Finite Group Databasebeta

← #10801767

Subgroups — #10801767

Order 768.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5171C211yesmaximal, characteristic
2C2×#5164C211yesmaximal, characteristic, complemented
3C2×D3×#97C211yesmaximal, characteristic, complemented
4#76479C211yesmaximal, characteristic, complemented
5#76291C211yesmaximal, characteristic
6C3×#1973C211yesmaximal, characteristic, complemented
7#70630C211yesmaximal, characteristic, complemented
8#70605C211yesmaximal, characteristic, complemented
9#70270C211yesmaximal, characteristic, complemented
10#70220C211yesmaximal, characteristic, complemented
11#70202C211yesmaximal, characteristic
12#70152C211yesmaximal, characteristic, complemented
13#69820C211yesmaximal, characteristic, complemented
14#69675C211yesmaximal, characteristic, complemented
15#69645C211yesmaximal, characteristic, complemented
16#21528—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×D4×Dic3C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24C2×#67⋊C4—21no—
25C2×C42×D3C2211yescharacteristic
26C2×C3×#107C2211yescharacteristic
27C2×C3×#103C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#97C2211yescharacteristic
30C3×#391C2211yescharacteristic
31C3×#390C2211yescharacteristic
32C2×#835C2211yescharacteristic
33C2×#835C2211yescharacteristic
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36#5171C418yescomplemented
37#5164—24no—
38C2×#818C2211yescharacteristic
39C2×#817C2211yescharacteristic
40C2×#815C2211yescharacteristic
41C2×#815C2211yescharacteristic
42#4987C2211yescharacteristic
43#4987C2211yescharacteristic
44Dic3×C4⋊C4C2211yescharacteristic
45Dic3×C4⋊C4C2211yescharacteristic
46#4956—21no—
47#4945—21no—
48Dic3×C22⋊C4—21no—
49#4928C2211yescharacteristic
50#4928C2211yescharacteristic
51C2×#803C2211yescharacteristic
52D3×#97—24no—
53#4668—21no—
54#4666—21no—
55#4655—21no—
56#4649—21no—
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#465—31no—
64C2×#440—31no—
65C22×#97—31no—
66C4×C22⋊Q8—31no—
67C4×#121—31no—
68#1973D311yescharacteristic, complemented
69#1944—31no—
70#1936—31no—
71#1935—31no—
72#1893—31no—
73#1892—31no—
74#1808—31no—
75#1776—31no—
76#1763—31no—
77#1762—31no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C22×#67—21no—
81C23×Dic3—21no—
82C22×C4×D3D411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16C2×C414yescomplemented
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C42C2311yescharacteristic
95C2×#217—21no—
96C2×#217—21no—
97#946—22no—
98#946C2×C414yescomplemented
99Q8×Dic3—22no—
100Q8×Dic3—22no—
101#938—22no—
102#938C2×C414yes—
103D4×Dic3—22no—
104D4×Dic3—22no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×C4⋊Dic3—21no—
109C2×C4⋊Dic3C2311yescharacteristic
110C2×C4⋊Dic3C2311yescharacteristic
111C2×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×Dic3⋊C4—21no—
115C2×Dic3⋊C4—21no—
116C2×C4×Dic3—21no—
117C2×C4×Dic3—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3D411yescharacteristic
120C2×C4×Dic3D411yescharacteristic
121C2×C4×Dic3C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124C2×D3×C8—22no—
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—22no—
128C2×D3×C8—22no—
129C2×D3×C8C2×C414yescomplemented
130#67⋊C4—44no—
131C42×D3—22no—
132C42×D3—22no—
133C3×#107—22no—
134C3×#103—22no—
135C3×#102—22no—
136C3×#97—22no—
137C3×#95—21no—
