Finite Group Databasebeta

← #35567304

Subgroups — #35567304

Order 21248.

1998 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic
2#24910625C214yesmaximal
3#24910489C212yesmaximal
4#24910486C212yesmaximal
5#24910422C211yesmaximal, characteristic, complemented
6#24910422C212yesmaximal, complemented
7#24910421C212yesmaximal, complemented
8#24910420C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic166C211yesmaximal, characteristic, complemented
10#24910261C214yesmaximal, complemented
11#24910210C212yesmaximal, complemented
12#24910179C212yesmaximal, complemented
13#24910071C212yesmaximal
14#24910068C212yesmaximal
15#24909868C211yesmaximal, characteristic
16#24909859C211yesmaximal, characteristic
17Q8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
18#19128255C4116yescomplemented
19C2×#14581791C2211yescharacteristic
20C2×#14581790C2211yescharacteristic
21C2×#14581782C2212yes—
22C2×#14581772C2211yescharacteristic
23C2×#14581770C2212yes—
24C2×#14581768C2211yescharacteristic
25C2×C4×Dic166C2212yes—
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×Dic166C2212yes—
28C2×#14581750C2212yes—
29C2×#14581749C2212yes—
30C2×C42×D83C2211yescharacteristic
31#19127608C2212yes—
32#19127606C2214yes—
33#19127606C2212yes—
34#19127605C2214yes—
35#19127599C2212yes—
36#19127598C2214yes—
37#19127592C2214yes—
38#19127591C2214yes—
39#19127591C2214yes—
40#19127590C2214yes—
41#19127587C2214yes—
42#19127585C2214yes—
43#19127585C2214yes—
44#19127584C2214yes—
45#19127583C2214yes—
46#19127582C2214yes—
47#19127582C2214yes—
48#19127582C2214yes—
49#19127582C2214yes—
50#19127582C2214yes—
51#19127571C2211yescharacteristic
52#19127570C2212yes—
53#19127568C2212yes—
54#19127567C2212yes—
55#19127566C2211yescharacteristic
56#19127566C2211yescharacteristic
57#19127566C2212yes—
58#19127566C2212yes—
59#19127563C2212yes—
60#19127558C2212yes—
61#19127558C2211yescharacteristic
62#19127558C2211yescharacteristic
63#19127558C2212yes—
64C4⋊C4×Dic83C2212yes—
65C4⋊C4×Dic83C2212yes—
66C4⋊C4×Dic83C2212yes—
67C4⋊C4×Dic83C2212yes—
68C4⋊C4×Dic83C2212yes—
69C4⋊C4×Dic83C2212yes—
70C4⋊C4×Dic83C2214yes—
71C4×Dic83⋊C4C2214yes—
72C4×C4⋊Dic83C2211yescharacteristic
73C4×C4⋊Dic83C2212yes—
74C4×(C2×D83)⋊C4C2212yes—
75#19127547C2212yes—
76C2×C4×Q8×C83C2212yes—
77C2×C4×Q8×C83C2211yescharacteristic
78#389×C83C2214yes—
79#389×C83C2212yes—
80#384×C83C2211yescharacteristic
81#384×C83C2212yes—
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×Dic166C2311yescharacteristic
85C22×Dic166C2312yes—
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2311yescharacteristic
88C22×C4×D83C2311yescharacteristic
89#14581791C2×C418yes—
90#14581790C2×C418yes—
91#14581782C2×C4116yes—
92#14581772C2×C418yes—
93#14581770C2×C4116yes—
94#14581768C2×C418yes—
95C4×Dic166—44no—
96C4×Dic166C2×C418yes—
97C4×Dic166C2×C4116yes—
98#14581750—44no—
99#14581749C2×C4116yes—
100C2×C4⋊Dic83C2311yescharacteristic
101C2×C4⋊Dic83C2311yescharacteristic
102C2×C4⋊Dic83C2312yes—
