Finite Group Databasebeta

← #25001837

Subgroups — #25001837

Order 11008.

1974 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4C2×#14582660C211yesmaximal, characteristic, complemented
5C2×#14582659C211yesmaximal, characteristic, complemented
6C2×#14582658C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C23×C4×D43—21no—
9C23×C4×D43C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C22×C4×Dic43—21no—
13C22×C4×Dic43C2211yescharacteristic
14C2×C42×D43—22no—
15C2×C42×D43—22no—
16C2×C42×D43—22no—
17C2×C42×D43—22no—
18C2×C42×D43—22no—
19C2×C42×D43C414yescomplemented
20#14582862—22no—
21#14582862C414yescomplemented
22C2×(C2×D43)⋊C8—22no—
23#14582760—21no—
24#14582756C414yescomplemented
25#14582754—21no—
26C4×(C2×D43)⋊C4—22no—
27#14582660—22no—
28#14582659—22no—
29#14582658—22no—
30C22×M16×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C22×C42×C43C2211yescharacteristic
33C43×#339—22no—
34C24×D43D411yescharacteristic
35C23×Dic43—21no—
36C23×Dic43D411yescharacteristic
37C22×C4×D43—24no—
38C22×C4×D43—24no—
39C22×C4×D43—216no—
40C22×C4×D43—24no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C4×D43—21no—
49C22×C4×D43C2×C412yes—
50C22×C4×D43C2×C412yes—
51C22×C4×D43C2×C412yes—
52C22×C4×D43D412yes—
53C22×C4×D43D412yes—
54C22×C4×D43Q812yes—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877C2×C412yescomplemented
61C22×C43⋊C8—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66C2×C4⋊Dic43C2×C412yescomplemented
67C2×C22⋊Dic43—21no—
68C2×(C2×D43)⋊C4—24no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43C2×C412yes—
77C2×C4×Dic43D412yes—
78C2×C4×Dic43D412yes—
79C42×D43—28no—
80C42×D43—28no—
81C42×D43—28no—
82C42×D43—28no—
83(C2×D43)⋊C8—28no—
84C43⋊#95—24no—
85C23×C4×C43—21no—
86C23×C4×C43C2311yescharacteristic
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43C2×C412yescomplemented
93C22×C8×C43—21no—
94#117×C43—21no—
95#117×C43—21no—
96#117×C43—21no—
97#117×C43—21no—
98C2×C4⋊C4×C43C2×C412yescomplemented
99C2×C22⋊C4×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43—21no—
102C2×C42×C43—21no—
103C2×C42×C43—21no—
104C2×C42×C43C2×C412yes—
105C2×C42×C43D412yes—
106C2×C42×C43D412yes—
107C24×C43C2×D411yescharacteristic
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—28no—
113C23×D43C22⋊C412yes—
114C23×D43C22⋊C412yes—
115C23×D43C4⋊C412yes—
116C22×C4×C43—28no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×Q811yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×Dic43—28no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C22⋊C412yes—
145C22×Dic43C22⋊C412yes—
146C22×Dic43C4⋊C412yes—
147C2×C4×D43—216no—
148C2×C4×D43—232no—
149C2×C4×D43—232no—
150C2×C4×D43—232no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43C4214yes—
176C2×C4×D43C22⋊C414yes—
177C2×C4×D43C4⋊C414yes—
178C2×C4×D43C4⋊C414yes—
179M16×C43—22no—
180M16×C43—22no—
181M16×C43—41no—
182M16×C43—41no—
183C2×C8×C43—22no—
184C2×C8×C43—41no—
185C2×C8×C43—41no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—22no—
191C42×C43—22no—
192C42×C43—22no—
193C42×C43—41no—
194C42×C43—41no—
195C42×C43C22⋊C414yescomplemented
196C22⋊Dic43—41no—
197C22⋊Dic43—41no—
198(C2×D43)⋊C4—48no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4×Dic43—216no—
