Finite Group Databasebeta

← C2×#328×D53 #27351172

Subgroups — C2×#328×D53 #27351172

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D53C211yesmaximal, characteristic
2C2×C22⋊C8×D53C211yesmaximal, characteristic
3C2×#95×D53C211yesmaximal, characteristic
4C2×#16810361C211yesmaximal, characteristic, complemented
5C2×#16810360C211yesmaximal, characteristic, complemented
6C2×#16810359C211yesmaximal, characteristic, complemented
7#328×D53C218yesmaximal, direct product factor
8C2×C53×#328C211yesmaximal, characteristic, complemented
9C22×Q8×D53C411yescharacteristic, complemented
10C23×C4×D53—21no—
11C23×C4×D53C2211yescharacteristic
12C22×C8×D53—21no—
13C2×#13133197C411yescharacteristic, complemented
14C2×#13133196C2211yescharacteristic
15C2×#13133195—21no—
16C2×#13133194—21no—
17C2×#13133193C411yescharacteristic, complemented
18C22⋊Q8×D53—22no—
19C22⋊Q8×D53—22no—
20C22⋊Q8×D53C414yescomplemented
21C22⋊Q8×D53C2214yes—
22C2×C4⋊C4×D53—21no—
23C2×C4⋊C4×D53C411yescharacteristic, complemented
24C2×C22⋊C4×D53—21no—
25C2×C22⋊#88322C2211yescharacteristic
26C2×#13133129—21no—
27C22⋊C8×D53—22no—
28C22⋊C8×D53C2214yes—
29C2×#13133124—21no—
30C2×#13133124C2211yescharacteristic
31#95×D53—22no—
32#95×D53C2214yes—
33#16810361C2214yescomplemented
34#16810360C2214yescomplemented
35#16810359C2214yescomplemented
36C2×C22⋊Q8×C53C2211yescharacteristic
37C2×C22⋊C8×C53C2211yescharacteristic
38C2×#95×C53C2211yescharacteristic
39C53×#328C2214yescomplemented
40C24×D53D411yescharacteristic
41C22×Dic106—21no—
42C22×Dic106C2×C411yescharacteristic, complemented
43C2×Q8×D53—22no—
44C2×Q8×D53—44no—
45C2×Q8×D53C2×C414yescomplemented
46C23×Dic53—21no—
47C23×Dic53D411yescharacteristic
48C22×C4×D53—28no—
49C22×C4×D53—21no—
50C22×C4×D53—21no—
51C22×C4×D53—24no—
52C22×C4×D53—44no—
53C22×C4×D53—44no—
54C22×C4×D53—44no—
55C22×C4×D53C2×C411yescharacteristic
56C22×C4×D53C2×C412yes—
57C22×C4×D53C2×C411yescharacteristic
58C22×C4×D53D411yescharacteristic
59C22×C4×D53D412yes—
60C22×C4×D53D412yes—
61C22×C4×D53D411yescharacteristic
62C22×C4×D53C2312yes—
63C22×#88322—21no—
64C2×C8×D53—24no—
65C2×C8×D53—44no—
66#13133197—22no—
67#13133197C2×C414yescomplemented
68#13133196—21no—
69#13133196—21no—
70#13133196C2×C412yescomplemented
71#13133196C2312yes—
72#13133195—24no—
73#13133195—24no—
74#13133194—24no—
75#13133194—24no—
76#13133193—22no—
77#13133193C2×C414yescomplemented
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53C2×C411yescharacteristic, complemented
80C2×#11719919—21no—
81C2×#11719919—21no—
82C2×#11719919—21no—
83C4⋊C4×D53—24no—