103C2×C4⋊Dic83C2312yes—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2312yes—
110C2×Dic83⋊C4C2312yes—
111C2×Dic83⋊C4C2312yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2312yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2312yes—
116C2×(C2×D83)⋊C4C2312yes—
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2312yes—
119C2×C4×Dic83C2312yes—
120C2×C4×Dic83C2314yes—
121C2×C4×Dic83C2314yes—
122C2×C4×Dic83C2314yes—
123C2×C4×Dic83C2314yes—
124C2×C4×Dic83C2311yescharacteristic
125C2×C4×Dic83C2312yes—
126C2×C4×Dic83C2311yescharacteristic
127C2×C4×Dic83C2311yescharacteristic
128C42×D83C2×C418yes—
129C83⋊#95C2312yes—
130C83⋊#95C2314yes—
131C83⋊#95C2312yes—
132C83⋊#95C2314yes—
133C83⋊#95C2312yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C22×Q8×C83C2311yescharacteristic
146C4×Q8×C83—44no—
147C4×Q8×C83C2×C418yes—
148C2×C4⋊C4×C83C2311yescharacteristic
149C2×C4⋊C4×C83C2312yes—
150C2×C4⋊C4×C83C2312yes—
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2314yes—
154C2×C4⋊C4×C83C2314yes—
155C2×C4⋊C4×C83C2311yescharacteristic
156C2×C4⋊C4×C83C2312yes—
157C2×C42×C83C2312yes—
158C2×C42×C83C2314yes—
159C2×C42×C83C2312yes—
160C2×C42×C83C2311yescharacteristic
161#95×C83C2312yes—
162#95×C83C2314yes—
163C23×D83C2411yescharacteristic
164C2×Dic166—22no—
165C2×Dic166—22no—
166C2×Dic166—42no—
167C2×Dic166—42no—
168C2×Dic166C22×C414yes—
169C2×Dic166C22×C418yes—
170C22×Dic83C2412yes—
171C22×Dic83C2412yes—
172C22×Dic83C2414yes—
173C22×Dic83C2411yescharacteristic
174C22×Dic83C2411yescharacteristic
175C22×Dic83C2411yescharacteristic
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C2×C4×D83—22no—
179C2×C4×D83—22no—
180C2×C4×D83—22no—
181C2×C4×D83—22no—
182C2×C4×D83—41no—
183C2×C4×D83—41no—
184C2×C4×D83C22×C414yes—
185C2×C4×D83C22×C414yes—
186C2×C4×D83C22×C414yes—
187C4⋊Dic83—24no—
188C4⋊Dic83—22no—
189C4⋊Dic83—22no—
190C4⋊Dic83—24no—
191C4⋊Dic83—42no—
192C4⋊Dic83C22×C414yes—
193C4⋊Dic83C22×C418yes—
194Dic83⋊C4—44no—
195Dic83⋊C4—44no—
196Dic83⋊C4C22×C418yes—
197Dic83⋊C4C22×C418yes—
198Dic83⋊C4C22×C418yes—
199Dic83⋊C4C22×C418yes—
200Dic83⋊C4C22×C418yes—
201(C2×D83)⋊C4—42no—
202(C2×D83)⋊C4—42no—
203(C2×D83)⋊C4—44no—
204(C2×D83)⋊C4C22×C418yes—
205(C2×D83)⋊C4C22×C418yes—
206C4×Dic83—24no—
207C4×Dic83—44no—
208C4×Dic83—44no—
209C4×Dic83—44no—
210C4×Dic83—44no—
211C4×Dic83C22×C414yes—
212C4×Dic83C22×C414yes—
213C4×Dic83C22×C414yes—
214C4×Dic83C22×C418yes—
215C2×Q8×C83—22no—
216C2×Q8×C83—22no—
217C2×Q8×C83C22×C414yes—
218C22×C4×C83C2412yes—
219C22×C4×C83C2412yes—
220C22×C4×C83C2414yes—
221C22×C4×C83C2411yescharacteristic
222C22×C4×C83C2412yes—
223C22×C4×C83C2412yes—
224C22×C4×C83C2411yescharacteristic
225C22×C4×C83C2411yescharacteristic
226C4⋊C4×C83—24no—
227C4⋊C4×C83—22no—
228C4⋊C4×C83—24no—
229C4⋊C4×C83—22no—
230C4⋊C4×C83—42no—
231C4⋊C4×C83—44no—
232C4⋊C4×C83—44no—
233C4⋊C4×C83C22×C418yes—
234C4⋊C4×C83C22×C414yes—
235C42×C83—24no—
236C42×C83—44no—
237C42×C83C22×C414yes—
238C42×C83C22×C418yes—
239C23×C83C2511yescharacteristic
240C22×D83—21no—
241C22×D83—21no—
