Finite Group Databasebeta

← #25101944

Subgroups — #25101944

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic
2#19136990C211yesmaximal, characteristic, complemented
3C4×#13063281C211yesmaximal, characteristic, complemented
4#19135580C211yesmaximal, characteristic, complemented
5#19135579C211yesmaximal, characteristic, complemented
6#19135432C211yesmaximal, characteristic
7#19135050C214yesmaximal, complemented
8#99×Dic43C214yesmaximal, complemented
9C43×#1964C211yesmaximal, characteristic
10#14583430—21no—
11#14583430—21no—
12#14583430—21no—
13#14583430—21no—
14#14583430—21no—
15#14583430—21no—
16#14583430—21no—
17#14583430—21no—
18C2×#13063318C412yescomplemented
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063312C411yescharacteristic, complemented
21C2×#13063306C2212yes—
22C2×#13063304C2211yescharacteristic
23C2×#13063290C411yescharacteristic, complemented
24C2×D4×Dic43C411yescharacteristic, complemented
25C2×D4×Dic43C2212yes—
26C2×#13063281C412yescomplemented
27C2×#13063281C2212yes—
28C22×C4×Dic43C2211yescharacteristic
29C2×#13063240C2214yes—
30#14582766—21no—
31#14582764—21no—
32#14582760C2212yes—
33#14582759C2211yescharacteristic
34C4⋊C4×Dic43—21no—
35C4×Dic43⋊C4—21no—
36#14582750—21no—
37C22⋊C4×Dic43C2212yes—
38C22⋊C4×Dic43C2212yes—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582744—21no—
41#14582744—21no—
42C42×Dic43—21no—
43#14582665C2214yes—
44#14582665C2214yes—
45C2×#121×C43C2211yescharacteristic
46C2×#99×C43C2214yes—
47C43×#380C2211yescharacteristic
48C4×C22⋊C4×C43C2211yescharacteristic
49C22×Dic86C2×C411yescharacteristic
50C23×Dic43C2×C412yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53#13063318—22no—
54#13063318—22no—
55#13063318—22no—
56#13063318—22no—
57#13063316—21no—
58#13063316—21no—
59#13063316—21no—
60#13063316—21no—
61#13063312—21no—
62#13063312—21no—
63#13063312—21no—
64#13063312—21no—
65#13063306—22no—
66#13063306—22no—
67#13063306—22no—
68#13063306—22no—
69#13063304—21no—
70#13063304—21no—
71#13063304—21no—
72#13063304—21no—
73#13063290—21no—
74#13063290—21no—
75#13063290—21no—
76#13063290—21no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43—22no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43—21no—
84D4×Dic43—21no—
85#13063281—24no—
86#13063281—24no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C412yes—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2×C412yes—
97C2×Dic43⋊C4C2×C412yes—
98C2×C22⋊Dic43C2×C412yes—
99C2×C22⋊Dic43C2×C412yes—
100C2×C22⋊Dic43C2×C412yes—
101C2×C22⋊Dic43C2312yes—
102C2×C22⋊Dic43C2312yes—
103C2×C22⋊Dic43C2312yes—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43C2×C412yes—
109C2×C4×Dic43C2×C411yescharacteristic
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43D411yescharacteristic
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121#13063240—28no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C22×D4×C43C2×C411yescharacteristic
129C22×D4×C43C2312yes—
130C23×C4×C43C2311yescharacteristic
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2×C412yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2312yes—
140C2×C42×C43—21no—
141#99×C43—28no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43C22×C412yes—
145C24×C43C2411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—24no—
151C2×D4×C43—24no—
152C2×D4×C43—42no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—42no—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—42no—
170C22×Dic43—44no—
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C412yes—
175C22×Dic43C22×C412yes—
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—42no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—24no—
195C22⋊C4×C43#4114yes—
196C42×C43—42no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C22⋊Dic43—24no—
207C22⋊Dic43#4114yes—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212C4⋊Dic43—42no—
213Dic43⋊C4—28no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220C4×Dic43—28no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—44no—
224C4×Dic43—44no—
225C4×Dic43—42no—
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22⋊C411yescharacteristic
