Finite Group Databasebeta

← #17056608

Subgroups — #17056608

Order 4352.

1034 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763024C211yesmaximal, characteristic
2C2×C4×#63229C211yesmaximal, characteristic, complemented
3C2×C4×#63228C211yesmaximal, characteristic
4#14531853C211yesmaximal, characteristic, complemented
5#14529593C211yesmaximal, characteristic, complemented
6#14529550C211yesmaximal, characteristic, complemented
7#14529466C211yesmaximal, characteristic, complemented
8#14529459C211yesmaximal, characteristic, complemented
9#14529132C211yesmaximal, characteristic
10#14529118C211yesmaximal, characteristic, complemented
11#14529044C211yesmaximal, characteristic, complemented
12#14529037C211yesmaximal, characteristic, complemented
13C4⋊C4×#3622C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C17×#2349C211yesmaximal, characteristic, complemented
16C22×#63229C2211yescharacteristic
17C22×#63228C2211yescharacteristic
18C2×#10587561C2211yescharacteristic
19C2×C4×Dic34C2211yescharacteristic
20C2×C4×D68C2211yescharacteristic
21#11763024C418yescomplemented
22C4×#63229—24no—
23C4×#63228—24no—
24C2×#10587478C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26C2×C4⋊#3622C2211yescharacteristic
27C2×#10587481C2211yescharacteristic
28C2×#10587481C2211yescharacteristic
29C2×#10587481C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587480C2211yescharacteristic
33C2×#10587480C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×C4×#3622C2211yescharacteristic
36C2×C4×#3622C2211yescharacteristic
37C2×C4×#3622C2211yescharacteristic
38#11762715C2211yescharacteristic
39#11762711C2211yescharacteristic
40#11762699—21no—
41#11762698—21no—
42#11762680—21no—
43C4×C4⋊Dic17C2211yescharacteristic
44#11762656—21no—
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762564C2211yescharacteristic
50#11762564C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C2×C4×D4×C17C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C17×#389C2211yescharacteristic
55C17×#389C2211yescharacteristic
56C17×#385—21no—
57C17×#385—21no—
58C17×#382C2211yescharacteristic
59C17×#380—21no—
60C4×C4⋊C4×C17C2211yescharacteristic
61C2×C17×#95—21no—
62C22×D4×C17C2311yescharacteristic
63C23×C4×C17—21no—
64C23×C4×C17—21no—
65C23×C4×C17—21no—
66C22×D68C2311yescharacteristic
67C22×C4×D17—21no—
68C22×Dic34C2311yescharacteristic
69C4×D4×C17—22no—
70C4×D4×C17—22no—
71C4×D4×C17—22no—
72C4×D4×C17—41no—
73C4×D4×C17—41no—
74C4×D4×C17C2×C414yescomplemented
75C2×C4⋊C4×C17—21no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17D411yescharacteristic
78C2×C4⋊C4×C17D411yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C42×C17C2311yescharacteristic
86C2×C42×C17C2311yescharacteristic
87C2×C42×C17C2311yescharacteristic
88C2×#63229—22no—
89C2×#63229—22no—
90C2×#63229C2×C414yescomplemented
91C2×#63228—22no—
92C2×#63228—22no—
93C2×#63228C2×C414yes—
94C2×#63227—21no—
95C2×#63227—21no—
96C2×#63227—21no—
97C2×#63227—21no—
98C2×#63227—21no—
99C2×C4⋊Dic17C2311yescharacteristic
100C2×C4⋊Dic17C2311yescharacteristic
101C2×#63225—21no—
102C2×C4×Dic17—21no—
103C2×C4×Dic17—21no—
104C22×#3622C2311yescharacteristic
105C22×#3622C2311yescharacteristic
106C22×#3622C2311yescharacteristic
107C22×#3622C2311yescharacteristic
108#10587561—22no—
109#10587561C2×C414yescomplemented
110C4×D68—22no—
111C4×D68—41no—
112C4×Dic34—22no—
113C4×Dic34—41no—
114C17×#95—21no—
115C17×#95—21no—
116C17×#95—21no—
117C17×#95—21no—
118C17×#95D411yescharacteristic
119C17×#95D411yescharacteristic
120#10587503—22no—
121#10587503D414yes—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587481—22no—
126#10587481—41no—
127#10587481C2×C414yescomplemented
