Finite Group Databasebeta

← #11660179

Subgroups — #11660179

Order 768.

1748 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5578C211yesmaximal, characteristic
2C3×#2983C211yesmaximal, characteristic, complemented
3#82435C211yesmaximal, characteristic, complemented
4#79967C214yesmaximal, complemented
5#79965C214yesmaximal, complemented
6#79960C214yesmaximal, complemented
7#79958C214yesmaximal, complemented
8#79333C214yesmaximal
9#79315C214yesmaximal, complemented
10#79282C211yesmaximal, characteristic
11D3×#431C211yesmaximal, characteristic
12#79264C211yesmaximal, characteristic, complemented
13#79263C211yesmaximal, characteristic, complemented
14#60250—31nomaximal, Sylow
15C2×C3×C4×Q8C2211yescharacteristic
16C2×#946C411yescharacteristic
17C2×#944C411yescharacteristic
18#5578C412yes—
19#5578C412yes—
20#5578C412yes—
21#5578C412yes—
22#5578C2212yes—
23#5578C2212yes—
24#5578C2212yes—
25#5578C2212yes—
26C2×#897C411yescharacteristic
27C2×#896C412yes—
28C2×#889C412yes—
29C2×#888C411yescharacteristic
30C2×#872C2212yes—
31C2×C42×D3C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2212yes—
34C3×#446C2214yescomplemented
35C3×#446C2214yescomplemented
36C3×#432C2214yes—
37C3×#431C2211yescharacteristic
38C3×#431C2211yescharacteristic
39Q8×C3⋊C8C2214yescomplemented
40Q8×C3⋊C8C2214yescomplemented
41#4925C2211yescharacteristic
42#4925C2211yescharacteristic
43#4925C2214yes—
44#4840C2218yes—
45#4839C2218yes—
46#4837C2212yes—
47#4835C2212yes—
48#4833C2212yes—
49D3×C4⋊C8C2212yes—
50#4831C2218yescomplemented
51#4831C2214yescomplemented
52#4830C2214yescomplemented
53#4830C2218yescomplemented
54#4726C2212yes—
55D3×C22⋊C8C2212yes—
56#4719C2214yes—
57#4719C2212yes—
58#4718C2214yes—
59#4718C2212yes—
60#4709C2218yes—
61#4708C2218yes—
62#4701C2218yescomplemented
63#4701C2218yescomplemented
64C4×ΓL(1,𝔽25)C2212yes—
65#4685C2212yes—
66#4685C2212yes—
67C4×D3×C8C2212yes—
68#4679C2214yescomplemented
69C8×Dic6C2214yescomplemented
70C2×#533—31no—
71#2986—34no—
72#2985—34no—
73#2984—34no—
74#2983—31no—
75#2983D311yescharacteristic, complemented
76#2982—31no—
77#2982—31no—
78#2962—34no—
79#2960—34no—
80#2924—34no—
81#2920—31no—
82C2×#431—31no—
83C22×C3×Q8C2×C411yescharacteristic
84C22×C4×D3C2×C411yescharacteristic
85C22×C4×D3C2×C411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2×C411yescharacteristic
88C22×Dic6C2×C412yes—
89C3×C4×Q8C2×C412yes—
90C3×C4×Q8C2×C412yes—
91C3×C4×Q8C2312yes—
92C3×C4×Q8C2312yes—
93C2×C3×C4⋊C4C2×C411yescharacteristic
94C2×C3×C4⋊C4C2×C412yes—
95C2×C3×C42C2311yescharacteristic
96C2×C3×C42C2312yes—
97#946C2×C412yes—
98#946C2×C412yes—
99#946C2×C412yes—
100#946C2×C412yes—
101#944C2×C412yes—
102#944C2×C412yes—
103#944C2×C412yes—
104#944C2×C412yes—
105C2×(C2×D3)⋊C4C2×C412yes—
106C2×(C2×D3)⋊C4C2×C412yes—
107C2×C4⋊Dic3C2×C411yescharacteristic
108C2×C4⋊Dic3C2×C412yes—
109C2×Dic3⋊C4C2×C412yes—
110C2×Dic3⋊C4C2×C412yes—
111C2×Dic3⋊C4C2×C412yes—
112C2×Dic3⋊C4C2×C412yes—
