Finite Group Databasebeta

← #27310857

Subgroups — #27310857

Order 13568.

2242 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C2×#16810540C211yesmaximal, characteristic
3C2×#16810494C212yesmaximal, complemented
4#20272979C211yesmaximal, characteristic, complemented
5#20272968C211yesmaximal, characteristic, complemented
6#20272963C212yesmaximal, complemented
7#20272959C212yesmaximal, complemented
8#20272955C211yesmaximal, characteristic
9#20272942C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal, complemented
11C2×C53×#387C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2212yes—
14C2×C4×D212—28no—
15C2×C4×D212—24no—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719919C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2212yes—
20C22×#11719921C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23#16810540C418yescomplemented
24#16810494—28no—
25C2×#13133124C2212yes—
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C22×C4⋊C4×C53C2211yescharacteristic
33C22×C4⋊C4×C53C2211yescharacteristic
34C22×C42×C53C2211yescharacteristic
35C53×#387—24no—
36C2×#95×C53C2211yescharacteristic
37C2×#95×C53C2211yescharacteristic
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C24×D53C2312yes—
41C22×D212—24no—
42C22×D212—24no—
43C22×D212—22no—
44C22×D212—22no—
45C22×D212C2×C414yes—
46C23×Dic53C2312yes—
47C23×Dic53C2312yes—
48C23×Dic53C2312yes—
49C22×C4×D53—24no—
50C22×C4×D53—24no—
51C22×C4×D53—42no—
52C22×C4×D53—42no—
53C22×C4×D53—42no—
54C22×C4×D53—42no—
55C22×C4×D53D418yes—
56C4×D212—232no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—24no—
59C2×#11719919—24no—
60C2×#11719919—42no—
61C2×#11719919—42no—
62C2×#11719921—24no—
63C2×#11719921—24no—
64C2×#11719921—24no—
65C2×#11719921—24no—
66C2×#11719921—24no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—42no—
70C2×#11719921—42no—
71C2×#11719921—42no—
72C2×#11719921—42no—
73C2×#11719921—42no—
74C2×#11719921—42no—
75C2×#11719921C2×C418yescomplemented
76C2×#11719921C2×C418yescomplemented
77#13133124—24no—
78#13133124—22no—
79#13133124—24no—
80#13133124—42no—
81#13133124—42no—
82#13133124—42no—
83#13133124C2×C414yescomplemented
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—24no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53C2×C414yescomplemented
96C2×C42×C53—24no—
97C2×C42×C53D414yes—
98#95×C53—22no—
99#95×C53—22no—
100#95×C53—22no—
101#95×C53—22no—
102C24×C53C2411yescharacteristic
103C23×D53—22no—
104C23×D53—22no—
105C23×D53—22no—
106C23×D53—22no—
107C23×D53—22no—
108C23×D53—22no—
109C23×D53—22no—
110C23×D53—22no—
111C23×D53—22no—
112C23×D53—22no—
113C23×D53—22no—
114C23×D53—22no—
115C23×D53C22×C414yes—
116C23×D53C2×D414yes—
117C23×D53#4114yes—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—21no—
121C22×C4×C53—22no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53C22×C412yes—
148C22×C4×C53C22×C412yes—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C2×D412yes—
151C22×C4×C53C2×D412yes—
152C22×C4×C53C2×D414yes—
153C22×C4×C53C2×D412yes—
154C22×C4×C53#4112yes—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53C22×C414yes—
175C22×Dic53C2×D414yes—
176C2×D212—28no—
177C2×D212—28no—
178C2×D212—216no—
179C2×D212—216no—
180C2×D212—28no—
181C2×C4×D53—216no—
182C2×C4×D53—48no—
183C2×C4×D53—48no—