242C22×D83—21no—
243C22×D83—21no—
244C22×D83—21no—
245C22×D83—21no—
246C22×D83C23×C412yes—
247Q8×C83—28no—
248C2×C4×C83—22no—
249C2×C4×C83—22no—
250C2×C4×C83—21no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—21no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—24no—
257C2×C4×C83—22no—
258C2×C4×C83—24no—
259C2×C4×C83—22no—
260C2×C4×C83—24no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83C23×C412yes—
264C2×C4×C83C23×C414yes—
265C2×C4×C83C23×C414yes—
266C2×C4×C83C23×C412yes—
267C2×C4×C83C23×C412yes—
268C2×C4×C83H(5,𝔽2)12yes—
269C2×C4×C832−1+412yes—
270C2×C4×C832−1+412yes—
271C2×C4×C832−1+412yes—
272C2×Dic83—21no—
273C2×Dic83—22no—
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—21no—
277C2×Dic83—22no—
278C2×Dic83—22no—
279C2×Dic83—22no—
280C2×Dic83—21no—
281C2×Dic83—21no—
282C2×Dic83—24no—
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—22no—
286C2×Dic83—24no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—24no—
291C2×Dic83C23×C412yes—
292C2×Dic83C23×C412yes—
293C2×Dic83C23×C412yes—
294C2×Dic83C23×C414yes—
295C2×Dic83C23×C414yes—
296C4×D83—28no—
297C4×D83—28no—
298C4×D83—44no—
299Dic166—28no—
300Dic166—48no—
301C22×C83C24×C411yescharacteristic
302C22×C83C2×H(5,𝔽2)11yescharacteristic
303C22×C83C2×2−1+411yescharacteristic
304C22×C83C2×2−1+411yescharacteristic
305C22×C83C2×2−1+411yescharacteristic
306C22×C83#58511yescharacteristic
307C22×C83#58511yescharacteristic
308C2×D83—22no—
309C2×D83—22no—
310C2×D83—22no—
311C2×D83—41no—
312C2×D83—41no—
313C2×D83—41no—
314C2×D83—41no—
315C4×C83—24no—
316C4×C83—24no—
317C4×C83—22no—
318C4×C83—42no—
319C4×C83—44no—
320C4×C83—42no—
321C4×C83#51914yes—
322C4×C83#52014yes—
323Dic83—22no—
324Dic83—24no—
325Dic83—22no—
326Dic83—22no—
327Dic83—24no—
328Dic83—44no—
329Dic83—42no—
330Dic83—42no—
331#34373—831nomaximal, Sylow
332C2×C83C2×#51911yescharacteristic
333C2×C83C2×#52011yescharacteristic
334C2×C83#342811yescharacteristic
335C2×C83#355411yescharacteristic
336C2×C83#355411yescharacteristic
337C2×C83#355511yescharacteristic
338C2×C83#355511yescharacteristic
339D83—42no—
340C2×#533—831no—
341#2378—834no—
342#2362—832no—
343#2362—832no—
344#2355—831no—
345#2355—832no—
346#2355—832no—
347#2355—831no—
348Q8×C4⋊C4—831no—
349Q8×C4⋊C4D8311yescharacteristic, complemented
350#2336—834no—
351#2331—832no—
352#2327—832no—
353#2314—832no—
354#2314—832no—
355#2285—831no—
356#2283—831no—
357C83#3437311yescharacteristic, complemented, Sylow
358#533—8316no—
359C2×C4⋊Q8—831no—
360C2×C4⋊Q8—831no—
361C2×#125—832no—
362C2×C22⋊Q8—831no—
363C2×C22⋊Q8—831no—
364C2×C22⋊Q8—832no—
365C2×C4×Q8—832no—
366C2×C4×Q8—831no—
367C2×C4×Q8—832no—
368C2×C4×Q8C2×D8312yes—
369C2×C4×Q8C2×D8311yescharacteristic
370C2×#117—832no—
371C2×#117—832no—
372C22×C42—831no—
373#391—832no—
374#391—832no—
375#391—834no—
376#391—834no—
377#389—832no—
378#389—834no—
379#389C2×D8312yes—
380#389C2×D8314yes—
381#388—834no—
382#388—834no—
383#388—834no—
384#388—834no—
385#387—834no—
386#387—834no—
387#387—834no—
388#387—834no—
