Finite Group Databasebeta

← #10794567

Subgroups — #10794567

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5522C211yesmaximal, characteristic
2C2×#4837C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊C8C211yesmaximal, characteristic, complemented
4C2×#4727C212yesmaximal
5C3×#1798C211yesmaximal, characteristic, complemented
6#71583C211yesmaximal, characteristic, complemented
7#70476C211yesmaximal, characteristic, complemented
8#70476C211yesmaximal, characteristic, complemented
9#69908C212yesmaximal, complemented
10#68662C212yesmaximal, complemented
11#68661C212yesmaximal, complemented
12#20629—31nomaximal, Sylow
13C22×#235C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C22×C4×Dic3C2211yescharacteristic
16C22×ΓL(1,𝔽25)C2212yes—
17C22×D3×C8C2212yes—
18#5522—24no—
19#5522—24no—
20C2×#893C411yescharacteristic
21C2×#893C411yescharacteristic
22C2×#887C411yescharacteristic
23C2×#887C411yescharacteristic
24C2×#67⋊C4C411yescharacteristic
25C2×#67⋊C4C411yescharacteristic
26C2×#67⋊C4C411yescharacteristic
27C2×#67⋊C4C411yescharacteristic
28C2×#872C2211yescharacteristic
29C2×#872C2211yescharacteristic
30C2×C42×D3C2211yescharacteristic
31C2×C42×D3C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×C4⋊C8C2211yescharacteristic
34C2×C3×C22⋊C8C2212yes—
35C2×#830C2212yes—
36C2×(C2×D3)⋊C8C2212yes—
37C2×(C2×D3)⋊C8C2212yes—
38C2×Dic3⋊C8C2212yes—
39C2×Dic3⋊C8C2212yes—
40C2×C4⋊(C3⋊C8)C2211yescharacteristic
41C2×C4⋊(C3⋊C8)C2211yescharacteristic
42#4837—24no—
43D3×C4⋊C8—24no—
44#4727—28no—
45C3×#336C2212yes—
46#4550C2212yes—
47#4550C2212yes—
48#4524C2212yes—
49C2×C4×#41—31no—
50C2×#423—31no—
51C22×C4⋊C8—31no—
52C2×#408—32no—
53#1798—31no—
54#1798—31no—
55#1798—31no—
56#1798D311yescharacteristic, complemented
57#1797—32no—
58#1797—32no—
59#1729—32no—
60C23×C3×C4C2311yescharacteristic
61C22×#67C2×C411yescharacteristic
62C22×#67C2×C411yescharacteristic
63C23×Dic3C2×C411yescharacteristic
64C23×Dic3C2×C411yescharacteristic
65C2×#235—22no—
66C2×#235—22no—
67C2×#235—22no—
68C2×#235—22no—
69C2×#235D414yes—
70C2×#235Q814yes—
71C22×D12C2×C411yescharacteristic
72C22×C4×D3C2×C411yescharacteristic
73C22×C4×D3C2×C411yescharacteristic
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3C2311yescharacteristic
77C22×C4×D3C2311yescharacteristic
78C22×Dic6C2×C411yescharacteristic
79C22×C3×C8C2312yes—
80C22×C3×C8C2312yes—
81C3×#117—22no—
82C3×#117—22no—
83C2×C3×C4⋊C4C2×C411yescharacteristic
84C2×C3×C4⋊C4C2×C411yescharacteristic
85C2×C3×C22⋊C4C2×C411yescharacteristic
86C2×C3×C22⋊C4C2×C411yescharacteristic
87C2×C3×C42C2311yescharacteristic
88C2×C3×C42C2311yescharacteristic
89C2×(C2×D3)⋊C4C2×C411yescharacteristic
90C2×(C2×D3)⋊C4C2×C411yescharacteristic
91C2×(C2×D3)⋊C4C2×C411yescharacteristic
92C2×(C2×D3)⋊C4C2×C411yescharacteristic
93C2×Dic3⋊C4C2×C411yescharacteristic
