Finite Group Databasebeta

← C107×#22979 #41048943

Subgroups — C107×#22979 #41048943

Order 27392.

850 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C107C211yesmaximal, characteristic
2C107×#2369C211yesmaximal, characteristic, complemented
3C107×#2349C211yesmaximal, characteristic
4C107×#1993C211yesmaximal, characteristic, complemented
5C107×#1949C211yesmaximal, characteristic, complemented
6C107×#1943C211yesmaximal, characteristic, complemented
7C107×#1942C211yesmaximal, characteristic, complemented
8C107×#1921C211yesmaximal, characteristic, complemented
9C107×#1918C211yesmaximal, characteristic, complemented
10C107×#1864C211yesmaximal, characteristic
11C107×#1862C211yesmaximal, characteristic
12C107×#1771C211yesmaximal, characteristic, complemented
13C107×#1762C211yesmaximal, characteristic
14C107×#1762C211yesmaximal, characteristic
15C4×#102×C107C211yesmaximal, characteristic
16C2×C4⋊Q8×C107C2211yescharacteristic
17C2×C4×D4×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20#474×C107C418yescomplemented
21C2×#107×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#107×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#97×C107C2211yescharacteristic
31C2×#97×C107C2211yescharacteristic
32C2×C4×C8×C107C2211yescharacteristic
33#391×C107—21no—
34#391×C107—21no—
35#389×C107—21no—
36#389×C107C2211yescharacteristic
37#389×C107C2211yescharacteristic
38#389×C107C2211yescharacteristic
39#389×C107C2211yescharacteristic
40#385×C107—21no—
41#385×C107—21no—
42#382×C107C2211yescharacteristic
43#380×C107—21no—
44C4×C4⋊C4×C107—21no—
45C4×C4⋊C4×C107C2211yescharacteristic
46C4×C4⋊C4×C107C2211yescharacteristic
47C4×C4⋊C4×C107C2211yescharacteristic
48C4×C4⋊C4×C107C2211yescharacteristic
49C2×#95×C107—21no—
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60C22×Q8×C107—21no—
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C23×C4×C107—21no—
64C23×C4×C107—21no—
65C22×C8×C107C2311yescharacteristic
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C4⋊Q8×C107—22no—
70C4⋊Q8×C107C2×C414yescomplemented
71C4×D4×C107—22no—
72C4×D4×C107—22no—
73C4×D4×C107—22no—
74C4×D4×C107—41no—
75C4×D4×C107—41no—
76C4×D4×C107C2×C414yes—
77C2×C4⋊C4×C107—21no—
78C2×C4⋊C4×C107—21no—
79C2×C4⋊C4×C107—21no—
80C2×C4⋊C4×C107—21no—
81C2×C4⋊C4×C107—21no—
82C2×C4⋊C4×C107D411yescharacteristic
83C2×C4⋊C4×C107D411yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
87C2×C4⋊C4×C107C2311yescharacteristic
88C2×C4⋊C4×C107C2311yescharacteristic
89C2×C4⋊C4×C107C2311yescharacteristic
90C2×C4⋊C4×C107C2311yescharacteristic
91C2×C22⋊C4×C107—21no—
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C42×C107—21no—
95C2×C42×C107—21no—
96C2×C42×C107—21no—
97C2×C42×C107C2311yescharacteristic
98C2×C42×C107C2311yescharacteristic
99C2×C42×C107C2311yescharacteristic
100#107×C107—41no—
101#107×C107C2×C414yescomplemented
102#107×C107C2×C414yescomplemented
103#106×C107—41no—
104C4⋊C8×C107C2×C414yescomplemented
105#102×C107—22no—
106#102×C107C2×C414yes—
107#102×C107C2×C414yes—
108#102×C107Q814yescomplemented
109#97×C107—22no—
110#97×C107—41no—
111C4×C8×C107—41no—
112#95×C107—21no—
113#95×C107—21no—
114#95×C107—21no—
115#95×C107—21no—
116#95×C107—21no—
117#95×C107—21no—
118#95×C107—21no—
119#95×C107—21no—
120#95×C107—21no—
121#95×C107D411yescharacteristic
122#95×C107D411yescharacteristic
123C24×C107—21no—
124C2×Q8×C107—24no—
125C2×Q8×C107—81no—
126C2×Q8×C107—81no—
