Finite Group Databasebeta

← #10813344

Subgroups — #10813344

Order 768.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×#67C211yesmaximal, characteristic
2C2×#4964C211yesmaximal, characteristic, complemented
3C2×D3×#106C211yesmaximal, characteristic, complemented
4C2×#4728C211yesmaximal, characteristic
5#74012C211yesmaximal, characteristic
6C3×#1853C211yesmaximal, characteristic, complemented
7#70579C211yesmaximal, characteristic, complemented
8#70564C211yesmaximal, characteristic, complemented
9#70556C211yesmaximal, characteristic, complemented
10#69929C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68874C211yesmaximal, characteristic, complemented
13#68869C211yesmaximal, characteristic, complemented
14#68796C211yesmaximal, characteristic, complemented
15#68786C211yesmaximal, characteristic, complemented
16#22659—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C2×C4×#67—21no—
19C2×C4×#67C2211yescharacteristic
20C2×#926C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23C2×D3×C4⋊C4C2211yescharacteristic
24C2×D3×C4⋊C4C2211yescharacteristic
25C2×C3×#106C2211yescharacteristic
26C2×C3×#106C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C3×#380C2211yescharacteristic
29#5212C2211yescharacteristic
30#5210—21no—
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×#818C2211yescharacteristic
33C2×#817C2211yescharacteristic
34C2×#815C2211yescharacteristic
35C2×Dic3⋊C8C2211yescharacteristic
36#4989—21no—
37#4987C2211yescharacteristic
38#4987C2211yescharacteristic
39#4977C2211yescharacteristic
40#4976—21no—
41#4975C2211yescharacteristic
42Dic3×C4⋊C4C2211yescharacteristic
43Dic3×C4⋊C4C2211yescharacteristic
44#4964—24no—
45C2×#808C2211yescharacteristic
46C2×#808C2211yescharacteristic
47C2×#808C2211yescharacteristic
48C2×#807C2211yescharacteristic
49C2×#807C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4956—21no—
52#4944—21no—
53D3×#106—24no—
54#4728C418yescomplemented
55#4666—21no—
56#4652—21no—
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#435—31no—
64C2×#428—31no—
65C22×#106—31no—
66#2352—31no—
67D4×C4⋊C4—31no—
68#1949—31no—
69#1948—31no—
70#1854—31no—
71#1853—31no—
72#1853D311yescharacteristic, complemented
73#1852—31no—
74#1847—31no—
75#1809—31no—
76#1808—31no—
77#1776—31no—
78C23×C3×C4—21no—
79C23×C3×C4C2311yescharacteristic
80C22×#67D411yescharacteristic
81C22×C4×D3—21no—
82C22×C4×D3—21no—
83C22×C4×D3C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—41no—
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C22⋊C4—21no—
94C2×#217—21no—
95C2×#217—21no—
96C2×#217D411yescharacteristic
97C4×#67—44no—
98C4×#67C2×C414yes—
99C4×#67Q814yes—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4D411yescharacteristic
103#926—22no—
104#926—41no—
105C2×C4⋊Dic3C2311yescharacteristic
106C2×C4⋊Dic3C2311yescharacteristic
107C2×C4⋊Dic3C2311yescharacteristic
108C2×C4⋊Dic3C2311yescharacteristic
109C2×Dic3⋊C4—21no—
110C2×Dic3⋊C4—21no—
111C2×Dic3⋊C4—21no—
112C2×Dic3⋊C4—21no—
113C2×Dic3⋊C4D411yescharacteristic
114C2×C4×Dic3—21no—
115C2×C4×Dic3—21no—
116C2×C4×Dic3—21no—
117C2×C4×Dic3C2311yescharacteristic
118C2×#208—22no—
119C2×#208—22no—
120C2×#208C2×C414yescomplemented
121C22×C3⋊C8C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C2×D3×C8—22no—