94C2×Dic3⋊C4C2×C411yescharacteristic
95C2×Dic3⋊C4C2×C411yescharacteristic
96C2×Dic3⋊C4C2×C411yescharacteristic
97C2×C4×Dic3—22no—
98C2×C4×Dic3—22no—
99C2×C4×Dic3C2×C411yescharacteristic
100C2×C4×Dic3C2×C411yescharacteristic
101C2×C4×Dic3C2×C411yescharacteristic
102C2×C4×Dic3C2×C411yescharacteristic
103C2×C4×Dic3C2×C411yescharacteristic
104C2×C4×Dic3C2×C411yescharacteristic
105C2×C4×Dic3C2311yescharacteristic
106C2×C4×Dic3C2311yescharacteristic
107C22×C3⋊C8C2312yes—
108C22×C3⋊C8C2312yes—
109C2×ΓL(1,𝔽25)—24no—
110C2×ΓL(1,𝔽25)—24no—
111C2×ΓL(1,𝔽25)—24no—
112C2×D3×C8—24no—
113C2×D3×C8—24no—
114C2×D3×C8—24no—
115#893—24no—
116#893—24no—
117#887—24no—
118#887—24no—
119#67⋊C4—24no—
120#67⋊C4—24no—
121#67⋊C4—24no—
122#67⋊C4—24no—
123#872—22no—
124#872—22no—
125#872—22no—
126#872—22no—
127C42×D3—22no—
128C42×D3—22no—
129C42×D3D414yes—
130C42×D3D414yes—
131C3×C4⋊C8—22no—
132C3×C4⋊C8—22no—
133C3×C22⋊C8—24no—
134#830—24no—
135(C2×D3)⋊C8—24no—
136(C2×D3)⋊C8—24no—
137Dic3⋊C8—24no—
138Dic3⋊C8—24no—
139C4⋊(C3⋊C8)—22no—
140C4⋊(C3⋊C8)—22no—
141C22×#41—31no—
142C22×M16—32no—
143C23×C8—32no—
144C4×#41—64no—
145C4×#41—64no—
146C2×C4×Q8—31no—
147C2×C4×Q8—31no—
148C2×C4×D4—31no—
149C2×C4×D4—31no—
150C2×C4×D4—31no—
151C2×C4×D4—31no—
152C2×C4×D4—31no—
153C2×C4×D4—31no—
154C2×#117—31no—
155C2×#117—31no—
156C2×#117C2×D311yescharacteristic
157C22×C42—31no—
158C22×C42—31no—
159C22×C42—31no—
160#423—64no—
161C2×C4⋊C8—32no—
162C2×C4⋊C8—32no—
163C2×C4⋊C8—31no—
164C2×C4⋊C8—31no—
165C2×C4⋊C8—64no—
166C2×C4⋊C8C2×D311yescharacteristic
167C2×C4⋊C8C2×D311yescharacteristic
168#408—68no—
169C2×C22⋊C8—32no—
170C2×C22⋊C8—32no—
171C2×C22⋊C8—32no—
172C2×C22⋊C8C2×D312yes—
173#336—32no—
174#336—32no—
175#336—32no—
176#336C2×D312yes—
177C24×C3C22×C411yescharacteristic
178C23×D3C22×C411yescharacteristic
179C23×D3C22×C411yescharacteristic
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4C22×C411yescharacteristic
185C22×C3×C4C22×C411yescharacteristic
186C22×C3×C4C22×C411yescharacteristic
187C22×C3×C4C22×C411yescharacteristic
188C22×C3×C4C22×C411yescharacteristic
189C22×C3×C4C2×D412yes—
190C22×C3×C4C2×Q812yes—
191C22×C3×C4C2411yescharacteristic
192C2×#67—22no—
193C2×#67—22no—
194C2×#67—22no—
195C2×#67—22no—
196C2×#67C4⋊C414yes—
197C2×#67C4⋊C414yes—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—24no—
201C22×Dic3—42no—
202C22×Dic3C22×C411yescharacteristic
203C22×Dic3C22×C411yescharacteristic
204C22×Dic3C22×C411yescharacteristic
205C22×Dic3C22×C411yescharacteristic
206C22×Dic3C22×C411yescharacteristic
207C22×Dic3C22×C411yescharacteristic
208#235—28no—
209#235—28no—
210#235—28no—
211#235—28no—
212C2×D12—22no—
213C2×D12—22no—
214C2×D12C4⋊C414yes—
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—24no—
220C2×C4×D3—22no—
221C2×C4×D3—22no—
222C2×C4×D3—24no—
223C2×C4×D3—42no—