128#10587480—22no—
129#10587480—41no—
130#10587480C2×C414yescomplemented
131#10587479—22no—
132#10587478—22no—
133C4⋊#3622C2×C414yescomplemented
134C4×#3622—22no—
135C4×#3622—22no—
136C4×#3622—22no—
137C24×C17—21no—
138C23×D17—21no—
139C2×D4×C17—21no—
140C2×D4×C17—21no—
141C2×D4×C17—21no—
142C2×D4×C17C22×C412yes—
143C2×D4×C17C2×D412yes—
144C2×D4×C17#4112yes—
145C22×C4×C17—21no—
146C22×C4×C17—24no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—42no—
150C22×C4×C17—42no—
151C22×C4×C17—42no—
152C22×C4×C17—42no—
153C22×C4×C17—81no—
154C22×C4×C17—81no—
155C22×C4×C17—81no—
156C22×C4×C17—81no—
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2411yescharacteristic
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C2×D68—21no—
168C2×D68—21no—
169C2×D68—21no—
170C2×D68—21no—
171C2×D68—21no—
172C2×D68C22×C412yes—
173C2×C4×D17—42no—
174C2×C4×D17—42no—
175C2×C4×D17—81no—
176C2×Dic34—21no—
177C2×Dic34—21no—
178C2×Dic34—21no—
179C2×Dic34—21no—
180C2×Dic34—21no—
181C2×Dic34C22×C412yes—
182C4⋊C4×C17—22no—
183C4⋊C4×C17—22no—
184C4⋊C4×C17—21no—
185C4⋊C4×C17—21no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17—21no—
188C4⋊C4×C17—21no—
189C4⋊C4×C17—81no—
190C4⋊C4×C17—81no—
191C4⋊C4×C17C22×C412yes—
192C22⋊C4×C17—24no—
193C22⋊C4×C17—42no—
194C22⋊C4×C17—42no—
195C42×C17—21no—
196C42×C17—21no—
197C42×C17—21no—
198C42×C17—21no—
199C42×C17C22×C412yes—
200C42×C17#4112yes—
201#63229—28no—
202#63228—28no—
203#63227—24no—
204#63227—24no—
205#63227—42no—
206#63227—42no—
207#63227—81no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17C2×D412yes—
212#63225—42no—
213C4×Dic17—42no—
214C4×Dic17—81no—
215C2×#3622—21no—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622C22×C412yes—
225C2×#3622C22×C412yes—
226C2×#3622C2×D412yes—
227#22999—171nomaximal, Sylow
228C23×C17—22no—
229C23×C17—22no—
230C23×C17—22no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17C22×D411yescharacteristic
236C22×D17—22no—
237C22×D17—41no—
238C22×D17—41no—
239C22×D17—41no—
240C22×D17—41no—
241C22×D17—41no—
242C22×D17—41no—
243D4×C17—22no—
244D4×C17—22no—
245D4×C17—22no—
246D4×C17C4×D414yes—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—21no—
253C2×C4×C17—21no—
254C2×C4×C17—21no—
255C2×C4×C17—22no—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—41no—
270C2×C4×C17—84no—
271C2×C4×C17—84no—
272C2×C4×C17—84no—
273C2×C4×C17C4×D412yes—
274C2×C4×C17C4×D412yes—
275C2×C4×C17#13512yes—
276C2×C4×C17#13512yes—
277C2×C4×C17C23×C411yescharacteristic
278C2×C4×C17C22×D411yescharacteristic
279C2×C4×C17C2×#4111yescharacteristic
280C2×C4×C17C2×#4111yescharacteristic
281C2×C4×C17H(5,𝔽2)11yescharacteristic
282C2×C4×C172−1+411yescharacteristic
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—41no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292D68—22no—
293D68—22no—
294D68—41no—
295D68—41no—
296C4×D17—84no—
297Dic34—22no—
298Dic34—22no—
299Dic34—41no—
300Dic34—41no—
301#3622—22no—
302#3622—22no—
303#3622—22no—
304#3622—41no—
305C2×#463—171no—
306C2×C4×SD16—171no—
307C2×C4×D8—171no—
308#2367—171no—
309#2349D1711yescharacteristic, complemented
310#1958—171no—
311#1949—171no—
312#1934—171no—
313#1933—171no—
314#1879—171no—
315#1877—171no—
316#1864—171no—
317#1863—171no—
318C8×C4⋊C4—171no—
319C4×#102—171no—
320C22×C17—24no—
321C22×C17—42no—
322C22×C17—42no—
323C22×C17—42no—
324C22×C17—42no—
325C22×C17—42no—
326C22×C17—42no—
327C22×C17C2×C4×D411yescharacteristic
328C22×C17D4211yescharacteristic
329C22×C17#54811yescharacteristic
330C22×C17C2×#13511yescharacteristic
331C22×C17C2×#13511yescharacteristic
332C22×C17#57611yescharacteristic
333C22×C17#57711yescharacteristic
334C2×D17—42no—
335C2×D17—42no—