84C4⋊C4×D53—22no—
85C4⋊C4×D53—24no—
86C4⋊C4×D53C2×C414yescomplemented
87C2×C22⋊Dic53—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C22⋊C4×D53—24no—
91C22⋊C4×D53—24no—
92C22⋊#88322—21no—
93C22⋊#88322C2312yes—
94#13133129—24no—
95#13133124—21no—
96#13133124—24no—
97#13133124C2312yes—
98C22×Q8×C53C2×C411yescharacteristic, complemented
99C23×C4×C53—21no—
100C23×C4×C53C2311yescharacteristic
101C22×C8×C53—21no—
102C22⋊Q8×C53—21no—
103C22⋊Q8×C53—21no—
104C22⋊Q8×C53C2×C412yescomplemented
105C22⋊Q8×C53C2312yes—
106C2×C4⋊C4×C53—21no—
107C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
108C2×C22⋊C4×C53—21no—
109C22⋊C8×C53—21no—
110C22⋊C8×C53C2312yes—
111#95×C53—21no—
112#95×C53C2312yes—
113C24×C53C2×D411yescharacteristic
114C23×D53—24no—
115C23×D53—24no—
116C23×D53C22⋊C412yes—
117C23×D53C22⋊C411yescharacteristic
118C23×D53C22⋊C411yescharacteristic
119C23×D53SD1614yes—
120C23×D53Q1614yes—
121C23×D53C2×D412yes—
122C2×Q8×C53—21no—
123C2×Q8×C53—42no—
124C2×Q8×C53C22×C412yescomplemented
125C22×C4×C53—24no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—22no—
129C22×C4×C53—42no—
130C22×C4×C53—42no—
131C22×C4×C53—42no—
132C22×C4×C53C22×C411yescharacteristic
133C22×C4×C53C22×C411yescharacteristic
134C22×C4×C53C2×D411yescharacteristic
135C22×C4×C53C2×D411yescharacteristic
136C22×C4×C53C2×D411yescharacteristic
137C22×C4×C53C2411yescharacteristic
138C22×Dic53—24no—
139C22×Dic53—21no—
140C22×Dic53—21no—
141C22×Dic53—22no—
142C22×Dic53—42no—
143C22×Dic53—42no—
144C22×Dic53—42no—
145C22×Dic53C22⋊C411yescharacteristic
146C22×Dic53C22⋊C411yescharacteristic
147C22×Dic53C22⋊C412yes—
148C22×Dic53C2×D412yes—
149Q8×D53—48no—
150Q8×D53—48no—
151C2×C4×D53—24no—
152C2×C4×D53—24no—
153C2×C4×D53—216no—
154C2×C4×D53—24no—
155C2×C4×D53—24no—
156C2×C4×D53—44no—
157C2×C4×D53—44no—
158C2×C4×D53—44no—
159C2×C4×D53—44no—
160C2×C4×D53—42no—
161C2×C4×D53—42no—
162C2×C4×D53—432no—
163C2×C4×D53—48no—
164C2×C4×D53—44no—
165C2×C4×D53—44no—
166C2×C4×D53—48no—
167C2×C4×D53C22⋊C412yes—
168C2×C4×D53C22⋊C412yes—
169C2×C4×D53C22⋊C412yes—
170C2×C4×D53C22⋊C412yes—
171C2×C4×D53C22×C412yes—
172C2×C4×D53C22×C412yes—
173C2×C4×D53C2×D412yes—
174C2×C4×D53C2×D412yes—
175C2×Dic106—21no—
176C2×Dic106—24no—
177C2×Dic106—44no—
178C2×Dic106—42no—
179C2×Dic106C22×C412yescomplemented
180C2×C8×C53—22no—
181C2×C8×C53—42no—
182C4⋊C4×C53—22no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—22no—
185C4⋊C4×C53C22×C412yescomplemented
186C22⋊C4×C53—22no—
187C22⋊C4×C53—22no—
188C22⋊Dic53—22no—
189C22⋊Dic53—22no—
190#11719921—24no—
191#11719921—24no—
