Finite Group Databasebeta

← #26139507

Subgroups — #26139507

Order 12032.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689021C211yesmaximal, characteristic
2C2×#15689019C211yesmaximal, characteristic
3C2×#15689019C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic
5#20241643C212yesmaximal
6#20241639C212yesmaximal
7#20241623C212yesmaximal
8#20241617C211yesmaximal, characteristic
9Dic47⋊#95C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C47×#382C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2212yes—
16C22×Dic47⋊C4C2212yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20#15689021C418yescomplemented
21#15689019—24no—
22#15689019—24no—
23C4⋊C4×Dic47—24no—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C47×#382—24no—
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47C2×C414yes—
49C2×C4⋊Dic47C2×C414yes—
50C2×C4⋊Dic47D414yes—
51C2×C4⋊Dic47Q814yes—
52C2×Dic47⋊C4—24no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—24no—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—42no—
57C2×Dic47⋊C4—42no—
58C2×Dic47⋊C4—42no—
59C2×Dic47⋊C4—42no—
60C2×Dic47⋊C4C2×C418yes—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—22no—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—24no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—42no—
69C2×C4×Dic47Q814yes—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—22no—
74C47⋊#95—22no—
75C47⋊#95—22no—
76C47⋊#95—24no—
77C47⋊#95—22no—
78C47⋊#95—42no—
79C47⋊#95C2×C418yes—
80C23×C4×C47C2312yes—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2312yes—
84C23×C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47D414yes—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47C2×C414yes—
94#95×C47—24no—
95#95×C47—24no—
96C24×C47C2411yescharacteristic
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—22no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C22×C412yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C2×D414yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×Q812yes—
129C22×C4×C47C2×Q812yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—21no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—22no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—21no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47C22×C414yes—
165C22×Dic47C22×C414yes—
166C22×Dic47C2×D414yes—
167C22×Dic47C2×Q812yes—
168C22×Dic47C2×Q814yes—
169C22×Dic47C2×Q812yes—
170C22×Dic47#4112yes—
171C22×Dic47#4112yes—
172C22×Dic47#4112yes—
173C22×Dic47#4112yes—
174C4⋊C4×C47—28no—
175C4⋊C4×C47—44no—
176C42×C47—28no—
177C4⋊Dic47—28no—
178C4⋊Dic47C4⋊C4116yescomplemented
179Dic47⋊C4—48no—
180Dic47⋊C4—48no—
181Dic47⋊C4—48no—
182C4×Dic47—28no—
183C4×Dic47—48no—
184C4×Dic47—44no—
185C23×C47C23×C411yescharacteristic
186C23×C47C22×D411yescharacteristic
187C23×C47C22×D411yescharacteristic
188C23×C47C22×Q811yescharacteristic
189C23×C47C22×Q811yescharacteristic
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4111yescharacteristic
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47C2×#4111yescharacteristic
195C23×C47C2×#4111yescharacteristic
196C23×C47H(5,𝔽2)11yescharacteristic
197C23×C47H(5,𝔽2)11yescharacteristic
198C23×C472−1+411yescharacteristic
199C23×C472−1+411yescharacteristic
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—42no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47C2×C4⋊C414yes—
229C2×C4×C47C4×D414yes—
230C2×C4×C47C4×Q814yes—
231C2×C4×C47#12114yes—
232C2×C4×C47C22⋊Q814yes—
233C2×C4×C47#12514yes—
234C2×C4×C47C4⋊Q814yes—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—42no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—41no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47C2×C4⋊C418yes—
276C2×Dic47#12514yes—
277#14006—471nomaximal, Sylow
278C22×C47C22×C4⋊C411yescharacteristic
279C22×C47C2×C4×D411yescharacteristic
280C22×C47C2×C4×Q811yescharacteristic
281C22×C47C4×#4111yescharacteristic
282C22×C47C4×#4111yescharacteristic
283C22×C47#51811yescharacteristic
284C22×C47#51911yescharacteristic
285C22×C47C2×#12111yescharacteristic
286C22×C47C2×C22⋊Q811yescharacteristic
