Finite Group Databasebeta

← C2×#14532229 #17202276

Subgroups — C2×#14532229 #17202276

Order 4352.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587583C211yesmaximal, characteristic, complemented
2C22×#10587610C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D17C211yesmaximal, characteristic
4#14532229C2116yesmaximal, direct product factor
5C2×#11762739C212yesmaximal, complemented
6C2×#11762731C212yesmaximal, complemented
7C2×#11762714C211yesmaximal, characteristic, complemented
8C2×#11762708C211yesmaximal, characteristic, complemented
9C2×#11762688C212yesmaximal
10C2×#11762669C212yesmaximal, complemented
11C2×#11762666C211yesmaximal, characteristic, complemented
12C23×C4⋊C4×C17C211yesmaximal, characteristic, complemented
13C23×Dic34C2211yescharacteristic
14C23×C22⋊D17C2211yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C2×#10587583—28no—
17C2×#10587583C2218yescomplemented
18C2×#10587610—28no—
19C2×#10587610C2218yescomplemented
20C2×C4×C22⋊D17—28no—
21C2×C4×C22⋊D17C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2212yes—
24C22×C4⋊Dic17C2212yes—
25C22×#63225C2211yescharacteristic
26C22×#63225C2212yes—
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2212yes—
29C22×#63227C2211yescharacteristic
30C22×#63227C2212yes—
31C22×#63227C2212yes—
32C22×C4×Dic17C2211yescharacteristic
33#11762739C22116yescomplemented
34#11762731C22116yescomplemented
35#11762714C2218yescomplemented
36#11762708C2218yescomplemented
37#11762688C22116yes—
38#11762669C22116yescomplemented
39#11762666C2218yescomplemented
40C2×#10587502C2212yes—
41C2×#10587502C2212yes—
42C2×#10587502C2212yes—
43C2×#10587502C2212yes—
44C24×C4×C17C2212yes—
45C24×C4×C17C2211yescharacteristic
46C22×C4⋊C4×C17—28no—
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C4⋊C4×C17C2212yes—
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C4⋊C4×C17C2218yescomplemented
51C25×C17C2311yescharacteristic
52C24×D17C2311yescharacteristic
53C23×C4×C17—24no—
54C23×C4×C17—24no—
55C23×C4×C17—28no—
56C23×C4×C17—28no—
57C23×C4×C17—44no—
58C23×C4×C17D418yes—
59C23×C4×C17C2312yes—
60C23×C4×C17C2318yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2312yes—
63C23×C4×C17C2314yes—
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—24no—
66C22×C22⋊D17—24no—
67C22×C22⋊D17Q818yescomplemented
68C22×C22⋊D17C2314yes—
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2312yes—
71C23×Dic17C2312yes—
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C22×C4×D17—24no—
75C22×C4×D17—24no—
76C22×C4×D17—24no—
77C22×C4×D17C2314yes—
78C22×Dic34—24no—
79C22×Dic34—24no—
80C22×Dic34—24no—
81C22×Dic34C2314yes—
82C2×C4⋊C4×C17—28no—
83C2×C4⋊C4×C17—24no—
84C2×C4⋊C4×C17—232no—
85C2×C4⋊C4×C17D418yescomplemented
86C2×C4⋊C4×C17C2314yes—
87C2×C4⋊C4×C17C2318yes—
88C2×C4⋊C4×C17C2314yes—
89C2×C22⋊Dic17—24no—
90C2×C22⋊Dic17—28no—
91C2×C22⋊Dic17C2318yes—
92C2×C22⋊Dic17C2314yes—
93C4×C22⋊D17—232no—
94C2×#63227—24no—
95C2×#63227—28no—
96C2×#63227—44no—
97C2×#63227C2318yes—
98C2×#63227C2314yes—
99C2×#63227C2318yes—
100C2×C4⋊Dic17—24no—
101C2×C4⋊Dic17—28no—
102C2×C4⋊Dic17—44no—
103C2×C4⋊Dic17C2314yes—
