Finite Group Databasebeta

← #29696903

Subgroups — #29696903

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840495C211yesmaximal, characteristic
2C2×#16839889C211yesmaximal, characteristic, complemented
3#21448771C211yesmaximal, characteristic, complemented
4#21446750C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic
7#21446641C211yesmaximal, characteristic
8#21446634C211yesmaximal, characteristic, complemented
9#21446628C211yesmaximal, characteristic, complemented
10#21445833C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445648C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16#16840495—24no—
17#16840495C418yescomplemented
18C2×#14519773C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519764C2211yescharacteristic
21C2×#14519763—21no—
22C2×#14519760—21no—
23C2×#14519759—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28#16839889—24no—
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519687C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43C2×C4×#92418C2211yescharacteristic
44#16839666—21no—
45#16839647—21no—
46#16839644—21no—
47#16839631C2211yescharacteristic
48#16839627C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51C4×C4⋊Dic61C2211yescharacteristic
52#16839613—21no—
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#382C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122D411yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C4×D61—21no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519773—22no—
71#14519773C2×C414yes—
72#14519765—22no—
73#14519765C2×C414yes—
74#14519764—22no—
75#14519764C2×C414yes—
76#14519763—28no—
77#14519760—28no—
78#14519759—28no—
79C4×Dic122C2×C414yes—
80C4×Dic122D414yes—
81#14519742—22no—
82#14519742C2×C414yes—
83#14519739—22no—
84#14519739C2×C414yes—
85C4×C22⋊D61—28no—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196D411yescharacteristic
93C2×#11758196D411yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519706—22no—
106#14519706—22no—
107#14519702—22no—
108#14519702—41no—
109#14519700—22no—
110#14519700—41no—
111#14519699—22no—
112#14519699—41no—
113#14519698—22no—
114#14519698—22no—
115#14519697—22no—
116#14519697—41no—
117#14519687—22no—
118#14519687—22no—
119C4×#92418—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61C2×C414yes—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—22no—
137#102×C61—41no—
138#102×C61—41no—
139#95×C61—21no—
140#95×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C412yes—
149C22×C4×C61—21no—
150C22×C4×C61—24no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—81no—
154C22×C4×C61—81no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244C22×C412yes—
177C2×C4×D61—24no—
178C2×C4×D61—81no—
179C2×C4×D61—81no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—41no—
186C2×Dic122—41no—
187C2×Dic122C22⋊C414yes—
188C2×Dic122C22×C412yes—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—24no—
202C42×C61C22×C412yes—
203C42×C61C2×D412yes—
204C22⋊Dic61—24no—
205C22⋊Dic61—24no—
206#11758198—24no—
207#11758198—24no—
208#11758198—24no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22⋊C414yes—
213C4⋊Dic61#4112yes—
214#11758196—24no—
215#11758196—42no—
216#11758196—81no—
217#11758196C22⋊C414yes—
218#11758196C22⋊C414yes—
219C4×Dic61—24no—
220C4×Dic61—42no—
221C4×Dic61—81no—
222C4×Dic61—81no—
223C4×Dic61C22×C412yes—
224C4×Dic61C22×C412yes—
225C4×Dic61C2×D412yes—
226C4×Dic61C2×D412yes—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418#4112yes—
233C23×C61—22no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61C22×D411yescharacteristic
241C22×D61—22no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248D4×C61—22no—
249D4×C61—22no—
250D4×C61—41no—
251D4×C61—41no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