234C4×Dic43C22⋊C411yescharacteristic
235C4×Dic43C22⋊C411yescharacteristic
236C4×Dic43C22⋊C411yescharacteristic
237C4×Dic43C22⋊C411yescharacteristic
238C4×Dic43C22⋊C411yescharacteristic
239C4×Dic43C22⋊C411yescharacteristic
240C4×Dic43C22⋊C411yescharacteristic
241C4×Dic43C22⋊C411yescharacteristic
242C23×C43—22no—
243C23×C43—24no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—42no—
247C23×C43—42no—
248C23×C43C23×C411yescharacteristic
249C23×C43C22×D411yescharacteristic
250C23×C43C22×D411yescharacteristic
251C23×C43C2×#4112yes—
252C23×C43C2×#4112yes—
253D4×C43—42no—
254D4×C43—44no—
255D4×C43—42no—
256D4×C43—42no—
257D4×C43—42no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—24no—
263C2×C4×C43—24no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43C2×C22⋊C411yescharacteristic
273C2×C4×C43C2×C22⋊C411yescharacteristic
274C2×C4×C43C2×C22⋊C411yescharacteristic
275C2×C4×C43C2×C22⋊C411yescharacteristic
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—24no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—44no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—44no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43C2×C22⋊C411yescharacteristic
303C2×Dic43C2×C22⋊C411yescharacteristic
304C2×Dic43C2×C22⋊C411yescharacteristic
305C2×Dic43C2×C22⋊C411yescharacteristic
306C2×Dic43C2×C22⋊C411yescharacteristic
307C2×Dic43C2×C22⋊C411yescharacteristic
308C2×Dic43C2×C22⋊C411yescharacteristic
309C2×Dic43C2×C22⋊C411yescharacteristic
310Dic86—42no—
311Dic86—42no—
312#21421—431nomaximal, Sylow
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—21no—
316C22×C43—21no—
317C22×C43—21no—
318C22×C43—21no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—84no—
325C22×C43C22×C22⋊C411yescharacteristic
326C22×C43C4×#4112yes—
327C22×C43#52512yes—
328C22×C43#53211yescharacteristic
329C22×C43#53211yescharacteristic
330C4×C43—21no—
331C4×C43—21no—
332C4×C43—21no—
333C4×C43—44no—
334C4×C43—42no—
335C4×C43—82no—
336C4×C43#41012yes—
337Dic43—21no—
338Dic43—21no—
339Dic43—21no—
340Dic43—21no—
341Dic43—21no—
342Dic43—21no—
343Dic43—21no—
344Dic43—44no—
345Dic43—42no—
346Dic43—42no—
347Dic43—82no—
348Dic43#41012yes—
349C2×#529—431no—
350#2283—431no—
351C4×#117—431no—
352#1996—431no—
353#1996—431no—
354#1964—431no—
355#1964D4311yescharacteristic
356#1899—434no—
357C4×#99—434no—
358C2×C43—22no—
359C2×C43—21no—
360C2×C43—21no—
361C2×C43—22no—
362C2×C43—82no—
363C2×C43#229711yescharacteristic
364C2×C43C2×#41011yescharacteristic
365C2×C43C2×#41011yescharacteristic
366#529—861no—
367#529—861no—
368#529—861no—
369#529—861no—
370#529—861no—
371#529—861no—
372#529—861no—
373#529—861no—
374C2×#126—432no—
375C2×#125—431no—
376C2×#124—431no—
377C2×#123—432no—
378C2×C22⋊Q8—431no—
379C2×#121C2×D4311yescharacteristic
380C2×C4×Q8—431no—
381C2×C4×D4—432no—
382C2×C4×D4—431no—
383C2×#117—432no—
384C2×#117—432no—
385C22×C42—431no—
386C2×#99—434no—
387C2×#99C2×D4314yes—
388#383—861no—
389#382—861no—
390#381—432no—
391#380—431no—
392#380C2×D4311yescharacteristic
393C4×C4⋊C4—861no—
394C4×C4⋊C4—861no—
395C4×C4⋊C4—861no—
396C4×C22⋊C4—431no—
397C4×C22⋊C4—432no—
398C4×C22⋊C4—432no—
399C4×C22⋊C4C2×D4311yescharacteristic
400#376—861no—
401#376—861no—
402C43—861no—
403#342—434no—
404#342—434no—
405C43#2142111yescharacteristic, complemented, Sylow
406C22×Q8—431no—
407C22×D4C4×D4311yescharacteristic
408C22×D4C22×D4312yes—
409C23×C4—431no—
410C23×C4—431no—
411C23×C4—432no—
412C23×C4C22×D4311yescharacteristic
413#126—862no—
414#126—862no—
415#126—862no—
416#126—862no—
417#125—861no—
418#125—861no—
419#125—861no—
420#125—861no—
421#124—861no—
422#124—861no—
423#124—861no—
424#124—861no—
425#123—862no—
426#123—862no—
427#123—862no—
428#123—862no—
429C22⋊Q8—861no—
430C22⋊Q8—861no—
431C22⋊Q8—861no—
432C22⋊Q8—861no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×Q8—861no—
440C4×Q8—861no—
441C4×D4—861no—
442C4×D4—861no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449#117—862no—
450#117—862no—
451#117—862no—
452#117—862no—
453#117—864no—
454#117—864no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—432no—
457C2×C4⋊C4—432no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—432no—