192C4⋊Dic53—21no—
193C4⋊Dic53—24no—
194C4⋊Dic53C22×C412yescomplemented
195#11719919—22no—
196#11719919—22no—
197#11719919—24no—
198#11719919—24no—
199C2×#88322—22no—
200C2×#88322—42no—
201C8×D53—48no—
202C23×C53—22no—
203C23×C53—22no—
204C23×C53C2×C22⋊C411yescharacteristic
205C23×C53C2×C22⋊C411yescharacteristic
206C23×C53C2×SD1612yes—
207C23×C53C2×Q1612yes—
208C23×C53C22×D411yescharacteristic
209C22×D53—22no—
210C22×D53—22no—
211C22×D53—216no—
212C22×D53—216no—
213C22×D53—24no—
214C22×D53—24no—
215C22×D53—24no—
216C22×D53—24no—
217C22×D53#9914yes—
218C22×D53#10314yes—
219C22×D53#10318yes—
220C22×D53#10314yes—
221C22×D53#10414yes—
222C22×D53C2×C22⋊C412yes—
223C22×D53C2×C22⋊C412yes—
224C22×D53C2×SD1614yes—
225C22×D53C2×Q1614yes—
226Q8×C53—42no—
227Q8×C53—42no—
228C2×C4×C53—22no—
229C2×C4×C53—22no—
230C2×C4×C53—24no—
231C2×C4×C53—22no—
232C2×C4×C53—22no—
233C2×C4×C53—41no—
234C2×C4×C53—41no—
235C2×C4×C53—41no—
236C2×C4×C53—41no—
237C2×C4×C53—42no—
238C2×C4×C53—48no—
239C2×C4×C53—42no—
240C2×C4×C53—42no—
241C2×C4×C53—42no—
242C2×C4×C53C2×C22⋊C411yescharacteristic
243C2×C4×C53C2×C22⋊C411yescharacteristic
244C2×C4×C53C23×C411yescharacteristic
245C2×C4×C53C22×D411yescharacteristic
246C2×Dic53—22no—
247C2×Dic53—22no—
248C2×Dic53—24no—
249C2×Dic53—22no—
250C2×Dic53—22no—
251C2×Dic53—42no—
252C2×Dic53—42no—
253C2×Dic53—42no—
254C2×Dic53—48no—
255C2×Dic53—42no—
256C2×Dic53—42no—
257C2×Dic53—42no—
258C2×Dic53C2×C22⋊C412yes—
259C2×Dic53C2×C22⋊C412yes—
260C4×D53—24no—
261C4×D53—24no—
262C4×D53—24no—
263C4×D53—24no—
264C4×D53—42no—
265C4×D53—42no—
266C4×D53—42no—
267C4×D53—42no—
268C4×D53—432no—
269C4×D53—48no—
270C4×D53—48no—
271Dic106—48no—
272Dic106—42no—
273Dic106—42no—
274C8×C53—42no—
275#88322—42no—
276C22×#328—531nomaximal, Sylow
277C22×C53—21no—
278C22×C53—21no—
279C22×C53—21no—
280C22×C53—21no—
281C22×C53—24no—
282C22×C53—24no—
283C22×C53C2×#9912yes—
284C22×C53C2×#10312yes—
285C22×C53C2×#10312yes—
286C22×C53C2×#10412yes—
287C22×C53C22×C22⋊C411yescharacteristic
288C22×C53C22×SD1611yescharacteristic
289C22×C53C22×Q1611yescharacteristic
290C2×D53—22no—
291C2×D53—22no—
292C2×D53—28no—
293C2×D53—28no—
294C2×D53—216no—
295C2×D53—28no—
296C2×D53#328116yesdirect product factor
297C2×D53C2×#9914yes—
298C2×D53C2×#10314yes—
299C2×D53C2×#10314yes—
300C2×D53C2×#10414yes—
301C4×C53—21no—
302C4×C53—21no—
303C4×C53—21no—
304C4×C53—21no—
305C4×C53—44no—
306C4×C53—42no—
307C4×C53—42no—
308Dic53—22no—
309Dic53—22no—
310Dic53—44no—
311Dic53—42no—
312Dic53—42no—
313C22×C22⋊Q8—531no—
314C22×C22⋊C8—531no—
315C22×#95—531no—
