Finite Group Databasebeta

← #17078229

Subgroups — #17078229

Order 4352.

966 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762971C211yesmaximal, characteristic
2C2×C4×#63231C211yesmaximal, characteristic, complemented
3#14532309C211yesmaximal, characteristic, complemented
4#14530312C211yesmaximal, characteristic, complemented
5#14530210C211yesmaximal, characteristic, complemented
6#14530101C211yesmaximal, characteristic, complemented
7#14529987C211yesmaximal, characteristic, complemented
8#14529470C211yesmaximal, characteristic, complemented
9#14529392C211yesmaximal, characteristic, complemented
10#14529142C211yesmaximal, characteristic, complemented
11#14529125C211yesmaximal, characteristic, complemented
12#14529038C211yesmaximal, characteristic, complemented
13#14528789C211yesmaximal, characteristic, complemented
14#14528724C211yesmaximal, characteristic
15C17×#2341C211yesmaximal, characteristic
16C22×#63231C2211yescharacteristic
17C22×#63229C2211yescharacteristic
18C2×#10587610C2211yescharacteristic
19C2×C4×Dic34C2211yescharacteristic
20#11762971—24no—
21C4×#63231—24no—
22C2×#10587478C2211yescharacteristic
23C2×#10587478C2211yescharacteristic
24C2×C4⋊#3622C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587481C2211yescharacteristic
29C2×#10587481C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34C2×C22⋊#3622C2211yescharacteristic
35C2×C4×#3622C2211yescharacteristic
36#11762745—21no—
37#11762743—21no—
38#11762715C2211yescharacteristic
39#11762707C2211yescharacteristic
40#11762702—21no—
41#11762692—21no—
42#11762679C2211yescharacteristic
43#11762669C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762564C2211yescharacteristic
49#11762564C2211yescharacteristic
50C22×#41×C17C2211yescharacteristic
51C2×C4×Q8×C17C2211yescharacteristic
52C2×C4×Q8×C17C2211yescharacteristic
53C17×#390—21no—
54C17×#390—21no—
55C17×#390C2211yescharacteristic
56C17×#390C2211yescharacteristic
57C17×#380—21no—
58C17×#380C2211yescharacteristic
59C4×C22⋊C4×C17—21no—
60C4×C22⋊C4×C17C2211yescharacteristic
61C2×#41×C17—22no—
62C2×#41×C17—22no—
63C2×#41×C17—22no—
64C2×#41×C17—22no—
65C2×#41×C17—41no—
66C2×#41×C17—41no—
67C22×Q8×C17C2311yescharacteristic
68C22×D4×C17—21no—
69C22×D4×C17C2311yescharacteristic
70C23×C4×C17—21no—
71C23×C4×C17C2311yescharacteristic
72C22×Dic34C2311yescharacteristic
73C4×Q8×C17—22no—
74C4×Q8×C17—22no—
75C4×Q8×C17—41no—
76C4×Q8×C17—41no—
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C22⋊C4×C17—21no—
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17D411yescharacteristic
87C2×C22⋊C4×C17D411yescharacteristic
88C2×C42×C17—21no—
89C2×C42×C17—21no—
90C2×C42×C17C2311yescharacteristic
91C2×C42×C17C2311yescharacteristic
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×#63231—22no—
95C2×#63231—22no—
96C2×#63231D414yes—
97C2×#63229—22no—
98C2×#63229—22no—
99C2×#63229—41no—
100C2×C4⋊Dic17—21no—
101C2×C4⋊Dic17—21no—
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104C2×C4⋊Dic17C2311yescharacteristic
105#10587610—22no—
106#10587610—41no—
107C2×#63225—21no—
108C2×#63225—21no—
109C2×#63225—21no—
110C2×C4×Dic17—21no—
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C4×Dic34—22no—
116C4×Dic34—41no—
117C17×#95—21no—
118C17×#95D411yescharacteristic
119C17×#95D411yescharacteristic
120#10587506—22no—
121#10587506—22no—
122#10587506—22no—
123#10587503—22no—
124#10587503—22no—
125#10587503—41no—
