Finite Group Databasebeta

← #29684655

Subgroups — #29684655

Order 15616.

1202 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic
2#21448221C211yesmaximal, characteristic
3C4×#14519733C211yesmaximal, characteristic
4#21446805C211yesmaximal, characteristic
5#21446804C211yesmaximal, characteristic
6#21446803C211yesmaximal, characteristic
7#21446802C214yesmaximal
8#21445550C214yesmaximal
9C61×#1996C211yesmaximal, characteristic
10#16840314—21no—
11#16840314—21no—
12#16840314—21no—
13#16840314—21no—
14#16840314—21no—
15#16840314—21no—
16#16840314—21no—
17#16840314—21no—
18C2×#14519776C411yescharacteristic, complemented
19C2×#14519775C411yescharacteristic, complemented
20C2×#14519767C412yescomplemented
21C2×#14519756C2211yescharacteristic
22C2×#14519754C2212yes—
23C2×Q8×Dic61C411yescharacteristic, complemented
24C2×#14519742C412yescomplemented
25C2×#14519742C411yescharacteristic, complemented
26C2×#14519733C2212yes—
27C2×#14519733C2212yes—
28C2×#14519733C2212yes—
29C22×C4×Dic61C2211yescharacteristic
30#16839631—21no—
31#16839626—21no—
32#16839622C2211yescharacteristic
33#16839620C2212yes—
34C4⋊C4×Dic61—21no—
35C4×#11758196—21no—
36#16839613—21no—
37#16839613—21no—
38C22⋊C4×Dic61C2212yes—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839607—21no—
41C42×Dic61—21no—
42#16839529C2214yes—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C22×Dic122C2×C412yes—
50C22×Dic122C2×C411yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53#14519776—21no—
54#14519776—21no—
55#14519776—21no—
56#14519776—21no—
57#14519775—21no—
58#14519775—21no—
59#14519775—21no—
60#14519775—21no—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519756—21no—
66#14519756—21no—
67#14519756—21no—
68#14519756—21no—
69#14519754—22no—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73Q8×Dic61—21no—
74Q8×Dic61—21no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77#14519742—21no—
78#14519742—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—22no—
82#14519742—22no—
83#14519742—22no—
84#14519742—22no—
85#14519733—22no—
86#14519733—22no—
87#14519733—22no—
88#14519733—22no—
89#14519733—24no—
90#14519733—28no—
91#14519733Q818yescomplemented
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C412yes—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196C2×C412yes—
99C2×#11758196C2×C412yes—
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2×C412yes—
103C2×C22⋊Dic61C2312yes—
104C2×C22⋊Dic61C2312yes—
105C2×C22⋊Dic61C2312yes—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61C2×C412yes—
111C2×C4×Dic61C2×C412yes—
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61D411yescharacteristic
122C2×C4×Dic61D411yescharacteristic
123C2×C4×Dic61D411yescharacteristic
124#14519684—21no—
125#14519684—21no—
126#14519684—22no—
127#14519684—22no—
128C22×Q8×C61C2×C411yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2×C412yes—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2312yes—
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C42×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143C24×C61C2411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—42no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—42no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C412yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—42no—
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C412yes—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×Q814yes—
176C22×Dic61#4114yes—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122—44no—
182C2×Dic122—42no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—42no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—24no—
192C22⋊C4×C61C2×Q814yes—
193C42×C61—42no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—24no—