287C22×C47C2×#12511yescharacteristic
288C22×C47C2×#12511yescharacteristic
289C22×C47#52911yescharacteristic
290C22×C47#52911yescharacteristic
291C22×C47C2×C4⋊Q811yescharacteristic
292C22×C47#53311yescharacteristic
293C22×C47#54211yescharacteristic
294C22×C47#54211yescharacteristic
295C22×C47#54411yescharacteristic
296C22×C47#54411yescharacteristic
297C22×C47#54611yescharacteristic
298C22×C47#54611yescharacteristic
299C22×C47#54611yescharacteristic
300C22×C47#54711yescharacteristic
301C22×C47#54811yescharacteristic
302C22×C47#54811yescharacteristic
303C22×C47#54811yescharacteristic
304C22×C47#55011yescharacteristic
305C22×C47#55211yescharacteristic
306C22×C47#55311yescharacteristic
307C22×C47#55411yescharacteristic
308C22×C47#55411yescharacteristic
309C22×C47#55511yescharacteristic
310C22×C47#55611yescharacteristic
311C22×C47#55711yescharacteristic
312C22×C47#55711yescharacteristic
313C4×C47—42no—
314C4×C47—42no—
315C4×C47—44no—
316C4×C47—82no—
317C4×C47#38918yes—
318Dic47—28no—
319Dic47—24no—
320Dic47—44no—
321Dic47—42no—
322Dic47—42no—
323Dic47—42no—
324C2×#389—471no—
325C2×#389—471no—
326C2×#389—471no—
327C2×#382D4711yescharacteristic
328C2×C4×C4⋊C4—471no—
329#1442—472no—
330#1441—472no—
331#1436—472no—
332C4⋊#95—472no—
333C4⋊#95—471no—
334C4×#95—471no—
335C2×C47C2×#38911yescharacteristic
336C2×C47C4×#12511yescharacteristic
337C2×C47#233111yescharacteristic
338C2×C47#234911yescharacteristic
339C2×C47#235111yescharacteristic
340C2×C47#236211yescharacteristic
341C2×C47#236311yescharacteristic
342C2×C47#242611yescharacteristic
343C2×C47#242711yescharacteristic
344C2×C47#243911yescharacteristic
345C2×C47#244211yescharacteristic
346C2×C47#250811yescharacteristic
347C2×C47#250911yescharacteristic
348C2×C47#255011yescharacteristic
349C2×C47#255211yescharacteristic
350C22×C4⋊C4—471no—
351C22×C4⋊C4—471no—
352C22×C4⋊C4—472no—
353C22×C4⋊C4—472no—
354C22×C4⋊C4—472no—
355C22×C4⋊C4C2×D4711yescharacteristic
356C22×C4⋊C4C2×D4711yescharacteristic
357C22×C42—471no—
358C22×C42—471no—
359C22×C42—472no—
360C22×C42C2×D4711yescharacteristic
361#389—478no—
362#389—944no—
363#389—944no—
364#382—24no—
365C4×C4⋊C4—944no—
366C2×#95—472no—
367C2×#95—471no—
368C2×#95—471no—
369C2×#95—471no—
370C2×#95—471no—
371C2×#95—472no—
372C2×#95—472no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95—472no—
376C2×#95C2×D4712yes—
377C2×#95C2×D4712yes—
378C47#1400611yescharacteristic, complemented, Sylow
379C23×C4—472no—
380C23×C4—471no—
381C23×C4—472no—
382C23×C4—471no—
383C23×C4—471no—
384C23×C4—471no—
385C23×C4C22×D4712yes—
386C23×C4C22×D4711yescharacteristic
387C23×C4C22×D4711yescharacteristic
388C23×C4C22×D4712yes—
389C23×C4C22×D4711yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—474no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—474no—
399C2×C4⋊C4—478no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—944no—
403C2×C4⋊C4—944no—
404C2×C4⋊C4—944no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—1882no—
407C2×C4⋊C4—1882no—
408C2×C4⋊C4—1882no—
409C2×C4⋊C4—1882no—
410C2×C4⋊C4C22⋊D4714yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—474no—
414C2×C42—942no—
415C2×C42—942no—
416C2×C42—944no—
417C2×C42—944no—
418C2×C42—942no—
419C2×C42—942no—
420C2×C42—942no—
421C2×C42—1882no—
422C2×C42C4×D4714yes—
423#95—24no—
424#95—24no—
425#95—478no—
426#95—942no—
427#95—942no—
428#95—942no—
429#95—942no—
430#95—944no—
431#95—944no—
432#95—944no—
433#95—944no—
434#95—1882no—
435C24C23×D4711yescharacteristic
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—474no—
462C22×C4—474no—
463C22×C4—472no—
464C22×C4—474no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—474no—
468C22×C4—472no—
469C22×C4—472no—
470C22×C4—472no—
471C22×C4—941no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—942no—
484C22×C4—941no—
485C22×C4—942no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—942no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—942no—
495C22×C4—941no—
496C22×C4—942no—
497C22×C4—941no—
498C22×C4—941no—
499C22×C4—942no—
500C22×C4—941no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4C2×C4×D4712yes—