202C4×Dic43—22no—
203C4×Dic43—22no—
204C4×Dic43—22no—
205C4×Dic43—41no—
206C4×Dic43—41no—
207C4×Dic43C22⋊C414yescomplemented
208#10621877—22no—
209#10621877—22no—
210#10621877—41no—
211#10621877—41no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—41no—
214C2×C43⋊C8—41no—
215C23×C43—24no—
216C23×C43C2×C22⋊C411yescharacteristic
217C23×C43C2×C22⋊C411yescharacteristic
218C23×C43C2×C4⋊C411yescharacteristic
219C23×C43#12011yescharacteristic
220C23×C43#12011yescharacteristic
221C23×C43#12311yescharacteristic
222C23×C43#12311yescharacteristic
223C22×D43—28no—
224C22×D43—28no—
225C22×D43—28no—
226C22×D43—28no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—24no—
234C22×D43—28no—
235C22×D43—28no—
236C22×D43#9514yes—
237C22×D43#10418yes—
238C2×C4×C43—28no—
239C2×C4×C43—28no—
240C2×C4×C43—28no—
241C2×C4×C43—24no—
242C2×C4×C43—42no—
243C2×C4×C43—44no—
244C2×C4×C43C2×C4211yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C4⋊C411yescharacteristic
249C2×C4×C43C2×C4⋊C411yescharacteristic
250C2×C4×C43#11711yescharacteristic
251C2×C4×C43#11711yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C4×D411yescharacteristic
256C2×C4×C43C4×D411yescharacteristic
257C2×C4×C43C4×D411yescharacteristic
258C2×C4×C43C4×D411yescharacteristic
259C2×C4×C43C4×D411yescharacteristic
260C2×C4×C43#12011yescharacteristic
261C2×C4×C43#12011yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43#12111yescharacteristic
266C2×C4×C43C22⋊Q811yescharacteristic
267C2×C4×C43C22⋊Q811yescharacteristic
268C2×C4×C43C22⋊Q811yescharacteristic
269C2×C4×C43C22⋊Q811yescharacteristic
270C2×C4×C43#12311yescharacteristic
271C2×C4×C43#12311yescharacteristic
272C2×Dic43—28no—
273C2×Dic43—28no—
274C2×Dic43—28no—
275C2×Dic43—22no—
276C2×Dic43—24no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—42no—
283C2×Dic43—44no—
284C2×Dic43#9514yes—
285C4×D43—264no—
286C4×D43—24no—
287C4×D43—24no—
288C4×D43—24no—
289C4×D43—24no—
290C4×D43—24no—
291C4×D43—24no—
292C4×D43—24no—
293C4×D43—24no—
294C8×C43—42no—
295C43⋊C8—42no—
296#10719—431nomaximal, Sylow
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—22no—
303C22×C43C2×#9511yescharacteristic
304C22×C43#37911yescharacteristic
305C22×C43#38111yescharacteristic
306C22×C43#38511yescharacteristic
307C22×C43#38511yescharacteristic
308C22×C43#38611yescharacteristic
309C22×C43#38611yescharacteristic
310C22×C43C2×#10414yes—
311C2×D43—28no—
312C2×D43—28no—
313C2×D43—28no—
314C2×D43—28no—
315C2×D43—28no—
316C2×D43—28no—
317C2×D43—24no—
318C2×D43—24no—
319C2×D43#33918yescomplemented
320C4×C43—28no—
321C4×C43—82no—
322C4×C43C4×C22⋊C411yescharacteristic
323C4×C43C4×C22⋊C411yescharacteristic
324C4×C43#38011yescharacteristic
325C4×C43#38011yescharacteristic
326C4×C43#38511yescharacteristic
327C4×C43#38511yescharacteristic
328C4×C43#38611yescharacteristic
329C4×C43#38611yescharacteristic
330Dic43—28no—
331Dic43—24no—
332Dic43—82no—
333C23×C42—431no—
334C2×#407—431no—
335#2280—431no—
336C2×#339—431no—
337C2×#339—431no—
338C2×#339—431no—
339C2×#339D4311yescharacteristic, complemented
340C2×C43—21no—
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—21no—
344C2×C43C22⋊#9511yescharacteristic
345C2×C43C2×#33912yes—
346C2×C43#189612yes—
