Finite Group Databasebeta

← #28618292

Subgroups — #28618292

Order 15104.

958 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837502C211yesmaximal, characteristic, complemented
2C2×#16837459C211yesmaximal, characteristic, complemented
3C4×#14273706C211yesmaximal, characteristic, complemented
4#21425587C211yesmaximal, characteristic, complemented
5#21425527C211yesmaximal, characteristic, complemented
6#21425484C211yesmaximal, characteristic, complemented
7#21425474C211yesmaximal, characteristic, complemented
8#21425413C211yesmaximal, characteristic, complemented
9#21425299C211yesmaximal, characteristic, complemented
10#21425282C211yesmaximal, characteristic
11#21425099C211yesmaximal, characteristic
12#21423994C211yesmaximal, characteristic, complemented
13#21423929C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C4×#121×C59C211yesmaximal, characteristic
16C22×#11745670C2211yescharacteristic
17C2×#14273706C2211yescharacteristic
18C2×C4×Dic118C2211yescharacteristic
19#16837502—24no—
20#16837459—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273650C2211yescharacteristic
27C2×#14273650C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837286—21no—
39#16837275—21no—
40#16837262C2211yescharacteristic
41C4×Dic59⋊C4—21no—
42C4×C4⋊Dic59C2211yescharacteristic
43C4×C22⋊Dic59—21no—
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C2×C4×D4×C59—21no—
52C2×C4×D4×C59C2211yescharacteristic
53C22×C42×C59C2211yescharacteristic
54C59×#390C2211yescharacteristic
55C59×#389C2211yescharacteristic
56C59×#388—21no—
57C59×#386—21no—
58C59×#380C2211yescharacteristic
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C22×Dic118C2311yescharacteristic
62C2×#11745670—22no—
63C2×#11745670—22no—
64C2×#11745670—22no—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69#14273706—22no—
70#14273706—22no—
71C4×Dic118—22no—
72C4×Dic118—22no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C4×Dic59—21no—
82C2×C4×Dic59—21no—
83#14273660—22no—
84#14273660—22no—
85#14273658—22no—
86C4⋊(C59⋊C8)—22no—
87C4⋊(C59⋊C8)—22no—
88#14273650—22no—
89#14273650—22no—
90#14273650—22no—
91#14273648—22no—
92#14273648—22no—
93#14273648—22no—
94C22⋊(C59⋊C8)—22no—
95C22⋊(C59⋊C8)—22no—
96#14273638—22no—
97#14273638D414yescomplemented
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C22×D4×C59—21no—
104C22×D4×C59C2311yescharacteristic
105C23×C4×C59—21no—
106C23×C4×C59D411yescharacteristic
107C23×C4×C59D411yescharacteristic
108C23×C4×C59C2311yescharacteristic
109#121×C59—22no—
110#121×C59—22no—
111C4×D4×C59—22no—
112C4×D4×C59—22no—
113C4×D4×C59—44no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C4⋊C4×C59C2311yescharacteristic
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C42×C59—22no—
124C2×C42×C59—22no—
125C2×C42×C59—21no—
126C2×C42×C59D411yescharacteristic
127C2×C42×C59D411yescharacteristic
128C2×C42×C59C2311yescharacteristic
129C2×C42×C59C2311yescharacteristic
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133C24×C59—21no—
134C24×C59C2×D411yescharacteristic
135C2×D4×C59—24no—
136C2×D4×C59—21no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—42no—
142C2×D4×C59—42no—
143C2×D4×C59#4112yes—
144C22×C4×C59—22no—