138C3×#95—21no—
139#835—22no—
140#835C2×C414yescomplemented
141#832—22no—
142#832C2×C414yescomplemented
143C3⋊#95—21no—
144C3⋊#95—21no—
145C3⋊#95—21no—
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149#818—22no—
150#817C2×C414yescomplemented
151#815—22no—
152#815D414yescomplemented
153#803—22no—
154C22×SD16C2×D311yescharacteristic
155C23×C8—31no—
156C23×C8—31no—
157C2×C22⋊Q8—31no—
158C2×#121—31no—
159C2×C4×Q8—31no—
160C2×C4×D4—31no—
161C2×C4×D4—61no—
162C22×C42—31no—
163#465—38no—
164#440—64no—
165C2×#107—31no—
166C2×#107C2×D311yescharacteristic
167C2×#106—31no—
168C2×#103—31no—
169C2×#103—31no—
170C2×#103C2×D311yescharacteristic
171C2×#102—31no—
172C2×#102—31no—
173C2×#102C2×D311yescharacteristic
174C2×#97—31no—
175C2×#97—31no—
176C2×#97—31no—
177C2×#97—64no—
178C2×#97C2×D311yescharacteristic
179#391C2×D311yescharacteristic
180#390C2×D311yescharacteristic
181#389—31no—
182#389—31no—
183#388—61no—
184#387—61no—
185#386—61no—
186#385—61no—
187#380—31no—
188#380—31no—
189C4×C4⋊C4—31no—
190C4×C4⋊C4—31no—
191C4×C4⋊C4—61no—
192C4×C22⋊C4—61no—
193C4×C22⋊C4—61no—
194#340—31no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199#340—31no—
200C24×C3—21no—
201C23×D3C2×D411yescharacteristic
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8C22×C412yes—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4C22×C412yes—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2411yescharacteristic
220C2×#67—24no—
221C2×#67—42no—
222C2×#67—42no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—42no—
228C22×Dic3—42no—
229C22×Dic3—42no—
230C22×Dic3C2×D411yescharacteristic
231C22×Dic3C2×D411yescharacteristic
232C22×Dic3C2×D411yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—22no—
241C2×C4×D3—41no—
242C2×C4×D3—41no—
243C2×C4×D3C22×C412yes—
244C2×C4×D3#4112yes—
245C3×SD16—28no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8C22×C412yes—
249C2×C3×C8C2×D412yes—
250C2×C3×C8#4112yes—
251C2×C3×C8#4112yes—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C22⋊C4—42no—
257C3×C22⋊C4—42no—
258C3×C42—21no—
259C3×C42—21no—
260#217—24no—
261#217—42no—
262(C2×D3)⋊C4—24no—
263(C2×D3)⋊C4—42no—
264(C2×D3)⋊C4—42no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—42no—
272C4⋊Dic3C22×C412yes—
273C4⋊Dic3C22×C412yes—
274Dic3⋊C4—24no—
275Dic3⋊C4—42no—
276Dic3⋊C4—42no—
277C4×Dic3—22no—
278C4×Dic3—22no—
279C4×Dic3—42no—
280C4×Dic3—42no—
281C4×Dic3—42no—
282C4×Dic3C2×D412yes—
283C4×Dic3#4112yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—21no—
288C2×C3⋊C8C22×C412yes—
289C2×C3⋊C8C2×D412yes—
290D3×C8—28no—
291D3×C8—28no—
292C22×Q8C22×D311yescharacteristic
293C22×D4—61no—
294C22×D4C22×D311yescharacteristic
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—61no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16C4×D314yescomplemented
302C22×C8—31no—
303C22×C8—31no—
304C22×C8—34no—
305C22×C8—62no—
306C22×C8—62no—
307C22×C8—62no—
308C22×C8—62no—
309C22×C8—62no—
310C22×C8C22×D311yescharacteristic
311C22×C8C22×D311yescharacteristic
312C22⋊Q8—34no—
313C22⋊Q8—62no—
314#121—34no—
315#121—62no—
316C4×Q8—62no—
317C4×Q8—62no—
318C4×D4—62no—
319C4×D4—62no—
320C4×D4—124no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—61no—
326C2×C4⋊C4—61no—
327C2×C4⋊C4—61no—
328C2×C4⋊C4—61no—
329C2×C4⋊C4C22×D311yescharacteristic
