Finite Group Databasebeta

← C2×#20244391 #26243068

Subgroups — C2×#20244391 #26243068

Order 12032.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625335C211yesmaximal, characteristic, complemented
2C22×#13094003C211yesmaximal, characteristic, complemented
3C22×#13093947C211yesmaximal, characteristic, complemented
4C22×#13093945C211yesmaximal, characteristic, complemented
5C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#20244391C218yesmaximal, direct product factor
7C2×#15688885C211yesmaximal, characteristic, complemented
8C22×#121×C47C211yesmaximal, characteristic
9C23×Dic94C2211yescharacteristic
10C22×#10625335—24no—
11C22×#10625335—24no—
12C22×#10625335—24no—
13C22×#10625335C2214yescomplemented
14C23×C47⋊C8C2211yescharacteristic
15C23×C47⋊C8C2211yescharacteristic
16C2×#13094003—24no—
17C2×#13094003—24no—
18C2×#13094003—22no—
19C2×#13094003C2214yescomplemented
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4—21no—
22C22×C22⋊Dic47—21no—
23C2×#13093947—24no—
24C2×#13093947C2214yescomplemented
25C2×#13093945—24no—
26C2×#13093945C2214yescomplemented
27C2×C22⋊(C47⋊C8)—24no—
28C2×C22⋊(C47⋊C8)C2214yescomplemented
29#15688885C2214yescomplemented
30C23×D4×C47—21no—
31C23×D4×C47C2211yescharacteristic
32C24×C4×C47C2211yescharacteristic
33C2×#121×C47—24no—
34C2×#121×C47—22no—
35C2×#121×C47—24no—
36C2×#121×C47C2214yes—
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47—21no—
39C22×Dic94—22no—
40C22×Dic94—22no—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—21no—
44C22×Dic94—22no—
45C22×Dic94D414yescomplemented
46C22×Dic94C2312yes—
47C23×Dic47—21no—
48C23×Dic47—21no—
49C2×#10625335—232no—
50C2×#10625335—28no—
51C2×#10625335—28no—
52C2×#10625335—28no—
53C22×C47⋊C8—22no—
54C22×C47⋊C8—22no—
55C22×C47⋊C8—22no—
56C22×C47⋊C8—22no—
57C22×C47⋊C8—22no—
58C22×C47⋊C8D414yescomplemented
59C22×C47⋊C8C2312yes—
60C22×C47⋊C8C2312yes—
61#13094003—216no—
62#13094003—28no—
63#13094003—28no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47D414yescomplemented
67C2×C4⋊Dic47C2312yes—
68C2×Dic47⋊C4—28no—
69C2×Dic47⋊C4—24no—
70C2×C22⋊Dic47—28no—
71C2×C22⋊Dic47—24no—
72#13093947—28no—
73#13093945—28no—
74C22⋊(C47⋊C8)—28no—
75C25×C47—21no—
76C25×C47D411yescharacteristic
77C22×D4×C47—28no—
78C22×D4×C47—24no—
79C22×D4×C47—22no—
80C22×D4×C47—22no—
81C22×D4×C47—22no—
82C22×D4×C47—21no—
83C22×D4×C47—22no—
84C22×D4×C47—22no—
85C22×D4×C47—44no—
86C22×D4×C47—44no—
87C22×D4×C47D414yes—
88C22×D4×C47C2312yes—
89C23×C4×C47—21no—
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47—22no—
93C23×C4×C47—22no—
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47D411yescharacteristic
97C23×C4×C47D412yes—
98C23×C4×C47C2312yes—
99C23×C4×C47C2311yescharacteristic
100#121×C47—216no—
101#121×C47—28no—
102#121×C47—28no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47D414yes—
106C2×C4⋊C4×C47C2312yes—
107C2×C22⋊C4×C47—28no—
108C2×C22⋊C4×C47—24no—
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—24no—
116C24×C47—22no—
117C24×C47—42no—
118C24×C47—42no—
119C24×C47—42no—
120C24×C47—42no—
121C24×C47—42no—
122C24×C47—42no—
123C24×C47SD1614yescomplemented
124C24×C47C2×D412yes—
125C24×C47C2×D411yescharacteristic
126C2×D4×C47—216no—
127C2×D4×C47—28no—
128C2×D4×C47—24no—
129C2×D4×C47—28no—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—22no—
133C2×D4×C47—22no—
134C2×D4×C47—22no—
135C2×D4×C47—48no—
136C2×D4×C47—432no—
137C2×D4×C47—48no—
138C2×D4×C47—42no—
139C2×D4×C47—44no—
140C2×D4×C47—42no—
141C2×D4×C47—44no—
142C2×D4×C47C2×D414yes—
143C22×C4×C47—22no—
144C22×C4×C47—24no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—24no—