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—84no—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C612−1+411yescharacteristic
274C22⋊D61—48no—
275C22⋊D61—84no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61C2×C22⋊C412yes—
294C2×Dic61C2×C22⋊C412yes—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C2×C22⋊C412yes—
297D244—22no—
298D244—22no—
299D244—41no—
300D244—41no—
301C4×D61—84no—
302Dic122—22no—
303Dic122—22no—
304Dic122—44no—
305Dic122—41no—
306Dic122—41no—
307C8×C61—41no—
308C8×C61—41no—
309#92418—22no—
310#92418—41no—
311#22549—611nomaximal, Sylow
312C22×C61—42no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61C22×C22⋊C411yescharacteristic
320C22×C61#54811yescharacteristic
321C22×C61#55011yescharacteristic
322C22×C61#57511yescharacteristic
323C22×C61#57511yescharacteristic
324C22×C61#57611yescharacteristic
325C22×C61#57711yescharacteristic
326C2×D61—42no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—81no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—42no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61C4×#4111yescharacteristic
339C4×C61#52011yescharacteristic
340C4×C61#54811yescharacteristic
341C4×C61#55011yescharacteristic
342Dic61—22no—
343Dic61—22no—
344Dic61—22no—
345Dic61—22no—
346Dic61—42no—
347Dic61—42no—
348Dic61—81no—
349C2×#559—611no—
350C2×#446—611no—
351#2355—611no—
352#1983—611no—
353#1983—611no—
354#1982—611no—
355#1961—611no—
356#1959—611no—
357#1958—611no—
358#1805—611no—
359#1804D6111yescharacteristic, complemented
360#1802—611no—
361#1763—611no—
362#1762—611no—
363C4×#102—611no—
364C2×C61—82no—
365C2×C61#234111yescharacteristic
366C2×C61#289611yescharacteristic
367C2×C61#289711yescharacteristic
368C2×C61#337011yescharacteristic
369C2×C61#337111yescharacteristic
370C2×C61#340111yescharacteristic
371C2×C61#340311yescharacteristic
372D61—82no—
373#559—618no—
374#559—1224no—
375C2×#127—611no—
376C2×#124—611no—
377C2×#124—611no—
378C2×#124—1221no—
379C2×#123—1221no—
380C2×#123—1221no—
381C2×C4×Q8—611no—
382C2×C4×Q8—611no—
383C2×C4×D4—611no—
384C2×C4×D4—1221no—
385C2×C4×D4C2×D6111yescharacteristic
386#446—1224no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8C2×D6111yescharacteristic
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102C2×D6111yescharacteristic
401C2×#102C2×D6111yescharacteristic
402C2×#97—611no—
403C2×#97—611no—
404C2×C4×C8—611no—
405#391—1221no—
406#387—1221no—
407#387—1221no—
408#384—611no—
409#382—611no—
410#382C2×D6111yescharacteristic
411C4×C4⋊C4—611no—
412C4×C4⋊C4—611no—
413C4×C4⋊C4—611no—
414C4×C4⋊C4—1221no—
415#340—611no—
416#340—611no—
417#340C2×D6111yescharacteristic
418#340C2×D6111yescharacteristic
419C61#2254911yescharacteristic, complemented, Sylow
420C22×Q8—611no—
421C22×Q8—611no—
422C22×D4—611no—
423C22×D4—1221no—
424C22×D4—1221no—
425C22×D4C22×D6111yescharacteristic
426C23×C4—21no—
427C23×C4—1221no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8C22×D6111yescharacteristic
431C22×C8C22×D6111yescharacteristic
432#127—614no—
433#127—1222no—
434#124—614no—
435#124—614no—
436#124—1222no—
437#124—1228no—
438#124—1222no—
439#123—1228no—
440#123—1228no—
441C4×Q8—614no—
442C4×Q8—614no—
443C4×Q8—614no—
444C4×Q8—1222no—
445C4×D4—22no—
446C4×D4—614no—
447C4×D4—1222no—
448C4×D4—1228no—
449C4×D4C4×D6114yes—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4C22×D6111yescharacteristic
459C2×C4⋊C4C22×D6111yescharacteristic
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—1221no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—1221no—
470C2×C42—1221no—
471C2×C42—1221no—
472C2×C42—1221no—
473C2×C42C22×D6111yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477#103—1222no—
478#103—1222no—
479#103—2441no—
480#103—2441no—
481#102—41no—
482#102—41no—
483#102—1222no—
484#102—1222no—
485#102—1222no—
486#102—1222no—
487#102—2441no—
488#102—2441no—
489#97—1222no—
490#97—1222no—
