Finite Group Databasebeta

← #32160352

Subgroups — #32160352

Order 18176.

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×#17986553C211yesmaximal, characteristic
2#22591502C214yesmaximal
3#22591366C212yesmaximal
4#22591363C212yesmaximal
5#22591299C211yesmaximal, characteristic, complemented
6#22591299C212yesmaximal, complemented
7#22591298C212yesmaximal, complemented
8#22591297C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic142C211yesmaximal, characteristic, complemented
10#22591138C214yesmaximal, complemented
11#22591087C212yesmaximal, complemented
12#22591056C212yesmaximal, complemented
13#22590948C212yesmaximal
14#22590945C212yesmaximal
15#22590745C211yesmaximal, characteristic
16#22590736C211yesmaximal, characteristic
17Q8×C4⋊C4×C71C211yesmaximal, characteristic, complemented
18#17986553C4116yescomplemented
19C2×#14556127C2211yescharacteristic
20C2×#14556126C2211yescharacteristic
21C2×#14556118C2212yes—
22C2×#14556108C2211yescharacteristic
23C2×#14556106C2212yes—
24C2×#14556104C2211yescharacteristic
25C2×C4×Dic142C2212yes—
26C2×C4×Dic142C2211yescharacteristic
27C2×C4×Dic142C2212yes—
28C2×#14556086C2212yes—
29C2×#14556085C2212yes—
30C2×C42×D71C2211yescharacteristic
31#17985906C2212yes—
32#17985904C2214yes—
33#17985904C2212yes—
34#17985903C2214yes—
35#17985897C2212yes—
36#17985896C2214yes—
37#17985890C2214yes—
38#17985889C2214yes—
39#17985889C2214yes—
40#17985888C2214yes—
41#17985885C2214yes—
42#17985883C2214yes—
43#17985883C2214yes—
44#17985882C2214yes—
45#17985881C2214yes—
46#17985880C2214yes—
47#17985880C2214yes—
48#17985880C2214yes—
49#17985880C2214yes—
50#17985880C2214yes—
51#17985869C2211yescharacteristic
52#17985868C2212yes—
53#17985866C2212yes—
54#17985865C2212yes—
55#17985864C2211yescharacteristic
56#17985864C2211yescharacteristic
57#17985864C2212yes—
58#17985864C2212yes—
59#17985861C2212yes—
60#17985856C2212yes—
61#17985856C2211yescharacteristic
62#17985856C2211yescharacteristic
63#17985856C2212yes—
64C4⋊C4×Dic71C2212yes—
65C4⋊C4×Dic71C2212yes—
66C4⋊C4×Dic71C2212yes—
67C4⋊C4×Dic71C2212yes—
68C4⋊C4×Dic71C2212yes—
69C4⋊C4×Dic71C2212yes—
70C4⋊C4×Dic71C2214yes—
71C4×Dic71⋊C4C2214yes—
72C4×C4⋊Dic71C2211yescharacteristic
73C4×C4⋊Dic71C2212yes—
74C4×(C2×D71)⋊C4C2212yes—
75#17985845C2212yes—
76C2×C4×Q8×C71C2212yes—
77C2×C4×Q8×C71C2211yescharacteristic
78#389×C71C2214yes—
79#389×C71C2212yes—
80#384×C71C2211yescharacteristic
81#384×C71C2212yes—
82C4×C4⋊C4×C71C2211yescharacteristic
83C4×C4⋊C4×C71C2212yes—
84C22×Dic142C2311yescharacteristic
85C22×Dic142C2312yes—
86C22×C4×D71C2311yescharacteristic
87C22×C4×D71C2311yescharacteristic
88C22×C4×D71C2311yescharacteristic
89#14556127C2×C418yes—
90#14556126C2×C418yes—
91#14556118C2×C4116yes—
92#14556108C2×C418yes—
93#14556106C2×C4116yes—
94#14556104C2×C418yes—
95C4×Dic142—44no—
96C4×Dic142C2×C418yes—
97C4×Dic142C2×C4116yes—
98#14556086—44no—
99#14556085C2×C4116yes—
100C2×C4⋊Dic71C2311yescharacteristic
101C2×C4⋊Dic71C2311yescharacteristic
102C2×C4⋊Dic71C2312yes—
103C2×C4⋊Dic71C2312yes—
104C2×C4⋊Dic71C2312yes—