149C22×C4×C47—24no—
150C22×C4×C47—24no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47—44no—
160C22×C4×C47—44no—
161C22×C4×C47—44no—
162C22×C4×C47—44no—
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D412yes—
166C22×C4×C47C2×D412yes—
167C22×C4×C47C2×D412yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47#4112yes—
171C22×C4×C47C2411yescharacteristic
172C22×Dic47—24no—
173C22×Dic47—24no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—42no—
177C22×Dic47—42no—
178C22×Dic47—42no—
179C22×Dic47—42no—
180C2×Dic94—28no—
181C2×Dic94—28no—
182C2×Dic94—22no—
183C2×Dic94—22no—
184C2×Dic94—22no—
185C2×Dic94—22no—
186C2×Dic94—24no—
187C2×Dic94—22no—
188C2×Dic94—42no—
189C2×Dic94—44no—
190C2×Dic94—42no—
191C2×Dic94—44no—
192C2×Dic94C2×D414yescomplemented
193C4⋊C4×C47—24no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47C2×D414yes—
196C22⋊C4×C47—216no—
197C22⋊Dic47—216no—
198#10625335—232no—
199C4⋊Dic47—24no—
200C4⋊Dic47—22no—
201C4⋊Dic47C2×D414yescomplemented
202Dic47⋊C4—216no—
203C2×C47⋊C8—28no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C2×C47⋊C8—44no—
210C2×C47⋊C8C2×D414yescomplemented
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—28no—
218C23×C47—28no—
219C23×C47—28no—
220C23×C47—24no—
221C23×C47—44no—
222C23×C47—44no—
223C23×C47—44no—
224C23×C47—44no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—48no—
232C23×C47—48no—
233C23×C47—48no—
234C23×C47—84no—
235C23×C47—84no—
236C23×C47—84no—
237C23×C47—84no—
238C23×C47#12012yes—
239C23×C47#12012yes—
240C23×C47#12112yes—
241C23×C47C2×SD1612yes—
242C23×C47C2×SD1614yescomplemented
243C23×C47#13512yes—
244C23×C47AGL(1,ℤ/8)12yes—
245C23×C47#13712yes—
246C23×C47C22×D411yescharacteristic
247D4×C47—24no—
248D4×C47—24no—
249D4×C47—432no—
250D4×C47—42no—
251D4×C47—42no—
252D4×C47—48no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—44no—
260C2×C4×C47—48no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47—48no—
266C2×C4×C47#12014yes—
267C2×C4×C47#12012yes—
268C2×C4×C47#12012yes—
269C2×C4×C47#12114yes—
270C2×C4×C47#12114yes—
271C2×C4×C47#12112yes—
272C2×C4×C47#12714yes—
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C22×D411yescharacteristic
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C22×D411yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×Dic47—24no—
280C2×Dic47—24no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—48no—
286C2×Dic47—48no—
287Dic94—24no—
288Dic94—24no—
289Dic94—42no—
290Dic94—42no—
291Dic94—48no—
292C47⋊C8—24no—
293C47⋊C8—42no—
294C2×#2000—471nomaximal, Sylow
295C22×C47—24no—
296C22×C47—24no—
297C22×C47—24no—
298C22×C47—42no—
299C22×C47—42no—
300C22×C47—42no—
301C22×C47—416no—
302C22×C47—42no—
303C22×C47—44no—
304C22×C47—44no—
305C22×C47—44no—
306C22×C47—82no—
307C22×C47—82no—
308C22×C47—816no—
309C22×C47—82no—
310C22×C47—82no—
311C22×C47#39214yes—
312C22×C47#44814yes—
313C22×C47#44914yes—
314C22×C47#45014yes—
315C22×C47#45214yes—
316C22×C47#46514yes—
317C22×C47#46814yes—
318C22×C47C2×#12011yescharacteristic
319C22×C47C2×#12011yescharacteristic
320C22×C47C2×#12111yescharacteristic
321C22×C47C22×SD1611yescharacteristic
322C22×C47C2×#13511yescharacteristic
323C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C47C2×#13711yescharacteristic
325C4×C47—42no—
326C4×C47—44no—
327C4×C47#39214yes—
328C4×C47C2×#12011yescharacteristic
329C4×C47C2×#12111yescharacteristic
330C4×C47C2×#12111yescharacteristic
331C4×C47C2×#12711yescharacteristic
332Dic47—44no—
333Dic47—44no—
334C23×SD16—471no—
335C22×C22⋊Q8—471no—
336C22×#121D4711yescharacteristic
337C22×#103—471no—
338C22×#102—471no—
