Finite Group Databasebeta

← #29721585

Subgroups — #29721585

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839965C211yesmaximal, characteristic
2C2×#16839965C211yesmaximal, characteristic
3C2×SD16×Dic61C211yesmaximal, characteristic
4#21450805C211yesmaximal, characteristic, complemented
5D4×#11758196C211yesmaximal, characteristic
6#21447199C211yesmaximal, characteristic, complemented
7#21447198C211yesmaximal, characteristic, complemented
8#21447063C211yesmaximal, characteristic, complemented
9#21447062C211yesmaximal, characteristic, complemented
10#21446619C211yesmaximal, characteristic, complemented
11#21446534C211yesmaximal, characteristic, complemented
12#21446155C211yesmaximal, characteristic
13#21446153C211yesmaximal, characteristic
14#21445822C211yesmaximal, characteristic, complemented
15C2×C61×#461C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519775C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C22×#11758196—21no—
23#16839965—24no—
24#16839965—24no—
25SD16×Dic61—24no—
26C2×#14519709C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839695—21no—
39#16839695—21no—
40#16839669C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839660C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839657—21no—
45#16839657—21no—
46#16839635—21no—
47#16839634—21no—
48#16839631C2211yescharacteristic
49#16839620—21no—
50C4×#11758196C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#461—24no—
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519775—22no—
72#14519775—22no—
73#14519775—22no—
74#14519775—41no—
75Q8×Dic61—22no—
76Q8×Dic61—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80D4×Dic61D414yes—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—44no—
94C2×#11758196D411yescharacteristic
95C2×#11758196D411yescharacteristic
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519709—22no—
102#14519706—22no—
103#14519706—22no—
104#14519702—22no—
105#14519702—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519701—41no—
110#14519700—41no—
111#14519698—22no—
112C8×Dic61—22no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C22×Q8×C61C2311yescharacteristic
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61D414yes—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C4⋊Q8×C61—22no—
134C4⋊Q8×C61—41no—
135C4×D4×C61—22no—
136C4×D4×C61—41no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C42×C61C2311yescharacteristic
142C4⋊C8×C61—22no—
143#103×C61—22no—
144#103×C61—22no—
145C24×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C2×D412yes—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61C2×D412yes—
162C2×D4×C61C2×D412yes—
163C2×D4×C61#4112yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—81no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—24no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61—42no—
182C22×Dic61—81no—
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193SD16×C61—28no—
194SD16×C61—44no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61C2×D412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C42×C61—21no—
207C42×C61—21no—
208C22⋊Dic61—24no—
209C22⋊Dic61—42no—
210#11758200—44no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—42no—
217C4⋊Dic61C2×D412yes—
218#11758196—22no—
219#11758196—42no—
220#11758196—42no—
221#11758196—42no—
222#11758196—42no—
223#11758196—42no—
224#11758196—42no—
225#11758196—42no—
226#11758196—81no—
227#11758196SD1614yescomplemented
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—42no—
231C4×Dic61C2×D412yes—
232C4×Dic61#4112yes—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22×D411yescharacteristic
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—41no—
250Q8×C61—41no—
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61#12114yes—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—84no—
274C2×C4×C61C2×SD1612yes—
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—22no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—48no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—84no—
302C2×Dic61#12112yes—
303C2×Dic61#12112yes—
304C2×Dic61C2×SD1612yes—
305C2×Dic61C2×SD1612yes—
306C2×Dic61#13712yes—
307Dic122—41no—
308Dic122—41no—
309Dic122—41no—
310Dic122—41no—
311C8×C61—22no—
312C8×C61—41no—
313#92418—41no—
314#92418—41no—
315#24730—611nomaximal, Sylow
316C22×C61—24no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61C2×#12111yescharacteristic
324C22×C61D4211yescharacteristic
325C22×C61#54811yescharacteristic
326C22×C61C22×SD1611yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57711yescharacteristic
329C22×C61#57811yescharacteristic
330C4×C61—22no—
331C4×C61—42no—
332C4×C61—41no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61C2×#12111yescharacteristic
336C4×C61#53711yescharacteristic
337C4×C61#54711yescharacteristic
338C4×C61#55311yescharacteristic
339Dic61—22no—
340Dic61—22no—
341Dic61—41no—
342Dic61—42no—
343Dic61—81no—
344Dic61—81no—
345Dic61—81no—
346Dic61#46114yescomplemented
347C2×#461—611no—
348C2×#461—611no—
349C2×#461D6111yescharacteristic
350C2×C4×SD16—611no—
351#2546—611no—
352D4×C4⋊C4—611no—
353#2066—611no—
354#2066—611no—
355#2043—611no—
356#2043—611no—
357#1956—611no—
358#1939—611no—
359#1877—611no—
360#1877—611no—
361#1803—611no—
362C2×C61—44no—
363C2×C61#241611yescharacteristic
364C2×C61C2×#46111yescharacteristic
365C2×C61#304611yescharacteristic
366C2×C61#327611yescharacteristic
367C2×C61D4×SD1611yescharacteristic
368C2×C61#335911yescharacteristic
369C2×C61#337211yescharacteristic
