Finite Group Databasebeta

← #26216163

Subgroups — #26216163

Order 12032.

1418 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093983C211yesmaximal, characteristic
2C2×#15689181C212yesmaximal, complemented
3#20243457C212yesmaximal, complemented
4#20243370C212yesmaximal, complemented
5#20243366C211yesmaximal, characteristic, complemented
6#20243366C211yesmaximal, characteristic, complemented
7#20243298C211yesmaximal, characteristic
8#20243156C212yesmaximal, complemented
9#20243152C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
11C47×#1779C211yesmaximal, characteristic
12C2×#13093983—28no—
13C2×#13093983C411yescharacteristic
14C2×#13093983C411yescharacteristic
15C2×#13093983C411yescharacteristic
16C2×#13093983C411yescharacteristic
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21C22×C4⋊Dic47C411yescharacteristic
22C22×C4⋊Dic47C411yescharacteristic
23C22×C22⋊Dic47C411yescharacteristic
24C22×C22⋊Dic47C411yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27#15689181—28no—
28C2×Dic47⋊C8C2212yescomplemented
29C2×Dic47⋊C8C2212yescomplemented
30C2×C22⋊(C47⋊C8)C2212yes—
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2212yes—
34C2×#13093934C2212yescomplemented
35C2×C8×Dic47C2212yescomplemented
36#15688877C2212yescomplemented
37#15688877C2212yescomplemented
38#15688877C2212yescomplemented
39#15688877C2212yescomplemented
40C24×C4×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2212yes—
42C2×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2212yes—
45C23×Dic47C2×C411yescharacteristic
46C23×Dic47C2×C411yescharacteristic
47C23×Dic47C2×C411yescharacteristic
48C23×Dic47C2×C411yescharacteristic
49C22×C47⋊C8C2312yes—
50C22×C47⋊C8C2312yes—
51#13093983—24no—
52#13093983—24no—
53#13093983—24no—
54#13093983—24no—
55#13093983—24no—
56#13093983—24no—
57#13093983—24no—
58#13093983D418yes—
59C2×C4⋊Dic47—24no—
60C2×C4⋊Dic47—24no—
61C2×C4⋊Dic47C2×C411yescharacteristic
62C2×C4⋊Dic47C2×C411yescharacteristic
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×C4⋊Dic47C2×C411yescharacteristic
66C2×C4⋊Dic47C2×C411yescharacteristic
67C2×C4⋊Dic47C2×C411yescharacteristic
68C2×C4⋊Dic47C2×C411yescharacteristic
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47C2×C411yescharacteristic
72C2×C22⋊Dic47C2×C411yescharacteristic
73C2×C22⋊Dic47C2×C411yescharacteristic
74C2×C22⋊Dic47C2×C411yescharacteristic
75C2×C22⋊Dic47C2×C411yescharacteristic
76C2×C22⋊Dic47C2×C411yescharacteristic
77C2×C22⋊Dic47C2×C411yescharacteristic
78C2×C22⋊Dic47C2×C411yescharacteristic
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47C2×C411yescharacteristic
83C2×C4×Dic47C2×C411yescharacteristic
84C2×C4×Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89Dic47⋊C8—24no—
90Dic47⋊C8—24no—
91C22⋊(C47⋊C8)—24no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—22no—
94C22⋊(C47⋊C8)—24no—
95#13093934—24no—
96C8×Dic47—24no—
97C25×C47C2×C411yescharacteristic
98C23×C4×C47—24no—
99C23×C4×C47—24no—
100C23×C4×C47—22no—
101C23×C4×C47—22no—
102C23×C4×C47C2×C411yescharacteristic
103C23×C4×C47C2×C411yescharacteristic
104C23×C4×C47C2×C411yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C22×C8×C47C2312yes—
109C22×C8×C47C2312yes—