105C2×C4⋊Dic71C2312yes—
106C2×C4⋊Dic71C2311yescharacteristic
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2312yes—
110C2×Dic71⋊C4C2312yes—
111C2×Dic71⋊C4C2312yes—
112C2×Dic71⋊C4C2312yes—
113C2×Dic71⋊C4C2312yes—
114C2×(C2×D71)⋊C4C2312yes—
115C2×(C2×D71)⋊C4C2312yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2312yes—
118C2×(C2×D71)⋊C4C2312yes—
119C2×C4×Dic71C2312yes—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C2×C4×Dic71C2314yes—
124C2×C4×Dic71C2311yescharacteristic
125C2×C4×Dic71C2311yescharacteristic
126C2×C4×Dic71C2312yes—
127C2×C4×Dic71C2311yescharacteristic
128C42×D71C2×C418yes—
129C71⋊#95C2312yes—
130C71⋊#95C2312yes—
131C71⋊#95C2312yes—
132C71⋊#95C2312yes—
133C71⋊#95C2312yes—
134C71⋊#95C2312yes—
135C71⋊#95C2312yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C22×Q8×C71C2311yescharacteristic
146C4×Q8×C71—44no—
147C4×Q8×C71C2×C418yes—
148C2×C4⋊C4×C71C2311yescharacteristic
149C2×C4⋊C4×C71C2312yes—
150C2×C4⋊C4×C71C2312yes—
151C2×C4⋊C4×C71C2311yescharacteristic
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2314yes—
154C2×C4⋊C4×C71C2314yes—
155C2×C4⋊C4×C71C2311yescharacteristic
156C2×C4⋊C4×C71C2312yes—
157C2×C42×C71C2312yes—
158C2×C42×C71C2314yes—
159C2×C42×C71C2312yes—
160C2×C42×C71C2311yescharacteristic
161#95×C71C2312yes—
162#95×C71C2314yes—
163C23×D71C2411yescharacteristic
164C2×Dic142—22no—
165C2×Dic142—22no—
166C2×Dic142—42no—
167C2×Dic142—42no—
168C2×Dic142C22×C414yes—
169C2×Dic142C22×C418yes—
170C22×Dic71C2412yes—
171C22×Dic71C2412yes—
172C22×Dic71C2414yes—
173C22×Dic71C2411yescharacteristic
174C22×Dic71C2411yescharacteristic
175C22×Dic71C2411yescharacteristic
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C2×C4×D71—22no—
179C2×C4×D71—22no—
180C2×C4×D71—22no—
181C2×C4×D71—22no—
182C2×C4×D71—41no—
183C2×C4×D71—41no—
184C2×C4×D71C22×C414yes—
185C2×C4×D71C22×C414yes—
186C2×C4×D71C22×C414yes—
187C4⋊Dic71—24no—
188C4⋊Dic71—22no—
189C4⋊Dic71—22no—
190C4⋊Dic71—24no—
191C4⋊Dic71—42no—
192C4⋊Dic71C22×C414yes—
193C4⋊Dic71C22×C418yes—
194Dic71⋊C4—44no—
195Dic71⋊C4—44no—
196Dic71⋊C4C22×C418yes—
197Dic71⋊C4C22×C418yes—
198Dic71⋊C4C22×C418yes—
199Dic71⋊C4C22×C418yes—
200Dic71⋊C4C22×C418yes—
201(C2×D71)⋊C4—42no—
202(C2×D71)⋊C4—42no—
203(C2×D71)⋊C4—44no—
204(C2×D71)⋊C4C22×C418yes—
205(C2×D71)⋊C4C22×C418yes—
206C4×Dic71—24no—
207C4×Dic71—44no—
208C4×Dic71—44no—
209C4×Dic71—44no—
210C4×Dic71—44no—
211C4×Dic71C22×C414yes—
212C4×Dic71C22×C414yes—
213C4×Dic71C22×C414yes—
214C4×Dic71C22×C418yes—
215C2×Q8×C71—22no—
216C2×Q8×C71—22no—
217C2×Q8×C71C22×C414yes—
218C22×C4×C71C2412yes—
219C22×C4×C71C2412yes—
220C22×C4×C71C2414yes—
221C22×C4×C71C2411yescharacteristic
222C22×C4×C71C2412yes—
223C22×C4×C71C2412yes—
224C22×C4×C71C2411yescharacteristic
225C22×C4×C71C2411yescharacteristic
226C4⋊C4×C71—24no—
227C4⋊C4×C71—22no—
228C4⋊C4×C71—24no—
229C4⋊C4×C71—22no—
230C4⋊C4×C71—42no—
231C4⋊C4×C71—44no—
232C4⋊C4×C71—44no—
233C4⋊C4×C71C22×C418yes—
234C4⋊C4×C71C22×C414yes—
235C42×C71—24no—
236C42×C71—44no—
237C42×C71C22×C414yes—
238C42×C71C22×C418yes—
