Finite Group Databasebeta

← #34324915

Subgroups — #34324915

Order 20224.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098867C211yesmaximal, characteristic, complemented
2C2×#19098663C211yesmaximal, characteristic
3#23768770C211yesmaximal, characteristic, complemented
4#23764735C211yesmaximal, characteristic, complemented
5#23764725C211yesmaximal, characteristic, complemented
6#23764548C211yesmaximal, characteristic, complemented
7#23764538C211yesmaximal, characteristic, complemented
8#23764370C211yesmaximal, characteristic, complemented
9#23764341C211yesmaximal, characteristic, complemented
10#23763734C211yesmaximal, characteristic
11#23763734C211yesmaximal, characteristic
12#23763661C211yesmaximal, characteristic
13#23763647C211yesmaximal, characteristic
14#23763400C211yesmaximal, characteristic
15C2×#554×C79C211yesmaximal, characteristic
16C22×#11929612C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18#19098867—24no—
19#19098663—24no—
20C2×#14579094C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×#14579084C2211yescharacteristic
25C2×#14579084C2211yescharacteristic
26C2×#14579084C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579072C2211yescharacteristic
31#19098496—21no—
32#19098496—21no—
33#19098470—21no—
34#19098469C2211yescharacteristic
35#19098469C2211yescharacteristic
36#19098461C2211yescharacteristic
37#19098461C2211yescharacteristic
38#19098459—21no—
39#19098433C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098318C2211yescharacteristic
47#19098318C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50#554×C79—24no—
51#554×C79—24no—
52C2×C4⋊Q8×C79C2211yescharacteristic
53C2×#125×C79C2211yescharacteristic
54C2×#125×C79C2211yescharacteristic
55C2×C22⋊Q8×C79—21no—
56C2×C22⋊Q8×C79—21no—
57C2×C22⋊Q8×C79—21no—
58C2×C4×Q8×C79C2211yescharacteristic
59C2×C4×D4×C79C2211yescharacteristic
60C2×C4×D4×C79C2211yescharacteristic
61C2×C4×D4×C79C2211yescharacteristic
62C22×C4⋊C4×C79—21no—
63C22×Dic158C2311yescharacteristic
64C2×#11929612—22no—
65C2×#11929612—22no—
66C2×#11929612Q814yescomplemented
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71C4×Dic158—22no—
72C4×Dic158—22no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×Dic79⋊C4—21no—
79C2×Dic79⋊C4—21no—
80C2×Dic79⋊C4—21no—
81C2×C4×Dic79—21no—
82#14579094—22no—
83#14579094—22no—
84#14579092—22no—
85C4⋊(C79⋊C8)—22no—
86#14579084—22no—
87#14579084—22no—
88#14579084—22no—
89#14579082—22no—
90#14579082—22no—
91#14579082—22no—
92#14579072—22no—
93C79⋊#95—21no—
94C79⋊#95—21no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C79⋊#95—21no—
98C79⋊#95—21no—
99C22×Q8×C79—21no—
100C22×Q8×C79D411yescharacteristic
101C22×D4×C79C2311yescharacteristic
102C23×C4×C79—21no—
103C23×C4×C79—21no—
104C23×C4×C79—21no—
105C4⋊Q8×C79—22no—
106C4⋊Q8×C79—22no—
107#125×C79—22no—
108#125×C79—22no—
109#125×C79—22no—
110#125×C79D414yes—
111C22⋊Q8×C79—28no—
112C22⋊Q8×C79—28no—
113C22⋊Q8×C79—28no—
114C4×Q8×C79—22no—
115C4×Q8×C79—22no—
116C4×D4×C79—22no—
117C4×D4×C79—22no—
118C4×D4×C79—22no—
119C4×D4×C79—22no—
120C4×D4×C79—22no—
121C4×D4×C79D414yes—
122C2×C4⋊C4×C79—28no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79—21no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C4⋊C4×C79D411yescharacteristic
129C2×C4⋊C4×C79D411yescharacteristic
130C2×C4⋊C4×C79D411yescharacteristic
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79C2311yescharacteristic
133C2×C4⋊C4×C79C2311yescharacteristic
134C2×C22⋊C4×C79—21no—
