Finite Group Databasebeta

← #29708566

Subgroups — #29708566

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839809C211yesmaximal, characteristic, complemented
2#21454406C211yesmaximal, characteristic, complemented
3#21454380C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic
5#418×D61C211yesmaximal, characteristic
6C2×#100×D61C211yesmaximal, characteristic
7#21447180C211yesmaximal, characteristic, complemented
8#21447179C211yesmaximal, characteristic, complemented
9#21447178C211yesmaximal, characteristic, complemented
10#21447177C211yesmaximal, characteristic, complemented
11#21447176C211yesmaximal, characteristic, complemented
12#21447175C211yesmaximal, characteristic, complemented
13#21447174C211yesmaximal, characteristic, complemented
14#21445556C211yesmaximal, characteristic, complemented
15C61×#2063C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22#117×D61C2211yescharacteristic
23#16839809—24no—
24C2×#14519713C2211yescharacteristic, complemented
25C2×#14519712C2211yescharacteristic, complemented
26C2×#14519712C2211yescharacteristic, complemented
27#16839805C2211yescharacteristic, complemented
28#16839804C2211yescharacteristic, complemented
29#16839803—21no—
30#16839802C2211yescharacteristic, complemented
31#16839801—21no—
32#16839799—21no—
33#16839797—21no—
34#16839790C2211yescharacteristic, complemented
35#16839789C2211yescharacteristic, complemented
36#16839788C2211yescharacteristic, complemented
37#16839787—22no—
38#16839784—22no—
39#16839768C2211yescharacteristic
40#16839767C2211yescharacteristic
41#16839766C2211yescharacteristic
42#16839765—22no—
43#16839765—22no—
44#16839765—21no—
45#16839765—21no—
46C2×#14519699C2211yescharacteristic
47C2×#14519698C2211yescharacteristic
48C2×#14519697C2211yescharacteristic
49#102×D61—21no—
50#102×D61—21no—
51C2×#14519694C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54#100×D61—24no—
55#16839531C2211yescharacteristic, complemented
56#16839530C2211yescharacteristic, complemented
57#16839530C2211yescharacteristic, complemented
58C2×#108×C61C2211yescharacteristic, complemented
59C61×#428C2211yescharacteristic, complemented
60C61×#424C2211yescharacteristic, complemented
61C61×#418C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#100×C61C2211yescharacteristic
64C61×#343C2211yescharacteristic, complemented
65C24×D61—21no—
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72C2×D4×D61—22no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61Q814yes—
76C22×C4×D61C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758189—21no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×#11758189D412yes—
86C2×#11758189D412yes—
87M16×D61—22no—
88M16×D61—22no—
89M16×D61—22no—
90M16×D61—22no—
91M16×D61—22no—
92M16×D61D414yes—
93C22×#92418C2311yescharacteristic
94C2×C8×D61—21no—
95C2×C8×D61—21no—
96C2×C8×D61—21no—
97#14519736C2311yescharacteristic
98#14519735—21no—
99#14519735—21no—
100#14519735—21no—
101#14519735—21no—
102#14519735D411yescharacteristic
103#14519735D411yescharacteristic
104#14519734—21no—
105#14519733—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C4⋊C4×D61D411yescharacteristic
108C4⋊C4×D61D411yescharacteristic
109C2×#11758198—21no—
110C22⋊C4×D61—21no—
111C2×C4×Dic61—21no—
112C42×D61—21no—
113#14519713—22no—
114#14519712—22no—
115#14519712—22no—
116#14519711—21no—
117#14519710—21no—
118#14519710—21no—
119#14519709—21no—
120#14519708—21no—
121#14519708—21no—
122C4⋊#92418—22no—
123#14519706—22no—
124#14519706—22no—
125#14519699—22no—
126#14519699—21no—
127#14519699—21no—
128#14519698—21no—
129#14519698—21no—
130#14519698—22no—
131#14519697—21no—
132#14519697—21no—
133#14519697—22no—
134#14519694—22no—
135#14519693—22no—
136#14519693—22no—
137C22×D4×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142#117×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144#108×C61—22no—
145#107×C61—21no—
146#106×C61—21no—
147C4⋊C8×C61—22no—
148#102×C61—22no—
149#102×C61—21no—
150#102×C61—21no—
151#100×C61—22no—
152C24×C61—21no—
153C23×D61—21no—
154C23×D61—24no—
155C23×D61—41no—
156C23×D61—41no—
157C23×D61—42no—
158C23×D61—82no—
159C23×D61—82no—
160C23×D61#4111yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61C2×Q812yes—
167C22×C4×C61—21no—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—24no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—42no—
173C22×Dic61—21no—
174C22×Dic61#4111yescharacteristic
175D4×D61—24no—
176D4×D61—24no—
177D4×D61—24no—
178D4×D61—24no—
179D4×D61—42no—
180D4×D61—42no—
181D4×D61—42no—
182D4×D61—42no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244C2×Q812yes—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61C2×D412yes—
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×Q812yes—
197C2×C4×D61#4112yes—