239C23×C71C2511yescharacteristic
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71—21no—
245C22×D71—21no—
246C22×D71C23×C412yes—
247Q8×C71—28no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—21no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—21no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—24no—
257C2×C4×C71—22no—
258C2×C4×C71—24no—
259C2×C4×C71—22no—
260C2×C4×C71—24no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71C23×C412yes—
264C2×C4×C71C23×C414yes—
265C2×C4×C71C23×C414yes—
266C2×C4×C71C23×C412yes—
267C2×C4×C71C23×C412yes—
268C2×C4×C71H(5,𝔽2)12yes—
269C2×C4×C712−1+412yes—
270C2×C4×C712−1+412yes—
271C2×C4×C712−1+412yes—
272C2×Dic71—21no—
273C2×Dic71—22no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—22no—
278C2×Dic71—22no—
279C2×Dic71—22no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—24no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—24no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—24no—
291C2×Dic71C23×C412yes—
292C2×Dic71C23×C412yes—
293C2×Dic71C23×C412yes—
294C2×Dic71C23×C414yes—
295C2×Dic71C23×C414yes—
296C4×D71—28no—
297C4×D71—28no—
298C4×D71—44no—
299Dic142—28no—
300Dic142—48no—
301C22×C71C24×C411yescharacteristic
302C22×C71C2×H(5,𝔽2)11yescharacteristic
303C22×C71C2×2−1+411yescharacteristic
304C22×C71C2×2−1+411yescharacteristic
305C22×C71C2×2−1+411yescharacteristic
306C22×C71#58511yescharacteristic
307C22×C71#58511yescharacteristic
308C2×D71—22no—
309C2×D71—22no—
310C2×D71—22no—
311C2×D71—41no—
312C2×D71—41no—
313C2×D71—41no—
314C2×D71—41no—
315C4×C71—24no—
316C4×C71—24no—
317C4×C71—22no—
318C4×C71—42no—
319C4×C71—44no—
320C4×C71—42no—
321C4×C71#51914yes—
322C4×C71#52014yes—
323Dic71—22no—
324Dic71—24no—
325Dic71—22no—
326Dic71—22no—
327Dic71—24no—
328Dic71—44no—
329Dic71—42no—
330Dic71—42no—
331#34373—711nomaximal, Sylow
332C2×C71C2×#51911yescharacteristic
333C2×C71C2×#52011yescharacteristic
334C2×C71#342811yescharacteristic
335C2×C71#355411yescharacteristic
336C2×C71#355411yescharacteristic
337C2×C71#355511yescharacteristic
338C2×C71#355511yescharacteristic
339D71—42no—
340C2×#533—711no—
341#2378—714no—
342#2362—712no—
343#2362—712no—
344#2355—711no—
345#2355—712no—
346#2355—712no—
347#2355—711no—
348Q8×C4⋊C4—711no—
349Q8×C4⋊C4D7111yescharacteristic, complemented
350#2336—714no—
351#2331—712no—
352#2327—712no—
353#2314—712no—
354#2314—712no—
355#2285—711no—
356#2283—711no—
357C71#3437311yescharacteristic, complemented, Sylow
358#533—7116no—
359C2×C4⋊Q8—711no—
360C2×C4⋊Q8—711no—
361C2×#125—712no—
362C2×C22⋊Q8—711no—
363C2×C22⋊Q8—711no—
364C2×C22⋊Q8—712no—
365C2×C4×Q8—712no—
366C2×C4×Q8—711no—
367C2×C4×Q8—712no—
368C2×C4×Q8C2×D7112yes—
369C2×C4×Q8C2×D7111yescharacteristic
370C2×#117—712no—
371C2×#117—712no—
372C22×C42—711no—
373#391—712no—
374#391—712no—
375#391—714no—
376#391—714no—
377#389—712no—
378#389—714no—
379#389C2×D7112yes—
380#389C2×D7114yes—
381#388—714no—
382#388—714no—
383#388—714no—
384#388—714no—
385#387—714no—
386#387—714no—
387#387—714no—
388#387—714no—
389#387—714no—