127C2×D4×C107—21no—
128C2×D4×C107—21no—
129C2×D4×C107—21no—
130C2×D4×C107C22×C412yes—
131C2×D4×C107C2×Q812yes—
132C2×D4×C107#4112yes—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—21no—
136C22×C4×C107—21no—
137C22×C4×C107—24no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—42no—
142C22×C4×C107—42no—
143C22×C4×C107—42no—
144C22×C4×C107—42no—
145C22×C4×C107—81no—
146C22×C4×C107—81no—
147C22×C4×C107—81no—
148C22×C4×C107—81no—
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155C22×C4×C107C2411yescharacteristic
156C2×C8×C107—21no—
157C2×C8×C107—21no—
158C2×C8×C107—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107—21no—
163C2×C8×C107—21no—
164C2×C8×C107—21no—
165C2×C8×C107C22×C412yes—
166C2×C8×C107C22×C412yes—
167C2×C8×C107C2×Q812yes—
168C4⋊C4×C107—24no—
169C4⋊C4×C107—22no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—21no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—21no—
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—21no—
180C4⋊C4×C107—41no—
181C4⋊C4×C107—81no—
182C4⋊C4×C107—81no—
183C4⋊C4×C107—81no—
184C4⋊C4×C107—81no—
185C4⋊C4×C107C22×C412yes—
186C4⋊C4×C107C22×C412yes—
187C4⋊C4×C107C22×C412yes—
188C4⋊C4×C107C2×Q812yes—
189C22⋊C4×C107—24no—
190C22⋊C4×C107—42no—
191C22⋊C4×C107—42no—
192C42×C107—21no—
193C42×C107—21no—
194C42×C107—21no—
195C42×C107—21no—
196C42×C107—42no—
197C42×C107—81no—
198C42×C107—81no—
199C42×C107C22×C412yes—
200C42×C107#4112yes—
201C23×C107—22no—
202C23×C107—22no—
203C23×C107—22no—
204C23×C107—41no—
205C23×C107—41no—
206C23×C107—41no—
207C23×C107—41no—
208C23×C107C22×D411yescharacteristic
209Q8×C107—84no—
210D4×C107—22no—
211D4×C107—22no—
212D4×C107—22no—
213D4×C107C4×Q814yes—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—22no—
221C2×C4×C107—22no—
222C2×C4×C107—22no—
223C2×C4×C107—21no—
224C2×C4×C107—21no—
225C2×C4×C107—21no—
226C2×C4×C107—22no—
227C2×C4×C107—21no—
228C2×C4×C107—21no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—41no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—41no—
249C2×C4×C107—41no—
250C2×C4×C107—84no—
251C2×C4×C107—84no—
252C2×C4×C107—84no—
253C2×C4×C107C4×D412yes—
254C2×C4×C107C4×D412yes—
255C2×C4×C107#13712yes—
256C2×C4×C107C23×C411yescharacteristic
257C2×C4×C107C22×Q811yescharacteristic
258C2×C4×C107C2×#4111yescharacteristic
259C2×C4×C107C2×#4111yescharacteristic
260C2×C4×C107H(5,𝔽2)11yescharacteristic
261C2×C4×C1072−1+411yescharacteristic
262C8×C107—22no—
263C8×C107—22no—
264C8×C107—22no—
265C8×C107—41no—
266C22×C107—24no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—42no—
270C22×C107—42no—
271C22×C107—42no—
272C22×C107—42no—
273C22×C107C2×C4×D411yescharacteristic
274C22×C107#54611yescharacteristic
275C22×C107D4×Q811yescharacteristic
276C22×C107C2×#13711yescharacteristic
277C22×C107#57511yescharacteristic
278C22×C107#57611yescharacteristic
279C22×C107#57611yescharacteristic
280C4×C107—22no—
281C4×C107—22no—
282C4×C107—22no—
283C4×C107—42no—
284C4×C107—42no—
285C4×C107—42no—
286C4×C107—42no—
287C4×C107—41no—
288C4×C107—41no—
289C4×C107—41no—
290C4×C107—81no—
291C4×C107—81no—
292C4×C107—81no—
293C4×C107C2×C4×Q811yescharacteristic
294C4×C107#52011yescharacteristic
295C4×C107#55211yescharacteristic
296C4×C107#55411yescharacteristic
297#22979C10711yesmaximal, characteristic, direct product factor, Sylow
298C2×C107—44no—
299C2×C107#236011yescharacteristic
300C2×C107C4×#13711yescharacteristic
301C2×C107#294811yescharacteristic