224C2×C4×D3—42no—
225C2×C4×D3C22⋊C414yes—
226C2×C4×D3C22⋊C414yes—
227C2×C4×D3C2×D412yes—
228C2×C4×D3C2×D412yes—
229C2×C4×D3C2×D412yes—
230C2×C4×D3C2×D412yes—
231C2×C4×D3C2×Q812yes—
232C2×C4×D3C2×Q812yes—
233C2×C4×D3#4112yes—
234C2×C4×D3#4112yes—
235C2×Dic6—22no—
236C2×Dic6—22no—
237C2×Dic6C4⋊C414yes—
238C2×C3×C8—22no—
239C2×C3×C8—22no—
240C2×C3×C8—22no—
241C2×C3×C8—22no—
242C2×C3×C8—22no—
243C2×C3×C8—22no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—22no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42C2×D412yes—
251C3×C42C2×D412yes—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255(C2×D3)⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258Dic3⋊C4—22no—
259Dic3⋊C4—22no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—22no—
263C4×Dic3—22no—
264C4×Dic3—22no—
265C4×Dic3—22no—
266C4×Dic3C22⋊C414yes—
267C4×Dic3C22⋊C414yes—
268C4×Dic3C2×D412yes—
269C4×Dic3C2×D412yes—
270C2×C3⋊C8—22no—
271C2×C3⋊C8—22no—
272C2×C3⋊C8—22no—
273C2×C3⋊C8—22no—
274C2×C3⋊C8—22no—
275C2×C3⋊C8—22no—
276ΓL(1,𝔽25)—48no—
277D3×C8—48no—
278C2×#41—34no—
279C2×#41—34no—
280C2×#41—62no—
281C2×#41—62no—
282C2×#41—62no—
283C2×#41—62no—
284C22×Q8—31no—
285C22×D4—31no—
286C22×D4—31no—
287C22×D4—31no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4—31no—
296C23×C4C22×D311yescharacteristic
297C2×M16—64no—
298C2×M16—64no—
299C2×M16—64no—
300C22×C8—32no—
301C22×C8—32no—
302C22×C8—64no—
303C22×C8—64no—
304C22×C8—64no—
305C22×C8C22×D312yes—
306C22×C8C22×D312yes—
307C4×Q8—64no—
308C4×Q8—64no—
309C4×D4—64no—
310C4×D4—64no—
311C4×D4—64no—
312C4×D4—64no—
313C4×D4—64no—
314C4×D4—64no—
315#117—22no—
316#117—22no—
317#117—62no—
318#117—62no—
319#117—62no—
320#117—62no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4C4×D311yescharacteristic
326C2×C4⋊C4C4×D311yescharacteristic
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—31no—
331C2×C22⋊C4C4×D311yescharacteristic
332C2×C22⋊C4C4×D311yescharacteristic
333C2×C42—31no—
334C2×C42—31no—
335C2×C42—31no—
336C2×C42—34no—
337C2×C42—34no—
338C2×C42—31no—
339C2×C42—31no—
340C2×C42—31no—
341C2×C42—31no—
342C2×C42—31no—
343C2×C42—62no—
344C2×C42—62no—
345C2×C42—62no—
346C2×C42—62no—
347C2×C42C22×D311yescharacteristic
348C2×C42C22×D311yescharacteristic
349C4⋊C8—22no—
350C4⋊C8—22no—
351C4⋊C8—64no—
352C4⋊C8—64no—
353C4⋊C8—62no—
354C4⋊C8—62no—
355C22⋊C8—24no—
356C22⋊C8—64no—
357C22⋊C8—64no—
358C22⋊C8—64no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3C2×C4⋊C412yes—
364C23×C3C23×C411yescharacteristic
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3C2×C22⋊C412yes—
372C22×D3C2×C4⋊C412yes—
373C22×D3C2×C4⋊C412yes—
374C22×D3#11712yes—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4C2×C22⋊C412yes—
388C2×C3×C4C2×C22⋊C412yes—
389C2×C3×C4C2×C4⋊C412yes—
390C2×C3×C4C22×D411yescharacteristic
391C2×C3×C4C22×D411yescharacteristic
