Finite Group Databasebeta

← #612828

Subgroups — #612828

Order 512.

3340 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2853C212yesmaximal
2C2×#2486C211yesmaximal, characteristic
3C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
4#14919C212yesmaximal, complemented
5#14912C212yesmaximal
6#14794C214yesmaximal, complemented
7#14784C214yesmaximal, complemented
8#14705C212yesmaximal, complemented
9#14697C211yesmaximal, characteristic, complemented
10#14133C212yesmaximal, complemented
11#14029C212yesmaximal, complemented
12#13974C212yesmaximal, complemented
13#13904C211yesmaximal, characteristic, complemented
14#13880C211yesmaximal, characteristic, complemented
15#13876C212yesmaximal, complemented
16#13872C211yesmaximal, characteristic
17C4×#386C211yesmaximal, characteristic
18C22×#123C2212yes—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C23×C42C2212yes—
24#2853—216no—
25#2486—28no—
26C2×#398C2212yes—
27C2×#397C2212yes—
28C2×#389C2211yescharacteristic
29C2×#389C2212yes—
30C2×#389C2211yescharacteristic
31C2×#388C2214yes—
32C2×#388C2214yes—
33C2×#387C2214yes—
34C2×#387C2214yes—
35C2×#386C2212yes—
36C2×#386C2211yescharacteristic
37C2×#386C2211yescharacteristic
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#384C2212yes—
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#381C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4—28no—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2214yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C22×#95C2212yes—
57#1445C2214yes—
58#1445C2214yes—
59#1444C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2212yes—
65#1441C2214yes—
66#1440C2214yes—
67#1439C2212yes—
68#1439C2214yes—
69#1437C2212yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2211yescharacteristic
84C22⋊#95C2211yescharacteristic
85C4×#95C2212yes—
86C23×D4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C2×#123—28no—
94C2×#123—28no—
95C2×#123—44no—
96C2×C4×D4—24no—
97C2×C4×D4—24no—
98C2×C4×D4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—28no—
103C22×C4⋊C4D418yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C22⋊C4C2311yescharacteristic
119C22×C22⋊C4C2311yescharacteristic
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C42—24no—
130C22×C42—28no—
131C22×C42—28no—
132C22×C42—28no—
133C22×C42—44no—
134C22×C42C2312yes—
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2314yes—
138C22×C42C2314yes—
139C22×C42C2312yes—
140#398—28no—
141#397—28no—
142#389—24no—
143#389—24no—
144#389—28no—
145#388—216no—
146#388—216no—
147#387—216no—
148#387—216no—
149#386—28no—
150#386—24no—
151#386D418yes—
152#385—28no—
153#385—28no—
154#385—44no—
155#384—28no—
156#381—28no—
157#381—28no—
158#381—28no—
159#380—24no—
160#380—24no—
161#380—24no—
162#380—24no—
163#380—28no—
164C4×C4⋊C4—28no—
165C4×C4⋊C4—28no—
166C4×C4⋊C4—216no—
167C4×C22⋊C4—24no—
168C4×C22⋊C4—28no—
169C2×#95—28no—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C25C2411yescharacteristic
198C25C2411yescharacteristic
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4C2×D414yes—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—22no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—28no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—42no—
232C23×C4—44no—
233C23×C4C2×D418yes—
234C23×C4C2×D414yes—
235C23×C4C2×D414yes—
236C23×C4#4114yes—
237C23×C4#4114yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2414yes—
241C23×C4C2411yescharacteristic
242C23×C4C2411yescharacteristic
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2414yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253#123—432no—
254C4×D4—416no—
255C2×C4⋊C4—232no—
256C2×C4⋊C4—232no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×D418yes—
295C2×C4⋊C4#4118yes—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4C2×D414yes—
327C2×C22⋊C4C2×D418yes—
328C2×C22⋊C4#4114yes—
329C2×C42—232no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—22no—
336C2×C42—28no—
337C2×C42—28no—
338C2×C42—28no—
339C2×C42—28no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—44no—
346C2×C42—44no—
347C2×C42—432no—
348C2×C42#4118yes—
349#95—28no—
350#95—28no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—28no—
355#95—28no—
356#95—24no—
357#95—24no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—24no—
369#95—28no—
370#95—24no—
371#95—44no—
372#95—42no—
373#95—44no—
374#95—44no—
375#95C2×D418yes—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—22no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—22no—
390C24C22×D412yes—
391C24C22×D412yes—
392C24C22×D412yes—
393C24C2×#4112yes—
394C24C2×#4112yes—
395C24C2×#4112yes—
396C24H(5,𝔽2)12yes—
397C242−1+412yes—