302C2×C107#331411yescharacteristic
303C2×C107#331911yescharacteristic
304C2×C107#338511yescharacteristic
305C2×C107#338911yescharacteristic
306C2×#474C2×C10711yescharacteristic
307#2369C2×C10711yescharacteristic, complemented
308#2349C2×C10711yescharacteristic
309#1993C2×C10711yescharacteristic, complemented
310#1949C2×C10711yescharacteristic, complemented
311#1943C2×C10711yescharacteristic, complemented
312#1942C2×C10711yescharacteristic, complemented
313#1921C2×C10711yescharacteristic, complemented
314#1918C2×C10711yescharacteristic, complemented
315#1864C2×C10711yescharacteristic
316#1862C2×C10711yescharacteristic
317#1771C2×C10711yescharacteristic, complemented
318#1762C2×C10711yescharacteristic
319#1762C2×C10711yescharacteristic
320C4×#102C2×C10711yescharacteristic
321C107#2297911yescharacteristic, direct product factor, Sylow
322C2×C4⋊Q8C22×C10711yescharacteristic
323C2×C4×D4C22×C10711yescharacteristic
324C2×C4×D4C22×C10711yescharacteristic
325C2×C4×D4C22×C10711yescharacteristic
326#474C4×C10718yescomplemented
327C2×#107C22×C10711yescharacteristic
328C2×#107C22×C10711yescharacteristic
329C2×#107C22×C10711yescharacteristic
330C2×#106C22×C10711yescharacteristic
331C2×C4⋊C8C22×C10711yescharacteristic
332C2×#102C22×C10711yescharacteristic
333C2×#102C22×C10711yescharacteristic
334C2×#102C22×C10711yescharacteristic
335C2×#102C22×C10711yescharacteristic
336C2×#97C22×C10711yescharacteristic
337C2×#97C22×C10711yescharacteristic
338C2×C4×C8C22×C10711yescharacteristic
339#391—21no—
340#391—21no—
341#389—21no—
342#389C22×C10711yescharacteristic
343#389C22×C10711yescharacteristic
344#389C22×C10711yescharacteristic
345#389C22×C10711yescharacteristic
346#385—21no—
347#385—21no—
348#382C22×C10711yescharacteristic
349#380—21no—
350C4×C4⋊C4—21no—
351C4×C4⋊C4C22×C10711yescharacteristic
352C4×C4⋊C4C22×C10711yescharacteristic
353C4×C4⋊C4C22×C10711yescharacteristic
354C4×C4⋊C4C22×C10711yescharacteristic
355C2×#95—21no—
356#340C22×C10711yescharacteristic
357#340C22×C10711yescharacteristic
358#340C22×C10711yescharacteristic
359#340C22×C10711yescharacteristic
360#340C22×C10711yescharacteristic
361#340C22×C10711yescharacteristic
362#340C22×C10711yescharacteristic
363#340C22×C10711yescharacteristic
364#336C22×C10711yescharacteristic
365#336C22×C10711yescharacteristic
366C22×Q8—21no—
367C22×D4C23×C10711yescharacteristic
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C22×C8C23×C10711yescharacteristic
372C22×C8C23×C10711yescharacteristic
373C22×C8C23×C10711yescharacteristic
374C22×C8C23×C10711yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8C2×C4×C10714yescomplemented
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—41no—
381C4×D4—41no—
382C4×D4C2×C4×C10714yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C10711yescharacteristic
389C2×C4⋊C4D4×C10711yescharacteristic
390C2×C4⋊C4C23×C10711yescharacteristic
391C2×C4⋊C4C23×C10711yescharacteristic
392C2×C4⋊C4C23×C10711yescharacteristic
393C2×C4⋊C4C23×C10711yescharacteristic
394C2×C4⋊C4C23×C10711yescharacteristic
395C2×C4⋊C4C23×C10711yescharacteristic
396C2×C4⋊C4C23×C10711yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C23×C10711yescharacteristic
404C2×C42C23×C10711yescharacteristic
405C2×C42C23×C10711yescharacteristic
406#107—41no—
407#107C2×C4×C10714yescomplemented
408#107C2×C4×C10714yescomplemented
409#106—41no—
410C4⋊C8C2×C4×C10714yescomplemented
411#102—22no—