110C22⋊C8×C47—24no—
111C22⋊C8×C47—22no—
112C22⋊C8×C47—22no—
113C22⋊C8×C47—24no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—41no—
120C24×C47—41no—
121C24×C47C22×C411yescharacteristic
122C24×C47C22×C411yescharacteristic
123C24×C47C22×C411yescharacteristic
124C22×C4×C47—216no—
125C22×C4×C47—216no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C2×D414yes—
147C22×C4×C47#4114yes—
148C22×C4×C47#4112yes—
149C22×C4×C47#4112yes—
150C22×C4×C47C2411yescharacteristic
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—41no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47C22×C411yescharacteristic
164C22×Dic47C22×C411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C22⋊Dic47—22no—
178C22⋊Dic47—22no—
179C22⋊Dic47—22no—
180C22⋊Dic47—22no—
181C22⋊Dic47—22no—
182C22⋊Dic47—22no—
183C22⋊Dic47C22⋊C414yes—
184C22⋊Dic47C22⋊C414yes—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—22no—
188C4⋊Dic47—22no—
189C4⋊Dic47—22no—
190C4⋊Dic47—22no—
191C4⋊Dic47C22⋊C414yes—
192C4⋊Dic47C22⋊C414yes—
193C4×Dic47—22no—
194C4×Dic47—22no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197C4×Dic47—22no—
198C4×Dic47—22no—
199C4×Dic47C2×D414yes—
200C4×Dic47C2×D414yes—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—28no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—44no—
225C23×C47—44no—
226C23×C47—44no—
227C23×C47—44no—
228C23×C47—44no—
229C23×C47—44no—
230C23×C47C2×C22⋊C412yes—
231C23×C47#11712yes—
232C23×C47#11712yes—
233C23×C47#13112yes—
234C23×C47#13112yes—
235C23×C47C23×C411yescharacteristic
236C2×C4×C47—28no—
237C2×C4×C47—28no—
238C2×C4×C47—28no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47C2×C22⋊C412yes—
252C2×C4×C47#11712yes—
253C2×C4×C47#11712yes—
254C2×C4×C47C22×D412yes—
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47C2×#4112yes—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—44no—
279C2×Dic47—44no—
280C2×Dic47—44no—
281C2×Dic47—44no—
282C2×Dic47C2×C22⋊C412yes—
283C2×Dic47C2×C22⋊C412yes—
284C2×Dic47C2×C22⋊C412yes—
285C2×Dic47C2×C22⋊C412yes—
286C8×C47—42no—
287C8×C47—42no—
288C47⋊C8—42no—
289C47⋊C8—42no—
290#20716—471nomaximal, Sylow
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—22no—
295C22×C47—22no—
296C22×C47—22no—
297C22×C47—22no—
298C22×C47—22no—
299C22×C47—22no—
300C22×C47—22no—
301C22×C47—22no—
302C22×C47—22no—
303C22×C47—416no—
304C22×C47—41no—
305C22×C47—41no—
306C22×C47—41no—
307C22×C47—41no—
308C22×C47—41no—
309C22×C47—41no—
310C22×C47—41no—
311C22×C47—41no—
312C22×C47#43314yescomplemented
313C22×C47C22×C22⋊C411yescharacteristic
314C22×C47C2×#11711yescharacteristic
315C22×C47C2×#11711yescharacteristic
316C22×C47C2×#13111yescharacteristic
317C22×C47C2×#13111yescharacteristic
318C22×C47#56811yescharacteristic
319C22×C47#56811yescharacteristic
320C4×C47—22no—
321C4×C47—22no—
322C4×C47—22no—
323C4×C47#52512yes—
324C4×C47#52512yes—
325Dic47—22no—
326Dic47—22no—
327Dic47—22no—
328Dic47—22no—
329Dic47—41no—
330Dic47—41no—
331Dic47—41no—
332Dic47—41no—
333C22×#117—471no—
334C2×#433—472no—
335#1818—472no—
336#1798—472no—
337#1797—471no—
338#1797—471no—
339#1779—471no—
340#1779D4711yescharacteristic
341#1750—472no—
342#1749—471no—
343C4×C22⋊C8—471no—
344C2×C47—24no—
