Finite Group Databasebeta

← #29698346

Subgroups — #29698346

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839872C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic
3C2×#16839842C211yesmaximal, characteristic
4#21448728C211yesmaximal, characteristic, complemented
5D4×#11758196C211yesmaximal, characteristic, complemented
6#21446559C211yesmaximal, characteristic, complemented
7#21446546C211yesmaximal, characteristic, complemented
8#21446083C211yesmaximal, characteristic, complemented
9#21446082C211yesmaximal, characteristic, complemented
10#21446063C211yesmaximal, characteristic, complemented
11#21445986C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic, complemented
14#21445692C211yesmaximal, characteristic, complemented
15C61×#1862C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C22×#11758196—21no—
23#16839872—24no—
24#16839871C418yescomplemented
25#16839842—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839636—21no—
42#16839635—21no—
43#16839634—21no—
44#16839633—21no—
45#16839631C2211yescharacteristic
46#16839627C2211yescharacteristic
47#16839620—21no—
48#16839619—21no—
49C4×#11758196C2211yescharacteristic
50#95×D61—21no—
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C23×Dic61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C2×#11758199C2×C414yes—
69C2×#11758199D414yes—
70C2×#11758199Q814yes—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C4×D244—22no—
74C4×D244—41no—
75D4×Dic61—22no—
76D4×Dic61—22no—
77D4×Dic61—41no—
78D4×Dic61C2×C414yescomplemented
79#14519739—22no—
80#14519739—22no—
81#14519739—41no—
82#14519739C2×C414yescomplemented
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—44no—
92C2×#11758196D411yescharacteristic
93C2×#11758196D411yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519710—22no—
102#14519709—41no—
103#14519708—22no—
104#14519708C2×C414yescomplemented
105#14519706—22no—
106#14519699—22no—
107#14519699C2×C414yescomplemented
108#14519698—22no—
109#14519697—22no—
110#14519688—22no—
111#14519687C2×C414yescomplemented
112C8×Dic61—22no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684D411yescharacteristic
119#14519684D411yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C4×D4×C61—22no—
125C4×D4×C61—41no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—41no—
133#102×C61—22no—
134#102×C61C2×C414yescomplemented
135#95×C61—21no—
136C24×C61—21no—
137C23×D61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61C22×C412yes—
142C2×D4×C61C2×D412yes—
143C2×D4×C61C2×Q812yes—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—81no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61—24no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C22×Dic61—42no—
160C22×Dic61—42no—
161C22×Dic61—81no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244C22×C412yes—
170C2×D244C2×D412yes—
171C2×D244C2×Q812yes—
172C2×C4×D61—24no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—81no—
178C2×C4×D61—81no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61C22×C412yes—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—81no—
193C4⋊C4×C61C22×C412yes—
194C22⋊C4×C61—42no—
195C42×C61—21no—
196C42×C61—21no—
197C22⋊Dic61—24no—
198C22⋊Dic61—42no—
199#11758199C4⋊C4116yescomplemented
200#11758198—24no—
201#11758198—42no—
202#11758198—42no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—81no—
209C4⋊Dic61C22×C412yes—
210#11758196—22no—
211#11758196—41no—
212#11758196—42no—
213#11758196—42no—
214#11758196—42no—
215#11758196—81no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61C22×C412yes—
219C4×Dic61#4112yes—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418C22×C412yes—
224C2×#92418C2×D412yes—
225C2×#92418C2×Q812yes—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61C22×D411yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61—41no—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61C2×C4⋊C414yes—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—84no—
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×Q811yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C2×C4×C612−1+411yescharacteristic