198C2×C4×D61#4112yes—
199M16×C61—21no—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61C2×D412yes—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61C2×D412yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C2×D411yescharacteristic
214C4⋊C4×C61C2×D411yescharacteristic
215C22⋊C4×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—21no—
218#11758198—21no—
219#11758198—21no—
220#11758198—41no—
221#11758198—41no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61C2×D411yescharacteristic
225C4⋊Dic61C2×D411yescharacteristic
226#11758196—21no—
227#11758196—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—41no—
232C4×Dic61—41no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236#11758194—21no—
237#11758194—21no—
238#11758194C2×D412yes—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C2×D412yes—
245#11758189—24no—
246#11758189—24no—
247#11758189—24no—
248#11758189—42no—
249#11758189—42no—
250C8×D61—24no—
251C8×D61—42no—
252C8×D61—42no—
253C23×C61—22no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—81no—
257C23×C61—81no—
258C23×C61C2×#4111yescharacteristic
259C22×D61—22no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61—82no—
267C22×D61—82no—
268C22×D61—82no—
269C22×D61—82no—
270C22×D61—88no—
271C22×D61—88no—
272C22×D61—81no—
273C22×D61—81no—
274C22×D61#12111yescharacteristic
275C22×D61#12111yescharacteristic
276C22×D61C22⋊Q812yes—
277C22×D61#12612yes—
278D4×C61—22no—
279D4×C61—22no—
280D4×C61—41no—
281D4×C61—41no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—81no—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×Q811yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C22⋊D61—44no—
293C22⋊D61—44no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—41no—
297C2×Dic61—81no—
298C2×Dic61#12111yescharacteristic
299C2×Dic61#12111yescharacteristic
300C2×Dic61C22⋊Q812yes—
301C2×Dic61#12612yes—
302D244—22no—
303D244—22no—
304D244—41no—
305D244—41no—
306C4×D61—81no—
307C4×D61—81no—
308C4×D61#12112yes—
309C4×D61#12112yes—
310C4×D61#12112yes—
311C4×D61#12112yes—
312C4×D61C22⋊Q812yes—
313C4×D61C22⋊Q812yes—
314C4×D61C22⋊Q812yes—
315C4×D61C22⋊Q812yes—
316C8×C61—22no—
317C8×C61—22no—
318C8×C61—41no—
319C8×C61—41no—
320#92418—22no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#23602—611nomaximal, Sylow
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—42no—
328C22×C61—82no—
329C22×C61—82no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×#12111yescharacteristic
333C22×C61C2×C22⋊Q811yescharacteristic
334C22×C61C2×#12611yescharacteristic
335C2×D61—21no—
336C2×D61—21no—
337C2×D61—21no—
338C2×D61—21no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—88no—
343C2×D61—88no—
344C2×D61—82no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—82no—
348C2×D61#39612yes—
349C2×D61#39612yes—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—81no—
353C4×C61C2×#12111yescharacteristic
354C4×C61C2×#12111yescharacteristic
355C4×C61C2×C22⋊Q811yescharacteristic
356C4×C61C2×C22⋊Q811yescharacteristic
357Dic61—41no—
358Dic61—41no—
359Dic61—81no—
360Dic61#39612yes—
361Dic61#39612yes—
362C2×#430—611no—
363#2911—611no—
364#2905—611no—
365C2×#418—611no—
366C2×#418—611no—
367C22×#100—611no—
368#2063—611no—
369#2063—611no—
370#2063—611no—
371#2063—611no—
372#2063—611no—
373#2063—611no—
374#2063—611no—
375#2063D6111yescharacteristic, complemented
376#1742—611no—
377C2×C61—21no—
378C2×C61—21no—
379C2×C61—82no—
380C2×C61C2×#39611yescharacteristic
381C2×C61#306811yescharacteristic
382C2×C61#306811yescharacteristic
383D61—22no—
384D61—22no—
385D61—82no—
386C23×D4—611no—
387C22×M16—611no—
388C22×M16—611no—
389C22×M16—611no—
390C22×M16—611no—
391C2×#117—611no—
392C2×#117—611no—
393#430—1224no—
394C2×#108—611no—
395C2×#108—611no—
396C2×#108—611no—
397C2×#108C2×D6111yescharacteristic, complemented
398#428—611no—
399#428—611no—
400#428—611no—
401#428—1221no—
402#428—1221no—
403#428C2×D6111yescharacteristic, complemented
404#427—1221no—
405#427—1221no—
406#424—611no—
407#424—611no—
408#424—611no—
409#424—1222no—
410#424C2×D6111yescharacteristic, complemented
411#423—1222no—
412#418—611no—
413#418—611no—
414#418—611no—
415#418—1221no—
416#418—1221no—
417#418—1222no—
418#418—1222no—
419#418C2×D6111yescharacteristic
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—1221no—
424C2×#102—1221no—
425C2×#102C2×D6111yescharacteristic
426C2×#100—611no—
427C2×#100—611no—
428C2×#100—611no—
429C2×#100—1224no—
430C2×#100C2×D6111yescharacteristic
431#343—611no—
432#343—611no—
433#343—611no—
434#343C2×D6111yescharacteristic, complemented
435C61#2360211yescharacteristic, complemented, Sylow
436C25—1221no—
437C22×D4—614no—
438C22×D4—611no—
439C22×D4—1222no—
440C22×D4—1222no—
441C22×D4—1221no—
