Finite Group Databasebeta

← #26121518

Subgroups — #26121518

Order 12032.

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×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3#20245767C211yesmaximal, characteristic
4C2×#15688884C211yesmaximal, characteristic, complemented
5C2×#15688883C211yesmaximal, characteristic, complemented
6C2×#15688882C211yesmaximal, characteristic, complemented
7C2×C47×#339C211yesmaximal, characteristic, complemented
8C23×C4×D47—21no—
9C23×C4×D47C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C22×C4×Dic47—21no—
13C22×C4×Dic47C2211yescharacteristic
14C2×C42×D47—22no—
15C2×C42×D47—22no—
16C2×C42×D47—22no—
17C2×C42×D47—22no—
18C2×C42×D47—22no—
19C2×C42×D47C414yescomplemented
20#15689086—22no—
21#15689086C414yescomplemented
22C2×(C2×D47)⋊C8—22no—
23#15688984—21no—
24#15688980C414yescomplemented
25#15688978—21no—
26C4×(C2×D47)⋊C4—22no—
27#15688884—22no—
28#15688883—22no—
29#15688882—22no—
30C22×M16×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C47×#339—22no—
34C24×D47D411yescharacteristic
35C23×Dic47—21no—
36C23×Dic47D411yescharacteristic
37C22×C4×D47—24no—
38C22×C4×D47—24no—
39C22×C4×D47—216no—
40C22×C4×D47—24no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—21no—
47C22×C4×D47—21no—
48C22×C4×D47—21no—
49C22×C4×D47C2×C412yes—
50C22×C4×D47C2×C412yes—
51C22×C4×D47C2×C412yes—
52C22×C4×D47D412yes—
53C22×C4×D47D412yes—
54C22×C4×D47Q812yes—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329C2×C412yescomplemented
61C22×C47⋊C8—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66C2×C4⋊Dic47C2×C412yescomplemented
67C2×C22⋊Dic47—21no—
68C2×(C2×D47)⋊C4—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—21no—
72C2×C4×Dic47—21no—
73C2×C4×Dic47—21no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47C2×C412yes—
77C2×C4×Dic47D412yes—
78C2×C4×Dic47D412yes—
79C42×D47—28no—
80C42×D47—28no—
81C42×D47—28no—
82C42×D47—28no—
83(C2×D47)⋊C8—28no—
84C47⋊#95—24no—
85C23×C4×C47—21no—
86C23×C4×C47C2311yescharacteristic
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47C2×C412yescomplemented
93C22×C8×C47—21no—
94#117×C47—21no—
95#117×C47—21no—
96#117×C47—21no—
97#117×C47—21no—
98C2×C4⋊C4×C47C2×C412yescomplemented
99C2×C22⋊C4×C47—21no—
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102C2×C42×C47—21no—
103C2×C42×C47—21no—
104C2×C42×C47C2×C412yes—
105C2×C42×C47D412yes—
106C2×C42×C47D412yes—
107C24×C47C2×D411yescharacteristic
108C23×D47—21no—
109C23×D47—21no—
110C23×D47—21no—
111C23×D47—21no—
112C23×D47—28no—
113C23×D47C22⋊C412yes—
114C23×D47C22⋊C412yes—
115C23×D47C4⋊C412yes—
116C22×C4×C47—28no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×Q811yescharacteristic
131C22×C4×C47#4111yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×Dic47—28no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—22no—
144C22×Dic47C22⋊C412yes—
145C22×Dic47C22⋊C412yes—
146C22×Dic47C4⋊C412yes—
147C2×C4×D47—216no—
148C2×C4×D47—232no—
149C2×C4×D47—232no—
150C2×C4×D47—232no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47C4214yes—
176C2×C4×D47C22⋊C414yes—
177C2×C4×D47C4⋊C414yes—
178C2×C4×D47C4⋊C414yes—
179M16×C47—22no—
180M16×C47—22no—
181M16×C47—41no—
182M16×C47—41no—
183C2×C8×C47—22no—
184C2×C8×C47—41no—
185C2×C8×C47—41no—
186C4⋊C4×C47—22no—
187C4⋊C4×C47—22no—
188C22⋊C4×C47—41no—
189C22⋊C4×C47—41no—
190C42×C47—22no—
191C42×C47—22no—
192C42×C47—22no—
193C42×C47—41no—
194C42×C47—41no—
195C42×C47C22⋊C414yescomplemented
196C22⋊Dic47—41no—
197C22⋊Dic47—41no—
198(C2×D47)⋊C4—48no—