336C2×D17—42no—
337C2×D17—81no—
338C2×D17—81no—
339C2×D17—81no—
340C2×D17—81no—
341C4×C17—22no—
342C4×C17—22no—
343C4×C17—22no—
344C4×C17—22no—
345C4×C17—42no—
346C4×C17—41no—
347C4×C17—41no—
348C4×C17—81no—
349C4×C17—81no—
350C4×C17C2×C4×D411yescharacteristic
351C4×C17#52011yescharacteristic
352C4×C17#54711yescharacteristic
353C4×C17#55311yescharacteristic
354Dic17—42no—
355Dic17—42no—
356Dic17—81no—
357C22×SD16—171no—
358C22×D8—171no—
359C2×#124—171no—
360C2×C4×Q8—171no—
361C2×C4×D4—171no—
362C2×C4×D4C2×D1711yescharacteristic
363C2×C4×D4C2×D1711yescharacteristic
364C2×C4×D4C2×D1711yescharacteristic
365#463—178no—
366C4×SD16—344no—
367C4×D8—344no—
368C2×#107—171no—
369C2×#106—171no—
370C2×C4⋊C8—171no—
371C2×#103—171no—
372C2×#103—171no—
373C2×#103—171no—
374C2×#102—171no—
375C2×#102—171no—
376C2×#102—171no—
377C2×#102—171no—
378C2×#102—171no—
379C2×C4×C8—171no—
380C2×C4×C8—171no—
381C2×C4×C8—171no—
382#391—171no—
383#390—171no—
384#389C2×D1711yescharacteristic
385#389C2×D1711yescharacteristic
386#388—341no—
387#388—341no—
388#385—21no—
389#385—21no—
390#385—341no—
391#382C2×D1711yescharacteristic
392#380—21no—
393C4×C4⋊C4—171no—
394C4×C4⋊C4C2×D1711yescharacteristic
395C4×C22⋊C4—341no—
396C2×#95—21no—
397#340—171no—
398#340—171no—
399#340—171no—
400#340—171no—
401#336—171no—
402#336—171no—
403C2×C17—44no—
404C2×C17#236111yescharacteristic
405C2×C17C4×#13511yescharacteristic
406C2×C17#294611yescharacteristic
407C2×C17#328011yescharacteristic
408C2×C17#328211yescharacteristic
409C2×C17#336011yescharacteristic
410C2×C17#336111yescharacteristic
411D17—82no—
412C22×Q8—171no—
413C22×D4—171no—
414C22×D4C22×D1711yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—341no—
419C2×SD16—174no—
420C2×SD16—342no—
421C2×SD16—342no—
422C2×D8—174no—
423C2×D8—342no—
424C2×D8—342no—
425C22×C8—171no—
426C22×C8—171no—
427C22×C8—171no—
428C22×C8—171no—
429#124—174no—
430#124—342no—
431C4×Q8—342no—
432C4×Q8—681no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—342no—
439C4×D4—681no—
440C4×D4C4×D1714yescomplemented
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—171no—
444C2×C4⋊C4—171no—
445C2×C4⋊C4—341no—
446C2×C4⋊C4C22⋊D1711yescharacteristic
447C2×C4⋊C4C22⋊D1711yescharacteristic
448C2×C4⋊C4C22×D1711yescharacteristic
449C2×C4⋊C4C22×D1711yescharacteristic
450C2×C4⋊C4C22×D1711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—341no—
455C2×C22⋊C4—341no—
456C2×C22⋊C4—341no—
457C2×C22⋊C4—341no—
458C2×C22⋊C4—341no—
459C2×C42—341no—
460C2×C42—341no—
461C2×C42C22×D1711yescharacteristic
462C2×C42C22×D1711yescharacteristic
463C2×C42C22×D1711yescharacteristic
464#107—342no—
465#106—342no—
466C4⋊C8—174no—
467#103—174no—
468#103—342no—
469#103—681no—
470#102—174no—
471#102—174no—
472#102—342no—
473#102—342no—
474#102—681no—
475C4×C8—342no—
476C4×C8—342no—
477C4×C8—342no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—341no—
483#95—341no—
484#95—341no—
485#95C22⋊D1711yescharacteristic
486#95C22⋊D1711yescharacteristic
487C17#2299911yescharacteristic, complemented, Sylow
488C24—21no—
489C24—341no—
490C2×Q8—172no—
491C2×Q8—341no—
492C2×Q8—341no—
493C2×Q8—341no—
494C2×Q8—341no—
495C2×Q8—341no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—172no—
500C2×D4—341no—
501C2×D4—341no—
502C2×D4—341no—
503C2×D4—341no—
504C2×D4—341no—
505C2×D4C2×C4×D1712yes—
506C2×D4D4×D1712yes—
507C2×D4#6325612yes—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—341no—
521C22×C4—341no—
522C22×C4—341no—
523C22×C4—682no—
524C22×C4—682no—
525C22×C4—1361no—
526C22×C4C2×C22⋊D1711yescharacteristic
527C22×C4C2×C22⋊D1711yescharacteristic
528C22×C4C2×C22⋊D1711yescharacteristic
529C22×C4C2×C22⋊D1711yescharacteristic