145C22×C4×C59—21no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—41no—
158C22×C4×C59—41no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—42no—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2411yescharacteristic
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C2×Dic118—21no—
173C2×Dic118—21no—
174C2×Dic118—21no—
175C2×Dic118—21no—
176C2×Dic118—21no—
177C2×Dic118#4112yes—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—42no—
184C4⋊C4×C59#4112yes—
185C22⋊C4×C59—24no—
186C22⋊C4×C59—42no—
187C22⋊C4×C59—42no—
188C22⋊C4×C59—42no—
189C22⋊C4×C59—42no—
190C42×C59—22no—
191C42×C59—22no—
192C42×C59—21no—
193C42×C59—21no—
194C42×C59—42no—
195C42×C59C2×D412yes—
196C42×C59#4112yes—
197C22⋊Dic59—24no—
198C22⋊Dic59—42no—
199#11745670—28no—
200C4⋊Dic59—21no—
201C4⋊Dic59—21no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59#4112yes—
206Dic59⋊C4—24no—
207Dic59⋊C4—42no—
208Dic59⋊C4—42no—
209C4×Dic59—42no—
210C4×Dic59—42no—
211C2×C59⋊C8—21no—
212C2×C59⋊C8—21no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8C2×D412yes—
222C2×C59⋊C8C2×D412yes—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—22no—
230C23×C59—41no—
231C23×C59—41no—
232C23×C59—41no—
233C23×C59—41no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59#13712yes—
237C23×C59C22×D411yescharacteristic
238D4×C59—22no—
239D4×C59—22no—
240D4×C59—48no—
241D4×C59—41no—
242D4×C59—41no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—22no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—44no—
257C2×C4×C59—44no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—84no—
271C2×C4×C59#12112yes—
272C2×C4×C59#12112yes—
273C2×C4×C59AGL(1,ℤ/8)12yes—
274C2×C4×C59C22×D411yescharacteristic
275C2×C4×C59C2×#4111yescharacteristic
276C2×C4×C59C2×#4111yescharacteristic
277C2×C4×C59C2×#4111yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×Dic59—22no—
281C2×Dic59—22no—
282C2×Dic59—41no—
283C2×Dic59—41no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292Dic118—22no—
293Dic118—22no—
294Dic118—41no—
295Dic118—41no—
296C59⋊C8—22no—
297C59⋊C8—22no—
298C59⋊C8—41no—
299C59⋊C8—41no—
300#23711—591nomaximal, Sylow
301C22×C59—22no—
302C22×C59—22no—
303C22×C59—22no—
304C22×C59—41no—
305C22×C59—41no—
306C22×C59—41no—
307C22×C59—41no—
308C22×C59—42no—
309C22×C59—42no—
310C22×C59—42no—
311C22×C59—81no—
312C22×C59—81no—
313C22×C59—81no—
314C22×C59—81no—
315C22×C59C2×#12111yescharacteristic
316C22×C59#52511yescharacteristic
317C22×C59#52511yescharacteristic
318C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C59C2×#13711yescharacteristic
320C22×C59#57511yescharacteristic
321C22×C59#57511yescharacteristic
322C4×C59—22no—
323C4×C59—22no—
324C4×C59—22no—
325C4×C59—42no—
326C4×C59—41no—
327C4×C59—41no—
328C4×C59—81no—
329C4×C59—81no—
330C4×C59#52511yescharacteristic
331C4×C59#52911yescharacteristic
332C4×C59#52911yescharacteristic
333C4×C59#53211yescharacteristic
334Dic59—42no—
335Dic59—42no—
336Dic59—81no—
337Dic59—81no—
338C2×#440—591no—
339C2×#432—591no—
340C4×C22⋊Q8—591no—
341C4×#121D5911yescharacteristic
342#2086—591no—
343#2076—591no—
344#2067—591no—
345#2066—591no—
346#2055—591no—
347#2036—591no—
348#2034—591no—
349#2000—591no—
