Finite Group Databasebeta

← #10824332

Subgroups — #10824332

Order 768.

1092 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4872C211yesmaximal, characteristic, complemented
2C2×#4756C211yesmaximal, characteristic, complemented
3#76293C211yesmaximal, characteristic, complemented
4#75961C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6#70619C211yesmaximal, characteristic, complemented
7#70481C211yesmaximal, characteristic, complemented
8Dic3×C4⋊C8C211yesmaximal, characteristic, complemented
9#70209C211yesmaximal, characteristic
10#70177C211yesmaximal, characteristic, complemented
11Dic3×#102C211yesmaximal, characteristic, complemented
12#69650C211yesmaximal, characteristic, complemented
13#69630C211yesmaximal, characteristic, complemented
14#68902C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#23676—31nomaximal, Sylow
17C2×#940C2211yescharacteristic
18C2×D4×Dic3C2211yescharacteristic
19C22×#213C2211yescharacteristic
20C22×D24C2211yescharacteristic
21C2×#893C2211yescharacteristic
22C2×#893C2211yescharacteristic
23C2×#892—21no—
24C2×#67⋊C4—21no—
25C2×#67⋊C4—21no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C3×#390C2211yescharacteristic
31C3×#389C2211yescharacteristic
32C2×#832C2211yescharacteristic
33C2×#821C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×C8×Dic3C2211yescharacteristic
36C2×C8×Dic3C2211yescharacteristic
37#4990—21no—
38#4988C2211yescharacteristic
39#4984C2211yescharacteristic
40#4975C2211yescharacteristic
41Dic3×C4⋊C4C2211yescharacteristic
42C2×#809C2211yescharacteristic
43C2×#809C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#807C2211yescharacteristic
46#4957—21no—
47#4957—21no—
48#4939C2211yescharacteristic
49#4939C2211yescharacteristic
50C42×Dic3C2211yescharacteristic
51C2×C4⋊(C3⋊C8)C2211yescharacteristic
52#4872—24no—
53#4756—24no—
54#4670—21no—
55#4666—21no—
56C3×#340C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62C2×C4×D8—31no—
63C2×C4×D8—31no—
64C4×#127—31no—
65#2293—31no—
66#2083—31no—
67#2071—31no—
68#2067—31no—
69#2067D311yescharacteristic, complemented
70#2054—31no—
71#2054—31no—
72#2041—31no—
73#2011—31no—
74C4×C4⋊C8—31no—
75C4×#102—31no—
76C4×#102—31no—
77C22×C3×D4C2311yescharacteristic
78C22×#67—21no—
79C22×#67—21no—
80C23×Dic3—21no—
81C22×D12C2311yescharacteristic
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3—21no—
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C22⋊C4—21no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C42C2311yescharacteristic
94C2×#217—21no—
95#940—22no—
96#940—22no—
97D4×Dic3—22no—
98D4×Dic3—22no—
99C2×#213—22no—
100C2×#213—22no—
101C2×#213—22no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×Dic3⋊C4—21no—
115C2×C4×Dic3—21no—
116C2×C4×Dic3D411yescharacteristic
117C2×C4×Dic3D411yescharacteristic
118C2×C4×Dic3D411yescharacteristic
119C2×C4×Dic3D411yescharacteristic
120C2×C4×Dic3C2311yescharacteristic
121C2×C4×Dic3C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124C2×D24—22no—
125C2×D24—22no—
126C2×D24—22no—
127#893—22no—
128#893—22no—
129#893—22no—
130#893D414yescomplemented
131#892—44no—
132#67⋊C4—44no—
133#67⋊C4—44no—
134C3×#107—22no—
135C3×C4⋊C8—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#95—21no—
139#832—22no—
140C3⋊#95—21no—
141C3⋊#95—21no—
142#821—22no—
143#821—22no—
144C8×Dic3—22no—
145C8×Dic3—22no—