184C2×C4×D53—48no—
185C2×C4×D53—48no—
186C2×C4×D53—48no—
187C2×C4×D53—48no—
188C4⋊C4×C53—28no—
189C4⋊C4×C53—44no—
190C42×C53—28no—
191#11719921—216no—
192#11719921—216no—
193#11719921—48no—
194#11719921—48no—
195#11719921—48no—
196C4⋊Dic53—28no—
197#11719919—48no—
198C23×C53C23×C411yescharacteristic
199C23×C53C22×D412yes—
200C23×C53C22×D411yescharacteristic
201C23×C53C2×#4112yes—
202C23×C53C2×#4111yescharacteristic
203C23×C53H(5,𝔽2)11yescharacteristic
204C23×C53H(5,𝔽2)11yescharacteristic
205C23×C53H(5,𝔽2)12yes—
206C23×C53H(5,𝔽2)11yescharacteristic
207C23×C532−1+411yescharacteristic
208C23×C532−1+412yes—
209C22×D53—24no—
210C22×D53—24no—
211C22×D53—24no—
212C22×D53—24no—
213C22×D53—24no—
214C22×D53—24no—
215C22×D53—24no—
216C22×D53—24no—
217C22×D53—24no—
218C22×D53—24no—
219C22×D53—24no—
220C22×D53—24no—
221C22×D53—24no—
222C22×D53—24no—
223C22×D53—24no—
224C22×D53—24no—
225C22×D53—24no—
226C22×D53—24no—
227C22×D53—42no—
228C22×D53—42no—
229C22×D53—42no—
230C22×D53—42no—
231C22×D53—42no—
232C22×D53—42no—
233C22×D53—42no—
234C22×D53—42no—
235C22×D53—42no—
236C22×D53—42no—
237C22×D53—42no—
238C22×D53—42no—
239C22×D53—42no—
240C22×D53—42no—
241C22×D53—42no—
242C22×D53—42no—
243C22×D53C4×D418yes—
244C2×C4×C53—24no—
245C2×C4×C53—22no—
246C2×C4×C53—22no—
247C2×C4×C53—24no—
248C2×C4×C53—24no—
249C2×C4×C53—24no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—24no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—42no—
263C2×C4×C53—41no—
264C2×C4×C53—42no—
265C2×C4×C53—41no—
266C2×C4×C53—42no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53C4×D414yes—
280C2×C4×C53#12014yes—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—24no—
285C2×Dic53—24no—
286C2×Dic53—24no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302D212—232no—
303C4×D53—432no—
304#14300—531nomaximal, Sylow
305C22×C53C2×C4×D412yes—
306C22×C53C2×C4×D411yescharacteristic
307C22×C53#51811yescharacteristic
308C22×C53#52011yescharacteristic
309C22×C53#52012yes—
310C22×C53C2×#12011yescharacteristic
311C22×C53#52511yescharacteristic
312C22×C53#52512yes—
313C22×C53#53412yes—
314C22×C53#53412yes—
315C22×C53#53511yescharacteristic
316C22×C53#53511yescharacteristic
317C22×C53#53612yes—
318C22×C53#53611yescharacteristic
319C22×C53#53711yescharacteristic
320C22×C53#53712yes—
321C22×C53#53812yes—
322C22×C53#53912yes—
323C22×C53#53912yes—
324C22×C53#53912yes—
325C22×C53#54011yescharacteristic
326C22×C53#54211yescharacteristic
327C22×C53#54212yes—
328C2×D53—28no—
329C2×D53—28no—
330C2×D53—28no—
331C2×D53—44no—
332C2×D53—44no—
333C2×D53—44no—
334C2×D53—44no—
335C2×D53—44no—
336C2×D53—44no—
337C2×D53—44no—
338C2×D53—44no—
339C2×D53—44no—
340C2×D53—44no—
341C2×D53—44no—
342C2×D53—44no—
343C4×C53—24no—
344C4×C53—24no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53—42no—
348C4×C53—81no—
349C4×C53—81no—
350Dic53—44no—
351Dic53—44no—
352Dic53—82no—
353C22×C4×D4—531no—
354C2×#394—531no—
355C2×#387D5311yescharacteristic, complemented
356C2×#385—532no—
357#1444—531no—
358#1441—531no—
359#1440—532no—
360#1439—532no—
361#1438—531no—
362#1434—531no—
363C22⋊#95—532no—
364C2×C53C4×#12011yescharacteristic
365C2×C53#232212yes—
366C2×C53#232411yescharacteristic
367C2×C53#232512yes—
368C2×C53#232611yescharacteristic
369C2×C53#261311yescharacteristic