389#387—834no—
390#387—834no—
391#387—834no—
392#387—834no—
393#387—834no—
394#387—834no—
395#384—832no—
396#384—831no—
397#384C2×D8312yes—
398#384C2×D8311yescharacteristic
399#383—832no—
400#382—832no—
401#382—832no—
402#382—831no—
403#382—831no—
404#382—832no—
405#381—832no—
406#380—831no—
407#380—831no—
408#380—832no—
409#380—832no—
410C4×C4⋊C4—832no—
411C4×C4⋊C4—832no—
412C4×C4⋊C4—832no—
413C4×C4⋊C4—832no—
414C4×C4⋊C4—832no—
415C4×C4⋊C4—834no—
416C4×C4⋊C4—832no—
417C4×C4⋊C4—832no—
418C4×C4⋊C4—831no—
419C4×C4⋊C4—834no—
420C4×C4⋊C4C2×D8312yes—
421C4×C4⋊C4C2×D8311yescharacteristic
422C4×C22⋊C4—832no—
423#376—832no—
424C22×Q8—832no—
425C22×Q8—831no—
426C22×Q8C22×D8311yescharacteristic
427C23×C4—831no—
428C23×C4—831no—
429C23×C4—831no—
430C4⋊Q8—838no—
431C4⋊Q8—838no—
432#125—8316no—
433C22⋊Q8—838no—
434C22⋊Q8—8316no—
435C22⋊Q8—838no—
436C4×Q8—44no—
437C4×Q8—3324no—
438C4×Q8—8316no—
439C4×Q8—838no—
440C4×Q8C4×D8318yes—
441#117—3324no—
442#117—8316no—
443C2×C4⋊C4—834no—
444C2×C4⋊C4—832no—
445C2×C4⋊C4—834no—
446C2×C4⋊C4—832no—
447C2×C4⋊C4—832no—
448C2×C4⋊C4—832no—
449C2×C4⋊C4—832no—
450C2×C4⋊C4—832no—
451C2×C4⋊C4—831no—
452C2×C4⋊C4—832no—
453C2×C4⋊C4—832no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—831no—
456C2×C4⋊C4—832no—
457C2×C4⋊C4C22×D8312yes—
458C2×C4⋊C4C22×D8311yescharacteristic
459C2×C4⋊C4C22×D8312yes—
460C2×C4⋊C4C22×D8311yescharacteristic
461C2×C4⋊C4C22×D8314yes—
462C2×C4⋊C4C22×D8312yes—
463C2×C4⋊C4C22×D8314yes—
464C2×C4⋊C4C22×D8312yes—
465C2×C4⋊C4C22×D8311yescharacteristic
466C2×C22⋊C4—834no—
467C2×C22⋊C4—832no—
468C2×C22⋊C4—832no—
469C2×C22⋊C4—832no—
470C2×C22⋊C4—832no—
471C2×C42—834no—
472C2×C42—834no—
473C2×C42—834no—
474C2×C42—834no—
475C2×C42—832no—
476C2×C42—831no—
477C2×C42—831no—
478C2×C42—831no—
479C2×C42—838no—
480C2×C42—832no—
481C2×C42C22×D8312yes—
482C2×C42C22×D8314yes—
483C2×C42C22×D8312yes—
484C2×C42C22×D8311yescharacteristic
485#95—832no—
486#95—832no—
487#95—832no—
488#95—832no—
489#95—832no—
490#95—832no—
491#95—834no—
492#95—834no—
493#95—832no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95C22×D8312yes—
502#95C22×D8314yes—
503C24—831no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—3322no—
507C2×Q8—3322no—
508C2×Q8—838no—
509C2×Q8—834no—
510C2×Q8—1662no—
511C2×Q8—1662no—
512C2×Q8C2×C4×D8314yes—
513C22×C4—3321no—
514C22×C4—3321no—
515C22×C4—834no—
516C22×C4—831no—
517C22×C4—831no—
518C22×C4—831no—
519C22×C4—832no—
520C22×C4—832no—
521C22×C4—834no—
522C22×C4—834no—
523C22×C4—832no—
524C22×C4—832no—
525C22×C4—834no—
526C22×C4—1662no—
527C22×C4—1662no—
528C22×C4—1662no—
529C22×C4—1662no—
530C22×C4C23×D8312yes—
531C22×C4C23×D8314yes—
532C22×C4C23×D8312yes—
533C22×C4C23×D8312yes—
534C22×C4C23×D8312yes—
535C22×C4C23×D8311yescharacteristic
536C22×C4C23×D8311yescharacteristic
537C22×C4C23×D8311yescharacteristic
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—44no—
543C4⋊C4—42no—
544C4⋊C4—44no—
545C4⋊C4—3324no—
546C4⋊C4—3324no—
547C4⋊C4—3322no—
548C4⋊C4—838no—
549C4⋊C4—838no—