347C2×C43#189612yes—
348D43—28no—
349C24×C4—431no—
350C24×C4—861no—
351C22×M16—431no—
352C22×M16C2×D4311yescharacteristic
353C2×#117—431no—
354C2×#117C2×D4311yescharacteristic
355C22×C42—431no—
356C22×C42—434no—
357C22×C42—862no—
358C22×C42—862no—
359C22×C42—862no—
360C22×C42—861no—
361C22×C42—862no—
362C22×C42—862no—
363C22×C42C2×D4311yescharacteristic
364#407—434no—
365#407—862no—
366C2×C22⋊C8—862no—
367#381—861no—
368#380—434no—
369#379—861no—
370C4×C22⋊C4—862no—
371#339—22no—
372#339—862no—
373#339—862no—
374#339—862no—
375C43#1071911yescharacteristic, complemented, Sylow
376C25—431no—
377C23×C4—21no—
378C23×C4—431no—
379C23×C4—432no—
380C23×C4—432no—
381C23×C4—432no—
382C23×C4—432no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4—864no—
386C23×C4—8616no—
387C23×C4—864no—
388C23×C4—864no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4C22×D4311yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—432no—
405C2×M16—861no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—861no—
409C2×M16—861no—
410C2×M16C4×D4312yescomplemented
411C22×C8—21no—
412C22×C8—861no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—861no—
418#117—861no—
419#117—861no—
420#117—861no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4C4×D4312yescomplemented
423C2×C22⋊C4—21no—
424C2×C22⋊C4—864no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—432no—
431C2×C42—432no—
432C2×C42—432no—
433C2×C42—868no—
434C2×C42—868no—
435C2×C42—868no—
436C2×C42—864no—
437C2×C42—864no—
438C2×C42—864no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—868no—
443C2×C42—861no—
444C2×C42C4×D4312yes—
445C2×C42D17212yes—
446C2×C42C22⋊D4312yes—
447C22⋊C8—868no—
448#95—864no—
449C24—432no—
450C24—432no—
451C24—432no—
452C24—868no—
453C24—861no—
454C24—861no—
455C24—861no—
456C24—861no—
457C24D4×D4311yescharacteristic
458C22×C4—28no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—434no—
469C22×C4—434no—
470C22×C4—8616no—
471C22×C4—8632no—
472C22×C4—8632no—
473C22×C4—8632no—
474C22×C4—868no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4C2×C4×D4311yescharacteristic
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4C2×D17211yescharacteristic
511C22×C4#1062189811yescharacteristic
512C22×C4#1062189811yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4#1062190011yescharacteristic
518C22×C4Q8×D4311yescharacteristic
519C22×C4#1062190211yescharacteristic
520C22×C4C2×C22⋊D4311yescharacteristic
521M16—22no—
522M16—22no—
523M16—41no—
524M16—41no—
525M16—862no—
526M16—862no—
527M16—1721no—
528M16—1721no—
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—862no—
533C2×C8—1721no—
534C2×C8—1721no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—1728no—
542C22⋊C4—1721no—
543C22⋊C4—1721no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—434no—
550C42—8616no—
551C42—862no—
552C42—862no—
553C42—862no—
554C42—1721no—
555C42—1721no—
556C42(C2×D43)⋊C414yescomplemented
557C23—24no—
558C23—438no—
559C23—434no—
560C23—868no—
561C23—868no—
562C23—868no—
563C23—868no—
564C23—868no—
565C23—868no—
566C23—864no—
567C23—862no—
568C23—862no—
569C23—862no—
570C23—862no—
571C23—862no—
572C23—862no—
573C23C22⋊C4×D4311yescharacteristic