504C22×C4C2×C4×D4712yes—
505C22×C4C2×C4×D4712yes—
506C22×C4#1062535012yes—
507C22×C4D4×D4712yes—
508C22×C4#1062535212yes—
509C22×C4Q8×D4712yes—
510C22×C4Q8×D4712yes—
511C22×C4C2×C22⋊D4714yes—
512C22×C4C2×C22⋊D4712yes—
513C4⋊C4—28no—
514C4⋊C4—44no—
515C4⋊C4—4716no—
516C4⋊C4—948no—
517C4⋊C4—1888no—
518C4⋊C4—1888no—
519C4⋊C4—1888no—
520C42—28no—
521C42—948no—
522C42—1888no—
523C42—1884no—
524C23C22×C4×D4711yescharacteristic
525C23C2×D4×D4711yescharacteristic
526C23C22×C22⋊D4711yescharacteristic
527C23C2×Q8×D4711yescharacteristic
528C23C2×Q8×D4711yescharacteristic
529C23#41×D4711yescharacteristic
530C23#41×D4711yescharacteristic
531C23#41×D4711yescharacteristic
532C23#41×D4711yescharacteristic
533C23C2×#1062535211yescharacteristic
534C23C2×#1062535011yescharacteristic
535C23#1309407011yescharacteristic
536C23#1309407011yescharacteristic
537C23#1309407111yescharacteristic
538C23#1309407111yescharacteristic
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—478no—
568C2×C4—474no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—944no—
577C2×C4—944no—
578C2×C4—944no—
579C2×C4—944no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—944no—
587C2×C4—944no—
588C2×C4—944no—
589C2×C4—942no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1882no—
596C2×C4—1881no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1882no—
602C2×C4—1881no—
603C2×C4—1882no—
604C2×C4—1881no—
605C2×C4—1882no—
606C2×C4—1881no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4C4⋊C4×D4714yes—
610C2×C4C4×C22⋊D4714yes—
611C2×C4#1309398914yes—
612C2×C4#1309399614yes—
613C2×C4#1309400214yes—
614C2×C4#1309401414yes—
615C2×C4#1309402214yes—
616C22C2×C4⋊C4×D4711yescharacteristic
617C22C2×C4×C22⋊D4711yescharacteristic
618C22C2×#1309398911yescharacteristic
619C22#1568959111yescharacteristic
620C22#1568959111yescharacteristic
621C22#1568959711yescharacteristic
622C22#1568960011yescharacteristic
623C22C2×#1309399611yescharacteristic
624C22C2×#1309400211yescharacteristic
625C22#125×D4711yescharacteristic
626C22C2×#1309401411yescharacteristic
627C22#1568965211yescharacteristic
628C22#1568965211yescharacteristic
629C22C2×#1309402211yescharacteristic
630C22#1568967911yescharacteristic
631C22#1568974211yescharacteristic
632C22#1568974211yescharacteristic
633C22#1568975311yescharacteristic
634C22#1568975311yescharacteristic
635C22#1568976111yescharacteristic
636C22#1568976611yescharacteristic
637C22#1568976611yescharacteristic
638C22#1568977211yescharacteristic
639C22#1568978011yescharacteristic
640C22#1568978111yescharacteristic
641C22#1568978111yescharacteristic
642C22#1568979211yescharacteristic
643C22#1568981211yescharacteristic
644C22#1568981711yescharacteristic
645C22#1568982911yescharacteristic
646C22#1568982911yescharacteristic
647C22#1568983611yescharacteristic
648C22#1568984111yescharacteristic
649C22#1568985011yescharacteristic
650C22#1568985011yescharacteristic
651C4—42no—
652C4—42no—
653C4—44no—
654C4—82no—
655C4—948no—
656C4—944no—
657C4—1882no—
658C4—1884no—
659C4—1882no—
660C4—1882no—
661C4#1568901818yes—
662C2C2×#1568901811yescharacteristic
663C2#2024594311yescharacteristic
664C2#2024613411yescharacteristic
665C2#2024629611yescharacteristic
666C2#2024630511yescharacteristic
667C2#2024641511yescharacteristic
668C2#2024642611yescharacteristic
669C2#2024695711yescharacteristic
670C2#2024696811yescharacteristic
671C2#2024708211yescharacteristic
672C2#2024711511yescharacteristic
673C2#2024792211yescharacteristic
674C2#2024793311yescharacteristic
675C2#2024840711yescharacteristic
676C2#2024842011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#382C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#382D47
hypocenterC47#14006
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
20. #15689021C4semidirect
178. C4⋊Dic47C4⋊C4semidirect
378. C47#14006semidirect

Maximal subgroups

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

subgroupindex
C2×#156890212
C2×#156890192
C2×C4⋊C4×Dic472
#202416432
#202416392
#202416232
#202416172
Dic47⋊#952
C4×C47⋊#952
C2×C47×#3822
#1400647