146#809—22no—
147#809—22no—
148#809—22no—
149#807—22no—
150C4⋊(C3⋊C8)—22no—
151C22×D8—31no—
152C22×D8—31no—
153C2×#127—31no—
154C2×C4×D4—31no—
155C2×C4×D4—31no—
156C2×C4×D4—31no—
157C2×C4×D4—61no—
158C2×C4×D4—61no—
159C2×#117—61no—
160C4×D8—64no—
161C4×D8—64no—
162C2×#107—31no—
163C2×#107C2×D311yescharacteristic
164C2×C4⋊C8—31no—
165C2×C4⋊C8C2×D311yescharacteristic
166C2×#102—31no—
167C2×#102—31no—
168C2×#102—31no—
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102C2×D311yescharacteristic
173C2×#102C2×D311yescharacteristic
174C2×C4×C8—31no—
175C2×C4×C8—31no—
176#390—31no—
177#390—31no—
178#390—31no—
179#390—61no—
180#390—61no—
181#390C2×D311yescharacteristic
182#389—31no—
183#389C2×D311yescharacteristic
184#388—61no—
185#388—61no—
186#384—31no—
187C4×C4⋊C4—31no—
188C4×C22⋊C4—61no—
189C43—31no—
190#340—31no—
191#340—31no—
192#340—31no—
193#340C2×D311yescharacteristic
194#336—31no—
195#336—31no—
196C24×C3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4#4112yes—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2411yescharacteristic
211C2×#67—24no—
212C2×#67—24no—
213C2×#67—42no—
214C2×#67—42no—
215C2×#67—42no—
216C2×#67—42no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—42no—
220C22×Dic3—42no—
221C22×Dic3—42no—
222C22×Dic3C2×D411yescharacteristic
223C22×Dic3C2×D411yescharacteristic
224C22×Dic3C2×D411yescharacteristic
225C22×Dic3C2×D411yescharacteristic
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12C2×D412yes—
237C2×D12#4112yes—
238C2×C4×D3—24no—
239C2×C4×D3—42no—
240C2×C4×D3—42no—
241C2×C4×D3—42no—
242C2×C4×D3—42no—
243C2×C4×D3—42no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8#4112yes—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—42no—
256C3×C4⋊C4C2×D412yes—
257C3×C22⋊C4—42no—
258C3×C22⋊C4—42no—
259C3×C42—21no—
260C3×C42—21no—
261#217—42no—
262#213—28no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—42no—
265(C2×D3)⋊C4—42no—
266(C2×D3)⋊C4—42no—
267(C2×D3)⋊C4—42no—
268(C2×D3)⋊C4—42no—
269(C2×D3)⋊C4—42no—
270(C2×D3)⋊C4—42no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—42no—
276Dic3⋊C4—42no—
277Dic3⋊C4—42no—
278C4×Dic3—21no—
279C4×Dic3—21no—
280C4×Dic3—22no—
281C4×Dic3—22no—
282C4×Dic3—41no—
283C4×Dic3—42no—
284C4×Dic3D814yescomplemented
285C4×Dic3C2×D412yes—
286C4×Dic3#4112yes—
287C2×C3⋊C8—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8#4112yes—
293D24—28no—
294C22×D4—31no—
295C22×D4—31no—
296C22×D4—61no—
297C22×D4—61no—
298C22×D4C22×D311yescharacteristic
299C23×C4—61no—
300C23×C4—61no—
301C23×C4—61no—
302C2×D8—62no—
303C2×D8—62no—
304C2×D8—62no—
305C2×D8—62no—
306C2×D8—62no—
307C2×D8—62no—
308C22×C8—31no—
309C22×C8—31no—
310C22×C8C22×D311yescharacteristic
311C22×C8C22×D311yescharacteristic
312#127—62no—
313#127—62no—
314C4×D4—34no—
315C4×D4—62no—
316C4×D4—62no—
317C4×D4—62no—
318C4×D4—62no—
319C4×D4—62no—
320C4×D4—124no—
321C4×D4—124no—
322#117—124no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—61no—
327C2×C4⋊C4—61no—
328C2×C4⋊C4—61no—
329C2×C4⋊C4C22×D311yescharacteristic
330C2×C4⋊C4C22×D311yescharacteristic
331C2×C4⋊C4C22×D311yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—61no—
335C2×C22⋊C4—61no—
336C2×C22⋊C4—61no—
337C2×C22⋊C4—61no—
338C2×C22⋊C4—61no—
339C2×C22⋊C4—61no—
340C2×C22⋊C4—61no—
341C2×C22⋊C4—61no—
342C2×C22⋊C4—61no—
343C2×C42—31no—
344C2×C42—31no—