392C2×C3×C4C22×D411yescharacteristic
393C2×C3×C4C22×Q811yescharacteristic
394C2×C3×C4C2×#4111yescharacteristic
395C2×C3×C4C2×#4111yescharacteristic
396#67—28no—
397#67—28no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—44no—
406C2×Dic3—44no—
407C2×Dic3C2×C22⋊C412yes—
408C2×Dic3C2×C22⋊C412yes—
409C2×Dic3C2×C22⋊C412yes—
410C2×Dic3C2×C4⋊C412yes—
411C2×Dic3C2×C4⋊C412yes—
412C2×Dic3#11712yes—
413C2×Dic3#13114yes—
414D12—28no—
415C4×D3—22no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—28no—
420C4×D3—44no—
421C4×D3—44no—
422C4×D3—44no—
423C4×D3#12114yes—
424C4×D3#12114yes—
425C4×D3C22⋊Q814yes—
426C4×D3C22⋊Q814yes—
427Dic6—28no—
428C3×C8—42no—
429C3×C8—42no—
430C3⋊C8—42no—
431C3⋊C8—42no—
432C24—31no—
433C24—31no—
434C24C2×C4×D311yescharacteristic
435#41—68no—
436#41—68no—
437#41—68no—
438#41—68no—
439C2×Q8—34no—
440C2×Q8—62no—
441C2×Q8—62no—
442C2×D4—34no—
443C2×D4—34no—
444C2×D4—34no—
445C2×D4—62no—
446C2×D4—62no—
447C2×D4—62no—
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—62no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—34no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—64no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—64no—
475C22×C4—62no—
476C22×C4—62no—
477C22×C4—64no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—122no—
483C22×C4—122no—
484C22×C4—122no—
485C22×C4C2×C4×D311yescharacteristic
486C22×C4C2×C4×D311yescharacteristic
487C22×C4C2×C4×D311yescharacteristic
488C22×C4C2×C4×D311yescharacteristic
489C22×C4C2×C4×D311yescharacteristic
490C22×C4D3×D412yes—
491C22×C4D3×Q812yes—
492C22×C4C23×D311yescharacteristic
493M16—128no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—62no—
501C2×C8—62no—
502C2×C8—62no—
503C2×C8—62no—
504C2×C8—62no—
505C2×C8—62no—
506C2×C8—128no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—62no—
510C4⋊C4—62no—
511C4⋊C4—62no—
512C4⋊C4—62no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—62no—
516C22⋊C4—62no—
517C22⋊C4—62no—
518C22⋊C4—62no—
519C42—21no—
520C42—21no—
521C42—34no—
522C42—34no—
523C42—32no—
524C42—32no—
525C42—62no—
526C42—62no—
527C42—62no—
528C42—62no—
529C42—61no—
530C42—61no—
531C42D3×D412yes—
532C42D3×D412yes—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3C22×C22⋊C411yescharacteristic
539C22×C3C22×C4⋊C411yescharacteristic
540C22×C3C2×#11711yescharacteristic
541C22×C3C2×#13112yes—
542C22×C3#56812yes—
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—24no—
546C2×D3—24no—
547C2×D3—24no—
548C2×D3—22no—
549C2×D3—41no—
550C2×D3—41no—
551C2×D3—42no—
552C2×D3#38014yes—
553C3×C4—22no—
554C3×C4—22no—
555C3×C4—22no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4C2×#12111yescharacteristic
559C3×C4C2×#12111yescharacteristic
560C3×C4C2×C22⋊Q811yescharacteristic
561C3×C4C2×C22⋊Q811yescharacteristic
562Dic3—22no—