330C2×C4⋊C4C22×D311yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—61no—
334C2×C22⋊C4—61no—
335C2×C22⋊C4—61no—
336C2×C22⋊C4—61no—
337C2×C22⋊C4—61no—
338C2×C42—31no—
339C2×C42—31no—
340C2×C42—31no—
341C2×C42—62no—
342C2×C42—62no—
343C2×C42—61no—
344C2×C42—61no—
345C2×C42—61no—
346C2×C42C22×D311yescharacteristic
347#107—22no—
348#107—62no—
349#106—34no—
350#103—22no—
351#103—34no—
352#103—62no—
353#102—22no—
354#102—34no—
355#102—62no—
356#97—22no—
357#97—34no—
358#97—62no—
359#97—62no—
360#95—21no—
361#95—21no—
362#95—61no—
363#95—61no—
364#95—61no—
365#95—61no—
366#95—61no—
367#95—61no—
368C23×C3—22no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3C22×D411yescharacteristic
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—21no—
380C22×D3C4×D412yes—
381C22×D3AGL(1,ℤ/8)12yes—
382C22×D3#13712yes—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—41no—
390C3×D4—41no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4C23×C411yescharacteristic
407C2×C3×C4C22×D411yescharacteristic
408C2×C3×C4C2×#4111yescharacteristic
409C2×C3×C4C2×#4111yescharacteristic
410C2×C3×C4C2×#4111yescharacteristic
411C2×C3×C4C2×#4111yescharacteristic
412#67—48no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—84no—
432C2×Dic3C4×D412yes—
433C2×Dic3#12112yes—
434C2×Dic3#12112yes—
435C4×D3—22no—
436C4×D3—22no—
437C4×D3—22no—
438C4×D3—22no—
439C4×D3—44no—
440C4×D3—44no—
441C3×C8—22no—
442C3×C8C4×D414yescomplemented
443C3⋊C8—22no—
444C3⋊C8—22no—
445C24—21no—
446C24—31no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×C4×D312yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—64no—
459C2×D4—122no—
460C2×D4—122no—
461C2×D4C2×C4×D312yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—32no—
469C22×C4—32no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—121no—
483C22×C4—121no—
484C22×C4—122no—
485C22×C4—122no—
486C22×C4—122no—
487C22×C4D3×D411yescharacteristic
488C22×C4D3×D411yescharacteristic
489C22×C4C23×D311yescharacteristic
490SD16—28no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—32no—
494C2×C8—32no—
495C2×C8—68no—
496C2×C8—61no—
497C2×C8—61no—
498C2×C8—61no—
499C2×C8—61no—
500C2×C8—68no—
501C2×C8C2×C4×D312yes—
502C2×C8D3×D412yes—
503C2×C8#23712yes—
504C2×C8#23712yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—32no—
510C4⋊C4—32no—
511C4⋊C4—64no—
512C4⋊C4—61no—
513C4⋊C4—61no—
514C4⋊C4—61no—
515C4⋊C4—61no—
516C4⋊C4—61no—
517C4⋊C4—61no—
518C4⋊C4—122no—
519C4⋊C4—122no—
520C4⋊C4—122no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—64no—
524C22⋊C4—64no—
525C22⋊C4—122no—
526C22⋊C4—122no—
527C22⋊C4—122no—
528C42—21no—
529C42—21no—
530C42—32no—
531C42—32no—
532C42—62no—
533C42—62no—
534C42—122no—
535C42—122no—
536C42—122no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3C2×C4×D411yescharacteristic
545C22×C3C2×#12111yescharacteristic
546C22×C3#53211yescharacteristic
547C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
548C22×C3C2×#13711yescharacteristic
549C22×C3#57511yescharacteristic
550C22×C3#57511yescharacteristic
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—22no—
554C2×D3—22no—
555C2×D3—22no—
556C2×D3—22no—
557C2×D3#44014yescomplemented
558C3×C4—41no—
559C3×C4—41no—
560C3×C4—42no—
561C3×C4—81no—
562C3×C4—81no—
563C3×C4C2×C4×D411yescharacteristic
564C3×C4C4×#4111yescharacteristic
565C3×C4#52511yescharacteristic
566C3×C4#52911yescharacteristic