104C2×C4⋊Dic17C2318yes—
105C2×C4⋊Dic17C2318yes—
106#10587610—232no—
107C2×#63225—24no—
108C2×#63225—28no—
109C2×#63225C2318yes—
110C2×#63225C2314yes—
111C2×C4×Dic17—24no—
112C2×C4×Dic17C2314yes—
113#10587583—232no—
114#10587502C2318yes—
115#10587502C2318yes—
116#10587502C2318yes—
117#10587502C2318yes—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17—22no—
122C24×C17C2×D414yes—
123C24×C17C2×Q814yes—
124C24×C17#4114yes—
125C24×C17C2412yes—
126C24×C17C2411yescharacteristic
127C23×D17—22no—
128C23×D17—22no—
129C23×D17—22no—
130C23×D17—22no—
131C23×D17—22no—
132C23×D17—22no—
133C23×D17C2×Q814yes—
134C23×D17C2412yes—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—24no—
138C22×C4×C17—24no—
139C22×C4×C17—232no—
140C22×C4×C17—28no—
141C22×C4×C17—28no—
142C22×C4×C17—24no—
143C22×C4×C17—216no—
144C22×C4×C17—24no—
145C22×C4×C17—24no—
146C22×C4×C17—216no—
147C22×C4×C17—48no—
148C22×C4×C17—432no—
149C22×C4×C17C2×D414yes—
150C22×C4×C17C2×D4116yes—
151C22×C4×C17C2×D414yes—
152C22×C4×C17C2×D418yes—
153C22×C4×C17C2×D414yes—
154C22×C4×C17#4114yes—
155C22×C4×C17C2414yes—
156C22×C4×C17C2414yes—
157C22×C4×C17C2412yes—
158C22×C4×C17C2412yes—
159C2×C22⋊D17—232no—
160C2×C22⋊D17—28no—
161C2×C22⋊D17—28no—
162C2×C22⋊D17C2×Q8116yescomplemented
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—24no—
166C22×Dic17—24no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—24no—
171C22×Dic17—24no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—24no—
175C22×Dic17—22no—
176C22×Dic17—24no—
177C22×Dic17C2×Q814yes—
178C22×Dic17C2414yes—
179C22×Dic17C2412yes—
180C22×Dic17C2412yes—
181C22×Dic17C2414yes—
182C22×Dic17C2412yes—
183C2×C4×D17—28no—
184C2×C4×D17—28no—
185C2×C4×D17—28no—
186C2×C4×D17—416no—
187C2×Dic34—28no—
188C2×Dic34—28no—
189C2×Dic34—28no—
190C2×Dic34—416no—
191C4⋊C4×C17—216no—
192C4⋊C4×C17—28no—
193C4⋊C4×C17C2×D4116yescomplemented
194C22⋊Dic17—216no—
195C22⋊Dic17—28no—
196#63227—216no—
197#63227—28no—
198#63227—48no—
199C4⋊Dic17—216no—
200C4⋊Dic17—28no—
201C4⋊Dic17—48no—
202#63225—216no—
203#63225—28no—
204C4×Dic17—28no—
205C2×#2417—171nomaximal, Sylow
206C23×C17—28no—
207C23×C17—28no—
208C23×C17—28no—
209C23×C17—28no—
210C23×C17—28no—
211C23×C17—28no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17C22⋊Q8116yescomplemented
217C23×C17C22×D414yes—
218C23×C17C22×D412yes—
219C23×C17C22×D412yes—
220C23×C17C22×Q814yes—
221C23×C17C22×Q812yes—
222C23×C17C2×#4112yes—
223C23×C17C2×#4114yes—
224C23×C17C2×#4112yes—
225C23×C17H(5,𝔽2)12yes—
226C23×C172−1+412yes—
227C23×C17C2511yescharacteristic
228C22×D17—28no—
229C22×D17—28no—
230C22×D17—28no—
231C22×D17—22no—
232C22×D17—22no—
233C22×D17—22no—
234C22×D17—22no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—44no—
238C22×D17—44no—
239C22×D17—44no—
240C22×D17—44no—
241C22×D17C22×Q814yes—
242C2×C4×C17—28no—
243C2×C4×C17—216no—
244C2×C4×C17—22no—
245C2×C4×C17—24no—
246C2×C4×C17—22no—
247C2×C4×C17—24no—
248C2×C4×C17—232no—
249C2×C4×C17—24no—
250C2×C4×C17—24no—
251C2×C4×C17—24no—
252C2×C4×C17—432no—
253C2×C4×C17—48no—
254C2×C4×C17#121116yes—
255C2×C4×C17C22×D414yes—
256C2×C4×C17C22×D414yes—
257C2×C4×C17C22×D418yes—