113C2×Dic3⋊C4C2×C412yes—
114C2×C4×Dic3C2×C411yescharacteristic
115C2×C4×Dic3C2×C411yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C2×C4×Dic3C2312yes—
118C2×ΓL(1,𝔽25)C2314yes—
119C2×D3×C8C2314yes—
120#897C2×C412yes—
121#897C2×C412yes—
122#897C2×C412yes—
123#897C2×C412yes—
124#896C2×C414yes—
125#896C2×C414yes—
126#896C2×C414yes—
127#896C2×C414yes—
128#889C2×C414yes—
129#889C2×C414yes—
130#889C2×C414yes—
131#889C2×C414yes—
132#888C2×C412yes—
133#888C2×C412yes—
134#888C2×C412yes—
135#888C2×C412yes—
136#872C2×C414yes—
137#872C2×C414yes—
138#872C2314yes—
139#872C2314yes—
140C42×D3C2×C411yescharacteristic
141C42×D3C2×C411yescharacteristic
142C42×D3C2×C411yescharacteristic
143C42×D3C2×C411yescharacteristic
144C42×D3C2311yescharacteristic
145C42×D3C2311yescharacteristic
146C42×D3C2311yescharacteristic
147C42×D3C2311yescharacteristic
148C4×Dic6C2×C414yes—
149C4×Dic6C2×C414yes—
150C4×Dic6C2×C412yes—
151C4×Dic6C2×C412yes—
152C4×Dic6C2312yes—
153C4×Dic6C2312yes—
154C4×Dic6C2314yes—
155C4×Dic6C2314yes—
156C3×C4⋊C8C2312yes—
157C3×C4⋊C8C2312yes—
158C3×C4⋊C8C2318yes—
159C3×C22⋊C8C2312yes—
160C3×C22⋊C8C2312yes—
161C3×#97C2318yes—
162C3×C4×C8C2312yes—
163C3×C4×C8C2312yes—
164#830C2312yes—
165#830C2312yes—
166(C2×D3)⋊C8C2314yes—
167(C2×D3)⋊C8C2314yes—
168#815C2318yes—
169#815C2314yes—
170Dic3⋊C8C2318yes—
171Dic3⋊C8C2318yes—
172Dic3⋊C8C2314yes—
173Dic3⋊C8C2314yes—
174C8×Dic3C2318yes—
175C8×Dic3C2314yes—
176C4⋊(C3⋊C8)C2312yes—
177C4⋊(C3⋊C8)C2312yes—
178C4⋊(C3⋊C8)C2318yes—
179C4×C3⋊C8C2312yes—
180C4×C3⋊C8C2312yes—
181C4×C3⋊C8C2318yes—
182#533—32no—
183#533—32no—
184#533—32no—
185#533—32no—
186#533—32no—
187#533—32no—
188#533—32no—
189#533—32no—
190C2×C4⋊Q8—31no—
191C2×C4⋊Q8—31no—
192C2×#125—32no—
193C2×C22⋊Q8—31no—
194C2×C22⋊Q8—32no—
195C2×C22⋊Q8—31no—
196C2×C4×Q8—31no—
197C2×C4×Q8—32no—
198C2×C4×Q8C2×D311yescharacteristic
199C2×#117—32no—
200C22×C42—31no—
201#446—34no—
202#446—38no—
203#446—38no—
204#446—38no—
205#446—34no—
206#446C2×D314yescomplemented
207#446C2×D314yescomplemented
208C8×Q8—34no—
209C8×Q8—34no—
210C8×Q8—34no—
211C8×Q8—38no—
212C8×Q8—34no—
213#433—38no—
214#433—38no—
215#432—32no—
216#432—32no—
217#432—34no—
218#432C2×D314yes—
219#431—31no—
220#431—31no—
221#431—34no—
222#431—32no—
223#431—32no—
224#431—34no—
225#431—32no—
226#431—32no—
227#431C2×D311yescharacteristic
228#431C2×D311yescharacteristic
229#424—38no—
230#423—32no—
231C2×C4⋊C8—32no—
232#407—32no—
233C2×C22⋊C8—32no—
234#405—38no—
235C4×M16—32no—
236C2×C4×C8—32no—
237C23×D3C22×C411yescharacteristic
238C2×C3×Q8—24no—
239C2×C3×Q8C22×C412yes—
240C2×C3×Q8C22×C412yes—
241C22×C3×C4C22×C412yes—
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C412yes—
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C22×Dic3C22×C411yescharacteristic
247C22×Dic3C22×C411yescharacteristic
248C22×Dic3C22×C411yescharacteristic
249C22×Dic3C22×C412yes—
250C22×Dic3C22×C412yes—
251C2×C4×D3—24no—
252C2×C4×D3—24no—
253C2×C4×D3—42no—