345C2×C47—42no—
346C2×C47—42no—
347C2×C47#228011yescharacteristic
348C2×C47#288011yescharacteristic
349C2×C47#288011yescharacteristic
350C2×C47C2×#43311yescharacteristic
351C2×C47#292111yescharacteristic
352C2×C47#292411yescharacteristic
353C2×C47#292411yescharacteristic
354C24×C4C2×D4711yescharacteristic
355C2×#117—471no—
356C2×#117—471no—
357C2×#117—471no—
358C2×#117—471no—
359C2×#117—471no—
360C2×#117—471no—
361C2×#117—471no—
362C2×#117—471no—
363C2×#117—948no—
364C22×C4⋊C4—471no—
365C22×C4⋊C4—471no—
366C22×C22⋊C4—471no—
367C22×C22⋊C4—471no—
368C22×C42—471no—
369C22×C42—471no—
370#433—948no—
371C2×C4⋊C8—472no—
372C2×C4⋊C8—472no—
373C2×C22⋊C8—471no—
374C2×C22⋊C8—471no—
375C2×C22⋊C8—472no—
376C2×C22⋊C8—472no—
377C2×C22⋊C8C2×D4711yescharacteristic
378C2×C22⋊C8C2×D4711yescharacteristic
379C2×C22⋊C8C2×D4712yes—
380C2×C22⋊C8C2×D4712yes—
381C2×#97—472no—
382C2×C4×C8—472no—
383#336—472no—
384#336—472no—
385#336—472no—
386#336—472no—
387C47#2071611yescharacteristic, complemented, Sylow
388C25C4×D4711yescharacteristic
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—471no—
394C23×C4—471no—
395C23×C4—471no—
396C23×C4—471no—
397C23×C4C4×D4711yescharacteristic
398C23×C4C4×D4711yescharacteristic
399C23×C4C4×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C23×C4C22×D4711yescharacteristic
402C23×C4C22×D4711yescharacteristic
403C22×C8—472no—
404C22×C8—472no—
405C22×C8C22×D4712yes—
406C22×C8C22×D4712yes—
407#117—478no—
408#117—944no—
409#117—944no—
410#117—944no—
411#117—944no—
412#117—944no—
413#117—944no—
414#117—944no—
415C2×C4⋊C4—471no—
416C2×C4⋊C4—471no—
417C2×C4⋊C4—471no—
418C2×C4⋊C4—471no—
419C2×C4⋊C4—471no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—944no—
424C2×C4⋊C4—944no—
425C2×C22⋊C4—471no—
426C2×C22⋊C4—471no—
427C2×C22⋊C4—471no—
428C2×C22⋊C4—471no—
429C2×C22⋊C4—471no—
430C2×C22⋊C4—471no—
431C2×C22⋊C4—471no—
432C2×C22⋊C4—471no—
433C2×C22⋊C4—944no—
434C2×C22⋊C4—944no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—471no—
438C2×C42—471no—
439C2×C42—471no—
440C2×C42—471no—
441C2×C42—471no—
442C2×C42—471no—
443C2×C42—944no—
444C2×C42—944no—
445C4⋊C8—944no—
446C4⋊C8—944no—
447C22⋊C8—24no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—24no—
451C22⋊C8—944no—
452C22⋊C8—942no—
453C22⋊C8—942no—
454C22⋊C8—944no—
455#97—944no—
456C4×C8—944no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24C2×C4×D4711yescharacteristic
465C24C2×C4×D4711yescharacteristic
466C24C2×C4×D4711yescharacteristic
467C22×C4—216no—
468C22×C4—216no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—471no—
487C22×C4—471no—
488C22×C4—471no—
489C22×C4—471no—
490C22×C4—471no—
491C22×C4—471no—
492C22×C4—471no—
493C22×C4—471no—
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—1881no—
503C22×C4—1881no—
504C22×C4—1881no—
505C22×C4—1881no—
506C22×C4C2×C4×D4711yescharacteristic
507C22×C4C2×C4×D4711yescharacteristic
508C22×C4C2×C4×D4711yescharacteristic
509C22×C4D4×D4714yes—
510C22×C4#1062535214yes—
511C22×C4#1062535212yes—
512C22×C4#1062535212yes—
513C22×C4C23×D4711yescharacteristic
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—942no—
521C2×C8—942no—
522C2×C8—942no—
523C2×C8—942no—
524C2×C8—942no—
525C2×C8—942no—