339C22×C22⋊C8—471no—
340#2000—478no—
341C2×#340—471no—
342C2×C47—44no—
343C2×C47—84no—
344C2×C47#200018yescomplemented
345C2×C47C2×#39211yescharacteristic
346C2×C47C2×#45011yescharacteristic
347C2×C47C2×#44811yescharacteristic
348C2×C47C2×#44911yescharacteristic
349C2×C47C2×#45211yescharacteristic
350C2×C47C2×#46511yescharacteristic
351C2×C47C2×#46811yescharacteristic
352C23×Q8—471no—
353C23×D4—21no—
354C23×D4C2×D4711yescharacteristic
355C24×C4C2×D4711yescharacteristic
356C22×SD16—474no—
357C22×SD16—944no—
358C22×SD16—944no—
359C22×SD16—944no—
360C23×C8—471no—
361C23×C8—471no—
362C2×C22⋊Q8—474no—
363C2×C22⋊Q8—944no—
364C2×C22⋊Q8—944no—
365C2×C22⋊Q8—942no—
366C2×#121—24no—
367C2×#121—22no—
368C2×#121—24no—
369C2×#121C2×D4714yes—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—941no—
372C22×C4⋊C4C2×D4711yescharacteristic
373C22×C22⋊C4—21no—
374C22×C22⋊C4—941no—
375C2×#103—474no—
376C2×#103—944no—
377C2×#102—474no—
378C2×#102—944no—
379C2×C22⋊C8—474no—
380C2×C22⋊C8—944no—
381#340—474no—
382C47C2×#200011yescharacteristic, complemented, Sylow
383C25—21no—
384C25C22⋊D4711yescharacteristic
385C22×Q8—474no—
386C22×Q8—472no—
387C22×Q8—942no—
388C22×Q8—941no—
389C22×Q8—942no—
390C22×Q8—942no—
391C22×Q8—942no—
392C22×Q8—942no—
393C22×D4—28no—
394C22×D4—24no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—21no—
400C22×D4—22no—
401C22×D4—44no—
402C22×D4—44no—
403C22×D4C22⋊D4714yes—
404C22×D4C22×D4712yes—
405C23×C4—21no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—941no—
413C23×C4—941no—
414C23×C4C22⋊D4712yes—
415C23×C4C22⋊D4711yescharacteristic
416C23×C4C22×D4712yes—
417C23×C4C22×D4711yescharacteristic
418C2×SD16—948no—
419C2×SD16—948no—
420C2×SD16—9432no—
421C2×SD16—948no—
422C22×C8—474no—
423C22×C8—472no—
424C22×C8—472no—
425C22×C8—942no—
426C22×C8—942no—
427C22×C8—942no—
428C22×C8—942no—
429C22×C8—942no—
430C22⋊Q8—948no—
431C22⋊Q8—948no—
432C22⋊Q8—9416no—
433#121—216no—
434#121—28no—
435#121—28no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—474no—
439C2×C4⋊C4—472no—
440C2×C4⋊C4—948no—
441C2×C4⋊C4—942no—
442C2×C4⋊C4—941no—
443C2×C4⋊C4—944no—
444C2×C4⋊C4C22⋊D4714yes—
445C2×C4⋊C4C22×D4712yes—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—948no—
449C2×C22⋊C4—944no—
450#103—948no—
451#102—948no—
452C22⋊C8—948no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24#1062533514yescomplemented
468C24C2×C22⋊D4712yes—
469C24C2×C22⋊D4711yescharacteristic
470C2×Q8—474no—
471C2×Q8—944no—
472C2×Q8—942no—
473C2×Q8—948no—
474C2×Q8—948no—
475C2×Q8—942no—
476C2×Q8—942no—
477C2×Q8—942no—
478C2×Q8—942no—
479C2×Q8—1882no—
480C2×Q8—1884no—
481C2×Q8—1882no—
482C2×Q8—1884no—
483C2×D4—216no—
484C2×D4—28no—
485C2×D4—24no—
486C2×D4—28no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—432no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4C2×C22⋊D4714yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—944no—
521C22×C4—944no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—1882no—
525C22×C4—1882no—
526C22×C4—1882no—
527C22×C4—1882no—
528C22×C4D4×D4712yes—
529C22×C4D4×D4712yes—
530C22×C4D4×D4712yes—
531C22×C4#1062535212yes—
532C22×C4C2×C22⋊D4712yes—
533C22×C4C2×C22⋊D4711yescharacteristic
534C22×C4C2×C22⋊D4712yes—
535C22×C4C2×C22⋊D4712yes—
536C22×C4C23×D4711yescharacteristic
537SD16—9432no—
538C2×C8—474no—
539C2×C8—948no—
540C2×C8—942no—
541C2×C8—942no—
542C2×C8—942no—
543C2×C8—942no—
544C2×C8—942no—
545C2×C8—1884no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—474no—
549C4⋊C4—9416no—
550C4⋊C4—944no—
551C4⋊C4—942no—
552C4⋊C4C2×C22⋊D4714yes—
553C22⋊C4—216no—
554C22⋊C4—9416no—
555C23—28no—
556C23—28no—
