Finite Group Databasebeta

← #28645755

Subgroups — #28645755

Order 15104.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837685C211yesmaximal, characteristic, complemented
2#21427781C211yesmaximal, characteristic, complemented
3#21426937C211yesmaximal, characteristic
4#21425619C211yesmaximal, characteristic, complemented
5#21425468C211yesmaximal, characteristic, complemented
6#21425466C211yesmaximal, characteristic, complemented
7#21425230C211yesmaximal, characteristic, complemented
8#21424366C211yesmaximal, characteristic, complemented
9#21424348C211yesmaximal, characteristic, complemented
10#21424295C211yesmaximal, characteristic, complemented
11#21424274C211yesmaximal, characteristic, complemented
12#21424121C211yesmaximal, characteristic, complemented
13#21424109C211yesmaximal, characteristic, complemented
14#21424036C211yesmaximal, characteristic
15C2×C59×#416C211yesmaximal, characteristic
16C2×#14273726C2211yescharacteristic
17C2×Q8×Dic59C2211yescharacteristic
18C2×Q8×Dic59C2211yescharacteristic
19#16837685—24no—
20C2×#14273660C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×Dic59⋊C8C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31#16837325—21no—
32#16837314—21no—
33#16837308—21no—
34#16837305—21no—
35#16837305—21no—
36#16837305C2211yescharacteristic
37#16837305C2211yescharacteristic
38#16837301C2211yescharacteristic
39#16837298C2211yescharacteristic
40#16837286—21no—
41#16837267C2211yescharacteristic
42#16837262—21no—
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45C4×C22⋊Dic59—21no—
46C4×C22⋊Dic59C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837156C2211yescharacteristic
52#16837156C2211yescharacteristic
53C22×#41×C59C2211yescharacteristic
54C23×C8×C59C2211yescharacteristic
55C2×#117×C59C2211yescharacteristic
56C59×#416—24no—
57C2×#103×C59C2211yescharacteristic
58C2×#103×C59C2211yescharacteristic
59C2×#102×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C22×Dic118—21no—
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64#14273726—22no—
65#14273726—41no—
66Q8×Dic59—22no—
67Q8×Dic59—22no—
68Q8×Dic59—41no—
69Q8×Dic59—41no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59—21no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59D411yescharacteristic
86C2×C22⋊Dic59D411yescharacteristic
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89C2×C4×Dic59C2311yescharacteristic
90C2×C4×Dic59C2311yescharacteristic
91#14273660—41no—
92#14273659—22no—
93#14273659—41no—
94#14273658—22no—
95Dic59⋊C8—22no—
96Dic59⋊C8—41no—
97#14273651—22no—
98#14273651—22no—
99#14273648—41no—
100#14273648—41no—
101C22⋊(C59⋊C8)—22no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95D411yescharacteristic
109C59⋊#95D411yescharacteristic
110C2×#41×C59—22no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—41no—
114C2×#41×C59—41no—
115C2×#41×C59Q814yescomplemented
116C22×Q8×C59C2311yescharacteristic
117C22×D4×C59—21no—
118C22×D4×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C23×C4×C59C2311yescharacteristic
121C22×C8×C59—22no—
122C22×C8×C59—22no—
123C22×C8×C59—41no—
124C22×C8×C59C2311yescharacteristic
125C22×C8×C59C2311yescharacteristic
126#117×C59—22no—
127#117×C59—41no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C42×C59—21no—
132#103×C59—22no—
133#103×C59D414yes—
134#102×C59—22no—
