Finite Group Databasebeta

← #29700340

Subgroups — #29700340

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839919C211yesmaximal, characteristic
2C2×#16839868C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic
4#21448826C211yesmaximal, characteristic
5#21448653C211yesmaximal, characteristic
6#21446689C211yesmaximal, characteristic, complemented
7#21446511C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic
9#21446159C211yesmaximal, characteristic, complemented
10#21446157C211yesmaximal, characteristic, complemented
11#21446088C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic
13#21445652C211yesmaximal, characteristic, complemented
14#21445594C211yesmaximal, characteristic
15C61×#1927C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×#14519742C2211yescharacteristic
24C2×C4⋊C4×D61C2211yescharacteristic
25#16839919C418yescomplemented
26#16839868—24no—
27C2×#14519708C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34#103×D61—24no—
35C2×#14519689C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839669C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839666—21no—
41#16839666—21no—
42#16839661C2211yescharacteristic
43#16839660—21no—
44#16839647—21no—
45#16839636—21no—
46#16839621—21no—
47#16839619C2211yescharacteristic
48C4×#11758198—21no—
49C4×#11758198C2211yescharacteristic
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—41no—
69C2×Q8×D61—41no—
70C2×Q8×D61C2×C414yes—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×Dic244—22no—
75C2×Dic244—22no—
76C2×Dic244C2×C414yescomplemented
77C2×#11758202—41no—
78C2×#11758202—41no—
79C2×#11758202C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85#14519757—22no—
86#14519757C2×C414yes—
87C4×Dic122—22no—
88C4×Dic122—41no—
89#14519742—22no—
90#14519742—22no—
91#14519742—41no—
92#14519742—41no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61—41no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198D411yescharacteristic
106C2×#11758198D411yescharacteristic
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519708—41no—
112#14519702—22no—
113#14519702—41no—
114#14519701—22no—
115#14519700—22no—
116#14519700C2×C414yescomplemented
117#14519700D414yes—
118#14519689C2×C414yes—
119#14519688—41no—
120#14519687—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127#14519684D411yescharacteristic
128#14519684D411yescharacteristic
129C22×Q8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137#106×C61—22no—
138#103×C61—22no—
139#103×C61C2×C414yescomplemented
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143C23×D61C2×D411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164Q8×D61—28no—
165Q8×D61—44no—
166Q8×D61—44no—
167Q8×D61—44no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
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×D61C22×C412yes—
179C2×C4×D61#4112yes—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—24no—
189C2×Dic122—42no—
190C2×Dic122—42no—
191C2×Dic122C22×C412yes—
192C2×Dic122C22×C412yes—
193C2×Dic122C2×D412yes—
194C2×Dic122#4112yes—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61C22×C412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22×C412yes—
206C4⋊C4×C61C2×D412yes—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—81no—
210#11758202—44no—
211#11758198—24no—
212#11758198—22no—
213#11758198—22no—
214#11758198—42no—
215C4⋊Dic61—24no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—81no—
221#11758196—42no—
222#11758196—42no—
223#11758196—42no—
224#11758196—42no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—42no—
228C4×Dic61—42no—
229C4×Dic61—42no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C22×C412yes—
235C2×#92418C2×D412yes—
236Dic244—28no—
237C8×D61—44no—
238C23×C61C22×D411yescharacteristic
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61C4×D412yes—
244C22×D61#13712yes—
245C22×D61#13712yes—
246Q8×C61—22no—
247Q8×C61—22no—
248Q8×C61—41no—