442C22×D4—1221no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4—1222no—
446C22×D4—1221no—
447C22×D4C22×D6111yescharacteristic
448C23×C4—611no—
449C2×M16—612no—
450C2×M16—612no—
451C2×M16—611no—
452C2×M16—614no—
453C2×M16—611no—
454C2×M16—611no—
455C2×M16—1221no—
456C2×M16—1222no—
457C2×M16—1222no—
458C2×M16—1221no—
459C2×M16—1221no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C2×M16—1222no—
464C2×M16—1222no—
465C2×M16C22×D6111yescharacteristic
466C2×M16C22×D6111yescharacteristic
467C2×M16C22×D6111yescharacteristic
468C22×C8—611no—
469C22×C8—1221no—
470C22×C8—1221no—
471C22×C8—1221no—
472C22×C8C22×D6111yescharacteristic
473#117—611no—
474#117—611no—
475#117—611no—
476#117—1221no—
477#117—1221no—
478#117—1221no—
479#117—1221no—
480#117—1221no—
481#117—1221no—
482#117C22×D6111yescharacteristic
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#108—22no—
492#108—1222no—
493#108—1222no—
494#108—1222no—
495#107—21no—
496#107—1221no—
497#107—1221no—
498#107—1221no—
499#106—21no—
500#106—1221no—
501#106—1221no—
502#106—1221no—
503C4⋊C8—22no—
504C4⋊C8—1222no—
505C4⋊C8—1222no—
506C4⋊C8—1222no—
507#102—22no—
508#102—21no—
509#102—21no—
510#102—1222no—
511#102—1221no—
512#102—1221no—
513#102—1221no—
514#102—1221no—
515#102—1222no—
516#102—1222no—
517#102—1221no—
518#102—1221no—
519#100—22no—
520#100—1222no—
521#100—1222no—
522#100—1222no—
523C24—21no—
524C24—611no—
525C24—1224no—
526C24—1221no—
527C24—4882no—
528C24—4882no—
529C24—2441no—
530C24—2441no—
531C24—2442no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—612no—
538C2×D4—1224no—
539C2×D4—1224no—
540C2×D4—1224no—
541C2×D4—1224no—
542C2×D4—1224no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—2442no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4—2441no—
553C2×D4—2441no—
554C2×D4—2442no—
555C2×D4Q8×D6112yes—
556C22×C4—21no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4C23×D6111yescharacteristic
570M16—21no—
571M16—21no—
572M16—21no—
573M16—21no—
574M16—21no—
575M16—612no—
576M16—1224no—
577M16—1224no—
578M16—1224no—
579M16—1221no—
580M16—1221no—
581M16—1221no—
582M16—1221no—
583M16—1221no—
584M16—2442no—
585M16—2442no—
586M16D4×D6112yes—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—612no—
593C2×C8—1224no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—2442no—
600C2×C8—2442no—
601C2×C8D4×D6112yes—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—611no—
605C4⋊C4—611no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4D4×D6111yescharacteristic
611C4⋊C4D4×D6111yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—1221no—
614C22⋊C4—1221no—
615C22⋊C4—1221no—
616C22⋊C4—2441no—
617C22⋊C4—2441no—
618C42—21no—
619C42—1221no—
620C42—1221no—
621C42—1221no—
622C42—2441no—
623C42—2441no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—81no—
628C23—81no—
629C23—611no—
630C23—611no—
631C23—612no—
632C23—612no—
633C23—1222no—
634C23—4881no—
635C23—4881no—
636C23—4882no—
637C23—4882no—
638C23—4882no—
639C23—4882no—
640C23—4888no—
641C23—4888no—
642C23—2441no—
643C23—2441no—
644C23—2444no—
645C23—2444no—
646C23—2441no—
647C23—2441no—
648C23#41×D6111yescharacteristic
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—1222no—
654D4—1222no—
655D4—2444no—
656D4—2444no—
657D4—2441no—
658D4—2441no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—81no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—4881no—
678C2×C4—4881no—
679C2×C4—4881no—
680C2×C4—2441no—
681C2×C4C2×D4×D6111yescharacteristic
682C2×C4C2×D4×D6111yescharacteristic
683C2×C4C2×D4×D6111yescharacteristic
684C2×C4C2×Q8×D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C8—22no—
688C8—22no—
689C8—41no—
690C8—41no—
691C8—1222no—
692C8—1222no—
693C8—2441no—
694C8—2441no—
695C22—21no—
696C22—21no—
697C22—42no—
698C22—82no—
699C22—82no—
700C22—81no—
701C22—81no—
702C22—612no—
703C22—612no—
704C22—1221no—
705C22—1221no—
706C22—1221no—
707C22—1221no—
708C22—4882no—
709C22—4882no—
710C22—4888no—
711C22—4888no—
712C22—4881no—
713C22—4881no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22#121×D6111yescharacteristic
718C22C22⋊Q8×D6111yescharacteristic
719C22#126×D6111yescharacteristic
720C4—41no—
721C4—41no—
722C4—81no—
723C4—612no—
724C4—612no—
725C4—4881no—
726C4—2441no—
727C4—2441no—
728C4#121×D6111yescharacteristic
729C4#121×D6111yescharacteristic
730C4C22⋊Q8×D6111yescharacteristic
731C4C22⋊Q8×D6111yescharacteristic
732C2—21no—
733C2—21no—
734C2—82no—
735C2—1222no—
736C2—1222no—
737C2—4882no—
738C2#396×D6111yescharacteristic
739C2#2145554211yescharacteristic
740C2#2145554511yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2063C2
socleC22×C61C2×#121
prime radicalC22×D4×D61C22
hypercenter#2063D61
hypocenterC61#23602
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2063