254C2×C4×D3C22×C411yescharacteristic
255C2×C4×D3C22×C411yescharacteristic
256C2×C4×D3C22×C411yescharacteristic
257C2×C4×D3C22×C411yescharacteristic
258C2×C4×D3C22×C411yescharacteristic
259C2×C4×D3C22×C411yescharacteristic
260C2×C4×D3C22×C411yescharacteristic
261C2×C4×D3C22×C411yescharacteristic
262C2×C4×D3C22×C411yescharacteristic
263C2×C4×D3C22×C411yescharacteristic
264C2×C4×D3C2411yescharacteristic
265C2×C4×D3C2411yescharacteristic
266C2×Dic6—24no—
267C2×Dic6—44no—
268C2×Dic6C22×C414yes—
269C2×Dic6C22×C412yes—
270C2×Dic6C22×C412yes—
271C2×Dic6C22×C414yes—
272C2×C3×C8C2414yes—
273C2×C3×C8C2414yes—
274C3×C4⋊C4C22×C412yes—
275C3×C4⋊C4C22×C412yes—
276C3×C4⋊C4C22×C414yes—
277C3×C4⋊C4C22×C414yes—
278C3×C42C22×C411yescharacteristic
279C3×C42C22×C411yescharacteristic
280C3×C42C22×C414yes—
281C3×C42C2411yescharacteristic
282C3×C42C2411yescharacteristic
283C3×C42C2414yes—
284(C2×D3)⋊C4C22×C414yes—
285(C2×D3)⋊C4C22×C414yes—
286(C2×D3)⋊C4C22×C414yes—
287(C2×D3)⋊C4C22×C414yes—
288C4⋊Dic3C22×C412yes—
289C4⋊Dic3C22×C412yes—
290C4⋊Dic3C22×C414yes—
291C4⋊Dic3C22×C414yes—
292Dic3⋊C4C22×C414yes—
293Dic3⋊C4C22×C414yes—
294Dic3⋊C4C22×C414yes—
295Dic3⋊C4C22×C414yes—
296Dic3⋊C4C22×C414yes—
297Dic3⋊C4C22×C414yes—
298Dic3⋊C4C22×C414yes—
299Dic3⋊C4C22×C414yes—
300Dic3⋊C4C22×C414yes—
301Dic3⋊C4C22×C414yes—
302C4×Dic3C22×C411yescharacteristic
303C4×Dic3C22×C411yescharacteristic
304C4×Dic3C22×C414yes—
305C4×Dic3C22×C411yescharacteristic
306C4×Dic3C22×C411yescharacteristic
307C4×Dic3C22×C411yescharacteristic
308C4×Dic3C22×C411yescharacteristic
309C4×Dic3C22×C411yescharacteristic
310C4×Dic3C22×C411yescharacteristic
311C4×Dic3C22×C411yescharacteristic
312C4×Dic3C22×C411yescharacteristic
313C4×Dic3C2411yescharacteristic
314C4×Dic3C2414yes—
315C4×Dic3C2411yescharacteristic
316C2×C3⋊C8C2414yes—
317C2×C3⋊C8C2414yes—
318ΓL(1,𝔽25)—28no—
319D3×C8—28no—
320C22×Q8—31no—
321C22×Q8—32no—
322C22×Q8C4×D311yescharacteristic
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C2×M16—34no—
327C22×C8—34no—
328C4⋊Q8—32no—
329C4⋊Q8—32no—
330C4⋊Q8—32no—
331C4⋊Q8—32no—
332C4⋊Q8—32no—
333C4⋊Q8—32no—
334C4⋊Q8—32no—
335C4⋊Q8—32no—
336#125—34no—
337#125—34no—
338#125—34no—
339#125—34no—
340C22⋊Q8—32no—
341C22⋊Q8—32no—
342C22⋊Q8—32no—
343C22⋊Q8—32no—
344C22⋊Q8—34no—
345C22⋊Q8—34no—
346C22⋊Q8—34no—
347C22⋊Q8—34no—
348C22⋊Q8—32no—
349C22⋊Q8—32no—
350C22⋊Q8—32no—
351C22⋊Q8—32no—
352C4×Q8—34no—
353C4×Q8—34no—
354C4×Q8—32no—
355C4×Q8—32no—
356C4×Q8—34no—
357C4×Q8—32no—
358C4×Q8—32no—
359C4×Q8—34no—
360C4×Q8C4×D312yes—
361C4×Q8C4×D312yes—
362C4×Q8C22×D312yes—
363C4×Q8C22×D312yes—
364#117—34no—
365#117—34no—
366#117—34no—
367#117—34no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4C4×D312yes—
376C2×C4⋊C4C4×D311yescharacteristic
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—32no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42C22×D312yes—
392C2×C42C22×D311yescharacteristic
393C4⋊C8—34no—
394C4⋊C8—34no—