135C2×C22⋊C4×C79—21no—
136C2×C22⋊C4×C79—21no—
137C2×C42×C79C2311yescharacteristic
138C2×C42×C79C2311yescharacteristic
139C2×C42×C79C2311yescharacteristic
140C2×Dic158—21no—
141C2×Dic158—21no—
142C2×Dic158—21no—
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158C2×Q812yes—
146C22×Dic79—21no—
147C22×Dic79—21no—
148C22×Dic79—21no—
149C22×Dic79—21no—
150#11929612—28no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8C2×Q812yes—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—21no—
168C4⋊Dic79—21no—
169C4⋊Dic79—42no—
170C4⋊Dic79—81no—
171Dic79⋊C4—42no—
172Dic79⋊C4—81no—
173Dic79⋊C4—81no—
174C4×Dic79—42no—
175C24×C79—21no—
176C2×Q8×C79—24no—
177C2×Q8×C79—22no—
178C2×Q8×C79—22no—
179C2×Q8×C79—41no—
180C2×Q8×C79—81no—
181C2×Q8×C79—81no—
182C2×D4×C79—21no—
183C2×D4×C79—21no—
184C2×D4×C79—21no—
185C2×D4×C79C2×D412yes—
186C2×D4×C79C2×Q812yes—
187C2×D4×C79#4112yes—
188C22×C4×C79—24no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—24no—
193C22×C4×C79—24no—
194C22×C4×C79—42no—
195C22×C4×C79—42no—
196C22×C4×C79—81no—
197C22×C4×C79—81no—
198C22×C4×C79—81no—
199C22×C4×C79—81no—
200C22×C4×C79C2×D411yescharacteristic
201C22×C4×C79C2×D411yescharacteristic
202C22×C4×C79C2×D411yescharacteristic
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2411yescharacteristic
207C4⋊C4×C79—24no—
208C4⋊C4×C79—24no—
209C4⋊C4×C79—24no—
210C4⋊C4×C79—22no—
211C4⋊C4×C79—24no—
212C4⋊C4×C79—24no—
213C4⋊C4×C79—22no—
214C4⋊C4×C79—22no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—21no—
218C4⋊C4×C79C2×D412yes—
219C4⋊C4×C79C2×D412yes—
220C4⋊C4×C79C2×D412yes—
221C22⋊C4×C79—24no—
222C22⋊C4×C79—24no—
223C22⋊C4×C79—24no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—21no—
227C42×C79—21no—
228C42×C79C2×D412yes—
229C42×C79C2×D412yes—
230C23×C79—22no—
231C23×C79—22no—
232C23×C79—22no—
233C23×C79—41no—
234C23×C79—41no—
235C23×C79—41no—
236C23×C79—41no—
237C23×C79C22×D411yescharacteristic
238Q8×C79—44no—
239Q8×C79—84no—
240D4×C79—22no—
241D4×C79—22no—
242D4×C79—22no—
243D4×C79C22⋊Q814yes—
244C2×C4×C79—21no—
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
249C2×C4×C79—21no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—22no—
254C2×C4×C79—22no—
255C2×C4×C79—22no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—48no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—41no—
268C2×C4×C79—41no—
269C2×C4×C79—84no—
270C2×C4×C79—84no—
271C2×C4×C79#12012yes—
272C2×C4×C79#12012yes—
273C2×C4×C79#13712yes—
274C2×C4×C79C22×D411yescharacteristic
275C2×C4×C79C22×D411yescharacteristic
276C2×C4×C79C22×Q811yescharacteristic
277C2×C4×C79C2×#4111yescharacteristic
278C2×C4×C792−1+411yescharacteristic
279C2×C4×C792−1+411yescharacteristic
280C2×Dic79—22no—
281C2×Dic79—41no—
282C2×Dic79—41no—
283C2×Dic79—41no—
284C2×Dic79—41no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292Dic158—22no—
293Dic158—22no—
294Dic158—41no—
295Dic158—41no—
296C79⋊C8—22no—
297C79⋊C8—41no—
298C79⋊C8—41no—
299C79⋊C8—41no—
300C22×C79—24no—
301C22×C79—42no—
302C22×C79—42no—
303C22×C79—42no—
304C22×C79—42no—
305C22×C79—42no—
306C22×C79—42no—
307C22×C79C2×#12011yescharacteristic
308C22×C79#54811yescharacteristic
309C22×C79D4×Q811yescharacteristic
310C22×C79C2×#13711yescharacteristic
311C22×C79#57511yescharacteristic
312C22×C79#57611yescharacteristic
313C22×C79#57711yescharacteristic
314C4×C79—22no—
315C4×C79—22no—
316C4×C79—22no—
317C4×C79—41no—
318C4×C79—42no—
319C4×C79—41no—
320C4×C79—41no—
321C4×C79—42no—