Complements

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

NH ≅ G/Ntype
1. C2×#16839809C2semidirect
2. #21454406C2semidirect
3. #21454380C2semidirect
7. #21447180C2semidirect
8. #21447179C2semidirect
9. #21447178C2semidirect
10. #21447177C2semidirect
11. #21447176C2semidirect
12. #21447175C2semidirect
13. #21447174C2semidirect
14. #21445556C2semidirect
15. C61×#2063C2semidirect
24. C2×#14519713C22semidirect
25. C2×#14519712C22semidirect
26. C2×#14519712C22semidirect
27. #16839805C22semidirect
28. #16839804C22semidirect
30. #16839802C22semidirect
34. #16839790C22semidirect
35. #16839789C22semidirect
36. #16839788C22semidirect
55. #16839531C22semidirect
56. #16839530C22semidirect
57. #16839530C22semidirect
58. C2×#108×C61C22semidirect
59. C61×#428C22semidirect
60. C61×#424C22semidirect
64. C61×#343C22semidirect
375. #2063D61semidirect
397. C2×#108C2×D61semidirect
403. #428C2×D61semidirect
410. #424C2×D61semidirect
434. #343C2×D61semidirect
435. C61#23602semidirect

Maximal subgroups

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

subgroupindex
C2×#168398092
#214544062
#214543802
C2×#168397652
#418×D612
C2×#100×D612
#214471802
#214471792
#214471782
#214471772
#214471762
#214471752
#214471742
#214455562
C61×#20632
#2360261