258C2×C4×C17C22×D414yes—
259C2×C4×C17C2×#4114yes—
260C22⋊D17—232no—
261C2×Dic17—28no—
262C2×Dic17—22no—
263C2×Dic17—22no—
264C2×Dic17—24no—
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—24no—
268C2×Dic17—24no—
269C2×Dic17—22no—
270C2×Dic17—24no—
271C2×Dic17—22no—
272C2×Dic17—22no—
273C2×Dic17—24no—
274C2×Dic17—22no—
275C2×Dic17—24no—
276C2×Dic17—48no—
277C2×Dic17—44no—
278C2×Dic17—44no—
279C2×Dic17—48no—
280C2×Dic17C22×Q814yes—
281C4×D17—416no—
282Dic34—416no—
283C22×C22⋊Q8—171no—
284C22×C22⋊Q8—171no—
285C22×C4×D4—171no—
286C23×C4⋊C4D1711yescharacteristic, complemented
287#2417—1716no—
288C2×#398—172no—
289C2×#396—172no—
290C2×#391—171no—
291C2×#389—171no—
292C2×#386—172no—
293C2×#380—172no—
294C2×#380—171no—
295C22×C17—24no—
296C22×C17—232no—
297C22×C17—24no—
298C22×C17—24no—
299C22×C17—24no—
300C22×C17—24no—
301C22×C17—24no—
302C22×C17C2×#12114yes—
303C22×C17C2×C22⋊Q814yes—
304C22×C17C2×C22⋊Q818yescomplemented
305C22×C17#53714yes—
306C22×C17#54614yes—
307C22×C17D4×Q814yes—
308C22×C17#55214yes—
309C22×C17#55414yes—
310C22×C17C23×D411yescharacteristic
311C22×C17C23×D411yescharacteristic
312C22×C17C23×Q811yescharacteristic
313C22×C17C22×#4111yescharacteristic
314C22×C17C22×#4111yescharacteristic
315C22×C17C2×H(5,𝔽2)11yescharacteristic
316C22×C17C2×2−1+411yescharacteristic
317C2×D17—24no—
318C2×D17—24no—
319C2×D17—24no—
320C2×D17—42no—
321C2×D17—416no—
322C2×D17—42no—
323C2×D17—42no—
324C2×D17—42no—
325C4×C17—24no—
326C4×C17—28no—
327C4×C17—44no—
328C4×C17C2×#12118yes—
329Dic17—24no—
330Dic17—44no—
331Dic17—42no—
332Dic17—42no—
333Dic17—44no—
334C23×Q8—171no—
335C23×D4—171no—
336C24×C4—171no—
337C24×C4C2×D1712yes—
338C24×C4C2×D1711yescharacteristic
339C2×C22⋊Q8—178no—
340C2×C22⋊Q8—178no—
341C2×C22⋊Q8—348no—
342C2×C22⋊Q8—348no—
343C2×C4×D4—178no—
344C2×C4×D4—348no—
345C22×C4⋊C4—28no—
346C22×C4⋊C4—172no—
347C22×C4⋊C4—171no—
348C22×C4⋊C4—172no—
349C22×C4⋊C4—171no—
350C22×C4⋊C4—172no—
351C22×C4⋊C4C2×D1712yes—
352C22×C4⋊C4C2×D1711yescharacteristic
353C22×C4⋊C4C2×D1711yescharacteristic
354C22×C4⋊C4C2×D1718yescomplemented
355C22×C22⋊C4—171no—
356C22×C22⋊C4—172no—
357C22×C22⋊C4—171no—
358C22×C22⋊C4—172no—
359C22×C22⋊C4—172no—
360C22×C42—171no—
361#398—1716no—
362#396—1716no—
363#391—178no—
364#389—178no—
365#386—1716no—
366#380—1716no—
367#380—178no—
368C2×#95—172no—
369C2×#95—172no—
370C2×#95—172no—
371C2×#95—172no—
372C2×C17—28no—
373C2×C17#241718yescomplemented
374C2×C17C22×#12111yescharacteristic
375C2×C17C22×C22⋊Q811yescharacteristic
376C2×C17C2×#53711yescharacteristic
377C2×C17C2×#54611yescharacteristic
378C2×C17C2×D4×Q811yescharacteristic
379C2×C17C2×#55211yescharacteristic
380C2×C17C2×#55411yescharacteristic
381D17—44no—
382C25—171no—
383C25C22×D1711yescharacteristic
384C22×Q8—174no—
385C22×Q8—344no—
386C22×Q8—344no—
387C22×Q8—344no—
388C22×D4—178no—
389C22×D4—174no—
390C22×D4—344no—
391C22×D4—344no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—28no—
395C23×C4—28no—
396C23×C4—44no—
397C23×C4—171no—
398C23×C4—172no—
399C23×C4—172no—
400C23×C4—171no—
401C23×C4—171no—
402C23×C4—174no—
403C23×C4—344no—