390#387—714no—
391#387—714no—
392#387—714no—
393#387—714no—
394#387—714no—
395#384—712no—
396#384—711no—
397#384C2×D7112yes—
398#384C2×D7111yescharacteristic
399#383—712no—
400#382—712no—
401#382—712no—
402#382—711no—
403#382—711no—
404#382—712no—
405#381—712no—
406#380—711no—
407#380—711no—
408#380—712no—
409#380—712no—
410C4×C4⋊C4—712no—
411C4×C4⋊C4—712no—
412C4×C4⋊C4—712no—
413C4×C4⋊C4—712no—
414C4×C4⋊C4—712no—
415C4×C4⋊C4—714no—
416C4×C4⋊C4—712no—
417C4×C4⋊C4—712no—
418C4×C4⋊C4—714no—
419C4×C4⋊C4—711no—
420C4×C4⋊C4C2×D7112yes—
421C4×C4⋊C4C2×D7111yescharacteristic
422C4×C22⋊C4—712no—
423#376—712no—
424C22×Q8—712no—
425C22×Q8—711no—
426C22×Q8C22×D7111yescharacteristic
427C23×C4—711no—
428C23×C4—711no—
429C23×C4—711no—
430C4⋊Q8—718no—
431C4⋊Q8—718no—
432#125—7116no—
433C22⋊Q8—718no—
434C22⋊Q8—7116no—
435C22⋊Q8—718no—
436C4×Q8—44no—
437C4×Q8—2844no—
438C4×Q8—7116no—
439C4×Q8—718no—
440C4×Q8C4×D7118yes—
441#117—2844no—
442#117—7116no—
443C2×C4⋊C4—714no—
444C2×C4⋊C4—712no—
445C2×C4⋊C4—714no—
446C2×C4⋊C4—712no—
447C2×C4⋊C4—712no—
448C2×C4⋊C4—712no—
449C2×C4⋊C4—712no—
450C2×C4⋊C4—712no—
451C2×C4⋊C4—711no—
452C2×C4⋊C4—712no—
453C2×C4⋊C4—712no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—711no—
456C2×C4⋊C4—712no—
457C2×C4⋊C4C22×D7112yes—
458C2×C4⋊C4C22×D7111yescharacteristic
459C2×C4⋊C4C22×D7112yes—
460C2×C4⋊C4C22×D7111yescharacteristic
461C2×C4⋊C4C22×D7114yes—
462C2×C4⋊C4C22×D7112yes—
463C2×C4⋊C4C22×D7114yes—
464C2×C4⋊C4C22×D7112yes—
465C2×C4⋊C4C22×D7111yescharacteristic
466C2×C22⋊C4—714no—
467C2×C22⋊C4—712no—
468C2×C22⋊C4—712no—
469C2×C22⋊C4—712no—
470C2×C22⋊C4—712no—
471C2×C42—714no—
472C2×C42—714no—
473C2×C42—714no—
474C2×C42—714no—
475C2×C42—712no—
476C2×C42—711no—
477C2×C42—711no—
478C2×C42—711no—
479C2×C42—718no—
480C2×C42—712no—
481C2×C42C22×D7112yes—
482C2×C42C22×D7114yes—
483C2×C42C22×D7112yes—
484C2×C42C22×D7111yescharacteristic
485#95—712no—
486#95—712no—
487#95—712no—
488#95—712no—
489#95—712no—
490#95—712no—
491#95—714no—
492#95—714no—
493#95—712no—
494#95—714no—
495#95—714no—
496#95—714no—
497#95—714no—
498#95—714no—
499#95—714no—
500#95—714no—
501#95C22×D7112yes—
502#95C22×D7114yes—
503C24—711no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—2842no—
507C2×Q8—2842no—
508C2×Q8—718no—
509C2×Q8—714no—
510C2×Q8—1422no—
511C2×Q8—1422no—
512C2×Q8C2×C4×D7114yes—
513C22×C4—2841no—
514C22×C4—2841no—
515C22×C4—714no—
516C22×C4—711no—
517C22×C4—711no—
518C22×C4—711no—
519C22×C4—712no—
520C22×C4—712no—
521C22×C4—714no—
522C22×C4—714no—
523C22×C4—712no—
524C22×C4—712no—
525C22×C4—714no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4C23×D7112yes—
531C22×C4C23×D7114yes—
532C22×C4C23×D7112yes—
533C22×C4C23×D7112yes—
534C22×C4C23×D7112yes—
535C22×C4C23×D7111yescharacteristic
536C22×C4C23×D7111yescharacteristic
537C22×C4C23×D7111yescharacteristic
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—42no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—2844no—
546C4⋊C4—2844no—
547C4⋊C4—2842no—
548C4⋊C4—718no—
549C4⋊C4—718no—
550C4⋊C4—718no—