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587502—21no—
130C22⋊#3622—22no—
131C22⋊#3622—41no—
132#10587481—22no—
133#10587481—41no—
134#10587478—22no—
135#10587478—41no—
136C4⋊#3622—41no—
137C4×#3622—22no—
138C24×C17—21no—
139C24×C17C2×D411yescharacteristic
140#41×C17—44no—
141#41×C17—44no—
142#41×C17—44no—
143#41×C17—44no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17C2×D412yes—
148C2×Q8×C17#4112yes—
149C2×Q8×C17#4112yes—
150C2×D4×C17—24no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—42no—
157C2×D4×C17—42no—
158C2×D4×C17#4112yes—
159C22×C4×C17—21no—
160C22×C4×C17—24no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—42no—
170C22×C4×C17—42no—
171C22×C4×C17C2×D411yescharacteristic
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17C2×D411yescharacteristic
174C22×C4×C17C2×D411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2411yescharacteristic
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C2×Dic34—21no—
182C2×Dic34—21no—
183C2×Dic34—21no—
184C2×Dic34—21no—
185C2×Dic34—21no—
186C2×Dic34C2×D412yes—
187C4⋊C4×C17—21no—
188C4⋊C4×C17—21no—
189C4⋊C4×C17—21no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—42no—
192C4⋊C4×C17—42no—
193C22⋊C4×C17—22no—
194C22⋊C4×C17—22no—
195C22⋊C4×C17—42no—
196C22⋊C4×C17—42no—
197C22⋊C4×C17—81no—
198C22⋊C4×C17—81no—
199C22⋊C4×C17—81no—
200C42×C17—21no—
201C42×C17—21no—
202C42×C17—21no—
203C42×C17—21no—
204C42×C17—42no—
205C42×C17—42no—
206C22⋊Dic17—42no—
207C22⋊Dic17—81no—
208#63231—28no—
209#63229—44no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—42no—
217C4⋊Dic17—81no—
218#63225—42no—
219#63225—42no—
220#63225—81no—
221C4×Dic17—42no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622C2×D412yes—
234#24904—171nomaximal, Sylow
235C23×C17—21no—
236C23×C17—22no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17C22×D411yescharacteristic
250Q8×C17—22no—
251Q8×C17—22no—
252Q8×C17—22no—
253Q8×C17#12314yes—
254D4×C17—22no—
255D4×C17—22no—
256D4×C17—48no—
257D4×C17—41no—
258D4×C17—41no—
259C2×C4×C17—22no—
260C2×C4×C17—21no—
261C2×C4×C17—22no—
262C2×C4×C17—21no—
263C2×C4×C17—22no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—48no—
276C2×C4×C17—41no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17#13512yes—
287C2×C4×C17#13712yes—
288C2×C4×C17C22×D411yescharacteristic
289C2×C4×C17C2×#4111yescharacteristic
290C2×C4×C17C2×#4111yescharacteristic
291C2×C4×C17C2×#4111yescharacteristic
292C2×C4×C17H(5,𝔽2)11yescharacteristic
293C2×C4×C17H(5,𝔽2)11yescharacteristic
294C2×Dic17—22no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306Dic34—22no—
307Dic34—22no—
308Dic34—41no—
309Dic34—41no—
310#3622—22no—
311#3622—41no—
312#3622—41no—
313#3622—41no—
314C2×#452—171no—
315C2×C4×Q16—171no—
316#2423—171no—
317#2341D1711yescharacteristic
318#2093—171no—
319#2075—171no—
320#2055—171no—
321#2036—171no—
322#1934—171no—
323#1923—171no—
324#1880—171no—
325#1878—171no—
326#1863—171no—
327#1803—171no—
328#1788—171no—
329C22×C17—41no—
330C22×C17—41no—
331C22×C17—42no—
332C22×C17—41no—
333C22×C17—42no—
334C22×C17—42no—
335C22×C17—41no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17—41no—
339C22×C17—81no—
340C22×C17—81no—
341C22×C17—81no—
342C22×C17—81no—
343C22×C17#52511yescharacteristic
344C22×C17D4211yescharacteristic
345C22×C17#54611yescharacteristic
346C22×C17C2×#13511yescharacteristic
347C22×C17C2×#13711yescharacteristic