404C23×C4—344no—
405C23×C4—344no—
406C23×C4D6818yes—
407C23×C4C22×D1712yes—
408C23×C4C22×D1718yes—
409C23×C4C22×D1714yes—
410C23×C4C22×D1711yescharacteristic
411C23×C4C22×D1712yes—
412C23×C4C22×D1711yescharacteristic
413C22⋊Q8—3432no—
414C22⋊Q8—3432no—
415C4×D4—3432no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—232no—
419C2×C4⋊C4—174no—
420C2×C4⋊C4—174no—
421C2×C4⋊C4—178no—
422C2×C4⋊C4—178no—
423C2×C4⋊C4—178no—
424C2×C4⋊C4—344no—
425C2×C4⋊C4—348no—
426C2×C4⋊C4—344no—
427C2×C4⋊C4—348no—
428C2×C4⋊C4—684no—
429C2×C4⋊C4C22⋊D1718yescomplemented
430C2×C4⋊C4C22×D1714yes—
431C2×C4⋊C4C22×D1718yes—
432C2×C4⋊C4C22×D1714yes—
433C2×C22⋊C4—174no—
434C2×C22⋊C4—178no—
435C2×C22⋊C4—174no—
436C2×C22⋊C4—178no—
437C2×C22⋊C4—178no—
438C2×C22⋊C4—344no—
439C2×C22⋊C4—348no—
440C2×C22⋊C4—344no—
441C2×C22⋊C4—348no—
442C2×C22⋊C4—684no—
443C2×C42—174no—
444C2×C42—344no—
445#95—178no—
446#95—178no—
447#95—178no—
448#95—178no—
449C17C2×#241711yescharacteristic, complemented, Sylow
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—174no—
455C24—172no—
456C24—342no—
457C24—342no—
458C24—342no—
459C24—342no—
460C24—342no—
461C24—342no—
462C24C2×D6814yes—
463C24#6325414yes—
464C24Q8×D1714yes—
465C24C23×D1712yes—
466C24C23×D1711yescharacteristic
467C2×Q8—348no—
468C2×Q8—348no—
469C2×Q8—348no—
470C2×Q8—6816no—
471C2×D4—1716no—
472C2×D4—348no—
473C2×D4—348no—
474C2×D4—3432no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—232no—
482C22×C4—216no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—216no—
487C22×C4—48no—
488C22×C4—432no—
489C22×C4—174no—
490C22×C4—172no—
491C22×C4—172no—
492C22×C4—174no—
493C22×C4—174no—
494C22×C4—172no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—344no—
499C22×C4—342no—
500C22×C4—344no—
501C22×C4—342no—
502C22×C4—344no—
503C22×C4—344no—
504C22×C4—342no—
505C22×C4—344no—
506C22×C4—342no—
507C22×C4—344no—
508C22×C4—342no—
509C22×C4—348no—
510C22×C4—348no—
511C22×C4—348no—
512C22×C4—6816no—
513C22×C4C2×D6814yes—
514C22×C4C2×D68116yes—
515C22×C4C2×D6814yes—
516C22×C4#6325214yes—
517C22×C4C2×C22⋊D1718yes—
518C22×C4C2×C22⋊D1714yes—
519C22×C4C23×D1714yes—
520C22×C4C23×D1712yes—
521C22×C4C23×D1714yes—
522C22×C4C23×D1712yes—
523C4⋊C4—216no—
524C4⋊C4—28no—
525C4⋊C4—348no—
526C4⋊C4—3416no—
527C4⋊C4—348no—
528C4⋊C4—3416no—
529C4⋊C4—688no—
530C4⋊C4C2×C22⋊D17116yescomplemented
531C22⋊C4—348no—
532C22⋊C4—3416no—
533C22⋊C4—348no—
534C22⋊C4—3416no—
535C22⋊C4—688no—
536C42—348no—
537C23—28no—
538C23—28no—
539C23—28no—
540C23—28no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—28no—
546C23—28no—
547C23—174no—
548C23—348no—
549C23—348no—
550C23—348no—
551C23—342no—
552C23—342no—
553C23—342no—
554C23—342no—
555C23—342no—
556C23—342no—
557C23—684no—
558C23—684no—
559C23—684no—
560C23—684no—
561C23#10587583116yescomplemented
562C23C22×D6814yes—
563C23C22×D6812yes—
564C23C2×#6325212yes—
565C23C2×#6325414yes—
566C23C2×#6325412yes—
567C23#1058769112yes—
568C23C2×Q8×D1714yes—
569C23C2×Q8×D1712yes—
570C23#1058769412yes—
571C23C22×C22⋊D1712yes—
572C23C24×D1711yescharacteristic
573Q8—6816no—
574D4—3432no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—216no—