551C4⋊C4—718no—
552C4⋊C4—718no—
553C4⋊C4—718no—
554C4⋊C4—714no—
555C4⋊C4—1424no—
556C4⋊C4—1422no—
557C4⋊C4—1422no—
558C4⋊C4—1424no—
559C4⋊C4C2×C4×D7118yes—
560C4⋊C4C2×C4×D7114yes—
561C22⋊C4—2842no—
562C22⋊C4—2842no—
563C22⋊C4—2844no—
564C22⋊C4—718no—
565C22⋊C4—718no—
566C42—24no—
567C42—44no—
568C42—2844no—
569C42—2844no—
570C42—2844no—
571C42—2844no—
572C42—714no—
573C42—714no—
574C42—714no—
575C42—718no—
576C42—1424no—
577C42C2×C4×D7114yes—
578C42C2×C4×D7118yes—
579C23—712no—
580C23—1421no—
581C23—1421no—
582C23—1421no—
583C23—1421no—
584C23—1421no—
585C23—1421no—
586C23C24×D7111yescharacteristic
587Q8—28no—
588Q8—2848no—
589Q8—1428no—
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—2844no—
606C2×C4—712no—
607C2×C4—712no—
608C2×C4—712no—
609C2×C4—714no—
610C2×C4—714no—
611C2×C4—1424no—
612C2×C4—1422no—
613C2×C4—1422no—
614C2×C4—1422no—
615C2×C4—1424no—
616C2×C4—1422no—
617C2×C4—1422no—
618C2×C4—1422no—
619C2×C4—1424no—
620C2×C4—1421no—
621C2×C4—1422no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1421no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1421no—
628C2×C4—1422no—
629C2×C4—1421no—
630C2×C4—1428no—
631C2×C4—1428no—
632C2×C4C22×C4×D7112yes—
633C2×C4C22×C4×D7114yes—
634C2×C4C22×C4×D7114yes—
635C2×C4C22×C4×D7112yes—
636C2×C4C22×C4×D7112yes—
637C2×C4#1455617312yes—
638C2×C4#1455617512yes—
639C2×C4#1455617612yes—
640C2×C4#1455617612yes—
641C22—2841no—
642C22—2841no—
643C22—2841no—
644C22—2841no—
645C22—1422no—
646C22—1422no—
647C22—1422no—
648C22C23×C4×D7111yescharacteristic
649C22C2×#1455617311yescharacteristic
650C22C2×#1455617511yescharacteristic
651C22C2×#1455617611yescharacteristic
652C22C2×#1455617611yescharacteristic
653C22#1798683411yescharacteristic
654C22#1798683611yescharacteristic
655C4—24no—
656C4—22no—
657C4—24no—
658C4—42no—
659C4—44no—
660C4—42no—
661C4—2844no—
662C4—2842no—
663C4—2842no—
664C4—1422no—
665C4—1422no—
666C4—1424no—
667C4—1422no—
668C4—1424no—
669C4#1798647514yes—
670C4#1798648014yes—
671C2—2842no—
672C2C2×#1798647511yescharacteristic
673C2C2×#1798648011yescharacteristic
674C2#2260154011yescharacteristic
675C2#2260280711yescharacteristic
676C2#2260281211yescharacteristic
677C2#2260282411yescharacteristic
678C2#2260282911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C4⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC23×D71C24
hypercenterQ8×C4⋊C4D71
hypocenterC71#34373
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #22591299C2semidirect
6. #22591299C2semidirect
7. #22591298C2semidirect
8. #22591297C2semidirect
9. C4⋊C4×Dic142C2semidirect
10. #22591138C2semidirect
11. #22591087C2semidirect
12. #22591056C2semidirect
17. Q8×C4⋊C4×C71C2semidirect
18. #17986553C4semidirect
349. Q8×C4⋊C4D71semidirect
357. C71#34373semidirect

Maximal subgroups

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

subgroupindex
C2×#179865532
#225915022
#225913662
#225913632
#225912992
#225912982
#225912972
C4⋊C4×Dic1422
#225911382
#225910872
#225910562
#225909482
#225909452
#225907452
#225907362
Q8×C4⋊C4×C712
#3437371