Finite Group Databasebeta

← #25115352

Subgroups — #25115352

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582977C211yesmaximal, characteristic
2#19137524C211yesmaximal, characteristic
3#19135363C211yesmaximal, characteristic, complemented
4#19135361C211yesmaximal, characteristic, complemented
5#19134794C211yesmaximal, characteristic, complemented
6#19134792C211yesmaximal, characteristic, complemented
7#19134783C211yesmaximal, characteristic, complemented
8#19134782C211yesmaximal, characteristic, complemented
9#19134725C211yesmaximal, characteristic, complemented
10#19134626C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12C4×#13063258C211yesmaximal, characteristic, complemented
13#19134316C211yesmaximal, characteristic, complemented
14#19134314C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14582977C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582792—21no—
32#14582785—21no—
33#14582779—21no—
34#14582765C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38C22⋊C4×Dic43—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C43×#388—21no—
53C43×#387—21no—
54C43×#386—21no—
55C43×#382C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C22⋊C4×C43—21no—
60C23×Dic43—21no—
61C2×#10621877—41no—
62C2×#10621877—41no—
63C2×#10621877—41no—
64C2×#10621877—41no—
65C2×#10621877C2×C414yescomplemented
66C2×#10621877C2×C414yescomplemented
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063284—22no—
72#13063284—41no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063258—22no—
87#13063258—41no—
88#13063258—41no—
89#13063256—41no—
90#13063256—41no—
91C4⋊(C43⋊C8)C2×C414yescomplemented
92C22⋊(C43⋊C8)C2×C414yescomplemented
93C22⋊(C43⋊C8)C2×C414yescomplemented
94C4×C43⋊C8C2×C414yescomplemented
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×D4×C43D411yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C4×D4×C43C2×C414yes—
105C4×D4×C43Q814yes—
106#117×C43—22no—
107#117×C43—41no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—41no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129C24×C43C2×D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C2×D4×C43C4⋊C414yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43C22×C412yes—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×Q812yes—
156C22×C4×C43C2×Q812yes—
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—81no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43C4⋊C414yes—
174C4⋊C4×C43#4112yes—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43C4⋊C414yes—
179C22⋊C4×C43C4⋊C414yes—
180C42×C43—42no—
181C42×C43—81no—
182C42×C43C22×C412yes—
183C42×C43C2×Q812yes—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195C4⋊Dic43#4112yes—
196C4×Dic43—42no—
197C4×Dic43—81no—
198#10621877—44no—
199#10621877—44no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C412yes—
209C2×C43⋊C8C22×C412yes—
210C2×C43⋊C8C22×C412yes—
211C2×C43⋊C8C22×C412yes—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43C2×C4⋊C412yes—
225C23×C43C2×C4⋊C412yes—
226C23×C43C22×D411yescharacteristic
227D4×C43—44no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—84no—
257C2×C4×C43C2×C4⋊C412yes—
258C2×C4×C43C2×C4⋊C412yes—
259C2×C4×C43C2×C4⋊C412yes—
260C2×C4×C43C2×C4⋊C412yes—
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×Q811yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—84no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282C43⋊C8—22no—
283C43⋊C8—22no—
284#22716—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43C22×C4⋊C411yescharacteristic
300C22×C43#54611yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43#57511yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57611yescharacteristic
305C22×C43#57811yescharacteristic
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43C4×#4111yescharacteristic
315C4×C43#51811yescharacteristic
316C4×C43#55411yescharacteristic
317C4×C43#55411yescharacteristic
318Dic43—42no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322C2×#436—431no—
323#2352—431no—
324#2352D4311yescharacteristic
325#1949—431no—
326#1949—431no—
327#1854—431no—
328#1854—431no—
329#1852—431no—
330#1852—431no—
331#1835—431no—
332#1809—431no—
333#1809—431no—
334C4×#107—431no—
335#1736—431no—
336#1736—431no—
337C2×C43—42no—
338C2×C43—42no—
339C2×C43#234911yescharacteristic
340C2×C43#291111yescharacteristic
341C2×C43#291311yescharacteristic
342C2×C43#332211yescharacteristic
343C2×C43#332211yescharacteristic
344C2×C43#332711yescharacteristic
345C2×C43#332711yescharacteristic
346C22×M16—431no—
347C22×M16—431no—
348C2×C4×D4C2×D4311yescharacteristic
349C2×#117—431no—
350C2×#117C2×D4311yescharacteristic
351C22×C4⋊C4—431no—