345C2×C42—31no—
346C2×C42—31no—
347C2×C42—31no—
348C2×C42—31no—
349C2×C42—61no—
350C2×C42C22×D311yescharacteristic
351#107—22no—
352#107—62no—
353C4⋊C8—22no—
354C4⋊C8—62no—
355#102—22no—
356#102—22no—
357#102—62no—
358#102—62no—
359#102—62no—
360#102—62no—
361#102—62no—
362#102—62no—
363C4×C8—62no—
364C4×C8—62no—
365#95—21no—
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—22no—
377C22×D3—22no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3—41no—
385C22×D3—41no—
386C22×D3—41no—
387C22×D3—41no—
388C22×D3—41no—
389C22×D3—41no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—41no—
393C3×D4—41no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
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×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4C2×D812yes—
409C2×C3×C4C22×D411yescharacteristic
410C2×C3×C4C2×#4111yescharacteristic
411C2×C3×C4C2×#4111yescharacteristic
412C2×C3×C4C2×#4111yescharacteristic
413C2×C3×C4C2×#4111yescharacteristic
414C2×C3×C4C2×#4111yescharacteristic
415#67—48no—
416#67—48no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—84no—
430C2×Dic3#12112yes—
431C2×Dic3#12112yes—
432C2×Dic3C2×D812yes—
433C2×Dic3C2×D812yes—
434C2×Dic3#13512yes—
435C2×Dic3AGL(1,ℤ/8)12yes—
436D12—22no—
437D12—22no—
438D12—22no—
439D12—22no—
440D12—41no—
441D12—41no—
442D12—41no—
443D12—41no—
444C4×D3—48no—
445C4×D3—84no—
446C3×C8—22no—
447C3×C8—41no—
448C3⋊C8—22no—
449C3⋊C8—41no—
450C24—21no—
451C24—61no—
452C24—61no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—32no—
459C2×D4—32no—
460C2×D4—64no—
461C2×D4—64no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—122no—
473C2×D4—122no—
474C2×D4—122no—
475C2×D4—122no—
476C2×D4#23912yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—64no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—122no—
488C22×C4—122no—
489C22×C4—122no—
490C22×C4—122no—
491C22×C4—122no—
492C22×C4—122no—
493C22×C4—122no—
494C22×C4—122no—
495C22×C4D3×D411yescharacteristic
496C22×C4D3×D411yescharacteristic
497C22×C4C23×D311yescharacteristic
498D8—68no—
499D8—68no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—32no—
506C2×C8—61no—
507C2×C8—61no—
508C2×C8—61no—
509C2×C8—61no—
510C2×C8—61no—
511C2×C8#23712yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—61no—
519C4⋊C4—61no—
520C4⋊C4—61no—
521C4⋊C4—61no—
522C4⋊C4—122no—
523C4⋊C4—122no—
524C4⋊C4—122no—
525C4⋊C4D3×D412yes—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—64no—
529C22⋊C4—122no—
530C22⋊C4—122no—
531C22⋊C4—122no—
532C22⋊C4—122no—
533C22⋊C4—122no—
534C22⋊C4—122no—
535C22⋊C4—122no—
536C22⋊C4—122no—
537C42—21no—
538C42—21no—
539C42—34no—
540C42—32no—
541C42—32no—
542C42—62no—
543C42—62no—
544C42—61no—
545C42—61no—
546C42—121no—
547C42—122no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—81no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3C2×#12111yescharacteristic
556C22×C3#52511yescharacteristic
557C22×C3#53211yescharacteristic
558C22×C3C22×D811yescharacteristic
559C22×C3C2×#13511yescharacteristic
560C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
561C22×C3#57511yescharacteristic
562C2×D3—42no—
563C2×D3—42no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3—81no—
569C2×D3—81no—
570C2×D3—81no—
571C2×D3—81no—
572C2×D3—81no—
573C2×D3—81no—
574C2×D3—81no—
575C2×D3—81no—
576C3×C4—22no—