557C23—28no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—48no—
570C23—48no—
571C23—48no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—84no—
579C23—84no—
580C23—84no—
581C23—84no—
582C23#1309399212yes—
583C23#1309399312yes—
584C23#1309399612yes—
585C23C2×#1062533512yes—
586C23C2×#1062533514yescomplemented
587C23#1309404412yes—
588C23#1309405012yes—
589C23#1309405412yes—
590C23C22×C22⋊D4711yescharacteristic
591Q8—944no—
592Q8—944no—
593Q8—1888no—
594Q8—1882no—
595Q8—1882no—
596D4—24no—
597D4—24no—
598D4—432no—
599D4—48no—
600D4—42no—
601D4—42no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—48no—
607C2×C4—44no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—48no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—944no—
616C2×C4—944no—
617C2×C4—1888no—
618C2×C4—1888no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4—1882no—
622C2×C4—1882no—
623C2×C4#1309399212yes—
624C2×C4#1309399214yes—
625C2×C4#1309399312yes—
626C2×C4#1309399514yes—
627C2×C4#1309399612yes—
628C2×C4#1309399614yes—
629C2×C4#1309402014yes—
630C2×C4C2×D4×D4711yescharacteristic
631C2×C4C2×D4×D4711yescharacteristic
632C2×C4C2×D4×D4711yescharacteristic
633C2×C4C22×C22⋊D4711yescharacteristic
634C2×C4C22×C22⋊D4711yescharacteristic
635C2×C4C2×#1062535211yescharacteristic
636C8—944no—
637C8—1882no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—416no—
644C22—42no—
645C22—42no—
646C22—44no—
647C22—44no—
648C22—44no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—816no—
653C22—82no—
654C22#1568903114yes—
655C22#1568926114yes—
656C22#1568926614yes—
657C22#1568927414yes—
658C22#1568928514yes—
659C22#1568935014yes—
660C22#1568936714yes—
661C22C2×#1309399211yescharacteristic
662C22C2×#1309399311yescharacteristic
663C22C2×#1309399611yescharacteristic
664C22C22×#1062533511yescharacteristic
665C22C2×#1309404411yescharacteristic
666C22C2×#1309405011yescharacteristic
667C22C2×#1309405411yescharacteristic
668C4—42no—
669C4—44no—
670C4—1884no—
671C4—1884no—
672C4#1568903114yes—
673C4C2×#1309399211yescharacteristic
674C4C2×#1309399511yescharacteristic
675C4C2×#1309399611yescharacteristic
676C4C2×#1309402011yescharacteristic
677C2—44no—
678C2—84no—
679C2#2024439118yesdirect product factor
680C2C2×#1568903111yescharacteristic
681C2C2×#1568927411yescharacteristic
682C2C2×#1568926111yescharacteristic
683C2C2×#1568926611yescharacteristic
684C2C2×#1568928511yescharacteristic
685C2C2×#1568935011yescharacteristic
686C2C2×#1568936711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
Fitting, prime radicalC22×#121×C47C2
socleC24×C47C2×D4
hypercenterC22×#121D47
hypocenterC47C2×#2000
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C23×#10625335C2semidirect
2. C22×#13094003C2semidirect
3. C22×#13093947C2semidirect
4. C22×#13093945C2semidirect
5. C22×C22⋊(C47⋊C8)C2semidirect
6. #20244391C2direct (N × H)
7. C2×#15688885C2semidirect
13. C22×#10625335C22semidirect
19. C2×#13094003C22semidirect
24. C2×#13093947C22semidirect
26. C2×#13093945C22semidirect
28. C2×C22⋊(C47⋊C8)C22semidirect
29. #15688885C22semidirect
45. C22×Dic94D4semidirect
58. C22×C47⋊C8D4semidirect
66. C2×C4⋊Dic47D4semidirect
123. C24×C47SD16semidirect
192. C2×Dic94C2×D4semidirect
201. C4⋊Dic47C2×D4semidirect
210. C2×C47⋊C8C2×D4semidirect
242. C23×C47C2×SD16semidirect
344. C2×C47#2000semidirect
382. C47C2×#2000semidirect
467. C24#10625335semidirect
586. C23C2×#10625335semidirect
679. C2#20244391direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253352
C22×#130940032
C22×#130939472
C22×#130939452
C22×C22⋊(C47⋊C8)2
#202443912
C2×#156888852
C22×#121×C472
C2×#200047