526C4⋊C4—474no—
527C4⋊C4—474no—
528C4⋊C4—942no—
529C4⋊C4—942no—
530C4⋊C4—942no—
531C4⋊C4—942no—
532C4⋊C4—942no—
533C4⋊C4—942no—
534C22⋊C4—474no—
535C22⋊C4—474no—
536C22⋊C4—942no—
537C22⋊C4—942no—
538C22⋊C4—942no—
539C22⋊C4—942no—
540C22⋊C4—942no—
541C22⋊C4—942no—
542C42—474no—
543C42—474no—
544C42—942no—
545C42—942no—
546C42—942no—
547C42—942no—
548C42—942no—
549C42—942no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—28no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23C22⋊C4×D4712yes—
574C23#1309398012yes—
575C23#1309398012yes—
576C23#1309403012yes—
577C23#1309403212yes—
578C23C22×C4×D4711yescharacteristic
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—472no—
595C2×C4—472no—
596C2×C4—472no—
597C2×C4—472no—
598C2×C4—941no—
599C2×C4—941no—
600C2×C4—941no—
601C2×C4—941no—
602C2×C4—941no—
603C2×C4—941no—
604C2×C4—941no—
605C2×C4—941no—
606C2×C4—941no—
607C2×C4—941no—
608C2×C4—941no—
609C2×C4—941no—
610C2×C4—941no—
611C2×C4—941no—
612C2×C4—941no—
613C2×C4—941no—
614C2×C4—941no—
615C2×C4—941no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—1884no—
619C2×C4—1884no—
620C2×C4—1884no—
621C2×C4—1884no—
622C2×C4C22⋊C4×D4712yes—
623C2×C4#1309398012yes—
624C2×C4#1309398012yes—
625C2×C4C2×D4×D4712yes—
626C2×C4C2×#1062535211yescharacteristic
627C2×C4C2×#1062535211yescharacteristic
628C2×C4C2×#1062535212yes—
629C8—42no—
630C8—42no—
631C8—1882no—
632C8—1882no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—416no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22#1568918114yescomplemented
655C22C2×C22⋊C4×D4711yescharacteristic
656C22C2×#1309398011yescharacteristic
657C22C2×#1309398011yescharacteristic
658C22C2×#1309403011yescharacteristic
659C22C2×#1309403211yescharacteristic
660C22#1568988911yescharacteristic
661C22#1568988911yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—942no—
666C4—942no—
667C4—942no—
668C4—942no—
669C4—1881no—
670C4—1881no—
671C4—1881no—
672C4—1881no—
673C4#1568962912yes—
674C4#1568962912yes—
675C2—24no—
676C2—42no—
677C2—42no—
678C2#2024576611yescharacteristic
679C2#2025183411yescharacteristic
680C2#2025183811yescharacteristic
681C2C2×#1568918111yescharacteristic
682C2#2025202311yescharacteristic
683C2#2025204211yescharacteristic
684C2#2025204811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1779C2
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenter#1779D47
hypocenterC47#20716
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#15689181C2semidirect
3. #20243457C2semidirect
4. #20243370C2semidirect
5. #20243366C2semidirect
6. #20243366C2semidirect
8. #20243156C2semidirect
9. #20243152C2semidirect
10. C22⋊C8×Dic47C2semidirect
28. C2×Dic47⋊C8C22semidirect
29. C2×Dic47⋊C8C22semidirect
34. C2×#13093934C22semidirect
35. C2×C8×Dic47C22semidirect
36. #15688877C22semidirect
37. #15688877C22semidirect
38. #15688877C22semidirect
39. #15688877C22semidirect
312. C22×C47#433semidirect
387. C47#20716semidirect
654. C22#15689181semidirect

Maximal subgroups

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

subgroupindex
C22×#130939832
C2×#156891812
#202434572
#202433702
#202433662
#202432982
#202431562
#202431522
C22⋊C8×Dic472
C47×#17792
#2071647