124C2×D3×C8—22no—
125C2×D3×C8C2×C414yescomplemented
126D3×C4⋊C4—22no—
127D3×C4⋊C4—22no—
128D3×C4⋊C4—41no—
129D3×C4⋊C4—41no—
130C3×#106—22no—
131C3×#106—41no—
132C3×C22⋊C8C2×C414yescomplemented
133C3×#95—21no—
134C3⋊#95—21no—
135C3⋊#95—21no—
136C3⋊#95—21no—
137C3⋊#95—21no—
138C3⋊#95—21no—
139C3⋊#95—21no—
140C3⋊#95—21no—
141(C2×D3)⋊C8C2×C414yescomplemented
142#818—41no—
143#817—22no—
144#815C2×C414yescomplemented
145Dic3⋊C8C2×C414yescomplemented
146#808—22no—
147#808—22no—
148#808D414yescomplemented
149#807—22no—
150#807—22no—
151#807—22no—
152C22×M16—31no—
153C23×C8—31no—
154C2×C4×D4—31no—
155C2×C4×D4—61no—
156C2×#117—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4C2×D311yescharacteristic
160#435—38no—
161#428—64no—
162C2×#107—31no—
163C2×#107—31no—
164C2×#107—31no—
165C2×#107—31no—
166C2×#106—31no—
167C2×#106—31no—
168C2×#106—31no—
169C2×#106—31no—
170C2×#106—64no—
171C2×#106C2×D311yescharacteristic
172C2×#106C2×D311yescharacteristic
173C2×C4⋊C8—31no—
174C2×C22⋊C8—31no—
175C2×C22⋊C8C2×D311yescharacteristic
176C2×#97—31no—
177#389—61no—
178#388—61no—
179#387—61no—
180#386—61no—
181#385—61no—
182#385—61no—
183#384—31no—
184#382—31no—
185#380—31no—
186#380—31no—
187#380—31no—
188#380C2×D311yescharacteristic
189C4×C4⋊C4—31no—
190C4×C4⋊C4—31no—
191C4×C22⋊C4—61no—
192#340—31no—
193#340—31no—
194#340—31no—
195#340—31no—
196#340C2×D311yescharacteristic
197#340C2×D311yescharacteristic
198C24×C3C2×D411yescharacteristic
199C23×D3C2×D411yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—42no—
209C22×C3×C4—42no—
210C22×C3×C4—81no—
211C22×C3×C4C22×C412yes—
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×Q812yes—
214C22×C3×C4C2411yescharacteristic
215C2×#67—22no—
216C2×#67—22no—
217C2×#67C4⋊C414yes—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3C2×D411yescharacteristic
223C22×Dic3C2×D411yescharacteristic
224C22×Dic3C2×D411yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—42no—
230C2×C4×D3—42no—
231C2×C4×D3—42no—
232C2×C4×D3—42no—
233C2×C4×D3—81no—
234C2×C4×D3—81no—
235C2×C4×D3C22×C412yes—
236C2×C4×D3C2×Q812yes—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8C22×C412yes—
242C2×C3×C8C22×C412yes—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—42no—
251C3×C4⋊C4C2×D412yes—
252C3×C22⋊C4—81no—
253#217—42no—
254#217—42no—
255#217C4⋊C414yes—
256(C2×D3)⋊C4—42no—
257(C2×D3)⋊C4—42no—
258(C2×D3)⋊C4C4⋊C414yes—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3C2×D412yes—
267Dic3⋊C4—42no—
268Dic3⋊C4—42no—
269Dic3⋊C4—42no—
270Dic3⋊C4—81no—
271Dic3⋊C4C4⋊C414yes—
272C4×Dic3—42no—
273C4×Dic3—42no—
274C4×Dic3—81no—
275C4×Dic3C22×C412yes—
276C4×Dic3C2×Q812yes—
277#208—28no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—21no—
280C2×C3⋊C8C22×C412yes—
281C2×C3⋊C8C22×C412yes—
282C2×C3⋊C8C2×D412yes—
283C2×C3⋊C8#4112yes—
284D3×C8—28no—
285C22×D4—31no—
286C23×C4—21no—
287C23×C4—31no—
288C23×C4—61no—
289C23×C4—61no—
290C23×C4C22×D311yescharacteristic
291C2×M16—34no—
292C2×M16—62no—
293C2×M16—62no—
294C22×C8—31no—
295C22×C8—31no—
296C22×C8—34no—
297C22×C8—62no—
298C22×C8—62no—
299C22×C8C22×D311yescharacteristic
300C22×C8C22×D311yescharacteristic
301C4×D4—34no—
302C4×D4—34no—
303C4×D4—124no—
304#117—62no—