316C2×#328—531no—
317C2×#328—531no—
318C2×#328—538no—
319C2×#328—531no—
320C2×#328D5311yescharacteristic, direct product factor
321C2×C53—21no—
322C2×C53—21no—
323C2×C53—22no—
324C2×C53C2×#32814yescomplemented
325C2×C53C22×#9911yescharacteristic
326C2×C53C22×#10311yescharacteristic
327C2×C53C22×#10411yescharacteristic
328D53—24no—
329D53C2×#32818yesdirect product factor
330C23×Q8—531no—
331C24×C4—531no—
332C24×C4—1061no—
333C23×C8—1061no—
334C2×C22⋊Q8—531no—
335C2×C22⋊Q8—531no—
336C2×C22⋊Q8—534no—
337C2×C22⋊Q8—534no—
338C2×C22⋊Q8—531no—
339C2×C22⋊Q8—1061no—
340C2×C22⋊Q8—1061no—
341C2×C22⋊Q8—1062no—
342C2×C22⋊Q8—1062no—
343C2×C22⋊Q8C2×D5311yescharacteristic
344C22×C4⋊C4—531no—
345C22×C4⋊C4—1061no—
346C22×C22⋊C4—1061no—
347C2×C22⋊C8—531no—
348C2×C22⋊C8—534no—
349C2×C22⋊C8—1062no—
350C2×C22⋊C8—1061no—
351C2×C22⋊C8C2×D5311yescharacteristic
352C2×#95—531no—
353C2×#95—534no—
354C2×#95—1062no—
355C2×#95—1061no—
356C2×#95C2×D5311yescharacteristic
357#328—534no—
358#328—534no—
359#328—534no—
360#328C2×D5314yesdirect product factor
361C53C22×#32811yescharacteristic, complemented, Sylow
362C25—531no—
363C22×Q8—534no—
364C22×Q8—531no—
365C22×Q8—1061no—
366C22×Q8—1062no—
367C22×Q8—2124no—
368C22×Q8C4×D5311yescharacteristic, complemented
369C23×C4—21no—
370C23×C4—531no—
371C23×C4—531no—
372C23×C4—531no—
373C23×C4—531no—
374C23×C4—532no—
375C23×C4—532no—
376C23×C4—531no—
377C23×C4—532no—
378C23×C4—532no—
379C23×C4—1061no—
380C23×C4—1061no—
381C23×C4—1064no—
382C23×C4—1068no—
383C23×C4—1061no—
384C23×C4—2124no—
385C23×C4—2124no—
386C23×C4—2124no—
387C23×C4C22×D5311yescharacteristic
388C22×C8—21no—
389C22×C8—1064no—
390C22×C8—1061no—
391C22×C8—2124no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—534no—
395C22⋊Q8—532no—
396C22⋊Q8—532no—
397C22⋊Q8—534no—
398C22⋊Q8—1064no—
399C22⋊Q8—1064no—
400C22⋊Q8—1064no—
401C22⋊Q8—1064no—
402C22⋊Q8—1062no—
403C22⋊Q8—1062no—
404C22⋊Q8—1061no—
405C22⋊Q8—1061no—
406C22⋊Q8C4×D5312yescomplemented
407C22⋊Q8C22×D5312yes—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—531no—
410C2×C4⋊C4—534no—
411C2×C4⋊C4—1062no—
412C2×C4⋊C4—1064no—
413C2×C4⋊C4—1064no—
414C2×C4⋊C4—1061no—
415C2×C4⋊C4—1061no—
416C2×C4⋊C4—1061no—
417C2×C4⋊C4—1061no—
418C2×C4⋊C4C4×D5311yescharacteristic, complemented
419C2×C22⋊C4—21no—
420C2×C22⋊C4—1064no—
421C2×C22⋊C4—1064no—
422C2×C22⋊C4—1061no—
423C2×C22⋊C4—1061no—
424C2×C22⋊C4—1061no—
425C22⋊C8—21no—
426C22⋊C8—532no—
427C22⋊C8—1064no—
428C22⋊C8—1061no—
429C22⋊C8C22×D5312yes—
430#95—21no—
431#95—532no—
432#95—1064no—
433#95—1061no—
434#95C22×D5312yes—