199C4⋊Dic47—22no—
200C4⋊Dic47—22no—
201C4×Dic47—216no—
202C4×Dic47—22no—
203C4×Dic47—22no—
204C4×Dic47—22no—
205C4×Dic47—41no—
206C4×Dic47—41no—
207C4×Dic47C22⋊C414yescomplemented
208#10625329—22no—
209#10625329—22no—
210#10625329—41no—
211#10625329—41no—
212C2×C47⋊C8—22no—
213C2×C47⋊C8—41no—
214C2×C47⋊C8—41no—
215C23×C47—24no—
216C23×C47C2×C22⋊C411yescharacteristic
217C23×C47C2×C22⋊C411yescharacteristic
218C23×C47C2×C4⋊C411yescharacteristic
219C23×C47#12011yescharacteristic
220C23×C47#12011yescharacteristic
221C23×C47#12311yescharacteristic
222C23×C47#12311yescharacteristic
223C22×D47—28no—
224C22×D47—28no—
225C22×D47—28no—
226C22×D47—28no—
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—24no—
234C22×D47—28no—
235C22×D47—28no—
236C22×D47#9514yes—
237C22×D47#10418yes—
238C2×C4×C47—28no—
239C2×C4×C47—28no—
240C2×C4×C47—28no—
241C2×C4×C47—24no—
242C2×C4×C47—42no—
243C2×C4×C47—44no—
244C2×C4×C47C2×C4211yescharacteristic
245C2×C4×C47C2×C22⋊C411yescharacteristic
246C2×C4×C47C2×C22⋊C411yescharacteristic
247C2×C4×C47C2×C22⋊C411yescharacteristic
248C2×C4×C47C2×C4⋊C411yescharacteristic
249C2×C4×C47C2×C4⋊C411yescharacteristic
250C2×C4×C47#11711yescharacteristic
251C2×C4×C47#11711yescharacteristic
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47C4×D411yescharacteristic
258C2×C4×C47C4×D411yescharacteristic
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47#12011yescharacteristic
261C2×C4×C47#12011yescharacteristic
262C2×C4×C47#12111yescharacteristic
263C2×C4×C47#12111yescharacteristic
264C2×C4×C47#12111yescharacteristic
265C2×C4×C47#12111yescharacteristic
266C2×C4×C47C22⋊Q811yescharacteristic
267C2×C4×C47C22⋊Q811yescharacteristic
268C2×C4×C47C22⋊Q811yescharacteristic
269C2×C4×C47C22⋊Q811yescharacteristic
270C2×C4×C47#12311yescharacteristic
271C2×C4×C47#12311yescharacteristic
272C2×Dic47—28no—
273C2×Dic47—28no—
274C2×Dic47—28no—
275C2×Dic47—22no—
276C2×Dic47—24no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—42no—
283C2×Dic47—44no—
284C2×Dic47#9514yes—
285C4×D47—264no—
286C4×D47—24no—
287C4×D47—24no—
288C4×D47—24no—
289C4×D47—24no—
290C4×D47—24no—
291C4×D47—24no—
292C4×D47—24no—
293C4×D47—24no—
294C8×C47—42no—
295C47⋊C8—42no—
296#10719—471nomaximal, Sylow
297C22×C47—22no—
298C22×C47—22no—
299C22×C47—22no—
300C22×C47—22no—
301C22×C47—22no—
302C22×C47—22no—
303C22×C47C2×#9511yescharacteristic
304C22×C47#37911yescharacteristic
305C22×C47#38111yescharacteristic
306C22×C47#38511yescharacteristic
307C22×C47#38511yescharacteristic
308C22×C47#38611yescharacteristic
309C22×C47#38611yescharacteristic
310C22×C47C2×#10414yes—
311C2×D47—28no—
312C2×D47—28no—
313C2×D47—28no—
314C2×D47—28no—
315C2×D47—28no—
316C2×D47—28no—
317C2×D47—24no—
318C2×D47—24no—
319C2×D47#33918yescomplemented
320C4×C47—28no—
321C4×C47—82no—
322C4×C47C4×C22⋊C411yescharacteristic
323C4×C47C4×C22⋊C411yescharacteristic
324C4×C47#38011yescharacteristic
325C4×C47#38011yescharacteristic
326C4×C47#38511yescharacteristic
327C4×C47#38511yescharacteristic
328C4×C47#38611yescharacteristic
329C4×C47#38611yescharacteristic
330Dic47—28no—
331Dic47—24no—
332Dic47—82no—
333C23×C42—471no—
334C2×#407—471no—
335#2280—471no—
336C2×#339—471no—
337C2×#339—471no—
338C2×#339—471no—
339C2×#339D4711yescharacteristic, complemented
340C2×C47—21no—
341C2×C47—21no—
342C2×C47—21no—
343C2×C47—21no—
344C2×C47C22⋊#9511yescharacteristic
345C2×C47C2×#33912yes—
346C2×C47#189612yes—
347C2×C47#189612yes—
348D47—28no—
349C24×C4—471no—
350C24×C4—941no—
351C22×M16—471no—