350#1776—591no—
351#1763—591no—
352#1762—591no—
353C2×C59—42no—
354C2×C59—82no—
355C2×C59#239211yescharacteristic
356C2×C59#305511yescharacteristic
357C2×C59#305611yescharacteristic
358C2×C59#311011yescharacteristic
359C2×C59#311111yescharacteristic
360C2×C59#311511yescharacteristic
361C2×C59#311711yescharacteristic
362C22×SD16—591no—
363C2×C22⋊Q8—591no—
364C2×#121C2×D5911yescharacteristic
365C2×C4×Q8—591no—
366C2×C4×D4—21no—
367C2×C4×D4C2×D5911yescharacteristic
368C22×C42C2×D5911yescharacteristic
369#440—1184no—
370#432—1184no—
371C2×#107—591no—
372C2×#107—591no—
373C2×#106—591no—
374C2×C4⋊C8—591no—
375C2×C4⋊C8—591no—
376C2×#103—591no—
377C2×#103—591no—
378C2×#103—591no—
379C2×#102—591no—
380C2×#102—591no—
381C2×#102—591no—
382C2×C22⋊C8—591no—
383C2×C22⋊C8—591no—
384C2×#97—591no—
385C2×#97—591no—
386#391—591no—
387#390C2×D5911yescharacteristic
388#389—591no—
389#389C2×D5911yescharacteristic
390#388—21no—
391#387—1181no—
392#386—21no—
393#385—1181no—
394#380—591no—
395#380C2×D5911yescharacteristic
396C4×C4⋊C4—591no—
397C4×C4⋊C4—1181no—
398C4×C4⋊C4C2×D5911yescharacteristic
399C4×C22⋊C4—21no—
400C4×C22⋊C4—1181no—
401#340—591no—
402#340—591no—
403#340—591no—
404#340—591no—
405#340—591no—
406#340—591no—
407C59#2371111yescharacteristic, complemented, Sylow
408C22×Q8—591no—
409C22×D4—21no—
410C22×D4C22×D5911yescharacteristic
411C23×C4—21no—
412C23×C4C22⋊D5911yescharacteristic
413C23×C4C22⋊D5911yescharacteristic
414C23×C4C22×D5911yescharacteristic
415C2×SD16—1182no—
416C2×SD16—1182no—
417C2×SD16—1182no—
418C22×C8—591no—
419C22×C8—591no—
420C22×C8—591no—
421C22×C8—591no—
422C22⋊Q8—1182no—
423C22⋊Q8—1182no—
424#121—22no—
425#121—22no—
426C4×Q8—1182no—
427C4×Q8—1182no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—44no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—591no—
433C2×C4⋊C4—591no—
434C2×C4⋊C4—591no—
435C2×C4⋊C4—1181no—
436C2×C4⋊C4—1181no—
437C2×C4⋊C4—1181no—
438C2×C4⋊C4C22×D5911yescharacteristic
439C2×C4⋊C4C22×D5911yescharacteristic
440C2×C4⋊C4C22×D5911yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—1181no—
447C2×C22⋊C4—1181no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—21no—
451C2×C42—1181no—
452C2×C42—1181no—
453C2×C42C22⋊D5911yescharacteristic
454C2×C42C22⋊D5911yescharacteristic
455C2×C42C22×D5911yescharacteristic
456C2×C42C22×D5911yescharacteristic
457#107—1182no—
458#107—1182no—
459#106—1182no—
460C4⋊C8—1182no—
461C4⋊C8—1182no—
462#103—1182no—
463#103—1182no—
464#103—1182no—
465#102—1182no—
466#102—1182no—
467#102—1182no—
468C22⋊C8—1182no—
469C22⋊C8—1182no—
470#97—594no—
471#97—1182no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—1181no—
476#95—1181no—
477#95—1181no—
478#95—1181no—
479#95—1181no—
480C24—21no—
481C24C2×C22⋊D5911yescharacteristic
482C2×Q8—592no—
483C2×Q8—1181no—
484C2×Q8—1181no—
485C2×Q8—1181no—
486C2×Q8—1181no—
487C2×Q8—1181no—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4#1174568512yes—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—1181no—
516C22×C4—1181no—
517C22×C4—1181no—
518C22×C4—1181no—
519C22×C4C2×C22⋊D5911yescharacteristic
520C22×C4C2×C22⋊D5911yescharacteristic
521C22×C4C2×C22⋊D5911yescharacteristic
522C22×C4C2×C22⋊D5911yescharacteristic