249Q8×C61—41no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—21no—
277C2×Dic61—22no—
278C2×Dic61—21no—
279C2×Dic61—22no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61C4×D412yes—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—48no—
300C4×D61—84no—
301Dic122—22no—
302Dic122—22no—
303Dic122—22no—
304Dic122—22no—
305Dic122—22no—
306Dic122—48no—
307Dic122—41no—
308Dic122—41no—
309Dic122C4×D414yes—
310C8×C61—22no—
311C8×C61—41no—
312#92418—22no—
313#92418—22no—
314#22859—611nomaximal, Sylow
315C22×C61C2×C4×D411yescharacteristic
316C22×C61D4211yescharacteristic
317C22×C61#54611yescharacteristic
318C22×C61C2×#13711yescharacteristic
319C22×C61C2×#13711yescharacteristic
320C22×C61#57711yescharacteristic
321C22×C61#57811yescharacteristic
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—22no—
326C2×D61—22no—
327C2×D61—22no—
328C2×D61#44114yescomplemented
329C4×C61—42no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—81no—
335C4×C61C2×C4×D411yescharacteristic
336C4×C61#51811yescharacteristic
337C4×C61#54611yescharacteristic
338C4×C61#55111yescharacteristic
339Dic61—24no—
340Dic61—22no—
341Dic61—42no—
342Dic61—41no—
343Dic61—41no—
344Dic61—81no—
345Dic61—81no—
346C2×#451—611no—
347C2×#441—611no—
348C22×#103—611no—
349#2360—611no—
350Q8×C22⋊C4—611no—
351#1971—611no—
352#1935—611no—
353#1927D6111yescharacteristic, complemented
354#1892—611no—
355#1878—611no—
356#1878—611no—
357#1865—611no—
358#1853—611no—
359#1763—611no—
360#1752—611no—
361C2×C61#235811yescharacteristic
362C2×C61C2×#44111yescharacteristic
363C2×C61#294711yescharacteristic
364C2×C61#326611yescharacteristic
365C2×C61#327011yescharacteristic
366C2×C61#331211yescharacteristic
367C2×C61#331611yescharacteristic
368D61—24no—
369C23×Q8—611no—
370C22×Q16—611no—
371C22×Q16—611no—
372C23×C8—611no—
373C2×C22⋊Q8—611no—
374C2×C4×Q8—611no—
375C2×C4×Q8—611no—
376C2×C4×Q8—611no—
377C22×C4⋊C4—611no—
378#451—618no—
379#441—1224no—
380C2×#106—611no—
381C2×#106C2×D6111yescharacteristic
382C2×#103—611no—
383C2×#103—611no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#103—611no—
387C2×#103—611no—
388C2×#103—1224no—
389C2×#103C2×D6111yescharacteristic
390C2×#103C2×D6111yescharacteristic
391C2×C22⋊C8—611no—
392C2×#97—611no—
393C2×#97—611no—
394#391—611no—
395#391—611no—
396#391—1221no—
397#391—1221no—
398#391C2×D6111yescharacteristic
399#389—611no—
400#389—1221no—
401#387—1221no—
402#385—1221no—
403#380—611no—
404#380—1221no—
405C4×C4⋊C4C2×D6111yescharacteristic
406C4×C22⋊C4—611no—
407C4×C22⋊C4—1221no—
408C4×C22⋊C4—1221no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340C2×D6111yescharacteristic
413#336—611no—
414#336C2×D6111yescharacteristic
415C61#2285911yescharacteristic, complemented, Sylow
416C22×Q8—614no—
417C22×Q8—611no—
418C22×Q8—611no—
419C22×Q8—1221no—
420C22×Q8—1222no—
421C22×Q8—1222no—
422C22×Q8—1222no—
423C22×Q8—2441no—
424C22×Q8—2441no—
425C22×Q8C22×D6111yescharacteristic
426C23×C4—611no—
427C23×C4—1221no—
428C23×C4—1221no—
429C2×Q16—614no—
430C2×Q16—614no—
431C2×Q16—1222no—
432C2×Q16—1222no—
433C2×Q16—2441no—
434C2×Q16—2441no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—1222no—
438C22×C8—1222no—
439C22×C8—2441no—
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C22⋊Q8—614no—
443C22⋊Q8—1222no—
444C4×Q8—1222no—
445C4×Q8—1222no—
446C4×Q8—1222no—
447C4×Q8—2441no—
448C4×Q8—2441no—
449C4×Q8—2441no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1221no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—2441no—
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C42—21no—
468C2×C42—611no—
469C2×C42—1221no—
470C2×C42—1221no—
471C2×C42—1221no—
472C2×C42C22×D6111yescharacteristic
473#106—22no—
474#106—2441no—
475#103—22no—
476#103—614no—
477#103—614no—
478#103—1222no—
479#103—1222no—
480#103—1222no—
481#103—2441no—
482#103C4×D6114yescomplemented
483C22⋊C8—614no—
484#97—1222no—
485#97—2441no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—611no—