352C22×M16C2×D4711yescharacteristic
353C2×#117—471no—
354C2×#117C2×D4711yescharacteristic
355C22×C42—471no—
356C22×C42—474no—
357C22×C42—942no—
358C22×C42—942no—
359C22×C42—942no—
360C22×C42—941no—
361C22×C42—942no—
362C22×C42—942no—
363C22×C42C2×D4711yescharacteristic
364#407—474no—
365#407—942no—
366C2×C22⋊C8—942no—
367#381—941no—
368#380—474no—
369#379—941no—
370C4×C22⋊C4—942no—
371#339—22no—
372#339—942no—
373#339—942no—
374#339—942no—
375C47#1071911yescharacteristic, complemented, Sylow
376C25—471no—
377C23×C4—21no—
378C23×C4—471no—
379C23×C4—472no—
380C23×C4—472no—
381C23×C4—472no—
382C23×C4—472no—
383C23×C4—472no—
384C23×C4—472no—
385C23×C4—944no—
386C23×C4—9416no—
387C23×C4—944no—
388C23×C4—944no—
389C23×C4—941no—
390C23×C4—941no—
391C23×C4—941no—
392C23×C4—941no—
393C23×C4—941no—
394C23×C4—941no—
395C23×C4—941no—
396C23×C4—941no—
397C23×C4—941no—
398C23×C4C22×D4711yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—472no—
405C2×M16—941no—
406C2×M16—941no—
407C2×M16—941no—
408C2×M16—941no—
409C2×M16—941no—
410C2×M16C4×D4712yescomplemented
411C22×C8—21no—
412C22×C8—941no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—941no—
418#117—941no—
419#117—941no—
420#117—941no—
421C2×C4⋊C4—472no—
422C2×C4⋊C4C4×D4712yescomplemented
423C2×C22⋊C4—21no—
424C2×C22⋊C4—944no—
425C2×C22⋊C4—941no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—472no—
431C2×C42—472no—
432C2×C42—472no—
433C2×C42—948no—
434C2×C42—948no—
435C2×C42—948no—
436C2×C42—944no—
437C2×C42—944no—
438C2×C42—944no—
439C2×C42—941no—
440C2×C42—941no—
441C2×C42—941no—
442C2×C42—948no—
443C2×C42—941no—
444C2×C42C4×D4712yes—
445C2×C42D18812yes—
446C2×C42C22⋊D4712yes—
447C22⋊C8—948no—
448#95—944no—
449C24—472no—
450C24—472no—
451C24—472no—
452C24—948no—
453C24—941no—
454C24—941no—
455C24—941no—
456C24—941no—
457C24D4×D4711yescharacteristic
458C22×C4—28no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—472no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—474no—
467C22×C4—474no—
468C22×C4—474no—
469C22×C4—474no—
470C22×C4—9416no—
471C22×C4—9432no—
472C22×C4—9432no—
473C22×C4—9432no—
474C22×C4—948no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4C2×C4×D4711yescharacteristic
508C22×C4C2×C4×D4711yescharacteristic
509C22×C4C2×C4×D4711yescharacteristic
510C22×C4C2×D18811yescharacteristic
511C22×C4#1062535011yescharacteristic
512C22×C4#1062535011yescharacteristic
513C22×C4D4×D4711yescharacteristic
514C22×C4D4×D4711yescharacteristic
515C22×C4D4×D4711yescharacteristic
516C22×C4D4×D4711yescharacteristic
517C22×C4#1062535211yescharacteristic
518C22×C4Q8×D4711yescharacteristic
519C22×C4#1062535411yescharacteristic
520C22×C4C2×C22⋊D4711yescharacteristic
521M16—22no—
522M16—22no—
523M16—41no—
524M16—41no—
525M16—942no—
526M16—942no—
527M16—1881no—
528M16—1881no—
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—942no—
533C2×C8—1881no—
534C2×C8—1881no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—942no—
538C4⋊C4—942no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—1888no—
542C22⋊C4—1881no—
543C22⋊C4—1881no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—474no—
550C42—9416no—
551C42—942no—
552C42—942no—
553C42—942no—
554C42—1881no—
555C42—1881no—
556C42(C2×D47)⋊C414yescomplemented
557C23—24no—
558C23—474no—
559C23—478no—
560C23—948no—
561C23—948no—
562C23—948no—
563C23—948no—
564C23—948no—
565C23—948no—
566C23—942no—
567C23—942no—
568C23—942no—
569C23—942no—
570C23—942no—
571C23—942no—
572C23—944no—
