristic
649C2×C4#1306337111yescharacteristic
650C2×C4#1306337211yescharacteristic
651C8—22no—
652C8—22no—
653C8—862no—
654C8—1721no—
655C22—864no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22—1722no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22C4×D4×D4311yescharacteristic
670C22#1458353311yescharacteristic
671C22#1458355711yescharacteristic
672C22#135×D4311yescharacteristic
673C22C2×#1306334811yescharacteristic
674C22#1458370111yescharacteristic
675C22#1458370511yescharacteristic
676C4—22no—
677C4—41no—
678C4—42no—
679C4—42no—
680C4—81no—
681C4—81no—
682C4—862no—
683C4—862no—
684C4—862no—
685C4—3441no—
686C4—1721no—
687C4—1722no—
688C4C4×D4×D4311yescharacteristic
689C4#1458337911yescharacteristic
690C4#1458354711yescharacteristic
691C4#1458360011yescharacteristic
692C2—3442no—
693C2—1724no—
694C2#1913760811yescharacteristic
695C2C4×#1306334811yescharacteristic
696C2#1914342211yescharacteristic
697C2#1914627711yescharacteristic
698C2#1914630911yescharacteristic
699C2#1914724911yescharacteristic
700C2#1914725211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×D344C22
cosocleC22×C4×C43C24
hypercenter#1933D43
hypocenterC43#22999
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. C2×#14582984C2semidirect
4. #19137671C2semidirect
5. #19137504C2semidirect
6. #19135403C2semidirect
7. #19135366C2semidirect
8. #19135279C2semidirect
10. #19134932C2semidirect
11. #19134855C2semidirect
12. #19134851C2semidirect
13. C8×Dic43⋊C4C2semidirect
14. #19134409C2semidirect
15. C43×#1933C2semidirect
24. #14583117C4semidirect
70. C2×#10621884C2×C4semidirect
77. #13063314C2×C4semidirect
87. #13063287C2×C4semidirect
108. Dic43⋊C8C2×C4semidirect
114. #13063245C2×C4semidirect
132. #103×C43C2×C4semidirect
350. #1933D43semidirect
412. C43#22999semidirect
470. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831172
C2×#145829842
C2×C4×D3442
#191376712
#191375042
#191354032
#191353662
#191352792
#191349442
#191349322
#191348552
#191348512
C8×Dic43⋊C42
#191344092
C43×#19332
#2299943