Finite Group Databasebeta

← #29718453

Subgroups — #29718453

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840100C211yesmaximal, characteristic, complemented
2C2×#16839758C211yesmaximal, characteristic
3#21448710C211yesmaximal, characteristic, complemented
4#21447214C211yesmaximal, characteristic, complemented
5#21447207C211yesmaximal, characteristic, complemented
6#21447062C211yesmaximal, characteristic, complemented
7#21447055C211yesmaximal, characteristic, complemented
8#21446752C211yesmaximal, characteristic, complemented
9#21446743C211yesmaximal, characteristic, complemented
10#21446450C211yesmaximal, characteristic, complemented
11#21446443C211yesmaximal, characteristic, complemented
12#21446243C211yesmaximal, characteristic, complemented
13#21445999C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic
15C61×#2432C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16840100—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23#16839758—24no—
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839656—21no—
40#16839656—21no—
41#16839629—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839613—21no—
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C61×#394—21no—
55C61×#394—21no—
56C61×#391C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#385—21no—
59C61×#385—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×#92418—22no—
62C22×#92418—41no—
63C22×#92418—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519736—22no—
69#14519736D414yes—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81#14519710—22no—
82#14519708—22no—
83C4⋊#92418—41no—
84C4⋊#92418—41no—
85#14519701—22no—
86#14519701—22no—
87#14519701—22no—
88#14519701—22no—
89#14519701—22no—
90#14519701—41no—
91#14519701—41no—
92#14519701—41no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—41no—
97C22⋊#92418—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—41no—
108C2×#41×C61—41no—
109C22×Q8×C61C2311yescharacteristic
110C22×Q8×C61C2311yescharacteristic
111C22×D4×C61—21no—
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C4⋊Q8×C61—22no—
116C4⋊Q8×C61—41no—
117#124×C61—22no—
118#124×C61—41no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134#95×C61—21no—
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140#41×C61—28no—
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144C2×Q8×C61—21no—
145C2×Q8×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#4112yes—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61#4112yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—42no—
190C4⋊C4×C61—42no—
191C4⋊C4×C61—42no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—42no—
195C22⋊C4×C61—42no—
196C22⋊C4×C61—42no—
197C22⋊C4×C61—42no—
198C22⋊C4×C61—42no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C22⋊Dic61—24no—
204C22⋊Dic61—81no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61C2×D412yes—
212C4⋊Dic61C2×D412yes—
213#11758196—42no—
214#11758196—42no—
215C4×Dic61—24no—
216C4×Dic61—81no—
217C4×Dic61—81no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—44no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—22no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61#12112yes—
245C23×C61C22×D411yescharacteristic
246Q8×C61—22no—
247Q8×C61—22no—
248Q8×C61—41no—
249Q8×C61—41no—
250Q8×C61—41no—
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—41no—
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—48no—
257D4×C61—41no—
258D4×C61—41no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—48no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61#12112yes—
287C2×C4×C61#13512yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306#92418—41no—
307#92418—41no—
308#92418—41no—
309#92418—41no—
310#24485—611nomaximal, Sylow
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61C2×#12111yescharacteristic
326C22×C61#54611yescharacteristic
327C22×C61#54611yescharacteristic
328C22×C61C2×#13511yescharacteristic
329C22×C61#57511yescharacteristic
330C22×C61#57711yescharacteristic
331C22×C61#57811yescharacteristic
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—42no—
335C4×C61—41no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61#52511yescharacteristic
341C4×C61#53511yescharacteristic
342C4×C61#55111yescharacteristic
343C4×C61#55111yescharacteristic
344Dic61—42no—
345Dic61—42no—
346Dic61—81no—
347Dic61—81no—
348C2×#485—611no—
349C2×#416—611no—
350#2432D6111yescharacteristic
351#2347—611no—
352#2068—611no—
353#2067—611no—
354#2043—611no—
355#2042—611no—
356#1983—611no—
357#1981—611no—
358#1927—611no—
359#1926—611no—
360#1892—611no—
361#1850—611no—
362#1788—611no—
363C2×C61—42no—
364C2×C61—82no—
365C2×C61#241111yescharacteristic
366C2×C61#303511yescharacteristic
367C2×C61#304611yescharacteristic
368C2×C61#330111yescharacteristic
369C2×C61#330211yescharacteristic
370C2×C61#330711yescharacteristic
371C2×C61#331311yescharacteristic
372C22×#41C2×D6111yescharacteristic
373C23×C8—611no—
374C2×C4⋊Q8C2×D6111yescharacteristic
375C2×#124C2×D6111yescharacteristic
376C2×C22⋊Q8C2×D6111yescharacteristic
377C2×#117—611no—
378#485—1224no—
379C2×#107—611no—
380C2×#106—611no—
381C2×C4⋊C8—611no—
382C2×C4⋊C8—611no—