460C2×C4⋊C4—432no—
461C2×C4⋊C4—862no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4C4×D4311yescharacteristic
464C2×C22⋊C4—432no—
465C2×C22⋊C4—432no—
466C2×C22⋊C4—432no—
467C2×C22⋊C4—432no—
468C2×C22⋊C4—432no—
469C2×C22⋊C4—432no—
470C2×C22⋊C4C4×D4312yes—
471C2×C22⋊C4C22×D4312yes—
472C2×C22⋊C4C22×D4312yes—
473C2×C42—21no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—431no—
477C2×C42—431no—
478C2×C42—431no—
479C2×C42—431no—
480C2×C42—431no—
481C2×C42—431no—
482C2×C42—431no—
483C2×C42—431no—
484C2×C42—431no—
485C2×C42—431no—
486C2×C42—432no—
487C2×C42—862no—
488C2×C42—862no—
489C2×C42—862no—
490C2×C42—861no—
491#99—28no—
492#99—868no—
493#95—21no—
494#95—21no—
495#95—862no—
496#95—862no—
497#95—862no—
498#95—862no—
499#95—861no—
500#95—861no—
501C24C2×C4×D4312yes—
502C24C23×D4311yescharacteristic
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—1722no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—42no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—1722no—
537C22×C4—1724no—
538C22×C4C2×C4×D4312yes—
539C22×C4C2×C4×D4311yescharacteristic
540C22×C4C2×C4×D4311yescharacteristic
541C22×C4D4×D4311yescharacteristic
542C22×C4D4×D4311yescharacteristic
543C22×C4D4×D4311yescharacteristic
544C22×C4D4×D4311yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—868no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1722no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—24no—
564C22⋊C4—434no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C22⋊C4—862no—
571C22⋊C4—862no—
572C22⋊C4—862no—
573C22⋊C4—862no—
574C22⋊C4—864no—
575C22⋊C4#1062190014yes—
576C42—42no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—431no—
583C42—431no—
584C42—431no—
585C42—431no—
586C42—431no—
587C42—431no—
588C42—431no—
589C42—431no—
590C42—431no—
591C42—431no—
592C42—431no—
593C42—862no—
594C42—862no—
595C42—868no—
596C42—1722no—
597C42—1724no—
598C42—1724no—
599C23—22no—
600C23—24no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23C22×C4×D4311yescharacteristic
606C23C2×D4×D4311yescharacteristic
607C23C2×D4×D4311yescharacteristic
608C23#41×D4312yes—
609C23C2×#1062190012yes—
610Q8—1722no—
611Q8—1722no—
612D4—42no—
613D4—44no—
614D4—42no—
615D4—42no—
616D4—42no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—431no—
632C2×C4—431no—
633C2×C4—431no—
634C2×C4—431no—
635C2×C4—431no—
636C2×C4—431no—
637C2×C4—431no—
638C2×C4—431no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—864no—
653C2×C4—1724no—
654C2×C4—1721no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4—1724no—
658C2×C4—1722no—
659C2×C4—1722no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4—1722no—
665C2×C4C22⋊C4×D4311yescharacteristic
666C2×C4C22⋊C4×D4311yescharacteristic
667C2×C4C22⋊C4×D4311yescharacteristic
668C2×C4C22⋊C4×D4311yescharacteristic
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—84no—
681C22C2×C22⋊C4×D4311yescharacteristic
682C22C4×#1062190012yes—
683C22#1458340912yes—
684C22#1458344711yescharacteristic
685C22#1458344811yescharacteristic
686C4—21no—
687C4—21no—
688C4—21no—
689C4—44no—
690C4—42no—
691C4—82no—
692C4—432no—
693C4—861no—
694C4—861no—
695C4—861no—
696C4—861no—
697C4—861no—
698C4—861no—
699C4—861no—
700C4—3442no—
701C4—1724no—
702C4—1722no—
703C4—1722no—
704C4#1458287112yes—
705C2—22no—
706C2—21no—
707C2—21no—
708C2—22no—
709C2—82no—
710C2#1913708211yescharacteristic
711C2#410×D4311yescharacteristic
712C2C2×#1458287111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1964C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC24×C43C24
hypercenter#1964D43
hypocenterC43#21421
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19136990C2semidirect
3. C4×#13063281C2semidirect
4. #19135580C2semidirect
5. #19135579C2semidirect
7. #19135050C2semidirect
8. #99×Dic43C2semidirect
18. C2×#13063318C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063312C4semidirect
23. C2×#13063290C4semidirect
24. C2×D4×Dic43C4semidirect
26. C2×#13063281C4semidirect
405. C43#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
#191369902
C4×#130632812
#191355802
#191355792
#191354322
#191350502
#99×Dic432
C43×#19642
#2142143