435C24—531no—
436C24—532no—
437C24—531no—
438C24—534no—
439C24—534no—
440C24—532no—
441C24—1064no—
442C24—1064no—
443C24D4×D5311yescharacteristic
444C2×Q8—21no—
445C2×Q8—42no—
446C2×Q8—532no—
447C2×Q8—1064no—
448C2×Q8—1061no—
449C2×Q8—2122no—
450C2×Q8—2124no—
451C2×Q8—2128no—
452C2×Q8—2128no—
453C2×Q8C2×C4×D5312yescomplemented
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—531no—
462C22×C4—531no—
463C22×C4—532no—
464C22×C4—532no—
465C22×C4—532no—
466C22×C4—532no—
467C22×C4—532no—
468C22×C4—532no—
469C22×C4—532no—
470C22×C4—532no—
471C22×C4—532no—
472C22×C4—532no—
473C22×C4—1064no—
474C22×C4—1064no—
475C22×C4—1064no—
476C22×C4—1064no—
477C22×C4—10616no—
478C22×C4—1064no—
479C22×C4—1061no—
480C22×C4—1061no—
481C22×C4—1062no—
482C22×C4—2122no—
483C22×C4—2122no—
484C22×C4—2124no—
485C22×C4—2124no—
486C22×C4—2124no—
487C22×C4—2124no—
488C22×C4—2124no—
489C22×C4—2128no—
490C22×C4—2124no—
491C22×C4—2128no—
492C22×C4—21232no—
493C22×C4—2122no—
494C22×C4—2122no—
495C22×C4—2122no—
496C22×C4C2×C4×D5311yescharacteristic
497C22×C4C2×C4×D5311yescharacteristic
498C22×C4D4×D5311yescharacteristic
499C22×C4D4×D5311yescharacteristic
500C22×C4D4×D5311yescharacteristic
501C22×C4C23×D5311yescharacteristic
502C2×C8—22no—
503C2×C8—42no—
504C2×C8—1062no—
505C2×C8—2128no—
506C2×C8—2122no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—532no—
511C4⋊C4—1064no—
512C4⋊C4—1064no—
513C4⋊C4—1064no—
514C4⋊C4—1061no—
515C4⋊C4—1062no—
516C4⋊C4—1062no—
517C4⋊C4C2×C4×D5312yescomplemented
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—1064no—
521C22⋊C4—1064no—
522C22⋊C4—1062no—
523C22⋊C4—1062no—
524C23—22no—
525C23—22no—
526C23—532no—
527C23—534no—
528C23—534no—
529C23—534no—
530C23—532no—
531C23—538no—
532C23—534no—
533C23—534no—
534C23—534no—
535C23—1064no—
536C23—1064no—
537C23—1064no—
538C23—10616no—
539C23—10616no—
540C23—1064no—
541C23—1062no—
542C23—1062no—
543C23C22⋊C4×D5311yescharacteristic
544C23C22⋊C4×D5311yescharacteristic
545C23SD16×D5312yes—
546C23Q16×D5312yes—
547C23C2×D4×D5311yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—2122no—
551Q8—2122no—
552Q8—2128no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—48no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—532no—
568C2×C4—532no—
569C2×C4—1064no—
570C2×C4—1064no—
571C2×C4—1064no—
572C2×C4—1064no—
573C2×C4—1062no—
574C2×C4—1062no—
575C2×C4—1064no—
576C2×C4—1062no—
577C2×C4—1062no—
578C2×C4—2122no—
579C2×C4—2122no—
580C2×C4—2122no—
581C2×C4—2122no—
582C2×C4—2128no—
583C2×C4—2128no—
584C2×C4—21232no—
585C2×C4—2122no—
586C2×C4—2122no—