370C2×C53#261611yescharacteristic
371C2×C53#263012yes—
372C2×C53#263311yescharacteristic
373C2×C53#263611yescharacteristic
374C2×C53#263812yes—
375D53—48no—
376C23×D4—531no—
377C24×C4—532no—
378C2×C4×D4—1068no—
379C2×C4×D4—1064no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—532no—
382C22×C4⋊C4C2×D5311yescharacteristic
383C22×C4⋊C4C2×D5311yescharacteristic
384C22×C22⋊C4—532no—
385C22×C22⋊C4—532no—
386C22×C22⋊C4—532no—
387C22×C22⋊C4—532no—
388C22×C22⋊C4—532no—
389C22×C42C2×D5311yescharacteristic
390#394—538no—
391#387—24no—
392#385—1068no—
393C2×#95—531no—
394C2×#95—532no—
395C2×#95—531no—
396C2×#95—532no—
397C2×#95—532no—
398C2×#95—532no—
399C2×#95—532no—
400C2×#95C2×D5311yescharacteristic
401C2×#95C2×D5311yescharacteristic
402C2×#95C2×D5311yescharacteristic
403C2×#95C2×D5311yescharacteristic
404C53#1430011yescharacteristic, complemented, Sylow
405C25—532no—
406C22×D4—534no—
407C22×D4—1064no—
408C22×D4—1064no—
409C22×D4—1062no—
410C22×D4—1062no—
411C23×C4—532no—
412C23×C4—532no—
413C23×C4—538no—
414C23×C4—532no—
415C23×C4—1064no—
416C23×C4—1064no—
417C23×C4—2122no—
418C23×C4—2122no—
419C23×C4—2122no—
420C23×C4—2122no—
421C23×C4C22×D5311yescharacteristic
422C23×C4C22×D5311yescharacteristic
423C23×C4C22×D5311yescharacteristic
424C23×C4C22×D5311yescharacteristic
425C23×C4C22×D5311yescharacteristic
426C23×C4C22×D5311yescharacteristic
427C23×C4C22×D5311yescharacteristic
428C4×D4—10632no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1062no—
435C2×C4⋊C4—1064no—
436C2×C4⋊C4—2122no—
437C2×C4⋊C4—2122no—
438C2×C4⋊C4C4×D5314yescomplemented
439C2×C22⋊C4—538no—
440C2×C22⋊C4—538no—
441C2×C22⋊C4—1064no—
442C2×C22⋊C4—1064no—
443C2×C22⋊C4—1064no—
444C2×C22⋊C4—1064no—
445C2×C22⋊C4—1064no—
446C2×C22⋊C4—1064no—
447C2×C22⋊C4—1064no—
448C2×C22⋊C4—2122no—
449C2×C22⋊C4—2122no—
450C2×C22⋊C4—2122no—
451C2×C22⋊C4—2122no—
452C2×C22⋊C4—2122no—
453C2×C22⋊C4—2122no—
454C2×C42—24no—
455C2×C42C22⋊D5314yes—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—534no—
461#95—1064no—
462#95—1062no—
463#95—1064no—
464#95—2122no—
465#95—2122no—
466#95—2122no—
467C24—534no—
468C24—534no—
469C24—534no—
470C24—1062no—
471C24—1062no—
472C24—1062no—
473C24—1062no—
474C24—1062no—
475C24—1062no—
476C24—1062no—
477C24—1062no—
478C24—1062no—
479C24—1062no—
480C24—1062no—
481C24—1062no—
482C24C23×D5311yescharacteristic
483C2×D4—10616no—
484C2×D4—1068no—
485C2×D4—1068no—
486C2×D4—10616no—
487C2×D4—1068no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—534no—
518C22×C4—534no—
519C22×C4—1062no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—10616no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—2128no—
540C22×C4—2128no—
541C22×C4—2128no—
542C22×C4—2128no—
543C22×C4—2128no—
544C22×C4—2128no—
545C22×C4C2×C4×D5312yes—
546C22×C4C2×C4×D5312yes—
547C22×C4C2×C4×D5312yes—
548C22×C4#1171994512yes—
549C22×C4D4×D5314yes—
550C22×C4C2×C22⋊D5312yes—
551C22×C4C2×C22⋊D5312yes—
552C22×C4C2×C22⋊D5312yes—
553C4⋊C4—28no—
554C4⋊C4—44no—
555C4⋊C4—1068no—
556C4⋊C4—2128no—
557C22⋊C4—10616no—
558C22⋊C4—10616no—
559C22⋊C4—2128no—
560C22⋊C4—2128no—
561C22⋊C4—2128no—
562C42—28no—
563C23—538no—
564C23—1064no—
565C23—1064no—
566C23—1064no—
567C23—1064no—
568C23—1064no—
569C23—1064no—
570C23—1064no—
571C23—1064no—
572C23—1064no—
573C23—1064no—
574C23—1064no—
575C23—1064no—