198C22⋊Dic61C2×Q814yes—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—42no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196—28no—
215#11758196—44no—
216#11758196—44no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—28no—
222C4×Dic61—44no—
223C4×Dic61—42no—
224C4×Dic61—44no—
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22⋊C411yescharacteristic
236C4×Dic61C22⋊C411yescharacteristic
237C4×Dic61C22⋊C411yescharacteristic
238C4×Dic61C22⋊C411yescharacteristic
239C4×Dic61C22⋊C411yescharacteristic
240C4×Dic61C22⋊C411yescharacteristic
241C23×C61—41no—
242C23×C61—41no—
243C23×C61C23×C411yescharacteristic
244C23×C61C22×D411yescharacteristic
245C23×C61C22×D411yescharacteristic
246C23×C61C22×Q812yes—
247C23×C61C2×#4112yes—
248Q8×C61—42no—
249Q8×C61—42no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—24no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61C2×C22⋊C411yescharacteristic
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—24no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C4×Q814yes—
295C2×Dic61C4×Q814yes—
296C2×Dic61C22⋊Q814yes—
297C2×Dic61C22⋊Q814yes—
298C2×Dic61#12412yes—
299C2×Dic61#12412yes—
300C2×Dic61C4⋊Q812yes—
301C2×Dic61C4⋊Q812yes—
302Dic122—44no—
303Dic122—42no—
304Dic122—42no—
305Dic122—44no—
306#21332—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61—21no—
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61C22×C22⋊C411yescharacteristic
316C22×C61C2×C4×Q812yes—
317C22×C61C2×C22⋊Q812yes—
318C22×C61C2×#12411yescharacteristic
319C22×C61C2×C4⋊Q811yescharacteristic
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—44no—
324C4×C61—42no—
325C4×C61—42no—
326C4×C61—82no—
327C4×C61#41012yes—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—44no—
332Dic61—42no—
333Dic61—42no—
334Dic61—82no—
335Dic61#39112yes—
336Dic61#39112yes—
337Dic61#39112yes—
338Dic61#39112yes—
339Dic61#41012yes—
340C2×#533—611no—
341#2285—611no—
342C4×#117—611no—
343#1996—611no—
344#1996—611no—
345#1996—614no—
346#1996—611no—
347#1996D6111yescharacteristic
348#1740—614no—
349C2×C61—22no—
350C2×C61—21no—
351C2×C61—22no—
352C2×C61—21no—
353C2×C61C2×#39111yescharacteristic
354C2×C61C2×#41011yescharacteristic
355C2×C61C2×#41011yescharacteristic
356#533—1221no—
357#533—1221no—
358#533—1221no—
359#533—1221no—
360#533—1221no—
361#533—1221no—
362#533—1221no—
363#533—1221no—
364C2×C4⋊Q8—611no—
365C2×C4⋊Q8—611no—
366C2×#125—612no—
367C2×C22⋊Q8—611no—
368C2×C22⋊Q8—612no—
369C2×C22⋊Q8C2×D6111yescharacteristic
370C2×C4×Q8—611no—
371C2×C4×Q8—611no—
372C2×C4×Q8—612no—
373C2×#117—612no—
374C2×#117—612no—
375C2×#117—612no—
376C22×C42—611no—
377#384—1221no—
378#382—1221no—
379#380—611no—
380#380—612no—
381#380C2×D6111yescharacteristic
382C4×C4⋊C4—1221no—
383C4×C4⋊C4—1221no—
384C4×C4⋊C4—1221no—
385C4×C4⋊C4—1221no—
386C4×C22⋊C4—611no—
387C4×C22⋊C4—612no—
388C4×C22⋊C4C2×D6111yescharacteristic
389#376—1221no—
390C43—1221no—
391#342—614no—
392#342—614no—
393#342—614no—
394#342C2×D6114yes—
395C61#2133211yescharacteristic, complemented, Sylow
396C22×Q8—612no—
397C22×Q8—611no—
398C22×Q8C4×D6111yescharacteristic
399C23×C4—611no—
400C23×C4—611no—
401C23×C4C22×D6111yescharacteristic
402C4⋊Q8—1221no—
403C4⋊Q8—1221no—
404C4⋊Q8—1221no—
405C4⋊Q8—1221no—
406C4⋊Q8—1221no—
407C4⋊Q8—1221no—
408C4⋊Q8—1221no—
409C4⋊Q8—1221no—
410#125—1222no—
411#125—1222no—
412#125—1222no—
413#125—1222no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—1222no—
419C22⋊Q8—1222no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C22⋊Q8—1221no—
423C22⋊Q8—1221no—
424C22⋊Q8—1221no—
425C22⋊Q8—1221no—
426C4×Q8—1222no—
427C4×Q8—1222no—
428C4×Q8—1222no—
429C4×Q8—1222no—
430C4×Q8—1221no—
431C4×Q8—1221no—
432C4×Q8—1221no—
433C4×Q8—1221no—
434C4×Q8—1221no—
435C4×Q8—1221no—
436C4×Q8—1221no—
437C4×Q8—1221no—
438#117—618no—
439#117—1222no—
440#117—1222no—
441#117—1222no—