370C22×SD16—611no—
371C22×SD16C2×D6111yescharacteristic
372C22×SD16C2×D6111yescharacteristic
373C2×C4⋊Q8—611no—
374C2×C4⋊Q8—611no—
375C2×C4⋊Q8C2×D6111yescharacteristic
376C2×C4×Q8—611no—
377C2×C4×D4—611no—
378C2×C4×D4—611no—
379C2×C4×D4C2×D6111yescharacteristic
380C22×C4⋊C4—1221no—
381#461—24no—
382#461—1224no—
383#461—1224no—
384C4×SD16—1224no—
385C2×#106—611no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8C2×D6111yescharacteristic
389C2×#103—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103C2×D6111yescharacteristic
397C2×#103C2×D6111yescharacteristic
398C2×#102—611no—
399C2×C4×C8—611no—
400#398—1221no—
401#398—1221no—
402#391—611no—
403#391—611no—
404#389—611no—
405#389—611no—
406#389—1221no—
407#389—1221no—
408#385—1221no—
409#385—1221no—
410#384—611no—
411#380—1221no—
412C4×C4⋊C4—611no—
413#340—611no—
414#340—611no—
415#336—611no—
416#336—611no—
417C61#2473011yescharacteristic, complemented, Sylow
418C22×Q8—611no—
419C22×Q8C22×D6111yescharacteristic
420C22×Q8C22×D6111yescharacteristic
421C22×D4C22×D6111yescharacteristic
422C23×C4—21no—
423C23×C4—1221no—
424C23×C4—1221no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—1222no—
431C2×SD16—1222no—
432C2×SD16—1222no—
433C2×SD16C22⋊D6114yes—
434C22×C8—611no—
435C22×C8—611no—
436C22×C8C22×D6111yescharacteristic
437C22×C8C22×D6111yescharacteristic
438C4⋊Q8—22no—
439C4⋊Q8—41no—
440C4⋊Q8—1222no—
441C4⋊Q8—1222no—
442C4⋊Q8—1222no—
443C4⋊Q8—2441no—
444C4×Q8—1222no—
445C4×Q8—1222no—
446C4×D4—22no—
447C4×D4—41no—
448C4×D4—614no—
449C4×D4—1222no—
450C4×D4—1222no—
451C4×D4—2441no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—2444no—
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—1221no—
476C2×C42C22×D6111yescharacteristic
477#106—1222no—
478C4⋊C8—22no—
479C4⋊C8—1222no—
480C4⋊C8—1222no—
481#103—22no—
482#103—22no—
483#103—1222no—
484#103—1222no—
485#103—1222no—
486#103—1222no—
487#103—1222no—
488#103—2441no—
489#103—2441no—
490#102—1222no—
491C4×C8—1222no—
492#95—611no—
493#95—611no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95—1221no—
499#95—1221no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—1221no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—1221no—
518C2×Q8C2×C22⋊D6112yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4D4×D6112yes—
523C2×D4#1175822412yes—
524C2×D4C2×C22⋊D6112yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—1224no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—4881no—
541C22×C4—2442no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4D4×D6111yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4C23×D6111yescharacteristic
548SD16—28no—
549SD16—44no—
550SD16—2444no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8C2×C22⋊D6112yes—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—614no—
568C4⋊C4—612no—
569C4⋊C4—1222no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—4881no—
576C4⋊C4—2442no—
577C4⋊C4—2442no—
578C4⋊C4—2442no—
579C4⋊C4—2442no—
580C4⋊C4—2442no—
581C4⋊C4—2442no—
582C4⋊C4—2442no—
583C4⋊C4—2442no—
584C22⋊C4—42no—
585C22⋊C4—1224no—
586C22⋊C4—2442no—
587C42—21no—
588C42—21no—
589C42—612no—
590C42—612no—
591C42—1221no—
592C42—1221no—
593C42—2442no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C2×D4×D6111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—2441no—
611Q8—2441no—
612Q8—2441no—
613Q8—2441no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4#1451974914yes—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—84no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1222no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—4884no—
647C2×C4—2448no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4SD16×D6112yes—
660C2×C4C2×D4×D6111yescharacteristic
661C2×C4C22×C22⋊D6111yescharacteristic
662C2×C4#41×D6111yescharacteristic
663C2×C4C2×#1175822411yescharacteristic
664C2×C4#1451982211yescharacteristic
665C2×C4#1451982411yescharacteristic
666C8—22no—
667C8—41no—
668C8—2441no—
669C8—2441no—
670C22—24no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22#121×D6111yescharacteristic
678C22D4×C22⋊D6111yescharacteristic
679C22#1684041811yescharacteristic
680C22C2×SD16×D6111yescharacteristic
681C22#137×D6111yescharacteristic
682C22#1684056811yescharacteristic
683C22#1684057811yescharacteristic
684C4—22no—
685C4—42no—
686C4—41no—
687C4—81no—
688C4—81no—
689C4—614no—
690C4—1222no—
691C4—1222no—
692C4—4881no—
693C4—4881no—
694C4—4881no—
695C4—2441no—
696C4—2442no—
697C4C2×#1451974911yescharacteristic
698C4#1684033911yescharacteristic
699C4#1684041111yescharacteristic
700C4#1684045511yescharacteristic
701C2—44no—
702C2#2144925611yescharacteristic
703C2#461×D6111yescharacteristic
704C2#2145536411yescharacteristic
705C2#2145745911yescharacteristic
706C2SD16×C22⋊D6111yescharacteristic
707C2#2145845611yescharacteristic
708C2#2145859511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenterC2×#461D61
hypocenterC61#24730
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
4. #21450805C2semidirect
6. #21447199C2semidirect
7. #21447198C2semidirect
8. #21447063C2semidirect
9. #21447062C2semidirect
10. #21446619C2semidirect
11. #21446534C2semidirect
14. #21445822C2semidirect
227. #11758196SD16semidirect
346. Dic61#461semidirect
417. C61#24730semidirect

Maximal subgroups

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

subgroupindex
C2×#168399652
C2×SD16×Dic612
#214508052
D4×#117581962
#214471992
#214471982
#214470632
#214470622
#214466192
#214465342
#214461552
#214461532
#214458222
C2×C61×#4612
#2473061