Finite Group Databasebeta

← C2×#29043 #6460376

Subgroups — C2×#29043 #6460376

Order 512.

2504 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2497C211yesmaximal, characteristic, complemented
2C2×#2428C211yesmaximal, characteristic
3#29043C2116yesmaximal, direct product factor
4C2×#2100C211yesmaximal, characteristic, complemented
5C2×#2041C211yesmaximal, characteristic, complemented
6C2×#2034C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#1957C211yesmaximal, characteristic, complemented
9C2×#1941C211yesmaximal, characteristic, complemented
10C2×#1934C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1893C211yesmaximal, characteristic, complemented
14C2×#1864C211yesmaximal, characteristic, complemented
15C2×C4×#102C211yesmaximal, characteristic, complemented
16C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C8C2211yescharacteristic
18C22×#127C2211yescharacteristic
19C22×#121—21no—
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36#2497—24no—
37#2497C2218yescomplemented
38#2428—24no—
39#2428C2218yes—
40C2×#400—21no—
41C2×#396—21no—
42C2×#394—21no—
43C2×#392—21no—
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#388—21no—
49C2×#387—21no—
50C2×#386—21no—
51C2×#384C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56#2100C2218yescomplemented
57#2041C2218yescomplemented
58#2034C2218yescomplemented
59#2034C2218yescomplemented
60#1957C2218yescomplemented
61#1941C2218yescomplemented
62#1934C2218yescomplemented
63#1926C2218yescomplemented
64#1893C2218yescomplemented
65#1893C2218yescomplemented
66#1864C2218yescomplemented
67C4×#102C2218yescomplemented
68C8×C22⋊C4C2218yescomplemented
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×D4—21no—
78C23×D4—21no—
79C23×D4—21no—
80C23×D4—21no—
81C23×D4C2311yescharacteristic
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4C2311yescharacteristic
85C23×C8—24no—
86C23×C8—42no—
87C23×C8—42no—
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2314yes—
93C2×#127—24no—
94C2×#127—22no—
95C2×#127—42no—
96C2×#127C2314yes—
97C2×#121—22no—
98C2×#121—22no—
99C2×#121—28no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—42no—
103C2×#121—42no—
104C2×#121—48no—
105C2×#121C2314yes—
106C2×#121C2314yes—
107C2×C4×D4—24no—
108C2×C4×D4—22no—
109C2×C4×D4—42no—
110C2×C4×D4C2314yes—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4D411yescharacteristic
130C22×C22⋊C4D411yescharacteristic
131C22×C42—21no—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C2×#106—24no—
135C2×#106—42no—
136C2×#106C2314yes—
137C2×#106C2314yes—
138C2×#102—24no—
139C2×#102—24no—
140C2×#102—24no—
141C2×#102—24no—
142C2×#102—24no—
143C2×#102—42no—
144C2×#102—42no—
145C2×#102—42no—
146C2×#102C2314yes—
147C2×#102C2314yes—
148C2×#102C2314yes—
149C2×#102C2314yes—
150C2×#102C2314yes—
151C2×#102C2314yes—
152C2×#102C2314yes—
153C2×#102C2314yes—
154C2×C22⋊C8—24no—
155C2×C22⋊C8C2314yes—
156C2×C4×C8—42no—
157C2×C4×C8—42no—
158C2×C4×C8C2314yes—
159C2×C4×C8C2314yes—
160#400—28no—
161#396—28no—
162#394—28no—
163#392—28no—
164#390—22no—
165#390C2314yes—
166#389—22no—
167#389—22no—
168#389—22no—
169#389C2314yes—
170#389C2314yes—
171#389C2314yes—
172#388—28no—
173#387—28no—
174#386—28no—
175#384—22no—
176#384C2314yes—
177#380—22no—
178#380—22no—
179#380C2314yes—
180#380C2314yes—
181C4×C4⋊C4—22no—
182C4×C4⋊C4C2314yes—
183C4×C22⋊C4D414yes—
184C4×C22⋊C4C2314yes—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95D411yescharacteristic
192C2×#95D411yescharacteristic