305#117—121no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—62no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—61no—
317C2×C4⋊C4—61no—
318C2×C4⋊C4—61no—
319C2×C4⋊C4—61no—
320C2×C4⋊C4—121no—
321C2×C4⋊C4—121no—
322C2×C4⋊C4C22×D311yescharacteristic
323C2×C4⋊C4C22×D311yescharacteristic
324C2×C4⋊C4C22×D311yescharacteristic
325C2×C4⋊C4C22×D311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—61no—
330C2×C22⋊C4—61no—
331C2×C22⋊C4—61no—
332C2×C22⋊C4—61no—
333C2×C42—31no—
334C2×C42—61no—
335C2×C42—61no—
336C2×C42—61no—
337#107—62no—
338#107—62no—
339#107—62no—
340#107—121no—
341#106—22no—
342#106—34no—
343#106—41no—
344#106—62no—
345#106—62no—
346#106—62no—
347C4⋊C8—34no—
348C22⋊C8—34no—
349C22⋊C8C4×D314yescomplemented
350#97—34no—
351#95—21no—
352#95—61no—
353#95—61no—
354#95—61no—
355#95—61no—
356#95—61no—
357#95—61no—
358#95—61no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3C2×C4⋊C412yes—
366C23×C3C22×D411yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—21no—
371C22×D3C2×C4⋊C412yes—
372C22×D3AGL(1,ℤ/8)12yes—
373C22×D3#13712yes—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—84no—
393C2×C3×C4C2×C4⋊C412yes—
394C2×C3×C4C23×C411yescharacteristic
395C2×C3×C4C22×D411yescharacteristic
396C2×C3×C4C22×Q811yescharacteristic
397C2×C3×C4C2×#4111yescharacteristic
398C2×C3×C4H(5,𝔽2)11yescharacteristic
399C2×C3×C42−1+411yescharacteristic
400#67—28no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—22no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—41no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3C2×C4⋊C412yes—
420C2×Dic3C2×C4⋊C412yes—
421C2×Dic3C2×C4⋊C412yes—
422C4×D3—22no—
423C4×D3—22no—
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—84no—
427C4×D3—84no—
428C3×C8—22no—
429C3×C8—22no—
430C3⋊C8—22no—
431C3⋊C8C4×D414yescomplemented
432C24—31no—
433C24D3×D411yescharacteristic
434C2×D4—34no—
435C2×D4—62no—
436C2×D4—62no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—81no—
461C22×C4—122no—
462C22×C4—122no—
463C22×C4—122no—
464C22×C4—122no—
465C22×C4—241no—
466C22×C4—241no—
467C22×C4C2×C4×D312yes—
468C22×C4D3×D411yescharacteristic
469C22×C4D3×Q812yes—
470C22×C4C23×D311yescharacteristic
471M16—68no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—32no—
477C2×C8—32no—
478C2×C8—32no—
479C2×C8—32no—
480C2×C8—68no—
481C2×C8—61no—
482C2×C8—61no—
483C2×C8C2×C4×D312yes—
484C2×C8C2×C4×D312yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—34no—
493C4⋊C4—32no—
494C4⋊C4—42no—
495C4⋊C4—61no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4—61no—
501C4⋊C4—61no—
502C4⋊C4—122no—
503C4⋊C4—122no—
504C4⋊C4—122no—
505C4⋊C4—241no—
506C4⋊C4D3×D412yes—
507C22⋊C4—34no—
508C22⋊C4—34no—
509C22⋊C4—81no—
510C22⋊C4—122no—
511C22⋊C4—122no—
512C22⋊C4—122no—
513C22⋊C4—122no—
514C42—32no—
515C42—32no—
516C42—122no—
517C42—122no—
518C42—241no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3C22×C4⋊C411yescharacteristic
527C22×C3D4211yescharacteristic
528C22×C3#54711yescharacteristic
529C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
530C22×C3C2×#13711yescharacteristic
531C22×C3#57711yescharacteristic
532C22×C3#57711yescharacteristic
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3#42814yescomplemented
540C3×C4—22no—
541C3×C4—42no—
542C3×C4—81no—
543C3×C4—81no—
544C3×C4—81no—