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—22no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—48no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—84no—
287C2×Dic61C4×D412yes—
288C2×Dic61C4×D412yes—
289C2×Dic61AGL(1,ℤ/8)12yes—
290D244—22no—
291D244—22no—
292D244—22no—
293D244C2×C4⋊C414yescomplemented
294C4×D61—84no—
295C4×D61—84no—
296C4×D61—84no—
297C8×C61—22no—
298C8×C61—41no—
299#92418—41no—
300#92418C2×C4⋊C414yescomplemented
301#22676—611nomaximal, Sylow
302C22×C61—24no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61C2×C4×D411yescharacteristic
310C22×C61D4211yescharacteristic
311C22×C61D4×Q811yescharacteristic
312C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C61#57511yescharacteristic
314C22×C61#57611yescharacteristic
315C22×C61#57711yescharacteristic
316C2×D61—24no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—42no—
323C4×C61—42no—
324C4×C61—41no—
325C4×C61—41no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61C22×C4⋊C411yescharacteristic
329C4×C61#52011yescharacteristic
330C4×C61#54711yescharacteristic
331C4×C61#55411yescharacteristic
332Dic61—22no—
333Dic61—22no—
334Dic61—22no—
335Dic61—42no—
336Dic61—41no—
337Dic61—81no—
338Dic61—81no—
339C2×#442—611no—
340C2×#442—611no—
341C2×C4×D8—611no—
342#2349—611no—
343D4×C4⋊C4—611no—
344#1944—611no—
345#1941—611no—
346#1864—611no—
347#1864—611no—
348#1862—611no—
349#1862D6111yescharacteristic, complemented
350#1847—611no—
351#1804—611no—
352#1802—611no—
353#1771—611no—
354C2×C61—44no—
355C2×C61D4×C4⋊C411yescharacteristic
356C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
357C2×C61#294611yescharacteristic
358C2×C61#326411yescharacteristic
359C2×C61#326711yescharacteristic
360C2×C61#338411yescharacteristic
361C2×C61#338911yescharacteristic
362D61—44no—
363C22×D8—611no—
364C2×C4×D4—611no—
365C2×C4×D4—611no—
366C2×C4×D4—611no—
367C2×C4×D4—611no—
368C2×C4×D4—611no—
369C2×C4×D4C2×D6111yescharacteristic
370C22×C4⋊C4—1221no—
371#442—618no—
372#442—1224no—
373C4×D8—1224no—
374C2×#107—611no—
375C2×#107C2×D6111yescharacteristic
376C2×#106—611no—
377C2×#106—611no—
378C2×#106—611no—
379C2×C4⋊C8—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102—611no—
383C2×#102—611no—
384C2×#102C2×D6111yescharacteristic
385C2×#102C2×D6111yescharacteristic
386C2×#97—611no—
387C2×#97—611no—
388C2×C4×C8—611no—
389#389—611no—
390#389—611no—
391#389—611no—
392#389C2×D6111yescharacteristic
393#385—1221no—
394#385—1221no—
395#385—1221no—
396#385—1221no—
397#384—611no—
398#382—611no—
399#380—1221no—
400#380—1221no—
401C4×C4⋊C4—611no—
402C2×#95—1221no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340C2×D6111yescharacteristic
407#336—611no—
408#336C2×D6111yescharacteristic
409C61#2267611yescharacteristic, complemented, Sylow
410C22×D4—611no—
411C22×D4C22×D6111yescharacteristic
412C23×C4—21no—
413C23×C4—1221no—
414C23×C4—1221no—
415C23×C4—1221no—
416C23×C4—1221no—
417C23×C4—1221no—
418C2×D8—614no—
419C2×D8—614no—
420C2×D8—614no—
421C22×C8—611no—
422C22×C8—611no—
423C22×C8C22×D6111yescharacteristic
424C22×C8C22×D6111yescharacteristic
425C4×D4—22no—
426C4×D4—41no—
427C4×D4—614no—
428C4×D4—614no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1222no—
434C4×D4—2441no—
435C4×D4—2441no—
436C4×D4—2441no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—2444no—
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C4⋊C4C22×D6111yescharacteristic
451C2×C4⋊C4C22×D6111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42C22×D6111yescharacteristic
461#107—41no—
462#107—1222no—
463#106—614no—
464#106—1222no—
465#106—2441no—
466C4⋊C8—1222no—
467#102—22no—
468#102—614no—
469#102—1222no—
470#102—1222no—
471#102—1222no—
472#102C4×D6114yescomplemented
473#97—614no—
474#97—1222no—
475C4×C8—1222no—
476#95—21no—
477#95—611no—
478#95—611no—
479#95—1221no—
480#95—1221no—
481#95—1221no—
482#95—1221no—
483#95—1221no—
484C24—21no—
485C24—1221no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—612no—
490C2×D4—612no—
491C2×D4—612no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4C2×C4×D6112yes—