395C4⋊C8—38no—
396C4⋊C8—38no—
397C4⋊C8—32no—
398C4⋊C8—32no—
399C4⋊C8—38no—
400C4⋊C8C22×D312yes—
401C4⋊C8C22×D312yes—
402C4⋊C8C22×D318yes—
403C22⋊C8—32no—
404C22⋊C8—32no—
405C22⋊C8—34no—
406C22⋊C8—34no—
407C22⋊C8C22×D312yes—
408C22⋊C8C22×D312yes—
409#97—34no—
410#97—38no—
411#97C22×D318yes—
412C4×C8—34no—
413C4×C8—38no—
414C4×C8—32no—
415C4×C8—32no—
416C4×C8—38no—
417C4×C8C22×D312yes—
418C4×C8C22×D312yes—
419C23×C3C23×C411yescharacteristic
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—41no—
423C22×D3C23×C411yescharacteristic
424C22×D3C23×C411yescharacteristic
425C3×Q8—24no—
426C3×Q8—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4#13114yes—
432C2×C3×C4C23×C411yescharacteristic
433C2×C3×C4C23×C411yescharacteristic
434C2×C3×C4C23×C411yescharacteristic
435C2×C3×C4C23×C414yes—
436C2×C3×C4C23×C414yes—
437C2×C3×C4C23×C411yescharacteristic
438C2×C3×C4C23×C411yescharacteristic
439C2×C3×C4C2511yescharacteristic
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—42no—
445C2×Dic3C23×C411yescharacteristic
446C2×Dic3C23×C411yescharacteristic
447C2×Dic3C23×C411yescharacteristic
448C2×Dic3C23×C411yescharacteristic
449C2×Dic3C23×C414yes—
450C2×Dic3C23×C414yes—
451C2×Dic3C23×C411yescharacteristic
452C2×Dic3C23×C411yescharacteristic
453C4×D3—22no—
454C4×D3—22no—
455C4×D3—22no—
456C4×D3—22no—
457C4×D3—22no—
458C4×D3—22no—
459C4×D3—22no—
460C4×D3—22no—
461C4×D3—22no—
462C4×D3—41no—
463C4×D3—41no—
464C4×D32−1+414yes—
465Dic6—24no—
466Dic6—24no—
467Dic6—28no—
468Dic6—44no—
469C3×C8—24no—
470C3×C8—24no—
471C3⋊C8—24no—
472C3⋊C8—24no—
473C24—31no—
474C2×Q8—24no—
475C2×Q8—34no—
476C2×Q8—32no—
477C2×Q8—32no—
478C2×Q8—34no—
479C2×Q8—64no—
480C2×Q8—124no—
481C2×Q8C2×C4×D312yes—
482C2×Q8C2×C4×D312yes—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—31no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—64no—
501C22×C4—64no—
502C22×C4—122no—
503C22×C4C2×C4×D312yes—
504C22×C4C2×C4×D311yescharacteristic
505C22×C4C2×C4×D312yes—
506C22×C4C2×C4×D311yescharacteristic
507C22×C4C23×D311yescharacteristic
508M16—68no—
509C2×C8—34no—
510C2×C8—34no—
511C2×C8—68no—
512C2×C8C23×D314yes—
513C2×C8C23×D314yes—
514C4⋊C4—34no—
515C4⋊C4—34no—
516C4⋊C4—34no—
517C4⋊C4—34no—
518C4⋊C4—34no—
519C4⋊C4—34no—
520C4⋊C4—34no—
521C4⋊C4—34no—
522C4⋊C4—34no—
523C4⋊C4—34no—
524C4⋊C4—34no—
525C4⋊C4—34no—
526C4⋊C4—32no—
527C4⋊C4—32no—
528C4⋊C4C2×C4×D314yes—
529C4⋊C4C2×C4×D314yes—
530C4⋊C4C2×C4×D312yes—
531C4⋊C4C2×C4×D312yes—
532C22⋊C4—34no—
533C22⋊C4—34no—
534C22⋊C4—34no—
535C22⋊C4—34no—
536C42—31no—
537C42—31no—
538C42—31no—
539C42—31no—
540C42—31no—
541C42—31no—
542C42—31no—
543C42—31no—
544C42—31no—
545C42—31no—
546C42—34no—
547C42—31no—
548C42—34no—
549C42—31no—
550C42C2×C4×D311yescharacteristic
551C42C2×C4×D311yescharacteristic
552C42C2×C4×D314yes—
553C42C23×D311yescharacteristic
554C42C23×D311yescharacteristic
555C42C23×D314yes—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3C2×#13112yes—