567Dic3—22no—
568Dic3—22no—
569Dic3—22no—
570Dic3—42no—
571Dic3—42no—
572Dic3—81no—
573Dic3—81no—
574C23—22no—
575C23—32no—
576C23—32no—
577C23—32no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—61no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23C2×D3×D411yescharacteristic
589Q8—22no—
590Q8—22no—
591Q8—41no—
592Q8—41no—
593D4—22no—
594D4—22no—
595D4—41no—
596D4—41no—
597D4—128no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—32no—
606C2×C4—32no—
607C2×C4—32no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—124no—
629C2×C4—124no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—121no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—121no—
638C2×C4—121no—
639C2×C4—121no—
640C2×C4—244no—
641C2×C4C22×C4×D311yescharacteristic
642C2×C4C2×D3×D411yescharacteristic
643C2×C4C2×#23711yescharacteristic
644C2×C4C2×#23711yescharacteristic
645C2×C4D3×#4111yescharacteristic
646C2×C4D3×#4111yescharacteristic
647C8—22no—
648C8—62no—
649C8—62no—
650C8#67⋊C414yescomplemented
651C2×C3—82no—
652C2×C3C4×#12111yescharacteristic
653C2×C3C2×#44011yescharacteristic
654C2×C3#294311yescharacteristic
655C2×C3#305511yescharacteristic
656C2×C3#305611yescharacteristic
657C2×C3#318011yescharacteristic
658C2×C3#318111yescharacteristic
659D3—24no—
660C22—34no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—62no—
665C22—62no—
666C22—62no—
667C22—62no—
668C22—62no—
669C22—62no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22C4×D3×D411yescharacteristic
675C22D3×#12111yescharacteristic
676C22#571611yescharacteristic
677C22D3×AGL(1,ℤ/8)11yescharacteristic
678C22#577311yescharacteristic
679C22D3×#13711yescharacteristic
680C22#577711yescharacteristic
681C4—42no—
682C4—41no—
683C4—41no—
684C4—62no—
685C4—62no—
686C4—62no—
687C4—81no—
688C4—81no—
689C4—122no—
690C4—122no—
691C4—241no—
692C4—241no—
693C4C2×#67⋊C411yescharacteristic
694C4C4×#23711yescharacteristic
695C4#560611yescharacteristic
696C4#568011yescharacteristic
697C3#2152811yescharacteristic, complemented, Sylow
698C2—64no—
699C2—82no—
700C2#7629111yescharacteristic
701C2D3×#44011yescharacteristic
702C2#7977211yescharacteristic
703C2#8080511yescharacteristic
704C2#8080611yescharacteristic
705C2#8183811yescharacteristic
706C2#8186311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1973C2
socleC23×C3C22×D4
prime radicalC2×#938C22
cosocleC22×C3×C4C24
hypercenter#1973D3
hypocenterC3#21528
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. C2×#5164C2semidirect
3. C2×D3×#97C2semidirect
4. #76479C2semidirect
6. C3×#1973C2semidirect
7. #70630C2semidirect
8. #70605C2semidirect
9. #70270C2semidirect
10. #70220C2semidirect
12. #70152C2semidirect
13. #69820C2semidirect
14. #69675C2semidirect
15. #69645C2semidirect
36. #5171C4semidirect
68. #1973D3semidirect
87. C2×C3×SD16C2×C4semidirect
98. #946C2×C4semidirect
129. C2×D3×C8C2×C4semidirect
140. #835C2×C4semidirect
142. #832C2×C4semidirect
150. #817C2×C4semidirect
152. #815D4semidirect
301. C2×SD16C4×D3semidirect
442. C3×C8C4×D4semidirect
557. C2×D3#440semidirect
650. C8#67⋊C4semidirect
697. C3#21528semidirect

Maximal subgroups

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

subgroupindex
C2×#51712
C2×#51642
C2×D3×#972
#764792
#762912
C3×#19732
#706302
#706052
#702702
#702202
#702022
#701522
#698202
#696752
#696452
#215283