135#102×C59—22no—
136C24×C59—21no—
137C24×C59C2×D411yescharacteristic
138#41×C59—28no—
139#41×C59—44no—
140#41×C59—44no—
141#41×C59—44no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59C2×D412yes—
146C2×Q8×C59C2×Q812yes—
147C2×Q8×C59#4112yes—
148C2×D4×C59—24no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—42no—
155C2×D4×C59—42no—
156C2×D4×C59C2×Q812yes—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—24no—
164C22×C4×C59—21no—
165C22×C4×C59—42no—
166C22×C4×C59—42no—
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×Q812yes—
169C22×C4×C59#4112yes—
170C22×C4×C59C2411yescharacteristic
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59C2×D411yescharacteristic
176C22×Dic59C2×D411yescharacteristic
177C22×Dic59C2×D411yescharacteristic
178C22×Dic59C2×D411yescharacteristic
179C2×Dic118—42no—
180C2×Dic118—42no—
181C2×Dic118—81no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—44no—
188C2×C8×C59C2×D412yes—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59C2×D412yes—
193C22⋊C4×C59—42no—
194C42×C59—42no—
195C22⋊Dic59—22no—
196C22⋊Dic59—41no—
197C22⋊Dic59—42no—
198C22⋊Dic59—42no—
199C22⋊Dic59—81no—
200C22⋊Dic59—81no—
201C22⋊Dic59—81no—
202C22⋊Dic59—81no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—42no—
212C4⋊Dic59—42no—
213C4⋊Dic59—81no—
214Dic59⋊C4—42no—
215Dic59⋊C4—42no—
216C4×Dic59—21no—
217C4×Dic59—21no—
218C4×Dic59—21no—
219C4×Dic59—21no—
220C4×Dic59—42no—
221C4×Dic59—42no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—22no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59C22⋊Q812yes—
242C23×C59C22×D411yescharacteristic
243Q8×C59—22no—
244Q8×C59—22no—
245Q8×C59—22no—
246Q8×C59C22⋊Q814yes—
247D4×C59—22no—
248D4×C59—22no—
249D4×C59—48no—
250D4×C59—41no—
251D4×C59—41no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—21no—
255C2×C4×C59—22no—
256C2×C4×C59—21no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—48no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59C22⋊Q812yes—
269C2×C4×C59C22×D411yescharacteristic
270C2×C4×C59C22×Q811yescharacteristic
271C2×C4×C59C2×#4111yescharacteristic
272C2×C4×C59C2×#4111yescharacteristic
273C2×C4×C59H(5,𝔽2)11yescharacteristic
274C2×C4×C59H(5,𝔽2)11yescharacteristic
275C2×Dic59—21no—
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59#13512yes—
299Dic118—84no—
300C8×C59—22no—
301C8×C59—41no—
302C59⋊C8—41no—
303C59⋊C8—41no—
304#25951—591nomaximal, Sylow
305C22×C59—22no—
306C22×C59—22no—
307C22×C59—22no—
308C22×C59—41no—
309C22×C59—41no—
310C22×C59—41no—
311C22×C59—41no—
312C22×C59—42no—
313C22×C59—42no—
314C22×C59—42no—
315C22×C59—81no—
316C22×C59—81no—
317C22×C59—81no—
318C22×C59—81no—
319C22×C59C2×C22⋊Q811yescharacteristic
320C22×C59D4211yescharacteristic
321C22×C59#54611yescharacteristic
322C22×C59C2×#13511yescharacteristic
323C22×C59#57511yescharacteristic
324C22×C59#57711yescharacteristic
325C22×C59#57711yescharacteristic
326C4×C59—22no—
327C4×C59—24no—
328C4×C59—42no—
329C4×C59—81no—
330C4×C59C2×C22⋊Q811yescharacteristic
331C4×C59#54311yescharacteristic
332C4×C59#54611yescharacteristic
333C4×C59#55111yescharacteristic
334Dic59—22no—
335Dic59—41no—
336Dic59—41no—
337Dic59—41no—
338Dic59—81no—
339Dic59—81no—
340Dic59—81no—
341Dic59—81no—
342C2×#475—591no—
343C2×#416D5911yescharacteristic
344#2439—591no—
345#2341—591no—