523C22×C4C2×C22⋊D5911yescharacteristic
524C22×C4C23×D5911yescharacteristic
525SD16—1188no—
526C2×C8—592no—
527C2×C8—592no—
528C2×C8—1181no—
529C2×C8—1181no—
530C2×C8—1181no—
531C2×C8—1181no—
532C2×C8—1181no—
533C2×C8—1181no—
534C2×C8—1181no—
535C2×C8—1181no—
536C2×C8—1181no—
537C2×C8—1181no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—592no—
545C4⋊C4—1184no—
546C4⋊C4—1181no—
547C4⋊C4—1181no—
548C4⋊C4—1181no—
549C4⋊C4—1181no—
550C4⋊C4—1181no—
551C4⋊C4—2362no—
552C4⋊C4—2362no—
553C4⋊C4#1174568512yes—
554C22⋊C4—24no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—1184no—
560C22⋊C4—2362no—
561C42—22no—
562C42—22no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—2362no—
567C42—2362no—
568C42D4×D5912yes—
569C42#1174568712yes—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23#1427375712yes—
584C23C22×C22⋊D5911yescharacteristic
585Q8—1182no—
586Q8—1182no—
587Q8—2361no—
588Q8—2361no—
589D4—22no—
590D4—22no—
591D4—48no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—1182no—
623C2×C4—1182no—
624C2×C4—2361no—
625C2×C4—2361no—
626C2×C4—2361no—
627C2×C4—2361no—
628C2×C4—2361no—
629C2×C4—2361no—
630C2×C4—2361no—
631C2×C4—2361no—
632C2×C4—2361no—
633C2×C4—2361no—
634C2×C4#1427369912yes—
635C2×C4#1427369912yes—
636C2×C4#1427375312yes—
637C2×C4C2×D4×D5911yescharacteristic
638C2×C4#41×D5911yescharacteristic
639C2×C4#41×D5911yescharacteristic
640C2×C4C2×#1174568711yescharacteristic
641C2×C4C2×#1174568511yescharacteristic
642C2×C4C2×#1174568511yescharacteristic
643C8—1182no—
644C8—1182no—
645C8—2361no—
646C8—2361no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×#1427369911yescharacteristic
662C22#1683790911yescharacteristic
663C22#1683791311yescharacteristic
664C22C2×#1427375311yescharacteristic
665C22C2×#1427375711yescharacteristic
666C22#1683820011yescharacteristic
667C22#1683820011yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—4721no—
677C4—4721no—
678C4—2362no—
679C4—2362no—
680C4#1683791111yescharacteristic
681C4#1683793211yescharacteristic
682C4#1683793411yescharacteristic
683C4#1683794911yescharacteristic
684C2—42no—
685C2—82no—
686C2#2142733811yescharacteristic
687C2#2143371111yescharacteristic
688C2#2143372811yescharacteristic
689C2#2143419511yescharacteristic
690C2#2143420511yescharacteristic
691C2#2143424111yescharacteristic
692C2#2143426311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×#121×C59C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC4×#121D59
hypocenterC59#23711
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16837502C2semidirect
2. C2×#16837459C2semidirect
3. C4×#14273706C2semidirect
4. #21425587C2semidirect
5. #21425527C2semidirect
6. #21425484C2semidirect
7. #21425474C2semidirect
8. #21425413C2semidirect
9. #21425299C2semidirect
12. #21423994C2semidirect
13. #21423929C2semidirect
14. #21423921C2semidirect
97. #14273638D4semidirect
407. C59#23711semidirect

Maximal subgroups

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

subgroupindex
C2×#168375022
C2×#168374592
C4×#142737062
#214255872
#214255272
#214254842
#214254742
#214254132
#214252992
#214252822
#214250992
#214239942
#214239292
#214239212
C4×#121×C592
#2371159