545C3×C4C2×C4×D411yescharacteristic
546C3×C4#52011yescharacteristic
547C3×C4D4×Q811yescharacteristic
548C3×C4#55411yescharacteristic
549Dic3—22no—
550Dic3—22no—
551Dic3—22no—
552Dic3—42no—
553Dic3—81no—
554Dic3—81no—
555Dic3—81no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—32no—
563C23—32no—
564C23—32no—
565C23—61no—
566C23—61no—
567C23—61no—
568C23—61no—
569C23D3×C4⋊C412yes—
570C23C2×D3×D411yescharacteristic
571D4—68no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—84no—
605C2×C4—121no—
606C2×C4—121no—
607C2×C4—121no—
608C2×C4—121no—
609C2×C4—121no—
610C2×C4—121no—
611C2×C4—121no—
612C2×C4—121no—
613C2×C4—121no—
614C2×C4—121no—
615C2×C4—121no—
616C2×C4—244no—
617C2×C4—244no—
618C2×C4D3×C4⋊C412yes—
619C2×C4C22×C4×D311yescharacteristic
620C2×C4C2×D3×D411yescharacteristic
621C2×C4#100411yescharacteristic
622C2×C4C2×D3×Q811yescharacteristic
623C2×C4D3×#4111yescharacteristic
624C2×C4#101011yescharacteristic
625C8—22no—
626C8—22no—
627C8—34no—
628C8—62no—
629C2×C3—42no—
630C2×C3D4×C4⋊C411yescharacteristic
631C2×C3C2×#42811yescharacteristic
632C2×C3#291211yescharacteristic
633C2×C3#326511yescharacteristic
634C2×C3#326611yescharacteristic
635C2×C3#334411yescharacteristic
636C2×C3#334511yescharacteristic
637D3—24no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—34no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—62no—
647C22—62no—
648C22—62no—
649C22—62no—
650C22—62no—
651C22—62no—
652C22C2×D3×C4⋊C411yescharacteristic
653C22#559011yescharacteristic
654C22#565511yescharacteristic
655C22#576211yescharacteristic
656C22#576211yescharacteristic
657C22D3×AGL(1,ℤ/8)11yescharacteristic
658C22D3×#13711yescharacteristic
659C4—22no—
660C4—42no—
661C4—62no—
662C4—62no—
663C4—62no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—122no—
668C4—241no—
669C4—241no—
670C4—241no—
671C4C4×D3×D411yescharacteristic
672C4#554611yescharacteristic
673C4#563211yescharacteristic
674C4#563611yescharacteristic
675C3#2265911yescharacteristic, complemented, Sylow
676C2—42no—
677C2—64no—
678C2#7439311yescharacteristic
679C2#7911611yescharacteristic
680C2D3×#42811yescharacteristic
681C2#8006111yescharacteristic
682C2#8015611yescharacteristic
683C2#8133511yescharacteristic
684C2#8143811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1853C2
socleC23×C3C22×D4
prime radicalC22×#67D4
cosocleC22×C3×C4C24
hypercenter#1853D3
hypocenterC3#22659
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#4964C2semidirect
3. C2×D3×#106C2semidirect
6. C3×#1853C2semidirect
7. #70579C2semidirect
8. #70564C2semidirect
9. #70556C2semidirect
10. #69929C2semidirect
11. #69513C2semidirect
12. #68874C2semidirect
13. #68869C2semidirect
14. #68796C2semidirect
15. #68786C2semidirect
54. #4728C4semidirect
72. #1853D3semidirect
120. C2×#208C2×C4semidirect
125. C2×D3×C8C2×C4semidirect
132. C3×C22⋊C8C2×C4semidirect
141. (C2×D3)⋊C8C2×C4semidirect
144. #815C2×C4semidirect
145. Dic3⋊C8C2×C4semidirect
148. #808D4semidirect
349. C22⋊C8C4×D3semidirect
431. C3⋊C8C4×D4semidirect
539. C2×D3#428semidirect
675. C3#22659semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#672
C2×#49642
C2×D3×#1062
C2×#47282
#740122
C3×#18532
#705792
#705642
#705562
#699292
#695132
#688742
#688692
#687962
#687862
#226593