322C4×C79—42no—
323C4×C79C2×C22⋊Q811yescharacteristic
324C4×C79#53611yescharacteristic
325C4×C79#54811yescharacteristic
326C4×C79D4×Q811yescharacteristic
327Dic79—42no—
328Dic79—81no—
329Dic79—81no—
330Dic79—81no—
331#24349—791nomaximal, Sylow
332C2×C79—44no—
333C2×C79#240911yescharacteristic
334C2×C79#300711yescharacteristic
335C2×C79#301211yescharacteristic
336C2×C79#337011yescharacteristic
337C2×C79#337211yescharacteristic
338C2×C79#338511yescharacteristic
339C2×C79#338811yescharacteristic
340C2×#554D7911yescharacteristic
341C2×#479—791no—
342C2×#440—791no—
343#2582—791no—
344#2059—791no—
345#2057—791no—
346#2026—791no—
347#2024—791no—
348#1992—791no—
349#1985—791no—
350#1877—791no—
351#1877—791no—
352#1864—791no—
353#1862—791no—
354#1802—791no—
355C79#2434911yescharacteristic, complemented, Sylow
356C22×SD16—791no—
357#554—24no—
358#554—24no—
359C2×C4⋊Q8C2×D7911yescharacteristic
360C2×#125C2×D7911yescharacteristic
361C2×#125C2×D7911yescharacteristic
362C2×C22⋊Q8—21no—
363C2×C22⋊Q8—21no—
364C2×C22⋊Q8—21no—
365C2×C4×Q8—791no—
366C2×C4×Q8C2×D7911yescharacteristic
367C2×C4×D4C2×D7911yescharacteristic
368C2×C4×D4C2×D7911yescharacteristic
369C2×C4×D4C2×D7911yescharacteristic
370C22×C4⋊C4—21no—
371#479—1584no—
372#440—1584no—
373C2×#107—791no—
374C2×#107—791no—
375C2×#106—791no—
376C2×C4⋊C8—791no—
377C2×#103—791no—
378C2×#103—791no—
379C2×#103—791no—
380C2×#102—791no—
381C2×#102—791no—
382C2×#102—791no—
383C2×#97—791no—
384#398—1581no—
385#398—1581no—
386#391—791no—
387#391—791no—
388#391—1581no—
389#389—791no—
390#389—791no—
391#389—1581no—
392#384—791no—
393#340—791no—
394#340—791no—
395#340—791no—
396#340—791no—
397#340—791no—
398#340—791no—
399#336—791no—
400#336—791no—
401#336—791no—
402#336—791no—
403C22×Q8—21no—
404C22×Q8—791no—
405C22×Q8C22⋊D7911yescharacteristic
406C22×D4C22×D7911yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—21no—
410C2×SD16—794no—
411C2×SD16—1582no—
412C2×SD16—1582no—
413C22×C8—791no—
414C22×C8—791no—
415C22×C8—791no—
416C22×C8—791no—
417C4⋊Q8—22no—
418C4⋊Q8—22no—
419#125—22no—
420#125—22no—
421#125—22no—
422#125C22⋊D7914yes—
423C22⋊Q8—28no—
424C22⋊Q8—28no—
425C22⋊Q8—28no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—1582no—
429C4×Q8—1582no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4C22⋊D7914yes—
436C2×C4⋊C4—28no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—791no—
443C2×C4⋊C4—791no—
444C2×C4⋊C4—791no—
445C2×C4⋊C4—1581no—
446C2×C4⋊C4—1581no—
447C2×C4⋊C4—1581no—
448C2×C4⋊C4—1581no—
449C2×C4⋊C4—1581no—
450C2×C4⋊C4C22⋊D7911yescharacteristic
451C2×C4⋊C4C22⋊D7911yescharacteristic
452C2×C4⋊C4C22⋊D7911yescharacteristic
453C2×C4⋊C4C22×D7911yescharacteristic
454C2×C4⋊C4C22×D7911yescharacteristic
455C2×C4⋊C4C22×D7911yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—1581no—
460C2×C42C22×D7911yescharacteristic
461C2×C42C22×D7911yescharacteristic
462C2×C42C22×D7911yescharacteristic
463#107—1582no—
464#107—1582no—
465#106—1582no—
466C4⋊C8—1582no—
467#103—1582no—
468#103—1582no—
469#103—1582no—
470#102—1582no—
471#102—1582no—
472#102—1582no—
473#97—1582no—
474#95—1581no—
475#95—1581no—
476#95—1581no—
477#95—1581no—
478#95—1581no—
479#95—1581no—
480C24—21no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—41no—
485C2×Q8—81no—
486C2×Q8—81no—
487C2×Q8—792no—
488C2×Q8—1581no—
489C2×Q8—1581no—
490C2×Q8—1581no—
491C2×Q8—1581no—
492C2×Q8—1581no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4C2×C22⋊D7912yes—
497C2×D4Q8×D7912yes—