346#2092—591no—
347#2065—591no—
348#2065—591no—
349#2023—591no—
350#1865—591no—
351#1863—591no—
352#1854—591no—
353#1850—591no—
354#1807—591no—
355#1805—591no—
356#1788—591no—
357C2×C59—42no—
358C2×C59—82no—
359C2×C59#243711yescharacteristic
360C2×C59#307611yescharacteristic
361C2×C59#308411yescharacteristic
362C2×C59#327111yescharacteristic
363C2×C59#328211yescharacteristic
364C2×C59#330411yescharacteristic
365C2×C59#332111yescharacteristic
366C22×#41C2×D5911yescharacteristic
367C23×C8C2×D5911yescharacteristic
368C2×C4⋊Q8—591no—
369C2×C4×Q8—591no—
370C2×C4×Q8—591no—
371C2×#117C2×D5911yescharacteristic
372#475—1184no—
373C2×#107—591no—
374C2×#106—591no—
375C2×#106—591no—
376C2×#106—591no—
377C2×C4⋊C8—591no—
378C2×C4⋊C8—591no—
379#416—24no—
380C2×#103—591no—
381C2×#103—591no—
382C2×#103C2×D5911yescharacteristic
383C2×#103C2×D5911yescharacteristic
384C2×#102—591no—
385C2×#102—591no—
386C2×#102C2×D5911yescharacteristic
387C2×#102C2×D5911yescharacteristic
388C2×C22⋊C8—591no—
389#396—1181no—
390#393—1181no—
391#391—1181no—
392#390—591no—
393#390—591no—
394#390—1181no—
395#390—1181no—
396#389—591no—
397#389—591no—
398#387—1181no—
399#382—591no—
400#380—591no—
401#380—591no—
402#380—1181no—
403C4×C22⋊C4—591no—
404C4×C22⋊C4—1181no—
405#340—591no—
406#340—591no—
407#340—591no—
408#340—591no—
409#336—591no—
410#336—591no—
411C59#2595111yescharacteristic, complemented, Sylow
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41Dic11814yescomplemented
418C22×Q8—1181no—
419C22×Q8C22×D5911yescharacteristic
420C22×D4—21no—
421C22×D4C22×D5911yescharacteristic
422C23×C4—21no—
423C23×C4C22×D5911yescharacteristic
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—591no—
428C22×C8—591no—
429C22×C8C22×D5911yescharacteristic
430C22×C8C22×D5911yescharacteristic
431C4⋊Q8—1182no—
432C4⋊Q8—2361no—
433C4×Q8—1182no—
434C4×Q8—1182no—
435C4×Q8—2361no—
436C4×Q8—2361no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—591no—
440C2×C4⋊C4—591no—
441C2×C4⋊C4—591no—
442C2×C4⋊C4—591no—
443C2×C4⋊C4—1181no—
444C2×C4⋊C4—1181no—
445C2×C4⋊C4—1181no—
446C2×C4⋊C4—1181no—
447C2×C4⋊C4—1181no—
448C2×C4⋊C4C22×D5911yescharacteristic
449C2×C4⋊C4C22×D5911yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—591no—
452C2×C22⋊C4—591no—
453C2×C22⋊C4—1181no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C42—21no—
460C2×C42—591no—
461C2×C42—591no—
462C2×C42—1181no—
463C2×C42—1181no—
464#107—2361no—
465#106—1182no—
466#106—1182no—
467#106—2361no—
468C4⋊C8—1182no—
469C4⋊C8—2361no—
470#103—22no—
471#103—1182no—
472#103—1182no—
473#103C22⋊D5914yes—
474#102—22no—
475#102—22no—
476#102—2361no—
477#102—2361no—
478C22⋊C8—1182no—
479#95—591no—
480#95—591no—
481#95—1181no—
482#95—1181no—
483#95—1181no—
484#95—1181no—
485#95—1181no—
486#95—1181no—
487C24—21no—
488C24D4×D5911yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—4721no—
497C2×Q8—2362no—
498C2×Q8—2362no—
499C2×Q8C2×Dic11812yes—
500C2×Q8#1174568512yes—
501C2×Q8C2×C22⋊D5912yes—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4C2×Dic11812yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—591no—
522C22×C4—591no—
523C22×C4—591no—
524C22×C4—591no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4C2×Dic11812yes—
530C22×C4D4×D5911yescharacteristic
531C22×C4#1174568712yes—