491C4×C8—1222no—
492#95—21no—
493#95—21no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95—1221no—
499C24—21no—
500C24—1221no—
501C2×Q8—614no—
502C2×Q8—612no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—2441no—
509C2×Q8—2441no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—612no—
516C2×D4—1224no—
517C2×D4—1224no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—1221no—
523C2×D4—4881no—
524C2×D4—4881no—
525C2×D4—2442no—
526C2×D4—2442no—
527C2×D4C2×C4×D6112yes—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—1224no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—4881no—
543C22×C4—4881no—
544C22×C4D4×D6111yescharacteristic
545C22×C4D4×D6111yescharacteristic
546C22×C4C23×D6111yescharacteristic
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—612no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—614no—
565C4⋊C4—614no—
566C4⋊C4—614no—
567C4⋊C4—612no—
568C4⋊C4—1224no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—4881no—
573C4⋊C4—2442no—
574C4⋊C4C2×C4×D6112yes—
575C22⋊C4—24no—
576C22⋊C4—1224no—
577C22⋊C4—1224no—
578C22⋊C4—1224no—
579C22⋊C4—1224no—
580C22⋊C4—1224no—
581C42—612no—
582C42—612no—
583C42—612no—
584C42—612no—
585C42—1224no—
586C42—4881no—
587C42—4881no—
588C42—2442no—
589C42C2×C4×D6112yes—
590C42D4×D6112yes—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—1222no—
599C23—2441no—
600C23—2441no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23—2441no—
605C23C2×D4×D6111yescharacteristic
606Q8—1222no—
607Q8—1222no—
608Q8—2444no—
609Q8—2441no—
610Q8—2441no—
611D4—22no—
612D4—22no—
613D4—41no—
614D4—41no—
615D4—1222no—
616D4—1222no—
617D4—4884no—
618D4—2448no—
619D4—2441no—
620D4—2441no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—4884no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4C22⋊C4×D6112yes—
658C2×C4C22⋊C4×D6112yes—
659C2×C4C22×C4×D6111yescharacteristic
660C2×C4C2×D4×D6111yescharacteristic
661C2×C4#41×D6111yescharacteristic
662C2×C4#41×D6111yescharacteristic
663C2×C4#1451982211yescharacteristic
664C2×C4#1451982511yescharacteristic
665C8—41no—
666C8—41no—
667C8—1222no—
668C8—2441no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—4881no—
677C22—4881no—
678C22—4881no—
679C22—4881no—
680C22—2442no—
681C22—2442no—
682C22—2442no—
683C22C2×C22⋊C4×D6111yescharacteristic
684C22#1684042211yescharacteristic
685C22#1684043011yescharacteristic
686C22#1684055911yescharacteristic
687C22#1684055911yescharacteristic
688C22#1684056611yescharacteristic
689C22#1684057211yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—81no—
694C4—81no—
695C4—1222no—
696C4—1222no—
697C4—1222no—
698C4—1222no—
699C4—4881no—
700C4—2442no—
701C4—2442no—
702C4#1684023011yescharacteristic
703C4#1684024311yescharacteristic
704C4#1684042211yescharacteristic
705C4#1684043011yescharacteristic
706C2—82no—
707C2—4882no—
708C2#2144865611yescharacteristic
709C2#2145433411yescharacteristic
710C2#2145434411yescharacteristic
711C2#2145857011yescharacteristic
712C2#2145858511yescharacteristic
713C2#2145888311yescharacteristic
714C2#2145890711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
cosocleC22×C4×C61C24
hypercenter#1804D61
hypocenterC61#22549
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#16839889C2semidirect
3. #21448771C2semidirect
4. #21446750C2semidirect
5. #21446749C2semidirect
8. #21446634C2semidirect
9. #21446628C2semidirect
10. #21445833C2semidirect
11. #21445818C2semidirect
12. #21445648C2semidirect
13. #21445643C2semidirect
14. C4×#14519698C2semidirect
15. C61×#1804C2semidirect
17. #16840495C4semidirect
359. #1804D61semidirect
419. C61#22549semidirect

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×#168398892
#214487712
#214467502
#214467492
#214467442
#214466412
#214466342
#214466282
#214458332
#214458182
#214456482
#214456432
C4×#145196982
C61×#18042
#2254961