383#416—1224no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#103—611no—
387C2×#103—611no—
388C2×#103—611no—
389C2×#103—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#102—611no—
393C2×#102—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×C22⋊C8—611no—
397#394—21no—
398#394—21no—
399#391C2×D6111yescharacteristic
400#390C2×D6111yescharacteristic
401#389—611no—
402#389—611no—
403#388—1221no—
404#388—1221no—
405#385—21no—
406#385—21no—
407#383—1221no—
408#380—611no—
409C4×C4⋊C4—611no—
410C4×C4⋊C4—611no—
411C4×C4⋊C4—1221no—
412C4×C22⋊C4C2×D6111yescharacteristic
413#340—611no—
414#340—611no—
415#336—611no—
416#336—611no—
417C61#2448511yescharacteristic, complemented, Sylow
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C22×Q8C22×D6111yescharacteristic
425C22×Q8C22×D6111yescharacteristic
426C22×D4—21no—
427C22×D4C22×D6111yescharacteristic
428C23×C4—21no—
429C23×C4C22×D6111yescharacteristic
430C22×C8—611no—
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—1222no—
435C22×C8—2441no—
436C22×C8—2441no—
437C4⋊Q8—22no—
438C4⋊Q8—41no—
439#124—22no—
440#124—41no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#117—614no—
444#117—1222no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4C22×D6111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—1221no—
461C2×C22⋊C4—1221no—
462C2×C22⋊C4C22⋊D6111yescharacteristic
463C2×C22⋊C4C22⋊D6111yescharacteristic
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42—1221no—
467C2×C42C22×D6111yescharacteristic
468C2×C42C22×D6111yescharacteristic
469#107—1222no—
470#106—1222no—
471C4⋊C8—2441no—
472C4⋊C8—2441no—
473#103—1222no—
474#103—1222no—
475#103—1222no—
476#103—1222no—
477#103—1222no—
478#103—2441no—
479#103—2441no—
480#103—2441no—
481#102—1222no—
482#102—1222no—
483#102—1222no—
484#102—2441no—
485C22⋊C8—1222no—
486#95—21no—
487#95—21no—
488#95—1221no—
489#95—1221no—
490#95—1221no—
491#95—1221no—
492#95—1221no—
493#95C22⋊D6111yescharacteristic
494#95C22⋊D6111yescharacteristic
495C24—21no—
496C24C2×C22⋊D6111yescharacteristic
497#41—28no—
498#41—44no—
499#41—44no—
500#41—44no—
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#1175822412yes—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4#1175822412yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4D4×D6112yes—
537C22×C4#1175822412yes—
538C22×C4C2×C22⋊D6111yescharacteristic
539C22×C4C2×C22⋊D6111yescharacteristic
540C22×C4C2×C22⋊D6111yescharacteristic
541C22×C4C2×C22⋊D6111yescharacteristic
542C22×C4C2×C22⋊D6111yescharacteristic
543C22×C4C23×D6111yescharacteristic
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—2444no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—612no—
563C4⋊C4—612no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C4⋊C4—2442no—
571C4⋊C4—2442no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—1224no—
580C22⋊C4—4881no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—1224no—
586C42—4881no—
587C42—4881no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#1451974812yes—
602C23C22×C22⋊D6111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—48no—
614D4—41no—
615D4—41no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4#1451974812yes—
656C2×C4#1451979712yes—
657C2×C4C2×D4×D6111yescharacteristic
658C2×C4C2×#1175822411yescharacteristic
659C2×C4C2×#1175822411yescharacteristic
660C2×C4C2×#1175822411yescharacteristic
661C2×C4#1451982211yescharacteristic
662C2×C4#1451982211yescharacteristic
663C8—2441no—
664C8—2441no—
665C8—2441no—
666C8—2441no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#1451974811yescharacteristic
682C22#1684040611yescharacteristic
683C22#1684040611yescharacteristic
684C22C2×#1451979711yescharacteristic
685C22#1684056011yescharacteristic
686C22#1684057011yescharacteristic
687C22#1684057711yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—4881no—
697C4—4881no—
698C4—2442no—
699C4—2442no—
700C4#1684026811yescharacteristic
701C4#1684032711yescharacteristic
702C4#1684044311yescharacteristic
703C4#1684044311yescharacteristic
704C2—42no—
705C2—82no—
706C2#2144920011yescharacteristic
707C2#2145526811yescharacteristic
708C2#2145536511yescharacteristic
709C2#2145772111yescharacteristic
710C2#2145773611yescharacteristic
711C2#2145779511yescharacteristic
712C2#2145788511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2432C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenter#2432D61
hypocenterC61#24485
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2432

Complements

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

NH ≅ G/Ntype
1. C2×#16840100C2semidirect
3. #21448710C2semidirect
4. #21447214C2semidirect
5. #21447207C2semidirect
6. #21447062C2semidirect
7. #21447055C2semidirect
8. #21446752C2semidirect
9. #21446743C2semidirect
10. #21446450C2semidirect
11. #21446443C2semidirect
12. #21446243C2semidirect
13. #21445999C2semidirect
417. C61#24485semidirect

Maximal subgroups

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

subgroupindex
C2×#168401002
C2×#168397582
#214487102
#214472142
#214472072
#214470622
#214470552
#214467522
#214467432
#214464502
#214464432
#214462432
#214459992
#214457592
C61×#24322
#2448561