532C22×C4C23×D5911yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—44no—
539C2×C8—1181no—
540C2×C8—1181no—
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8C2×C22⋊D5912yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—1181no—
550C4⋊C4—1181no—
551C4⋊C4—1181no—
552C4⋊C4—1181no—
553C4⋊C4—1181no—
554C4⋊C4—1181no—
555C4⋊C4—1181no—
556C4⋊C4—1181no—
557C4⋊C4—4721no—
558C4⋊C4—2362no—
559C4⋊C4—2362no—
560C4⋊C4—2362no—
561C4⋊C4—2362no—
562C4⋊C4C2×C22⋊D5912yes—
563C22⋊C4—42no—
564C22⋊C4—1182no—
565C22⋊C4—4721no—
566C22⋊C4—4721no—
567C22⋊C4—4721no—
568C22⋊C4—4721no—
569C22⋊C4—2362no—
570C22⋊C4—2361no—
571C22⋊C4—2362no—
572C42—42no—
573C42—1181no—
574C42—1181no—
575C42—1181no—
576C42—1181no—
577C42—2362no—
578C42—2362no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23#1427370412yes—
593C23C2×D4×D5911yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—4724no—
598Q8#1427370614yes—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—48no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—592no—
621C2×C4—1181no—
622C2×C4—1181no—
623C2×C4—1181no—
624C2×C4—1181no—
625C2×C4—1181no—
626C2×C4—1181no—
627C2×C4—1181no—
628C2×C4—1181no—
629C2×C4—1181no—
630C2×C4—1181no—
631C2×C4—1181no—
632C2×C4—2361no—
633C2×C4—2361no—
634C2×C4—2361no—
635C2×C4—2361no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4#1427370412yes—
645C2×C4C22×C22⋊D5911yescharacteristic
646C2×C4C22×Dic11811yescharacteristic
647C2×C4C2×#1174568711yescharacteristic
648C2×C4C2×#1174568511yescharacteristic
649C2×C4#1427377211yescharacteristic
650C2×C4#1427377211yescharacteristic
651C8—22no—
652C8—41no—
653C8—2361no—
654C8—2361no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×#1427370411yescharacteristic
670C22D4×C22⋊D5911yescharacteristic
671C22#1683804211yescharacteristic
672C22#135×D5911yescharacteristic
673C22#1683819911yescharacteristic
674C22#1683820911yescharacteristic
675C22#1683820911yescharacteristic
676C4—22no—
677C4—24no—
678C4—42no—
679C4—81no—
680C4—1182no—
681C4—4721no—
682C4—4721no—
683C4—4721no—
684C4—4721no—
685C4—2361no—
686C4—2361no—
687C4—2361no—
688C4C2×#1427370611yescharacteristic
689C4#1683802811yescharacteristic
690C4#1683804611yescharacteristic
691C4#1683807811yescharacteristic
692C2—42no—
693C2—82no—
694C2#2142775711yescharacteristic
695C2#2143388011yescharacteristic
696C2#2143395611yescharacteristic
697C2#2143568111yescharacteristic
698C2#2143579711yescharacteristic
699C2#2143603111yescharacteristic
700C2#2143627811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#416C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
hypercenterC2×#416D59
hypocenterC59#25951
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16837685C2semidirect
2. #21427781C2semidirect
4. #21425619C2semidirect
5. #21425468C2semidirect
6. #21425466C2semidirect
7. #21425230C2semidirect
8. #21424366C2semidirect
9. #21424348C2semidirect
10. #21424295C2semidirect
11. #21424274C2semidirect
12. #21424121C2semidirect
13. #21424109C2semidirect
115. C2×#41×C59Q8semidirect
411. C59#25951semidirect
417. C2×#41Dic118semidirect

Maximal subgroups

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

subgroupindex
C2×#168376852
#214277812
#214269372
#214256192
#214254682
#214254662
#214252302
#214243662
#214243482
#214242952
#214242742
#214241212
#214241092
#214240362
C2×C59×#4162
#2595159