576C23—1064no—
577C23—1064no—
578C23—1064no—
579C23—1064no—
580C23—1064no—
581C23—1064no—
582C23—2122no—
583C23—2122no—
584C23—2122no—
585C23—2122no—
586C23—2122no—
587C23—2122no—
588C23—2122no—
589C23—2122no—
590C23—2122no—
591C23—2122no—
592C23—2122no—
593C23—2122no—
594C23—2122no—
595C23—2122no—
596C23—2122no—
597C23—2122no—
598C23C22×C4×D5311yescharacteristic
599C23C2×D4×D5312yes—
600C23C22×C22⋊D5311yescharacteristic
601C23#41×D5312yes—
602C23C2×#1171994511yescharacteristic
603C23#1313326311yescharacteristic
604C23#1313326311yescharacteristic
605C23#1313326311yescharacteristic
606C23#1313326312yes—
607C23#1313326411yescharacteristic
608C23#1313326512yes—
609D4—10632no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—1064no—
646C2×C4—1064no—
647C2×C4—1064no—
648C2×C4—1064no—
649C2×C4—1064no—
650C2×C4—1064no—
651C2×C4—21232no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4—2122no—
656C2×C4—2122no—
657C2×C4—2122no—
658C2×C4—2122no—
659C2×C4—2122no—
660C2×C4—2122no—
661C2×C4—2122no—
662C2×C4—2122no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4C4×C22⋊D5314yes—
668C2×C4#1313318514yes—
669C22—1068no—
670C22—1068no—
671C22—1068no—
672C22—2124no—
673C22—2124no—
674C22—2124no—
675C22—2124no—
676C22—2124no—
677C22—2124no—
678C22—2124no—
679C22—2124no—
680C22—2124no—
681C22—2124no—
682C22—2124no—
683C22—2124no—
684C22C4×D4×D5312yes—
685C22C2×C4×C22⋊D5311yescharacteristic
686C22#1681109711yescharacteristic
687C22#1681110311yescharacteristic
688C22#1681110512yes—
689C22C2×#1313318511yescharacteristic
690C22#1681113011yescharacteristic
691C22#1681113212yes—
692C22#1681118412yes—
693C22#1681118412yes—
694C22#1681118711yescharacteristic
695C22#1681118711yescharacteristic
696C22#1681119612yes—
697C22#1681119711yescharacteristic
698C22#1681120111yescharacteristic
699C22#1681120312yes—
700C22#1681121212yes—
701C22#1681121412yes—
702C22#1681122112yes—
703C22#1681122112yes—
704C22#1681122811yescharacteristic
705C22#1681124411yescharacteristic
706C22#1681124512yes—
707C4—24no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—81no—
713C4—81no—
714C4—4242no—
715C4—2124no—
716C4—2124no—
717C2—2128no—
718C2C4×#1313318511yescharacteristic
719C2#2027738812yes—
720C2#2027740811yescharacteristic
721C2#2027741412yes—
722C2#2027742211yescharacteristic
723C2#2028043111yescharacteristic
724C2#2028044511yescharacteristic
725C2#2028056412yes—
726C2#2028058411yescharacteristic
727C2#2028061211yescharacteristic
728C2#2028063912yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#387C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×#387D53
hypocenterC53#14300
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C2×#16810494C2semidirect
4. #20272979C2semidirect
5. #20272968C2semidirect
6. #20272963C2semidirect
7. #20272959C2semidirect
9. #20272942C2semidirect
10. #20272936C2semidirect
11. C2×C53×#387C2semidirect
23. #16810540C4semidirect
75. C2×#11719921C2×C4semidirect
76. C2×#11719921C2×C4semidirect
83. #13133124C2×C4semidirect
95. C2×C4⋊C4×C53C2×C4semidirect
355. C2×#387D53semidirect
404. C53#14300semidirect
438. C2×C4⋊C4C4×D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C2×#168105402
C2×#168104942
#202729792
#202729682
#202729632
#202729592
#202729552
#202729422
#202729362
C2×C53×#3872
#1430053