442#117—1222no—
443#117—1224no—
444#117—1228no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—612no—
447C2×C4⋊C4—612no—
448C2×C4⋊C4—612no—
449C2×C4⋊C4—612no—
450C2×C4⋊C4—612no—
451C2×C4⋊C4—612no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4C4×D6112yes—
458C2×C4⋊C4C4×D6111yescharacteristic
459C2×C22⋊C4—612no—
460C2×C22⋊C4—612no—
461C2×C22⋊C4—612no—
462C2×C22⋊C4C22×D6112yes—
463C2×C22⋊C4C22×D6112yes—
464C2×C22⋊C4C22×D6112yes—
465C2×C42—21no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—612no—
479C2×C42—612no—
480C2×C42—1222no—
481C2×C42—1222no—
482C2×C42—1222no—
483C2×C42—1221no—
484#95—21no—
485#95—21no—
486#95—1222no—
487#95—1222no—
488#95—1221no—
489#95—1221no—
490C24C23×D6111yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—42no—
494C2×Q8—1222no—
495C2×Q8—1222no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8—2442no—
499C2×Q8—2444no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—42no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—614no—
510C22×C4—614no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—2442no—
522C22×C4C2×C4×D6111yescharacteristic
523C22×C4C2×C4×D6112yes—
524C22×C4C2×C4×D6112yes—
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4D4×D6111yescharacteristic
527C22×C4D4×D6111yescharacteristic
528C22×C4D4×D6111yescharacteristic
529C22×C4D4×D6111yescharacteristic
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—1222no—
542C4⋊C4—1222no—
543C4⋊C4—1222no—
544C4⋊C4—1222no—
545C4⋊C4—1228no—
546C4⋊C4—1222no—
547C4⋊C4—1222no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—2442no—
551C4⋊C4—2444no—
552C4⋊C4—2444no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—24no—
557C22⋊C4—614no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1224no—
562C22⋊C4Q8×D6114yes—
563C42—42no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—1222no—
581C42—1222no—
582C42—1222no—
583C42—1222no—
584C42—1228no—
585C42—2442no—
586C42—2444no—
587C42—2444no—
588C23—41no—
589C23—41no—
590C23C22×C4×D6111yescharacteristic
591C23C2×D4×D6111yescharacteristic
592C23C2×D4×D6111yescharacteristic
593C23C2×Q8×D6112yes—
594C23#41×D6112yes—
595Q8—42no—
596Q8—42no—
597Q8—2442no—
598Q8—2444no—
599Q8—2444no—
600Q8—2442no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—614no—
623C2×C4—614no—
624C2×C4—614no—
625C2×C4—614no—
626C2×C4—612no—
627C2×C4—612no—
628C2×C4—612no—
629C2×C4—612no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1224no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4C22⋊C4×D6111yescharacteristic
650C2×C4C22⋊C4×D6111yescharacteristic
651C2×C4C22⋊C4×D6111yescharacteristic
652C2×C4C22⋊C4×D6111yescharacteristic
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—42no—
660C22—42no—
661C22C2×C22⋊C4×D6111yescharacteristic
662C22C4×Q8×D6112yes—
663C22C22⋊Q8×D6112yes—
664C22#124×D6111yescharacteristic
665C22C4⋊Q8×D6111yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—44no—
670C4—42no—
671C4—42no—
672C4—82no—
673C4—612no—
674C4—612no—
675C4—612no—
676C4—612no—
677C4—612no—
678C4—1221no—
679C4—1221no—
680C4—1221no—
681C4—4882no—
682C4—2444no—
683C4—2442no—
684C4—2442no—
685C4#1683973412yes—
686C2—22no—
687C2—21no—
688C2—22no—
689C2—21no—
690C2#391×D6111yescharacteristic
691C2#410×D6111yescharacteristic
692C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radical, cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21332
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
18. C2×#14519776C4semidirect
19. C2×#14519775C4semidirect
20. C2×#14519767C4semidirect
23. C2×Q8×Dic61C4semidirect
24. C2×#14519742C4semidirect
25. C2×#14519742C4semidirect
91. #14519733Q8semidirect
395. C61#21332semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
#214482212
C4×#145197332
#214468052
#214468042
#214468032
#214468022
#214455502
C61×#19962
#2133261