559C22×C3C24×C411yescharacteristic
560C2×D3—21no—
561C2×D3—21no—
562C2×D3—21no—
563C2×D3—21no—
564C2×D3—21no—
565C2×D3—44no—
566C2×D3#51912yes—
567C3×C4—21no—
568C3×C4—24no—
569C3×C4—24no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4C2×#13112yes—
573C3×C4C2×#13112yes—
574C3×C4C2×2−1+412yes—
575Dic3—21no—
576Dic3—24no—
577Dic3—21no—
578Dic3—21no—
579Dic3—24no—
580Dic3—21no—
581Dic3#51912yes—
582Dic3#56812yes—
583C23—31no—
584C23—31no—
585C23—62no—
586C23—62no—
587C23—121no—
588C23C22×C4×D311yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—68no—
592Q8—64no—
593Q8—64no—
594Q8—124no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—31no—
598C2×C4—31no—
599C2×C4—34no—
600C2×C4—31no—
601C2×C4—31no—
602C2×C4—31no—
603C2×C4—31no—
604C2×C4—34no—
605C2×C4—34no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—64no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—122no—
624C2×C4#90714yes—
625C2×C4C22×C4×D311yescharacteristic
626C2×C4C22×C4×D311yescharacteristic
627C2×C4C22×C4×D311yescharacteristic
628C2×C4C22×C4×D314yes—
629C2×C4C22×C4×D314yes—
630C2×C4C22×C4×D311yescharacteristic
631C2×C4C22×C4×D311yescharacteristic
632C2×C4C24×D311yescharacteristic
633C8—24no—
634C8—24no—
635C8—64no—
636C8—64no—
637C2×C3—22no—
638C2×C3C2×#51911yescharacteristic
639C2×C3C22×#13111yescharacteristic
640C2×C3C2×#56811yescharacteristic
641D3—22no—
642D3—41no—
643C22—21no—
644C22—21no—
645C22—32no—
646C22—61no—
647C22—61no—
648C22—61no—
649C22—61no—
650C22—61no—
651C22—124no—
652C22C2×#90712yes—
653C22C23×C4×D311yescharacteristic
654C4—24no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—24no—
659C4—32no—
660C4—32no—
661C4—61no—
662C4—61no—
663C4—64no—
664C4—61no—
665C4—61no—
666C4—64no—
667C4C2×#90712yes—
668C4C2×#90712yes—
669C4D3×2−1+412yes—
670C3#6025011yescharacteristic, complemented, Sylow
671C2—22no—
672C2—62no—
673C2—121no—
674C2D3×#51911yescharacteristic
675C2C22×#90711yescharacteristic
676C2D3×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2983C2
prime radicalC23×D3C22×C4
cosocleC2×C3×C4C25
hypercenter#2983D3
hypocenterC3#60250
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. C3×#2983C2semidirect
3. #82435C2semidirect
4. #79967C2semidirect
5. #79965C2semidirect
6. #79960C2semidirect
7. #79958C2semidirect
9. #79315C2semidirect
12. #79264C2semidirect
13. #79263C2semidirect
34. C3×#446C22semidirect
35. C3×#446C22semidirect
39. Q8×C3⋊C8C22semidirect
40. Q8×C3⋊C8C22semidirect
50. #4831C22semidirect
51. #4831C22semidirect
52. #4830C22semidirect
53. #4830C22semidirect
62. #4701C22semidirect
63. #4701C22semidirect
68. #4679C22semidirect
69. C8×Dic6C22semidirect
75. #2983D3semidirect
206. #446C2×D3semidirect
207. #446C2×D3semidirect
670. C3#60250semidirect

Maximal subgroups

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

subgroupindex
C2×#55782
C3×#29832
#824352
#799672
#799652
#799602
#799582
#793332
#793152
#792822
D3×#4312
#792642
#792632
#602503