193#340C2314yes—
194#340C2314yes—
195#340C2314yes—
196#340C2314yes—
197#340C2314yes—
198#340C2314yes—
199#336C2314yes—
200#336C2314yes—
201C25—21no—
202C25—21no—
203C25C2×D411yescharacteristic
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—82no—
230C22×D4—82no—
231C22×D4—82no—
232C22×D4—82no—
233C22×D4#4114yes—
234C22×D4C2412yes—
235C22×D4C2412yes—
236C23×C4—21no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—24no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—82no—
252C23×C4C2×D412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—28no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8—416no—
274C22×C8#4114yes—
275C22×C8#4114yes—
276C22×C8C2412yes—
277C22×C8C2412yes—
278C22×C8C2412yes—
279C22×C8C2412yes—
280#127—28no—
281#127—44no—
282#127—48no—
283#121—28no—
284#121—28no—
285#121—44no—
286#121—44no—
287#121—48no—
288#121—48no—
289#121—432no—
290C4×D4—28no—
291C4×D4—44no—
292C4×D4—48no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—82no—
318C2×C4⋊C4—82no—
319C2×C4⋊C4—82no—
320C2×C4⋊C4#4114yes—
321C2×C4⋊C4C2412yes—
322C2×C4⋊C4C2412yes—
323C2×C4⋊C4C2412yes—
324C2×C4⋊C4C2412yes—
325C2×C4⋊C4C2412yes—
326C2×C4⋊C4C2412yes—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—82no—
340C2×C22⋊C4—82no—
341C2×C22⋊C4—82no—
342C2×C22⋊C4SD1618yes—
343C2×C22⋊C4C2×D414yes—
344C2×C22⋊C4C2×D414yes—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—82no—
351C2×C42C2×D412yes—
352C2×C42C2×D412yes—
353C2×C42C2412yes—
354C2×C42C2412yes—
355#106—28no—
356#106—44no—
357#102—28no—
358#102—28no—
359#102—28no—
360#102—28no—
361#102—28no—
362#102—44no—
363#102—44no—
364#102—44no—
365C22⋊C8—28no—
366C4×C8—44no—
367C4×C8—44no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95C2×D414yes—
375#95C2×D414yes—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—22no—
384C24—22no—
385C24—42no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24C2×SD1614yes—
399C24C22×D412yes—
400C24C22×D411yescharacteristic
401C2×D4—28no—
402C2×D4—24no—
403C2×D4—28no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—48no—
421C2×D4—44no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—84no—
435C2×D4—84no—
436C2×D4—816no—
437C2×D4—816no—
438C2×D4—84no—
439C2×D4—84no—
440C2×D4—816no—
441C2×D4—816no—
442C2×D4C2×#4114yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—48no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—48no—
494C22×C4—84no—
495C22×C4—816no—
496C22×C4C2×SD1614yes—
497C22×C4C2×SD1614yes—
498C22×C4#13514yes—
499C22×C4C22×D412yes—
500C22×C4C22×D412yes—
501C22×C4C22×D412yes—
502C22×C4C22×D412yes—
503C22×C4C22×D412yes—
504C22×C4C22×D411yescharacteristic
505C22×C4C2×#4112yes—
506C22×C4C2×#4112yes—
507C22×C4C2×#4112yes—
508C22×C4C2×#4112yes—
509C22×C4H(5,𝔽2)12yes—
510C22×C4H(5,𝔽2)12yes—
511C22×C4C2511yescharacteristic
512C2×C8—28no—
513C2×C8—28no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—416no—
525C2×C8—44no—
526C2×C8—44no—
527C2×C8C2×#4114yes—
528C2×C8C2×#4114yes—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—84no—
549C4⋊C4—84no—
550C4⋊C4—84no—
551C4⋊C4C2×#4114yes—
552C22⋊C4—28no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—84no—
558C22⋊C4—84no—
559C22⋊C4—84no—
560C22⋊C4C2×SD16116yes—
561C42—24no—
562C42—24no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—84no—
568C23—28no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—28no—
573C23—28no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—42no—
583C23—42no—
584C23—48no—