490#95—611no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497C24—611no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—612no—
504C2×Q8—612no—
505C2×Q8—612no—
506C2×Q8—612no—
507C2×Q8—1224no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×Q8—1228no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—2442no—
518C2×Q8—2442no—
519C2×Q8—2444no—
520C2×Q8—2444no—
521C2×Q8—2444no—
522C2×Q8C2×C4×D6112yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—611no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1224no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—4881no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4—2442no—
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4C23×D6111yescharacteristic
549Q16—1228no—
550Q16—2444no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—612no—
557C2×C8—612no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—2444no—
563C2×C8C2×C4×D6112yes—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—1224no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—4881no—
574C4⋊C4—2442no—
575C4⋊C4—2442no—
576C4⋊C4—2442no—
577C4⋊C4—2442no—
578C4⋊C4C2×C4×D6112yes—
579C4⋊C4D4×D6112yes—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4—1224no—
583C22⋊C4—2442no—
584C42—21no—
585C42—21no—
586C42—81no—
587C42—1221no—
588C42—1221no—
589C42—2442no—
590C42—2442no—
591C42—2442no—
592C23—612no—
593C23—612no—
594C23—612no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23C2×D4×D6111yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—41no—
603Q8—41no—
604Q8—614no—
605Q8—1222no—
606Q8—1222no—
607Q8—1222no—
608Q8—1222no—
609Q8—1222no—
610Q8—2448no—
611Q8—2441no—
612Q8—2441no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—612no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1221no—
635C2×C4—1222no—
636C2×C4—1221no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—4884no—
649C2×C4—2448no—
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×C4C22×C4×D6111yescharacteristic
659C2×C4C2×D4×D6111yescharacteristic
660C2×C4#41×D6111yescharacteristic
661C2×C4#41×D6111yescharacteristic
662C2×C4#1451982311yescharacteristic
663C2×C4#1451982311yescharacteristic
664C8—22no—
665C8—41no—
666C8—1222no—
667C8—1222no—
668C22—614no—
669C22—1222no—
670C22—1222no—
671C22—1222no—
672C22—1222no—
673C22—1222no—
674C22—1222no—
675C22C4×D4×D6111yescharacteristic
676C22#1684039611yescharacteristic
677C22#1684040411yescharacteristic
678C22#137×D6111yescharacteristic
679C22#137×D6111yescharacteristic
680C22#1684056811yescharacteristic
681C22#1684057611yescharacteristic
682C4—41no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—81no—
688C4—1222no—
689C4—1224no—
690C4—4881no—
691C4—4881no—
692C4—2442no—
693C4—2441no—
694C4—2441no—
695C4C4×D4×D6111yescharacteristic
696C4#1684023611yescharacteristic
697C4#1684040511yescharacteristic
698C4#1684043711yescharacteristic
699C2—1224no—
700C2#2144879711yescharacteristic
701C2#441×D6111yescharacteristic
702C2#2145465511yescharacteristic
703C2#2145733511yescharacteristic
704C2#2145738411yescharacteristic
705C2#2145787311yescharacteristic
706C2#2145793311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1927C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1927D61
hypocenterC61#22859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
2. C2×#16839868C2semidirect
6. #21446689C2semidirect
7. #21446511C2semidirect
9. #21446159C2semidirect
10. #21446157C2semidirect
11. #21446088C2semidirect
13. #21445652C2semidirect
15. C61×#1927C2semidirect
25. #16839919C4semidirect
76. C2×Dic244C2×C4semidirect
79. C2×#11758202C2×C4semidirect
116. #14519700C2×C4semidirect
139. #103×C61C2×C4semidirect
328. C2×D61#441semidirect
353. #1927D61semidirect
415. C61#22859semidirect
482. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399192
C2×#168398682
C2×#103×D612
#214488262
#214486532
#214466892
#214465112
#214462412
#214461592
#214461572
#214460882
#214460102
#214456522
#214455942
C61×#19272
#2285961