Finite Group Databasebeta

← #29585449

Subgroups — #29585449

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2C2×#16839744C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4#21445538C211yesmaximal, characteristic, complemented
5#21445530C211yesmaximal, characteristic, complemented
6#21445529C211yesmaximal, characteristic, complemented
7C61×#1736C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840243—22no—
11#16840243—22no—
12#16840243—22no—
13#16840243—22no—
14C2×#14519742—21no—
15C2×#14519739—21no—
16C2×C4×C22⋊D61—22no—
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519735C412yescomplemented
20C2×C4⋊C4×D61C412yescomplemented
21#16839744—22no—
22#16839744C414yescomplemented
23C2×#14519695—21no—
24C2×#14519693—21no—
25#16839735—22no—
26#16839735C414yescomplemented
27C2×#14519691—22no—
28#16839524—22no—
29#16839523—22no—
30#16839522—22no—
31C22×M16×C61C2211yescharacteristic
32C2×#117×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C61×#340—22no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C2×#11758222D412yes—
46C2×#11758222Q812yes—
47C22×Dic122D411yescharacteristic
48C22×D244D411yescharacteristic
49C22×C22⋊D61D412yes—
50C22×C4×D61—22no—
51C22×C4×D61C2×C412yes—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194C2×C412yescomplemented
58C22×#92418—21no—
59#14519742—24no—
60#14519742—24no—
61#14519739—24no—
62#14519739—24no—
63C4×C22⋊D61—28no—
64C4×C22⋊D61—28no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68#14519736—21no—
69#14519736—21no—
70#14519736C2×C412yescomplemented
71#14519736D412yes—
72#14519736D412yes—
73#14519735—24no—
74#14519735—24no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×#11758196—22no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—24no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—22no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—21no—
87#14519695—24no—
88#14519693—24no—
89#14519691—28no—
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61C2×C412yescomplemented
98C22×C8×C61—21no—
99#117×C61—21no—
100#117×C61—21no—
101#117×C61—21no—
102#117×C61C2×C412yescomplemented
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61C2×C412yes—
108C2×C4⋊C4×C61D412yes—
109C2×C4⋊C4×C61D412yes—
110C2×C22⋊C4×C61—21no—
111C2×C42×C61—21no—
112C24×C61C2×D411yescharacteristic
113C23×D61C22⋊C412yes—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—41no—
118C22×C4×C61—82no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×Q811yescharacteristic
129C22×C4×C61#4111yescharacteristic
130C22×C4×C61#4111yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61#4111yescharacteristic
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61—22no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61C22⋊C414yes—
138C2×C22⋊D61C4⋊C414yes—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—41no—
142C22×Dic61C22⋊C412yes—
143#11758222—22no—
144#11758222—22no—
145#11758222—22no—
146#11758222—22no—
147#11758222—22no—
148#11758222—22no—
149#11758222—22no—
150#11758222—22no—
151#11758222—22no—
152#11758222—22no—
153#11758222—22no—
154#11758222—22no—
155#11758222—22no—
156#11758222—22no—
157#11758222—22no—
158#11758222—22no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244C22⋊C412yes—
164C2×D244C4⋊C412yes—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—28no—
170C2×C4×D61—84no—
171C2×C4×D61C4214yes—
172C2×C4×D61C4⋊C414yes—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122C22⋊C412yes—
178C2×Dic122C4⋊C412yes—
179M16×C61—22no—
180M16×C61—22no—
181M16×C61—41no—
182M16×C61—41no—