530C22×C4C2×C22⋊D1711yescharacteristic
531C22×C4C2×C22⋊D1711yescharacteristic
532C22×C4C23×D1711yescharacteristic
533SD16—348no—
534D8—348no—
535C2×C8—172no—
536C2×C8—172no—
537C2×C8—172no—
538C2×C8—341no—
539C2×C8—341no—
540C2×C8—341no—
541C2×C8—341no—
542C2×C8—341no—
543C2×C8—341no—
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C4⋊C4—21no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—172no—
557C4⋊C4—341no—
558C4⋊C4—341no—
559C4⋊C4—341no—
560C4⋊C4—682no—
561C4⋊C4C2×C4×D1712yes—
562C22⋊C4—24no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—344no—
566C22⋊C4—344no—
567C22⋊C4—682no—
568C22⋊C4—682no—
569C22⋊C4—1361no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—682no—
575C42—1361no—
576C42C2×C4×D1712yes—
577C42#6325212yes—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—342no—
586C23—681no—
587C23—681no—
588C23—681no—
589C23—681no—
590C23—681no—
591C23—681no—
592C23C22×C22⋊D1711yescharacteristic
593Q8—342no—
594Q8—342no—
595Q8—681no—
596Q8—681no—
597D4—22no—
598D4—22no—
599D4—22no—
600D4—342no—
601D4—342no—
602D4—681no—
603D4—681no—
604D4#1058757914yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4—342no—
632C2×C4—342no—
633C2×C4—681no—
634C2×C4—681no—
635C2×C4—681no—
636C2×C4—681no—
637C2×C4—681no—
638C2×C4—681no—
639C2×C4—681no—
640C2×C4—1364no—
641C2×C4C4×C22⋊D1712yes—
642C2×C4C4×C22⋊D1712yes—
643C2×C4#1058763612yes—
644C2×C4#1058763612yes—
645C2×C4C22×C4×D1711yescharacteristic
646C2×C4C2×#6325211yescharacteristic
647C2×C4C2×D4×D1711yescharacteristic
648C2×C4#1058769111yescharacteristic
649C2×C4C2×#6325611yescharacteristic
650C2×C4#1058769411yescharacteristic
651C8—342no—
652C8—342no—
653C8—342no—
654C8—681no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—682no—
663C22—682no—
664C22—682no—
665C22—1361no—
666C22—1361no—
667C22—1361no—
668C22—1361no—
669C22C2×C4×C22⋊D1711yescharacteristic
670C22D4×C22⋊D1711yescharacteristic
671C22#1176347011yescharacteristic
672C22C2×#1058763611yescharacteristic
673C22C2×#1058763611yescharacteristic
674C22#1176361211yescharacteristic
675C22#1176362011yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—682no—
686C4—682no—
687C4—1361no—
688C4C2×#1058757911yescharacteristic
689C4#1176329011yescharacteristic
690C4#1176346011yescharacteristic
691C4#1176350711yescharacteristic
692C2—44no—
693C2—1362no—
694C2#1453180011yescharacteristic
695C2C4×#1058763611yescharacteristic
696C2#1453761611yescharacteristic
697C2#1454046511yescharacteristic
698C2#1454048711yescharacteristic
699C2#1454143311yescharacteristic
700C2#1454144411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2349C2
socleC23×C17C22×D4
prime radicalC22×#63228C22
cosocleC22×C4×C17C24
hypercenter#2349D17
hypocenterC17#22999
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63229C2semidirect
4. #14531853C2semidirect
5. #14529593C2semidirect
6. #14529550C2semidirect
7. #14529466C2semidirect
8. #14529459C2semidirect
10. #14529118C2semidirect
11. #14529044C2semidirect
12. #14529037C2semidirect
13. C4⋊C4×#3622C2semidirect
14. C4×#10587503C2semidirect
15. C17×#2349C2semidirect
21. #11763024C4semidirect
74. C4×D4×C17C2×C4semidirect
90. C2×#63229C2×C4semidirect
109. #10587561C2×C4semidirect
127. #10587481C2×C4semidirect
130. #10587480C2×C4semidirect
133. C4⋊#3622C2×C4semidirect
309. #2349D17semidirect
440. C4×D4C4×D17semidirect
487. C17#22999semidirect

Maximal subgroups

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

subgroupindex
C2×#117630242
C2×C4×#632292
C2×C4×#632282
#145318532
#145295932
#145295502
#145294662
#145294592
#145291322
#145291182
#145290442
#145290372
C4⋊C4×#36222
C4×#105875032
C17×#23492
#2299917