496C2×D4D4×D6112yes—
497C2×D4Q8×D6112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—1224no—
509C22×C4—1224no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—4881no—
514C22×C4—4881no—
515C22×C4—4881no—
516C22×C4—4881no—
517C22×C4—4881no—
518C22×C4—2442no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4—2442no—
523C22×C4—2442no—
524C22×C4—2442no—
525C22×C4—2442no—
526C22×C4D4×D6111yescharacteristic
527C22×C4D4×D6111yescharacteristic
528C22×C4C23×D6111yescharacteristic
529D8—6116no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—612no—
536C2×C8—612no—
537C2×C8—612no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8C2×C4×D6112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—81no—
548C4⋊C4—612no—
549C4⋊C4—1222no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—4881no—
556C4⋊C4—4881no—
557C4⋊C4—2441no—
558C4⋊C4—2442no—
559C4⋊C4—2442no—
560C4⋊C4—2442no—
561C4⋊C4C2×C4×D6112yes—
562C22⋊C4—42no—
563C22⋊C4—1224no—
564C22⋊C4—1224no—
565C22⋊C4—2442no—
566C22⋊C4—2442no—
567C22⋊C4—2442no—
568C42—21no—
569C42—21no—
570C42—612no—
571C42—612no—
572C42—1221no—
573C42—1221no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—1222no—
582C23—1222no—
583C23—1222no—
584C23—2441no—
585C23—2441no—
586C23—2441no—
587C23—2441no—
588C23C2×D4×D6111yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—614no—
593D4—1222no—
594D4—1222no—
595D4—1222no—
596D4C4⋊C4×D6114yes—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4—612no—
614C2×C4—612no—
615C2×C4—612no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1222no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—4884no—
627C2×C4—4884no—
628C2×C4—4884no—
629C2×C4—4884no—
630C2×C4—2448no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4C22×C4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4C2×Q8×D6111yescharacteristic
642C2×C4#41×D6111yescharacteristic
643C2×C4#1451982211yescharacteristic
644C2×C4#1451982411yescharacteristic
645C8—22no—
646C8—41no—
647C8—614no—
648C8—2441no—
649C22—24no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—1224no—
657C22—2442no—
658C22—2442no—
659C22—2442no—
660C22—2442no—
661C22—2442no—
662C22—2442no—
663C22C4×D4×D6111yescharacteristic
664C22#1684039411yescharacteristic
665C22#1684042511yescharacteristic
666C22AGL(1,ℤ/8)×D6111yescharacteristic
667C22#1684056111yescharacteristic
668C22#1684056311yescharacteristic
669C22#1684056911yescharacteristic
670C4—42no—
671C4—41no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—1222no—
676C4—1222no—
677C4—1222no—
678C4—4881no—
679C4—4881no—
680C4—2442no—
681C4—2441no—
682C4C2×C4⋊C4×D6111yescharacteristic
683C4#1684024111yescharacteristic
684C4#1684041011yescharacteristic
685C4#1684046611yescharacteristic
686C2—44no—
687C2—2444no—
688C2#2144871711yescharacteristic
689C2#2145462411yescharacteristic
690C2#2145464411yescharacteristic
691C2#2145729711yescharacteristic
692C2#2145734711yescharacteristic
693C2#2145872111yescharacteristic
694C2#2145877211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1862C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#1862D61
hypocenterC61#22676
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
4. #21448728C2semidirect
5. D4×#11758196C2semidirect
6. #21446559C2semidirect
7. #21446546C2semidirect
8. #21446083C2semidirect
9. #21446082C2semidirect
10. #21446063C2semidirect
11. #21445986C2semidirect
12. #21445827C2semidirect
13. #21445818C2semidirect
14. #21445692C2semidirect
15. C61×#1862C2semidirect
24. #16839871C4semidirect
78. D4×Dic61C2×C4semidirect
82. #14519739C2×C4semidirect
104. #14519708C2×C4semidirect
107. #14519699C2×C4semidirect
111. #14519687C2×C4semidirect
134. #102×C61C2×C4semidirect
199. #11758199C4⋊C4semidirect
293. D244C2×C4⋊C4semidirect
300. #92418C2×C4⋊C4semidirect
349. #1862D61semidirect
409. C61#22676semidirect
472. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398722
C2×#168398712
C2×#168398422
#214487282
D4×#117581962
#214465592
#214465462
#214460832
#214460822
#214460632
#214459862
#214458272
#214458182
#214456922
C61×#18622
#2267661