398C24C2511yescharacteristic
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—28no—
402C2×D4—44no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—44no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—216no—
409C22×C4—28no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—216no—
419C22×C4—216no—
420C22×C4—216no—
421C22×C4—28no—
422C22×C4—216no—
423C22×C4—216no—
424C22×C4—216no—
425C22×C4—216no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—416no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—416no—
499C22×C4—48no—
500C22×C4—44no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—44no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4#123116yes—
513C22×C4C22×D414yes—
514C22×C4C22×D412yes—
515C22×C4C22×D414yes—
516C22×C4C22×D414yes—
517C22×C4C22×D412yes—
518C22×C4C22×D414yes—
519C22×C4C22×D412yes—
520C22×C4C2×#4114yes—
521C22×C4C2×#4114yes—
522C22×C4C2×#4118yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4114yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4114yes—
529C22×C4C2×#4114yes—
530C22×C42−1+414yes—
531C4⋊C4—216no—
532C4⋊C4—216no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—216no—
536C4⋊C4—416no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—48no—
543C4⋊C4—416no—
544C4⋊C4—88no—
545C22⋊C4—28no—
546C22⋊C4—28no—
547C22⋊C4—216no—
548C22⋊C4—48no—
549C22⋊C4—416no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—44no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—44no—
556C42—216no—
557C42—216no—
558C42—416no—
559C42—416no—
560C42—44no—
561C42—48no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—22no—
582C23—24no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—41no—
589C23—42no—
590C23—41no—
591C23—41no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23C2×#12314yes—
602C23#53214yes—
603C23#54214yes—
604C23D4214yes—
605C23#54714yes—
606C23#54714yes—
607C23#55314yes—
608C23C23×D411yescharacteristic
609C23C23×D411yescharacteristic
610C23C22×#4111yescharacteristic
611C23C22×#4111yescharacteristic
612C23C22×#4112yes—
613C23C22×#4112yes—
614C23C22×#4111yescharacteristic
615C23C2×H(5,𝔽2)11yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23C2×2−1+412yes—
618C23#58512yes—
619D4—416no—
620C2×C4—232no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—232no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—28no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—28no—
653C2×C4—432no—
654C2×C4—416no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—432no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—88no—
712C2×C4C2×#12314yes—
713C2×C4C2×#12314yes—
714C2×C4#52514yes—
715C2×C4#52514yes—
716C2×C4#52918yes—
717C2×C4#52918yes—
718C2×C4#54718yes—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—28no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—28no—
727C22—28no—
728C22—28no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—42no—
733C22—44no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—82no—
739C22—82no—
740C22#242218yes—
741C22C22×#12311yescharacteristic
742C22C2×#52511yescharacteristic
743C22C2×#52511yescharacteristic
744C22C2×#52912yes—
745C22C2×#52912yes—
746C22C2×#53211yescharacteristic
747C22C2×#54211yescharacteristic
748C22#346112yes—
749C22C2×D4211yescharacteristic
750C22C2×#54712yes—
751C22C2×#54711yescharacteristic
752C22C2×#54711yescharacteristic
753C22D4×#4112yes—
754C22C2×#55311yescharacteristic
755C22#347512yes—
756C22#348212yes—
757C22#348611yescharacteristic
758C22#348711yescharacteristic
759C22#349212yes—
760C22#349512yes—
761C22#350712yes—
762C22#351312yes—
763C22#352312yes—
764C4—28no—
765C4—24no—
766C4—48no—
767C4—44no—
768C4—44no—
769C4—44no—
770C4—44no—
771C4—42no—
772C4—44no—
773C4—82no—
774C4—82no—
775C4—81no—
776C4—81no—
777C4—84no—
778C4#285318yescomplemented
779C2—28no—
780C2—82no—
781C2C2×#242211yescharacteristic
782C2#3476312yes—
783C2#3518211yescharacteristic
784C2#3522812yes—
785C2#3610211yescharacteristic
786C2#3610311yescharacteristic
787C2#3611612yes—
788C2#3642311yescharacteristic
789C2#3642711yescharacteristic
790C2#3648612yes—
791C2C2×#285311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×C4×C4⋊C4C2semidirect
4. #14919C2semidirect
6. #14794C2semidirect
7. #14784C2semidirect
8. #14705C2semidirect
9. #14697C2semidirect
10. #14133C2semidirect
11. #14029C2semidirect
12. #13974C2semidirect
13. #13904C2semidirect
14. #13880C2semidirect
15. #13876C2semidirect
778. C4#2853semidirect

Maximal subgroups

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

subgroupindex
C2×#28532
C2×#24862
C22×C4×C4⋊C42
#149192
#149122
#147942
#147842
#147052
#146972
#141332
#140292
#139742
#139042
#138802
#138762
#138722
C4×#3862