183C2×C8×C61—22no—
184C2×C8×C61—41no—
185C2×C8×C61—41no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61C22⋊C414yes—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—41no—
194C42×C61—22no—
195C42×C61—41no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—41no—
200#11758198—28no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—22no—
204C4⋊Dic61—41no—
205C4⋊Dic61C22⋊C412yes—
206C4⋊Dic61C22⋊C412yes—
207#11758196—28no—
208C4×Dic61—28no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—41no—
213#11758194—22no—
214#11758194—22no—
215#11758194—41no—
216#11758194—41no—
217C2×#92418—22no—
218C2×#92418—41no—
219C2×#92418—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61C2×C22⋊C411yescharacteristic
224C23×C61C2×C4⋊C411yescharacteristic
225C23×C61#12011yescharacteristic
226C23×C61#12011yescharacteristic
227C23×C61#12311yescharacteristic
228C23×C61#12311yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61#9514yes—
234C2×C4×C61—24no—
235C2×C4×C61—44no—
236C2×C4×C61—42no—
237C2×C4×C61—82no—
238C2×C4×C61—82no—
239C2×C4×C61—81no—
240C2×C4×C61—81no—
241C2×C4×C61C2×C4211yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C4⋊C411yescharacteristic
246C2×C4×C61C2×C4⋊C411yescharacteristic
247C2×C4×C61#11711yescharacteristic
248C2×C4×C61#11711yescharacteristic
249C2×C4×C61C4×D411yescharacteristic
250C2×C4×C61C4×D411yescharacteristic
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C4×D411yescharacteristic
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61#12111yescharacteristic
260C2×C4×C61#12111yescharacteristic
261C2×C4×C61#12111yescharacteristic
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61C22⋊Q811yescharacteristic
264C2×C4×C61C22⋊Q811yescharacteristic
265C2×C4×C61C22⋊Q811yescharacteristic
266C2×C4×C61C22⋊Q811yescharacteristic
267C2×C4×C61#12311yescharacteristic
268C2×C4×C61#12311yescharacteristic
269C22⋊D61—24no—
270C22⋊D61—24no—
271C22⋊D61—24no—
272C22⋊D61—24no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—81no—
281C2×Dic61—81no—
282C2×Dic61#9514yes—
283D244—22no—
284D244—22no—
285D244—22no—
286D244—22no—
287C4×D61—24no—
288C4×D61—24no—
289C4×D61—24no—
290C4×D61—24no—
291C4×D61—88no—
292Dic122—22no—
293Dic122—22no—
294Dic122—22no—
295Dic122—22no—
296C8×C61—42no—
297#92418—42no—
298#10765—611nomaximal, Sylow
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61C2×#9511yescharacteristic
310C22×C61#37911yescharacteristic
311C22×C61#38111yescharacteristic
312C22×C61#38511yescharacteristic
313C22×C61#38511yescharacteristic
314C22×C61#38611yescharacteristic
315C22×C61#38611yescharacteristic
316C2×D61—24no—
317C2×D61—44no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—44no—
321C4×C61—44no—
322C4×C61—82no—
323C4×C61C4×C22⋊C411yescharacteristic
324C4×C61C4×C22⋊C411yescharacteristic
325C4×C61#38011yescharacteristic
326C4×C61#38011yescharacteristic
327C4×C61#38511yescharacteristic
328C4×C61#38511yescharacteristic
329C4×C61#38611yescharacteristic
330C4×C61#38611yescharacteristic
331Dic61—24no—
332Dic61—42no—
333Dic61—42no—
334Dic61—82no—
335C2×#520—611no—
336C2×#413—611no—
337C2×#410—611no—
338#1736—611no—
339#1736D6111yescharacteristic, complemented
340#1733—611no—
341#1733—611no—
342C2×C61—21no—
343C2×C61—21no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—21no—
348C2×C61C22⋊#9511yescharacteristic
349C2×C61#179511yescharacteristic
350C2×C61#179611yescharacteristic
351D61—44no—
352C22×#41—611no—
353C22×M16—611no—
354C22×M16C2×D6111yescharacteristic
355#520—1222no—
356#520—1222no—
357#520—1222no—
358#520—1222no—