348C22×C17#57611yescharacteristic
349C22×C17#57811yescharacteristic
350C4×C17—24no—
351C4×C17—22no—
352C4×C17—22no—
353C4×C17—41no—
354C4×C17—41no—
355C4×C17—41no—
356C4×C17—81no—
357C4×C17—81no—
358C4×C17C2×#12311yescharacteristic
359C4×C17#53811yescharacteristic
360C4×C17#54611yescharacteristic
361C4×C17#55111yescharacteristic
362Dic17—42no—
363Dic17—81no—
364Dic17—81no—
365Dic17—81no—
366C22×#41C2×D1711yescharacteristic
367C22×Q16—171no—
368C22×SD16—171no—
369C2×C22⋊Q8—171no—
370C2×C4×Q8—171no—
371C2×C4×Q8C2×D1711yescharacteristic
372C2×C4×Q8C2×D1711yescharacteristic
373#452—344no—
374C4×Q16—344no—
375C2×#107—171no—
376C2×#107—171no—
377C2×C4⋊C8—171no—
378C2×#103—171no—
379C2×#103—171no—
380C2×#103—171no—
381C2×#103—171no—
382C2×#103—171no—
383C2×#102—171no—
384C2×#102—171no—
385C2×#102—171no—
386C2×C22⋊C8—171no—
387C2×C22⋊C8—171no—
388C2×C4×C8—171no—
389#399—341no—
390#398—341no—
391#391—171no—
392#390—21no—
393#390—21no—
394#390C2×D1711yescharacteristic
395#390C2×D1711yescharacteristic
396#389—171no—
397#388—341no—
398#387—341no—
399#384—171no—
400#380—21no—
401#380—171no—
402#380C2×D1711yescharacteristic
403C4×C22⋊C4—21no—
404C4×C22⋊C4C2×D1711yescharacteristic
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#336—171no—
410#336—171no—
411C2×C17—81no—
412C2×C17—82no—
413C2×C17#241811yescharacteristic
414C2×C17#310711yescharacteristic
415C2×C17#312411yescharacteristic
416C2×C17#327011yescharacteristic
417C2×C17#328711yescharacteristic
418C2×C17#330011yescharacteristic
419C2×C17#333311yescharacteristic
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—41no—
425C2×#41—41no—
426C22×Q8—171no—
427C22×Q8C22×D1711yescharacteristic
428C22×D4—21no—
429C22×D4C22×D1711yescharacteristic
430C23×C4—21no—
431C23×C4C22×D1711yescharacteristic
432C2×Q16—174no—
433C2×Q16—342no—
434C2×Q16—342no—
435C2×SD16—342no—
436C2×SD16—342no—
437C2×SD16—681no—
438C22×C8—171no—
439C22×C8—171no—
440C22×C8—171no—
441C22×C8—171no—
442C22⋊Q8—342no—
443C22⋊Q8—681no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—41no—
447C4×Q8—41no—
448C4×Q8—342no—
449C4×Q8—681no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—171no—
453C2×C4⋊C4—171no—
454C2×C4⋊C4—171no—
455C2×C4⋊C4—341no—
456C2×C4⋊C4—341no—
457C2×C4⋊C4—341no—
458C2×C4⋊C4—341no—
459C2×C4⋊C4—341no—
460C2×C4⋊C4C22×D1711yescharacteristic
461C2×C4⋊C4C22×D1711yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—341no—
468C2×C22⋊C4—341no—
469C2×C22⋊C4C22⋊D1711yescharacteristic
470C2×C22⋊C4C22⋊D1711yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—341no—
474C2×C42C22×D1711yescharacteristic
475C2×C42C22×D1711yescharacteristic
476#107—342no—
477#107—681no—
478C4⋊C8—681no—
479#103—342no—
480#103—342no—
481#103—342no—
482#103—342no—
483#103—681no—
484#102—342no—
485#102—342no—
486#102—681no—
487C22⋊C8—342no—
488C22⋊C8—681no—
489C4×C8—342no—
490#95—21no—
491#95—341no—
492#95—341no—
493#95—341no—
494#95—341no—
495#95C22⋊D1711yescharacteristic
496#95C22⋊D1711yescharacteristic
497C17#2490411yescharacteristic, complemented, Sylow
498C24—21no—
499C24C2×C22⋊D1711yescharacteristic
500#41—44no—
501#41—44no—
502#41—44no—
503#41—44no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—172no—
508C2×Q8—341no—
509C2×Q8—341no—
510C2×Q8—341no—
511C2×Q8—341no—
512C2×Q8—341no—
513C2×Q8#6325212yes—
514C2×Q8D4×D1712yes—