550C4⋊C4—838no—
551C4⋊C4—838no—
552C4⋊C4—838no—
553C4⋊C4—838no—
554C4⋊C4—834no—
555C4⋊C4—1664no—
556C4⋊C4—1662no—
557C4⋊C4—1662no—
558C4⋊C4—1664no—
559C4⋊C4C2×C4×D8318yes—
560C4⋊C4C2×C4×D8314yes—
561C22⋊C4—3324no—
562C22⋊C4—3322no—
563C22⋊C4—3322no—
564C22⋊C4—838no—
565C22⋊C4—838no—
566C42—24no—
567C42—44no—
568C42—3324no—
569C42—3324no—
570C42—3324no—
571C42—3324no—
572C42—834no—
573C42—834no—
574C42—834no—
575C42—838no—
576C42—1664no—
577C42C2×C4×D8314yes—
578C42C2×C4×D8318yes—
579C23—832no—
580C23—1661no—
581C23—1661no—
582C23—1661no—
583C23—1661no—
584C23—1661no—
585C23—1661no—
586C23C24×D8311yescharacteristic
587Q8—28no—
588Q8—3328no—
589Q8—1668no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—3324no—
606C2×C4—832no—
607C2×C4—832no—
608C2×C4—832no—
609C2×C4—834no—
610C2×C4—834no—
611C2×C4—1664no—
612C2×C4—1662no—
613C2×C4—1662no—
614C2×C4—1662no—
615C2×C4—1664no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1662no—
619C2×C4—1664no—
620C2×C4—1661no—
621C2×C4—1662no—
622C2×C4—1661no—
623C2×C4—1661no—
624C2×C4—1661no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1661no—
628C2×C4—1662no—
629C2×C4—1661no—
630C2×C4—1668no—
631C2×C4—1668no—
632C2×C4C22×C4×D8312yes—
633C2×C4C22×C4×D8314yes—
634C2×C4C22×C4×D8314yes—
635C2×C4C22×C4×D8312yes—
636C2×C4C22×C4×D8312yes—
637C2×C4#1458183712yes—
638C2×C4#1458183912yes—
639C2×C4#1458184012yes—
640C2×C4#1458184012yes—
641C22—3321no—
642C22—3321no—
643C22—3321no—
644C22—3321no—
645C22—1662no—
646C22—1662no—
647C22—1662no—
648C22C23×C4×D8311yescharacteristic
649C22C2×#1458183711yescharacteristic
650C22C2×#1458183911yescharacteristic
651C22C2×#1458184011yescharacteristic
652C22C2×#1458184011yescharacteristic
653C22#1912853611yescharacteristic
654C22#1912853811yescharacteristic
655C4—24no—
656C4—22no—
657C4—24no—
658C4—42no—
659C4—44no—
660C4—42no—
661C4—3324no—
662C4—3322no—
663C4—3322no—
664C4—1662no—
665C4—1662no—
666C4—1664no—
667C4—1662no—
668C4—1664no—
669C4#1912817714yes—
670C4#1912818214yes—
671C2—3322no—
672C2C2×#1912817711yescharacteristic
673C2C2×#1912818211yescharacteristic
674C2#2492066311yescharacteristic
675C2#2492193011yescharacteristic
676C2#2492193511yescharacteristic
677C2#2492194711yescharacteristic
678C2#2492195211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC23×D83C24
hypercenterQ8×C4⋊C4D83
hypocenterC83#34373
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #24910422C2semidirect
6. #24910422C2semidirect
7. #24910421C2semidirect
8. #24910420C2semidirect
9. C4⋊C4×Dic166C2semidirect
10. #24910261C2semidirect
11. #24910210C2semidirect
12. #24910179C2semidirect
17. Q8×C4⋊C4×C83C2semidirect
18. #19128255C4semidirect
349. Q8×C4⋊C4D83semidirect
357. C83#34373semidirect

Maximal subgroups

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

subgroupindex
C2×#191282552
#249106252
#249104892
#249104862
#249104222
#249104212
#249104202
C4⋊C4×Dic1662
#249102612
#249102102
#249101792
#249100712
#249100682
#249098682
#249098592
Q8×C4⋊C4×C832
#3437383