359C2×C4×Q8—1221no—
360C2×C4×D4—1221no—
361C2×C4×D4—1222no—
362C2×#117—611no—
363C2×#117—612no—
364C2×#117—611no—
365C2×#117C2×D6111yescharacteristic
366C22×C4⋊C4—612no—
367C22×C4⋊C4C2×D6111yescharacteristic
368#413—614no—
369#413—1222no—
370C2×#101—1221no—
371C2×#100—1221no—
372#410—614no—
373#410—1222no—
374C2×#99—1222no—
375#340—22no—
376#340—1222no—
377#339—1222no—
378#339—1222no—
379C61#1076511yescharacteristic, complemented, Sylow
380C2×#41—612no—
381C2×#41—612no—
382C2×#41—612no—
383C2×#41—612no—
384C2×#41—1221no—
385C2×#41—1221no—
386C2×#41—1221no—
387C2×#41—1221no—
388C2×#41—1221no—
389C2×#41—1221no—
390C2×#41—1221no—
391C2×#41—1221no—
392C22×Q8—611no—
393C22×D4—612no—
394C22×D4—611no—
395C23×C4—21no—
396C23×C4—612no—
397C23×C4—1222no—
398C23×C4C22×D6111yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—612no—
405C2×M16—1221no—
406C2×M16—1221no—
407C2×M16—1221no—
408C2×M16—1221no—
409C2×M16—1221no—
410C2×M16C4×D6112yescomplemented
411C22×C8—21no—
412C22×C8—1221no—
413C4×Q8—1224no—
414C4×Q8—1224no—
415C4×D4—1224no—
416C4×D4—1224no—
417C4×D4—1228no—
418C4×D4—1228no—
419#117—21no—
420#117—21no—
421#117—21no—
422#117—612no—
423#117—612no—
424#117—612no—
425#117—1224no—
426#117—1221no—
427#117—1221no—
428#117—1224no—
429#117—1221no—
430#117—1221no—
431#117—1221no—
432#117C4×D6112yescomplemented
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—1224no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1224no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4C4×D6112yes—
444C2×C4⋊C4D24412yes—
445C2×C4⋊C4C22⋊D6112yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1222no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C42—21no—
451C2×C42—1222no—
452C2×C42—1221no—
453C2×C42—1221no—
454#101—1224no—
455#100—1224no—
456#99—1228no—
457C24—612no—
458C24D4×D6111yescharacteristic
459#41—1222no—
460#41—1222no—
461#41—1222no—
462#41—1222no—
463#41—1222no—
464#41—1222no—
465#41—1222no—
466#41—1222no—
467#41—1222no—
468#41—1222no—
469#41—1222no—
470#41—1222no—
471#41—1222no—
472#41—1222no—
473#41—1222no—
474#41—1222no—
475C2×Q8—612no—
476C2×Q8—612no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×D4—614no—
482C2×D4—614no—
483C2×D4—612no—
484C2×D4—612no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1221no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—41no—
497C22×C4—82no—
498C22×C4—612no—
499C22×C4—614no—
500C22×C4—614no—
501C22×C4—1228no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—4884no—
509C22×C4—2441no—
510C22×C4C2×C4×D6111yescharacteristic
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4C2×C4×D6111yescharacteristic
513C22×C4C2×D24411yescharacteristic
514C22×C4#1175822211yescharacteristic
515C22×C4#1175822211yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C22×C4D4×D6111yescharacteristic
518C22×C4D4×D6111yescharacteristic
519C22×C4D4×D6111yescharacteristic
520C22×C4#1175822411yescharacteristic
521C22×C4Q8×D6111yescharacteristic
522C22×C4#1175822611yescharacteristic
523C22×C4C2×C22⋊D6111yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—1222no—
529M16—1222no—
530M16—2441no—
531M16—2441no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—1222no—
536C2×C8—2441no—
537C2×C8—2441no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—41no—
543C4⋊C4—612no—
544C4⋊C4—612no—
545C4⋊C4—1228no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1222no—
549C4⋊C4—2441no—
550C4⋊C4#1175819814yes—
551C22⋊C4—22no—
552C22⋊C4—41no—
553C22⋊C4—1228no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—2441no—