587C2×C4—2122no—
588C2×C4—2128no—
589C2×C4—2122no—
590C2×C4—2122no—
591C2×C4—2122no—
592C2×C4C22⋊C4×D5311yescharacteristic
593C2×C4C22⋊C4×D5311yescharacteristic
594C2×C4C22×C4×D5311yescharacteristic
595C2×C4C2×D4×D5311yescharacteristic
596C8—42no—
597C8—2122no—
598C22—21no—
599C22—21no—
600C22—24no—
601C22—24no—
602C22—21no—
603C22—21no—
604C22—534no—
605C22—5316no—
606C22—534no—
607C22—534no—
608C22—534no—
609C22—1068no—
610C22—10616no—
611C22—1068no—
612C22—1062no—
613C22—1068no—
614C22—1062no—
615C22#99×D5312yes—
616C22#103×D5312yes—
617C22#103×D5312yes—
618C22#104×D5312yes—
619C22C2×C22⋊C4×D5311yescharacteristic
620C22C2×SD16×D5311yescharacteristic
621C22C2×Q16×D5311yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—44no—
627C4—42no—
628C4—42no—
629C4—1062no—
630C4—1062no—
631C4—2124no—
632C4—2122no—
633C4—2122no—
634C2—21no—
635C2—22no—
636C2—21no—
637C2—538no—
638C2—1064no—
639C2#328×D5314yesdirect product factor
640C2C2×#99×D5311yescharacteristic
641C2C2×#103×D5311yescharacteristic
642C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#328C2
socleC23×C53C2×C22⋊C4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenterC2×#328D53
hypocenterC53C22×#328
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×#16810361C2semidirect
5. C2×#16810360C2semidirect
6. C2×#16810359C2semidirect
7. #328×D53C2direct (N × H)
8. C2×C53×#328C2semidirect
9. C22×Q8×D53C4semidirect
13. C2×#13133197C4semidirect
17. C2×#13133193C4semidirect
20. C22⋊Q8×D53C4semidirect
23. C2×C4⋊C4×D53C4semidirect
33. #16810361C22semidirect
34. #16810360C22semidirect
35. #16810359C22semidirect
39. C53×#328C22semidirect
42. C22×Dic106C2×C4semidirect
45. C2×Q8×D53C2×C4semidirect
67. #13133197C2×C4semidirect
70. #13133196C2×C4semidirect
77. #13133193C2×C4semidirect
79. C2×C4⋊Dic53C2×C4semidirect
86. C4⋊C4×D53C2×C4semidirect
98. C22×Q8×C53C2×C4semidirect
104. C22⋊Q8×C53C2×C4semidirect
107. C2×C4⋊C4×C53C2×C4semidirect
124. C2×Q8×C53C22×C4semidirect
179. C2×Dic106C22×C4semidirect
185. C4⋊C4×C53C22×C4semidirect
194. C4⋊Dic53C22×C4semidirect
296. C2×D53#328direct (N × H)
320. C2×#328D53direct (N × H)
324. C2×C53C2×#328semidirect
329. D53C2×#328direct (N × H)
360. #328C2×D53direct (N × H)
361. C53C22×#328semidirect
368. C22×Q8C4×D53semidirect
406. C22⋊Q8C4×D53semidirect
418. C2×C4⋊C4C4×D53semidirect
453. C2×Q8C2×C4×D53semidirect
517. C4⋊C4C2×C4×D53semidirect
639. C2#328×D53direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D532
C2×C22⋊C8×D532
C2×#95×D532
C2×#168103612
C2×#168103602
C2×#168103592
#328×D532
C2×C53×#3282
C22×#32853