573C23C22⋊C4×D4711yescharacteristic
574C23C22⋊C4×D4711yescharacteristic
575C23C4⋊C4×D4711yescharacteristic
576C23#1309399211yescharacteristic
577C23#1309399411yescharacteristic
578C23#1309400611yescharacteristic
579C23#1309400911yescharacteristic
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—28no—
583C2×C4—24no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—474no—
587C2×C4—9464no—
588C2×C4—948no—
589C2×C4—948no—
590C2×C4—948no—
591C2×C4—944no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—944no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—944no—
605C2×C4—944no—
606C2×C4—1882no—
607C2×C4—1884no—
608C2×C4C42×D4711yescharacteristic
609C2×C4C22⋊C4×D4711yescharacteristic
610C2×C4C22⋊C4×D4711yescharacteristic
611C2×C4C2×(C2×D47)⋊C411yescharacteristic
612C2×C4C4⋊C4×D4711yescharacteristic
613C2×C4C4⋊C4×D4711yescharacteristic
614C2×C4#1309398111yescharacteristic
615C2×C4#1309398211yescharacteristic
616C2×C4(C22⋊D47)⋊C411yescharacteristic
617C2×C4(C22⋊D47)⋊C411yescharacteristic
618C2×C4C4×C22⋊D4711yescharacteristic
619C2×C4C4×C22⋊D4711yescharacteristic
620C2×C4#1309398611yescharacteristic
621C2×C4#1309398611yescharacteristic
622C2×C4C4×D18811yescharacteristic
623C2×C4C4×D18811yescharacteristic
624C2×C4#1309399211yescharacteristic
625C2×C4#1309399411yescharacteristic
626C2×C4#1309399511yescharacteristic
627C2×C4#1309399711yescharacteristic
628C2×C4#1309399711yescharacteristic
629C2×C4#1309399911yescharacteristic
630C2×C4#1309400011yescharacteristic
631C2×C4#1309400211yescharacteristic
632C2×C4#1309400211yescharacteristic
633C2×C4#1309400411yescharacteristic
634C2×C4#1309400611yescharacteristic
635C2×C4#1309400911yescharacteristic
636C8—42no—
637C8—1882no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—478no—
645C22—948no—
646C22—948no—
647C22—948no—
648C22—948no—
649C22—948no—
650C22—948no—
651C22—944no—
652C22—944no—
653C22#95×D4711yescharacteristic
654C22#1568897811yescharacteristic
655C22#1568898511yescharacteristic
656C22#1568899411yescharacteristic
657C22#1568899711yescharacteristic
658C22#1568899911yescharacteristic
659C22#1568900111yescharacteristic
660C22#104×D4714yes—
661C4—28no—
662C4—82no—
663C4—948no—
664C4—944no—
665C4—3762no—
666C4#1568897011yescharacteristic
667C4C4×(C2×D47)⋊C411yescharacteristic
668C4#1568898011yescharacteristic
669C4#1568898211yescharacteristic
670C4#1568899411yescharacteristic
671C4#1568899711yescharacteristic
672C4#1568899911yescharacteristic
673C4#1568900111yescharacteristic
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—948no—
679C2(C2×D47)⋊#9511yescharacteristic
680C2#339×D4712yes—
681C2#2024382812yes—
682C2#2024383012yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#339C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×#339D47
hypocenterC47#10719
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#15688884C2semidirect
5. C2×#15688883C2semidirect
6. C2×#15688882C2semidirect
7. C2×C47×#339C2semidirect
19. C2×C42×D47C4semidirect
21. #15689086C4semidirect
24. #15688980C4semidirect
60. C2×#10625329C2×C4semidirect
66. C2×C4⋊Dic47C2×C4semidirect
92. C2×M16×C47C2×C4semidirect
98. C2×C4⋊C4×C47C2×C4semidirect
195. C42×C47C22⋊C4semidirect
207. C4×Dic47C22⋊C4semidirect
319. C2×D47#339semidirect
339. C2×#339D47semidirect
375. C47#10719semidirect
410. C2×M16C4×D47semidirect
422. C2×C4⋊C4C4×D47semidirect
556. C42(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D472
C2×#156890862
#202457672
C2×#156888842
C2×#156888832
C2×#156888822
C2×C47×#3392
#1071947