558C42—22no—
559C42—41no—
560C42—1228no—
561C42—1222no—
562C42—1222no—
563C42—1222no—
564C42—2441no—
565C23—41no—
566C23—41no—
567C23—614no—
568C23—1222no—
569C23—1222no—
570C23—2442no—
571C23—2442no—
572C23C22⋊C4×D6111yescharacteristic
573C23C22⋊C4×D6111yescharacteristic
574C23C4⋊C4×D6111yescharacteristic
575C23#1451974511yescharacteristic
576C23#1451974711yescharacteristic
577C23#1451975911yescharacteristic
578C23#1451976211yescharacteristic
579Q8—1222no—
580Q8—1222no—
581Q8—1222no—
582Q8—1222no—
583D4—1224no—
584D4—1224no—
585D4—1224no—
586D4—1224no—
587D4—1222no—
588D4—1222no—
589D4—1222no—
590D4—1222no—
591C2×C4—24no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—614no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—4888no—
608C2×C4—4881no—
609C2×C4—4881no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4C42×D6111yescharacteristic
614C2×C4C22⋊C4×D6111yescharacteristic
615C2×C4C22⋊C4×D6111yescharacteristic
616C2×C4C2×#1175819811yescharacteristic
617C2×C4C4⋊C4×D6111yescharacteristic
618C2×C4C4⋊C4×D6111yescharacteristic
619C2×C4#1451973411yescharacteristic
620C2×C4#1451973511yescharacteristic
621C2×C4#1451973711yescharacteristic
622C2×C4#1451973711yescharacteristic
623C2×C4C4×C22⋊D6111yescharacteristic
624C2×C4C4×C22⋊D6111yescharacteristic
625C2×C4#1451973911yescharacteristic
626C2×C4#1451973911yescharacteristic
627C2×C4C4×D24411yescharacteristic
628C2×C4C4×D24411yescharacteristic
629C2×C4#1451974511yescharacteristic
630C2×C4#1451974711yescharacteristic
631C2×C4#1451974811yescharacteristic
632C2×C4#1451975011yescharacteristic
633C2×C4#1451975011yescharacteristic
634C2×C4#1451975211yescharacteristic
635C2×C4#1451975311yescharacteristic
636C2×C4#1451975511yescharacteristic
637C2×C4#1451975511yescharacteristic
638C2×C4#1451975711yescharacteristic
639C2×C4#1451975911yescharacteristic
640C2×C4#1451976211yescharacteristic
641C8—42no—
642C8—2442no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—1224no—
654C22—2444no—
655C22—2444no—
656C22—2442no—
657C22—2442no—
658C22#95×D6111yescharacteristic
659C22#1683961711yescharacteristic
660C22#1683962411yescharacteristic
661C22#1683963311yescharacteristic
662C22#1683963611yescharacteristic
663C22#1683963811yescharacteristic
664C22#1683964011yescharacteristic
665C4—44no—
666C4—82no—
667C4—1224no—
668C4—4882no—
669C4—2442no—
670C4—2442no—
671C4#1683960911yescharacteristic
672C4C4×#1175819811yescharacteristic
673C4#1683961911yescharacteristic
674C4#1683962111yescharacteristic
675C4#1683963311yescharacteristic
676C4#1683963611yescharacteristic
677C4#1683963811yescharacteristic
678C4#1683964011yescharacteristic
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—2444no—
686C2#2144404011yescharacteristic
687C2#2144578611yescharacteristic
688C2#2144579111yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1736C2
socleC22×C61#379
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1736D61
hypocenterC61#10765
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #21445538C2semidirect
5. #21445530C2semidirect
6. #21445529C2semidirect
7. C61×#1736C2semidirect
19. C2×#14519735C4semidirect
20. C2×C4⋊C4×D61C4semidirect
22. #16839744C4semidirect
26. #16839735C4semidirect
57. C2×#11758194C2×C4semidirect
70. #14519736C2×C4semidirect
97. C2×M16×C61C2×C4semidirect
102. #117×C61C2×C4semidirect
339. #1736D61semidirect
379. C61#10765semidirect
410. C2×M16C4×D61semidirect
432. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402432
C2×#168397442
C2×#168397352
#214455382
#214455302
#214455292
C61×#17362
#1076561