577C3×C4—41no—
578C3×C4—42no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4#52511yescharacteristic
582C3×C4#52511yescharacteristic
583C3×C4#52911yescharacteristic
584C3×C4#52911yescharacteristic
585Dic3—22no—
586Dic3—22no—
587Dic3—22no—
588Dic3—81no—
589Dic3—81no—
590Dic3#45914yes—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—62no—
599C23—62no—
600C23—121no—
601C23—121no—
602C23—121no—
603C23—121no—
604C23—121no—
605C23—121no—
606C23—121no—
607C23—121no—
608C23—121no—
609C23—121no—
610C23—121no—
611C23—121no—
612C23C2×D3×D411yescharacteristic
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—62no—
618D4—62no—
619D4—62no—
620D4—62no—
621D4—128no—
622D4—128no—
623D4—121no—
624D4—121no—
625D4—121no—
626D4—121no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—128no—
654C2×C4—121no—
655C2×C4—121no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—244no—
661C2×C4—244no—
662C2×C4D3×D812yes—
663C2×C4C2×D3×D411yescharacteristic
664C2×C4C2×#23711yescharacteristic
665C2×C4C2×#23911yescharacteristic
666C2×C4D3×#4111yescharacteristic
667C2×C4D3×#4111yescharacteristic
668C2×C4D3×#4111yescharacteristic
669C8—22no—
670C8—41no—
671C8—62no—
672C8—121no—
673C2×C3—82no—
674C2×C3#239211yescharacteristic
675C2×C3C2×#45911yescharacteristic
676C2×C3#303511yescharacteristic
677C2×C3#310011yescharacteristic
678C2×C3#310511yescharacteristic
679C2×C3#316911yescharacteristic
680C2×C3#317111yescharacteristic
681D3—82no—
682D3—82no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—122no—
691C22—122no—
692C22—122no—
693C22—122no—
694C22—122no—
695C22—122no—
696C22—241no—
697C22—241no—
698C22—241no—
699C22—241no—
700C22—241no—
701C22—241no—
702C22—241no—
703C22—241no—
704C22#559611yescharacteristic
705C22D3×#12111yescharacteristic
706C22#562711yescharacteristic
707C22C2×D3×D811yescharacteristic
708C22D3×#13511yescharacteristic
709C22D3×AGL(1,ℤ/8)11yescharacteristic
710C22#577711yescharacteristic
711C4—22no—
712C4—34no—
713C4—41no—
714C4—42no—
715C4—62no—
716C4—62no—
717C4—62no—
718C4—81no—
719C4—81no—
720C4—241no—
721C4—241no—
722C4#560611yescharacteristic
723C4#562411yescharacteristic
724C4#562711yescharacteristic
725C4#570611yescharacteristic
726C3#2367611yescharacteristic, complemented, Sylow
727C2—82no—
728C2—242no—
729C2—242no—
730C2#7728111yescharacteristic
731C2D3×#45911yescharacteristic
732C2#8059711yescharacteristic
733C2#8069711yescharacteristic
734C2#8078411yescharacteristic
735C2#8094811yescharacteristic
736C2#8114111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2067C2
socleC23×C3C22×D4
prime radical#70209C2
hypercenter#2067D3
hypocenterC3#23676
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#4872C2semidirect
2. C2×#4756C2semidirect
3. #76293C2semidirect
4. #75961C2semidirect
5. C3×#2067C2semidirect
6. #70619C2semidirect
7. #70481C2semidirect
8. Dic3×C4⋊C8C2semidirect
10. #70177C2semidirect
11. Dic3×#102C2semidirect
12. #69650C2semidirect
13. #69630C2semidirect
14. #68902C2semidirect
15. #68780C2semidirect
69. #2067D3semidirect
130. #893D4semidirect
284. C4×Dic3D8semidirect
726. C3#23676semidirect

Maximal subgroups

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

subgroupindex
C2×#48722
C2×#47562
#762932
#759612
C3×#20672
#706192
#704812
Dic3×C4⋊C82
#702092
#701772
Dic3×#1022
#696502
#696302
#689022
#687802
#236763