515C2×Q8#6325412yes—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4#6325212yes—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—341no—
538C22×C4—341no—
539C22×C4—341no—
540C22×C4—341no—
541C22×C4C2×C22⋊D1711yescharacteristic
542C22×C4C2×C22⋊D1711yescharacteristic
543C22×C4C2×C22⋊D1711yescharacteristic
544C22×C4C2×C22⋊D1711yescharacteristic
545C22×C4C2×C22⋊D1711yescharacteristic
546C22×C4C23×D1711yescharacteristic
547Q16—348no—
548SD16—684no—
549C2×C8—172no—
550C2×C8—341no—
551C2×C8—341no—
552C2×C8—341no—
553C2×C8—341no—
554C2×C8—341no—
555C2×C8—341no—
556C2×C8—341no—
557C2×C8—341no—
558C2×C8—341no—
559C2×C8—341no—
560C2×C8—341no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—341no—
568C4⋊C4—341no—
569C4⋊C4—341no—
570C4⋊C4—341no—
571C4⋊C4—341no—
572C4⋊C4—341no—
573C4⋊C4—682no—
574C4⋊C4—682no—
575C4⋊C4—682no—
576C4⋊C4—1361no—
577C4⋊C4—1361no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—682no—
586C22⋊C4—1361no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—42no—
593C42—682no—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C22×C22⋊D1711yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—342no—
613Q8—342no—
614Q8—681no—
615Q8—681no—
616Q8#1058756914yes—
617D4—22no—
618D4—22no—
619D4—48no—
620D4—41no—
621D4—41no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—48no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—342no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—681no—
661C2×C4#1058763612yes—
662C2×C4#1058763712yes—
663C2×C4C2×#6325211yescharacteristic
664C2×C4C2×#6325211yescharacteristic
665C2×C4C2×D4×D1711yescharacteristic
666C2×C4C2×#6325411yescharacteristic
667C2×C4#1058769111yescharacteristic
668C2×C4#1058769111yescharacteristic
669C8—342no—
670C8—681no—
671C8—681no—
672C8—681no—
673C22—41no—
674C22—42no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—41no—
680C22—42no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22#1176332011yescharacteristic
688C22D4×C22⋊D1711yescharacteristic
689C22#1176345311yescharacteristic
690C22C2×#1058763611yescharacteristic
691C22C2×#1058763711yescharacteristic
692C22#1176361211yescharacteristic
693C22#1176362411yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4—81no—
702C4—682no—
703C4—1361no—
704C4—1361no—
705C4—1361no—
706C4C2×#1058756911yescharacteristic
707C4#1176339711yescharacteristic
708C4#1176344911yescharacteristic
709C4#1176348511yescharacteristic
710C2—81no—
711C2—82no—
712C2#1453224611yescharacteristic
713C2#1453885511yescharacteristic
714C2#1453904611yescharacteristic
715C2#1454035011yescharacteristic
716C2#1454054011yescharacteristic
717C2#1454067111yescharacteristic
718C2#1454112211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2341C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
hypercenter#2341D17
hypocenterC17#24904
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63231C2semidirect
3. #14532309C2semidirect
4. #14530312C2semidirect
5. #14530210C2semidirect
6. #14530101C2semidirect
7. #14529987C2semidirect
8. #14529470C2semidirect
9. #14529392C2semidirect
10. #14529142C2semidirect
11. #14529125C2semidirect
12. #14529038C2semidirect
13. #14528789C2semidirect
497. C17#24904semidirect

Maximal subgroups

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

subgroupindex
C2×#117629712
C2×C4×#632312
#145323092
#145303122
#145302102
#145301012
#145299872
#145294702
#145293922
#145291422
#145291252
#145290382
#145287892
#145287242
C17×#23412
#2490417