563Dic3—22no—
564Dic3—41no—
565Dic3—41no—
566Dic3#38014yes—
567Dic3#40814yescomplemented
568C23—21no—
569C23—22no—
570C23—22no—
571C23—21no—
572C23—32no—
573C23—32no—
574C23—32no—
575C23—32no—
576C23—62no—
577C23—62no—
578C23—61no—
579C23—62no—
580C23—62no—
581C23—61no—
582C23D3×C4⋊C412yes—
583C23C22×C4×D311yescharacteristic
584Q8—68no—
585D4—68no—
586D4—68no—
587D4—68no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—32no—
601C2×C4—32no—
602C2×C4—34no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—34no—
606C2×C4—34no—
607C2×C4—34no—
608C2×C4—34no—
609C2×C4—32no—
610C2×C4—32no—
611C2×C4—68no—
612C2×C4—61no—
613C2×C4—62no—
614C2×C4—61no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—124no—
624C2×C4—124no—
625C2×C4—124no—
626C2×C4—124no—
627C2×C4—124no—
628C2×C4D3×C22⋊C412yes—
629C2×C4D3×C22⋊C412yes—
630C2×C4D3×C4⋊C412yes—
631C2×C4C2×D3×D411yescharacteristic
632C2×C4C2×D3×D411yescharacteristic
633C2×C4C2×D3×D411yescharacteristic
634C2×C4C2×D3×Q811yescharacteristic
635C2×C4D3×#4111yescharacteristic
636C2×C4D3×#4111yescharacteristic
637C8—42no—
638C8—42no—
639C8—122no—
640C8—122no—
641C2×C3—42no—
642C2×C3C2×#38011yescharacteristic
643C2×C3C2×#40811yescharacteristic
644C2×C3#287911yescharacteristic
645C2×C3#290612yes—
646C2×C3#292512yes—
647D3—24no—
648D3—42no—
649C22—22no—
650C22—24no—
651C22—34no—
652C22—42no—
653C22—41no—
654C22—41no—
655C22—64no—
656C22—62no—
657C22—62no—
658C22—64no—
659C22—62no—
660C22—64no—
661C22—122no—
662C22—121no—
663C22—121no—
664C22C2×D3×C22⋊C411yescharacteristic
665C22C2×D3×C4⋊C411yescharacteristic
666C22D3×#11711yescharacteristic
667C22D3×#13112yes—
668C22#575012yes—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—34no—
673C4—34no—
674C4—41no—
675C4—41no—
676C4—62no—
677C4—62no—
678C4—121no—
679C4—121no—
680C4D3×#12111yescharacteristic
681C4D3×#12111yescharacteristic
682C4D3×C22⋊Q811yescharacteristic
683C4D3×C22⋊Q811yescharacteristic
684C3#2062911yescharacteristic, complemented, Sylow
685C2—42no—
686C2—64no—
687C2—122no—
688C2D3×#38011yescharacteristic
689C2D3×#40811yescharacteristic
690C2#7866211yescharacteristic
691C2#7908112yes—
692C2#7937512yes—
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1798C2
prime radicalC22×#235C22
cosocleC22×C3×C4C24
hypercenter#1798D3
hypocenterC3#20629
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#4837C2semidirect
3. C2×D3×C4⋊C8C2semidirect
5. C3×#1798C2semidirect
6. #71583C2semidirect
7. #70476C2semidirect
8. #70476C2semidirect
9. #69908C2semidirect
10. #68662C2semidirect
11. #68661C2semidirect
56. #1798D3semidirect
567. Dic3#408semidirect
684. C3#20629semidirect

Maximal subgroups

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

subgroupindex
C2×#55222
C2×#48372
C2×D3×C4⋊C82
C2×#47272
C3×#17982
#715832
#704762
#699082
#686622
#686612
#206293