498C2×D4#1192962512yes—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—1581no—
512C22×C4—1581no—
513C22×C4—1581no—
514C22×C4—1581no—
515C22×C4C2×C22⋊D7911yescharacteristic
516C22×C4C2×C22⋊D7911yescharacteristic
517C22×C4C2×C22⋊D7911yescharacteristic
518C22×C4C2×C22⋊D7911yescharacteristic
519C22×C4C2×C22⋊D7911yescharacteristic
520C22×C4C2×C22⋊D7911yescharacteristic
521C22×C4C23×D7911yescharacteristic
522SD16—1588no—
523C2×C8—792no—
524C2×C8—1581no—
525C2×C8—1581no—
526C2×C8—1581no—
527C2×C8—1581no—
528C2×C8—1581no—
529C2×C8—1581no—
530C2×C8—1581no—
531C2×C8—1581no—
532C2×C8—1581no—
533C2×C8—1581no—
534C2×C8—1581no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—3162no—
547C4⋊C4—3162no—
548C4⋊C4—6321no—
549C4⋊C4—6321no—
550C4⋊C4—6321no—
551C4⋊C4—1581no—
552C4⋊C4—1581no—
553C4⋊C4—1581no—
554C4⋊C4—1581no—
555C4⋊C4—1581no—
556C4⋊C4—1581no—
557C4⋊C4C2×C22⋊D7912yes—
558C4⋊C4C2×C22⋊D7912yes—
559C4⋊C4C2×C22⋊D7912yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—3162no—
568C42C2×C22⋊D7912yes—
569C42C2×C22⋊D7912yes—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×C22⋊D7911yescharacteristic
578Q8—44no—
579Q8—84no—
580Q8—3161no—
581Q8—3161no—
582Q8—1582no—
583Q8—1582no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4#1457913714yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—48no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—84no—
614C2×C4—84no—
615C2×C4—3161no—
616C2×C4—3161no—
617C2×C4—3161no—
618C2×C4—3161no—
619C2×C4—3161no—
620C2×C4—3161no—
621C2×C4—3161no—
622C2×C4—3161no—
623C2×C4—3161no—
624C2×C4—3161no—
625C2×C4—3161no—
626C2×C4—1582no—
627C2×C4#1457913012yes—
628C2×C4#1457913012yes—
629C2×C4#1457919112yes—
630C2×C4C22×C22⋊D7911yescharacteristic
631C2×C4C22×C22⋊D7911yescharacteristic
632C2×C4C2×Q8×D7911yescharacteristic
633C2×C4C2×#1192962511yescharacteristic
634C2×C4#1457920911yescharacteristic
635C2×C4#1457920911yescharacteristic
636C8—3161no—
637C8—3161no—
638C8—3161no—
639C8—1582no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22C2×#1457913011yescharacteristic
648C22#1909922411yescharacteristic
649C22Q8×C22⋊D7911yescharacteristic
650C22C2×#1457919111yescharacteristic
651C22#1909936111yescharacteristic
652C22#1909936611yescharacteristic
653C22#1909937411yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—42no—
663C4—3162no—
664C4—6321no—
665C4—6321no—
666C4—6321no—
667C4C2×#1457913711yescharacteristic
668C4#1909913711yescharacteristic
669C4#1909922411yescharacteristic
670C4Q8×C22⋊D7911yescharacteristic
671C2—44no—
672C2#2376675911yescharacteristic
673C2#2377266011yescharacteristic
674C2#2377270411yescharacteristic
675C2#2377615311yescharacteristic
676C2#2377618111yescharacteristic
677C2#2377631011yescharacteristic
678C2#2377634511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC2×#554×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#554D79
hypocenterC79#24349
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#19098867C2semidirect
3. #23768770C2semidirect
4. #23764735C2semidirect
5. #23764725C2semidirect
6. #23764548C2semidirect
7. #23764538C2semidirect
8. #23764370C2semidirect
9. #23764341C2semidirect
66. C2×#11929612Q8semidirect
355. C79#24349semidirect

Maximal subgroups

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

subgroupindex
C2×#190988672
C2×#190986632
#237687702
#237647352
#237647252
#237645482
#237645382
#237643702
#237643412
#237637342
#237636612
#237636472
#237634002
C2×#554×C792
#2434979