352C22×C4⋊C4C2×D4311yescharacteristic
353#436—438no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#107—431no—
357C2×#107—431no—
358C2×#106—431no—
359C2×#106—431no—
360C2×C4⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8—431no—
363C2×C4×C8—431no—
364#388—21no—
365#388—861no—
366#387—21no—
367#387—861no—
368#386—21no—
369#386—861no—
370#382—431no—
371#382C2×D4311yescharacteristic
372#380—431no—
373#380—431no—
374#380C2×D4311yescharacteristic
375#380C2×D4311yescharacteristic
376C4×C4⋊C4—431no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C22⋊C4—21no—
379C4×C22⋊C4—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390C43#2271611yescharacteristic, complemented, Sylow
391C22×D4C22⋊D4311yescharacteristic
392C23×C4—21no—
393C23×C4—861no—
394C23×C4C22×D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×M16—434no—
397C2×M16—434no—
398C2×M16—1721no—
399C2×M16—1721no—
400C2×M16—1721no—
401C2×M16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
406C4×D4Dic8614yes—
407C4×D4C4×D4314yes—
408#117—22no—
409#117—41no—
410#117—862no—
411#117—1721no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4C22⋊D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4C22⋊D4311yescharacteristic
434C2×C22⋊C4C22⋊D4311yescharacteristic
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440#107—862no—
441#107—862no—
442#107—1721no—
443#107—1721no—
444#106—1721no—
445#106—1721no—
446C4⋊C8—434no—
447C22⋊C8—434no—
448C22⋊C8—434no—
449C4×C8—434no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24C2×C22⋊D4311yescharacteristic
461C24C2×C22⋊D4311yescharacteristic
462C2×D4—41no—
463C2×D4—41no—
464C2×D4Dic43⋊C414yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—81no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×Dic8612yes—
488C22×C4C2×Dic8612yes—
489C22×C4C2×C4×D4312yes—
490C22×C4C2×C4×D4312yes—
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496M16—1724no—
497M16—1724no—
498C2×C8—432no—
499C2×C8—432no—
500C2×C8—432no—
501C2×C8—432no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—432no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1722no—
527C4⋊C4Dic43⋊C414yes—
528C4⋊C4#1062190012yes—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—81no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4Dic43⋊C414yes—
536C22⋊C4Dic43⋊C414yes—
537C42—42no—
538C42—81no—
539C42—3441no—
540C42—1722no—
541C42C2×Dic8612yes—
542C42C2×C4×D4312yes—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23C2×Dic43⋊C412yes—
556C23C2×Dic43⋊C412yes—
557C23C22×C22⋊D4311yescharacteristic
558D4—44no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—862no—
589C2×C4—3444no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C2×Dic43⋊C412yes—
602C2×C4C2×Dic43⋊C412yes—
603C2×C4C2×Dic43⋊C412yes—
604C2×C4C2×Dic43⋊C412yes—
605C2×C4C22×C4×D4311yescharacteristic
606C2×C4C22×Dic8611yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062190011yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—862no—
612C8—862no—
613C8—862no—
614C8—862no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22C22×Dic43⋊C411yescharacteristic
630C22#1458353711yescharacteristic
631C22#1458354311yescharacteristic
632C22#1458369711yescharacteristic
633C22#1458369711yescharacteristic
634C22#1458370211yescharacteristic
635C22#1458371411yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4C4×#1062190011yescharacteristic
649C4#1458337111yescharacteristic
650C4#1458360611yescharacteristic
651C4#1458360811yescharacteristic
652C2—42no—
653C2—42no—
654C2#1913750011yescharacteristic
655C2#1914318411yescharacteristic
656C2#1914319311yescharacteristic
657C2#1914679011yescharacteristic
658C2#1914679611yescharacteristic
659C2#1914685711yescharacteristic
660C2#1914686311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22716
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #19135363C2semidirect
4. #19135361C2semidirect
5. #19134794C2semidirect
6. #19134792C2semidirect
7. #19134783C2semidirect
8. #19134782C2semidirect
9. #19134725C2semidirect
10. #19134626C2semidirect
11. #19134626C2semidirect
12. C4×#13063258C2semidirect
13. #19134316C2semidirect
14. #19134314C2semidirect
20. #14582977C4semidirect
65. C2×#10621877C2×C4semidirect
66. C2×#10621877C2×C4semidirect
91. C4⋊(C43⋊C8)C2×C4semidirect
92. C22⋊(C43⋊C8)C2×C4semidirect
93. C22⋊(C43⋊C8)C2×C4semidirect
94. C4×C43⋊C8C2×C4semidirect
390. C43#22716semidirect

Maximal subgroups

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

subgroupindex
C2×#145829772
#191375242
#191353632
#191353612
#191347942
#191347922
#191347832
#191347822
#191347252
#191346262
C4×#130632582
#191343162
#191343142
C43×#23522
#2271643