574C23C22⋊C4×D4311yescharacteristic
575C23C4⋊C4×D4311yescharacteristic
576C23#1306329311yescharacteristic
577C23#1306329511yescharacteristic
578C23#1306330711yescharacteristic
579C23#1306331011yescharacteristic
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—28no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—434no—
587C2×C4—8664no—
588C2×C4—868no—
589C2×C4—868no—
590C2×C4—868no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—1724no—
607C2×C4—1722no—
608C2×C4C42×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C2×(C2×D43)⋊C411yescharacteristic
612C2×C4C4⋊C4×D4311yescharacteristic
613C2×C4C4⋊C4×D4311yescharacteristic
614C2×C4#1306328211yescharacteristic
615C2×C4#1306328311yescharacteristic
616C2×C4(C22⋊D43)⋊C411yescharacteristic
617C2×C4(C22⋊D43)⋊C411yescharacteristic
618C2×C4C4×C22⋊D4311yescharacteristic
619C2×C4C4×C22⋊D4311yescharacteristic
620C2×C4#1306328711yescharacteristic
621C2×C4#1306328711yescharacteristic
622C2×C4C4×D17211yescharacteristic
623C2×C4C4×D17211yescharacteristic
624C2×C4#1306329311yescharacteristic
625C2×C4#1306329511yescharacteristic
626C2×C4#1306329611yescharacteristic
627C2×C4#1306329811yescharacteristic
628C2×C4#1306329811yescharacteristic
629C2×C4#1306330011yescharacteristic
630C2×C4#1306330111yescharacteristic
631C2×C4#1306330311yescharacteristic
632C2×C4#1306330311yescharacteristic
633C2×C4#1306330511yescharacteristic
634C2×C4#1306330711yescharacteristic
635C2×C4#1306331011yescharacteristic
636C8—42no—
637C8—1722no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—438no—
645C22—868no—
646C22—868no—
647C22—868no—
648C22—868no—
649C22—868no—
650C22—868no—
651C22—864no—
652C22—864no—
653C22#95×D4311yescharacteristic
654C22#1458275411yescharacteristic
655C22#1458276111yescharacteristic
656C22#1458277011yescharacteristic
657C22#1458277311yescharacteristic
658C22#1458277511yescharacteristic
659C22#1458277711yescharacteristic
660C22#104×D4314yes—
661C4—28no—
662C4—82no—
663C4—868no—
664C4—864no—
665C4—3442no—
666C4#1458274611yescharacteristic
667C4C4×(C2×D43)⋊C411yescharacteristic
668C4#1458275611yescharacteristic
669C4#1458275811yescharacteristic
670C4#1458277011yescharacteristic
671C4#1458277311yescharacteristic
672C4#1458277511yescharacteristic
673C4#1458277711yescharacteristic
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—868no—
679C2(C2×D43)⋊#9511yescharacteristic
680C2#339×D4312yes—
681C2#1913503512yes—
682C2#1913503712yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#10719
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#14582660C2semidirect
5. C2×#14582659C2semidirect
6. C2×#14582658C2semidirect
7. C2×C43×#339C2semidirect
19. C2×C42×D43C4semidirect
21. #14582862C4semidirect
24. #14582756C4semidirect
60. C2×#10621877C2×C4semidirect
66. C2×C4⋊Dic43C2×C4semidirect
92. C2×M16×C43C2×C4semidirect
98. C2×C4⋊C4×C43C2×C4semidirect
195. C42×C43C22⋊C4semidirect
207. C4×Dic43C22⋊C4semidirect
319. C2×D43#339semidirect
339. C2×#339D43semidirect
375. C43#10719semidirect
410. C2×M16C4×D43semidirect
422. C2×C4⋊C4C4×D43semidirect
556. C42(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D432
C2×#145828622
#191369742
C2×#145826602
C2×#145826592
C2×#145826582
C2×C43×#3392
#1071943