412#102C2×C4×C10714yes—
413#102C2×C4×C10714yes—
414#102Q8×C10714yescomplemented
415#97—22no—
416#97—41no—
417C4×C8—41no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95D4×C10711yescharacteristic
428#95D4×C10711yescharacteristic
429C24—21no—
430C2×Q8—24no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4C22×C4×C10712yes—
437C2×D4C2×Q8×C10712yes—
438C2×D4#41×C10712yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×D4×C10711yescharacteristic
456C22×C4C2×D4×C10711yescharacteristic
457C22×C4C2×D4×C10711yescharacteristic
458C22×C4C2×D4×C10711yescharacteristic
459C22×C4C2×D4×C10711yescharacteristic
460C22×C4C2×D4×C10711yescharacteristic
461C22×C4C24×C10711yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C22×C4×C10712yes—
472C2×C8C22×C4×C10712yes—
473C2×C8C2×Q8×C10712yes—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4C22×C4×C10712yes—
492C4⋊C4C22×C4×C10712yes—
493C4⋊C4C22×C4×C10712yes—
494C4⋊C4C2×Q8×C10712yes—
495C22⋊C4—24no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—81no—
504C42—81no—
505C42C22×C4×C10712yes—
506C42#41×C10712yes—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23C22×D4×C10711yescharacteristic
515Q8—84no—
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Q8×C10714yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4C4×D4×C10712yes—
560C2×C4C4×D4×C10712yes—
561C2×C4#137×C10712yes—
562C2×C4C23×C4×C10711yescharacteristic
563C2×C4C22×Q8×C10711yescharacteristic
564C2×C4C2×#41×C10711yescharacteristic
565C2×C4C2×#41×C10711yescharacteristic
566C2×C4H(5,𝔽2)×C10711yescharacteristic
567C2×C42−1+4×C10711yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C4×D4×C10711yescharacteristic
580C22#546×C10711yescharacteristic
581C22D4×Q8×C10711yescharacteristic
582C22C2×#137×C10711yescharacteristic
583C22#575×C10711yescharacteristic
584C22#576×C10711yescharacteristic
585C22#576×C10711yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4C2×C4×Q8×C10711yescharacteristic
600C4#520×C10711yescharacteristic
601C4#552×C10711yescharacteristic
602C4#554×C10711yescharacteristic
603C2—44no—
604C2C107×#236011yescharacteristic
605C2C4×#137×C10711yescharacteristic
606C2C107×#294811yescharacteristic
607C2C107×#331411yescharacteristic
608C2C107×#331911yescharacteristic
609C2C107×#338511yescharacteristic
610C2C107×#338911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2369C2semidirect
4. C107×#1993C2semidirect
5. C107×#1949C2semidirect
6. C107×#1943C2semidirect
7. C107×#1942C2semidirect
8. C107×#1921C2semidirect
9. C107×#1918C2semidirect
12. C107×#1771C2semidirect
20. #474×C107C4semidirect
70. C4⋊Q8×C107C2×C4semidirect
101. #107×C107C2×C4semidirect
102. #107×C107C2×C4semidirect
104. C4⋊C8×C107C2×C4semidirect
108. #102×C107Q8semidirect
297. #22979C107direct (N × H)
307. #2369C2×C107semidirect
309. #1993C2×C107semidirect
310. #1949C2×C107semidirect
311. #1943C2×C107semidirect
312. #1942C2×C107semidirect
313. #1921C2×C107semidirect
314. #1918C2×C107semidirect
317. #1771C2×C107semidirect
321. C107#22979direct (N × H)
326. #474C4×C107semidirect
376. C4⋊Q8C2×C4×C107semidirect
407. #107C2×C4×C107semidirect
408. #107C2×C4×C107semidirect
410. C4⋊C8C2×C4×C107semidirect
414. #102Q8×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1072
C107×#23692
C107×#23492
C107×#19932
C107×#19492
C107×#19432
C107×#19422
C107×#19212
C107×#19182
C107×#18642
C107×#18622
C107×#17712
C107×#17622
C4×#102×C1072
#22979107