581C2×C4—232no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—432no—
586C2×C4—48no—
587C2×C4—174no—
588C2×C4—348no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—344no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—344no—
595C2×C4—342no—
596C2×C4—344no—
597C2×C4—342no—
598C2×C4—344no—
599C2×C4—344no—
600C2×C4—342no—
601C2×C4—342no—
602C2×C4—344no—
603C2×C4—684no—
604C2×C4—688no—
605C2×C4—684no—
606C2×C4—688no—
607C2×C4—6816no—
608C2×C4#10587616116yes—
609C2×C4C22×D6814yes—
610C2×C4C22×D6814yes—
611C2×C4C2×#6325214yes—
612C2×C4C22×C22⋊D1718yes—
613C2×C4C22×C22⋊D1714yes—
614C22—24no—
615C22—232no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—344no—
622C22—344no—
623C22—344no—
624C22—682no—
625C22—6816no—
626C22—682no—
627C22—682no—
628C22—682no—
629C22C2×#1058761614yes—
630C22C2×#1058758314yes—
631C22C2×#1058758318yescomplemented
632C22#1176339014yes—
633C22#1176345314yes—
634C22Q8×C22⋊D1714yes—
635C22#1176349414yes—
636C22#1176351414yes—
637C22C23×C22⋊D1711yescharacteristic
638C22C23×D6811yescharacteristic
639C22C22×Q8×D1711yescharacteristic
640C22C22×#6325411yescharacteristic
641C22C22×#6325211yescharacteristic
642C22C2×#1058769111yescharacteristic
643C22C2×#1058769411yescharacteristic
644C4—28no—
645C4—24no—
646C4—44no—
647C4—344no—
648C4—682no—
649C4—684no—
650C4—682no—
651C4—684no—
652C4C2×#1058761618yes—
653C2—28no—
654C2—684no—
655C2#1453222918yesdirect product factor
656C2C22×#1058761611yescharacteristic
657C2C22×#1058758311yescharacteristic
658C2C2×#1176339011yescharacteristic
659C2C2×#1176345311yescharacteristic
660C2C2×Q8×C22⋊D1711yescharacteristic
661C2C2×#1176349411yescharacteristic
662C2C2×#1176351411yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC23×C4⋊C4×C17C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC23×C4⋊C4D17
hypocenterC17C2×#2417
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#10587583C2semidirect
2. C22×#10587610C2semidirect
4. #14532229C2direct (N × H)
5. C2×#11762739C2semidirect
6. C2×#11762731C2semidirect
7. C2×#11762714C2semidirect
8. C2×#11762708C2semidirect
10. C2×#11762669C2semidirect
11. C2×#11762666C2semidirect
12. C23×C4⋊C4×C17C2semidirect
17. C2×#10587583C22semidirect
19. C2×#10587610C22semidirect
33. #11762739C22semidirect
34. #11762731C22semidirect
35. #11762714C22semidirect
36. #11762708C22semidirect
38. #11762669C22semidirect
39. #11762666C22semidirect
50. C22×C4⋊C4×C17C22semidirect
67. C22×C22⋊D17Q8semidirect
85. C2×C4⋊C4×C17D4semidirect
162. C2×C22⋊D17C2×Q8semidirect
193. C4⋊C4×C17C2×D4semidirect
216. C23×C17C22⋊Q8semidirect
286. C23×C4⋊C4D17semidirect
304. C22×C17C2×C22⋊Q8semidirect
354. C22×C4⋊C4C2×D17semidirect
373. C2×C17#2417semidirect
429. C2×C4⋊C4C22⋊D17semidirect
449. C17C2×#2417semidirect
530. C4⋊C4C2×C22⋊D17semidirect
561. C23#10587583semidirect
631. C22C2×#10587583semidirect
655. C2#14532229direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875832
C22×#105876102
C22×C4×C22⋊D172
#145322292
C2×#117627392
C2×#117627312
C2×#117627142
C2×#117627082
C2×#117626882
C2×#117626692
C2×#117626662
C23×C4⋊C4×C172
C2×#241717