585C23—48no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—48no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—84no—
599C23—84no—
600C23—84no—
601C23—84no—
602C23—84no—
603C23—84no—
604C23—84no—
605C23—84no—
606C23—84no—
607C23—84no—
608C23—84no—
609C23#53212yes—
610C23#54612yes—
611C23#54612yes—
612C23C22×SD1614yes—
613C23C22×SD1612yes—
614C23C2×#13512yes—
615C23#57612yes—
616C23#57612yes—
617C23C23×D411yescharacteristic
618D4—24no—
619D4—24no—
620D4—42no—
621D4—42no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—42no—
626D4—48no—
627D4—816no—
628D4—816no—
629D4—816no—
630D4—816no—
631D4—84no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—28no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—48no—
649C2×C4—44no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—816no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4#52914yes—
680C2×C4#53212yes—
681C2×C4#53814yes—
682C2×C4#54612yes—
683C2×C4#54612yes—
684C2×C4#55314yes—
685C2×C4#55314yes—
686C2×C4C22×SD1614yes—
687C2×C4C22×SD1614yes—
688C2×C4C2×#13514yes—
689C2×C4C22×#4111yescharacteristic
690C2×C4C22×#4111yescharacteristic
691C2×C4C22×#4111yescharacteristic
692C2×C4C22×#4111yescharacteristic
693C2×C4C2×H(5,𝔽2)11yescharacteristic
694C2×C4C2×H(5,𝔽2)11yescharacteristic
695C8—24no—
696C8—24no—
697C8—42no—
698C8—42no—
699C22—24no—
700C22—24no—
701C22—24no—
702C22—42no—
703C22—42no—
704C22—416no—
705C22—42no—
706C22—42no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—82no—
711C22—816no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—82no—
722C22—168no—
723C22#255914yes—
724C22#316714yes—
725C22#317614yes—
726C22#329514yes—
727C22#329514yes—
728C22#329714yes—
729C22#330514yes—
730C22C2×#53211yescharacteristic
731C22C2×#54611yescharacteristic
732C22C2×#54611yescharacteristic
733C22C23×SD1611yescharacteristic
734C22C22×#13511yescharacteristic
735C22C2×#57611yescharacteristic
736C22C2×#57611yescharacteristic
737C4—24no—
738C4—24no—
739C4—24no—
740C4—42no—
741C4—44no—
742C4—42no—
743C4—82no—
744C4—82no—
745C4—82no—
746C4—82no—
747C4—82no—
748C4#255914yes—
749C4C2×#52911yescharacteristic
750C4C2×#53811yescharacteristic
751C4C2×#55311yescharacteristic
752C4C2×#55311yescharacteristic
753C2—44no—
754C2—84no—
755C2—162no—
756C2#2904318yesdirect product factor
757C2C2×#255911yescharacteristic
758C2C2×#316711yescharacteristic
759C2C2×#317611yescharacteristic
760C2C2×#329511yescharacteristic
761C2C2×#329511yescharacteristic
762C2C2×#329711yescharacteristic
763C2C2×#330511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2497C2semidirect
3. #29043C2direct (N × H)
4. C2×#2100C2semidirect
5. C2×#2041C2semidirect
6. C2×#2034C2semidirect
7. C2×#2034C2semidirect
8. C2×#1957C2semidirect
9. C2×#1941C2semidirect
10. C2×#1934C2semidirect
11. C2×#1926C2semidirect
12. C2×#1893C2semidirect
13. C2×#1893C2semidirect
14. C2×#1864C2semidirect
15. C2×C4×#102C2semidirect
16. C2×C8×C22⋊C4C2semidirect
37. #2497C22semidirect
56. #2100C22semidirect
57. #2041C22semidirect
58. #2034C22semidirect
59. #2034C22semidirect
60. #1957C22semidirect
61. #1941C22semidirect
62. #1934C22semidirect
63. #1926C22semidirect
64. #1893C22semidirect
65. #1893C22semidirect
66. #1864C22semidirect
67. C4×#102C22semidirect
68. C8×C22⋊C4C22semidirect
756. C2#29043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24972
C2×#24282
#290432
C2×#21002
C2×#20412
C2×#20342
C2×#19572
C2×#19412
C2×#19342
C2×#19262
C2×#18932
C2×#18642
C2×C4×#1022
C2×C8×C22⋊C42