Finite Group Databasebeta

← #4453593

Subgroups — #4453593

Order 512.

3356 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic
2C2×#2582C211yesmaximal, characteristic, complemented
3C2×#2581C211yesmaximal, characteristic, complemented
4C2×#2396C211yesmaximal, characteristic
5#16674C212yesmaximal
6#16659C214yesmaximal
7#16656C212yesmaximal
8#16634C212yesmaximal, complemented
9#16608C212yesmaximal, complemented
10#16605C214yesmaximal, complemented
11#15218C212yesmaximal, complemented
12#15180C212yesmaximal, complemented
13#15179C212yesmaximal
14#15179C212yesmaximal
15#14340C211yesmaximal, characteristic
16#13942C211yesmaximal, characteristic, complemented
17#13926C211yesmaximal, characteristic, complemented
18C2×#541—28no—
19C2×#541—28no—
20C2×#541—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#126C2212yes—
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#125C2212yes—
26C22×#125C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2582—28no—
34#2581—28no—
35#2396—28no—
36C2×#400C2212yes—
37C2×#400C2211yescharacteristic
38C2×#399C2211yescharacteristic
39C2×#398C2214yes—
40C2×#398C2212yes—
41C2×#396C2212yes—
42C2×#395C2212yes—
43C2×#395C2211yescharacteristic
44C2×#393C2211yescharacteristic
45C2×#391C2212yes—
46C2×#391C2212yes—
47C2×#391C2212yes—
48C2×#391C2212yes—
49C2×#391C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#389C2212yes—
53C2×#387C2214yes—
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2212yes—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60#1444C2214yes—
61#1444C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87#1434C2212yes—
88#1434C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C24×C4C2311yescharacteristic
93#541—2128no—
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×#126—28no—
98C2×#126—28no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#126—28no—
102C2×#126—28no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—28no—
106C2×#125—28no—
107C2×#125—28no—
108C2×#125—28no—
109C2×#125—24no—
110C2×#125—28no—
111C2×#125—28no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8D418yes—
126C2×C4×Q8D418yes—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117D418yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2314yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#400—28no—
167#400—24no—
168#399—24no—
169#398—216no—
170#398—28no—
171#396—28no—
172#395—28no—
173#395—24no—
174#393—24no—
175#391—28no—
176#391—28no—
177#391—28no—
178#391—44no—
179#391—44no—
180#389—28no—
181#389—28no—
182#389—28no—
183#387—216no—
184#384—24no—
185#382—24no—
186#380—44no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—24no—
189C4×C22⋊C4—28no—
190C2×#95C2312yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—42no—
233C22×Q8C2×D414yes—
234C22×Q8C2×D414yes—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4C2×D414yes—
242C23×C4C2412yes—
243C23×C4C2414yes—
244C23×C4C2414yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C4⋊Q8—232no—
259#126—264no—
260#126—264no—
261#125—232no—
262#125—264no—
263#125—264no—
264C22⋊Q8—232no—
265C22⋊Q8—232no—
266C4×Q8—232no—
267C4×Q8—232no—
268C4×Q8—416no—
269#117—232no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D418yes—
336C2×C4⋊C4C2×D418yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×D414yes—
357C2×C22⋊C4C2×D414yes—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42C2×D414yes—
371C2×C42C2×D418yes—
372C2×C42C2×D418yes—
373C2×C42C2×D414yes—
374C2×C42C2×D414yes—
375C2×C42C2×D414yes—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—22no—
380#95—22no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24C22×D412yes—
412C24C2511yescharacteristic
413C2×Q8—28no—
414C2×Q8—28no—
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—48no—
421C2×Q8—48no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
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—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4C22×D414yes—
518C22×C4C22×D414yes—
519C22×C4C22×D412yes—
520C22×C4C22×D414yes—
521C22×C4C22×D414yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C42−1+414yes—
535C22×C42−1+414yes—
536C22×C42−1+412yes—
537C22×C42−1+412yes—
538C22×C42−1+412yes—
539C4⋊C4—216no—
540C4⋊C4—216no—
541C4⋊C4—216no—
542C4⋊C4—216no—
543C4⋊C4—216no—
544C4⋊C4—216no—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—216no—
550C4⋊C4—216no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—416no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—44no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—84no—
561C4⋊C4—88no—
562C22⋊C4—216no—
563C22⋊C4—216no—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—88no—
569C42—28no—
570C42—216no—
571C42—216no—
572C42—48no—
573C42—48no—
574C42#120116yes—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23C23×D411yescharacteristic
599C23C23×D411yescharacteristic
600C23C23×D411yescharacteristic
601C23C2×H(5,𝔽2)11yescharacteristic
602C23C2×2−1+411yescharacteristic
603C23C2×2−1+411yescharacteristic
604C23C2×2−1+411yescharacteristic
605C23C2×2−1+412yes—
606C23C2×2−1+412yes—
607C23#58512yes—
608C23#58512yes—
609Q8—416no—
610Q8—416no—
611Q8—416no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—44no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—416no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4C2×#12014yes—
705C2×C4C2×#12014yes—
706C2×C4C2×#12014yes—
707C2×C4#53614yes—
708C2×C4#53614yes—
709C2×C4#53614yes—
710C2×C4#53714yes—
711C2×C4#53714yes—
712C2×C4#53714yes—
713C22—44no—
714C22—44no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—82no—
721C22—82no—
722C22—81no—
723C22—81no—
724C22C22×#12011yescharacteristic
725C22C2×#53611yescharacteristic
726C22C2×#53611yescharacteristic
727C22C2×#53611yescharacteristic
728C22C2×#53711yescharacteristic
729C22C2×#53711yescharacteristic
730C22C2×#53711yescharacteristic
731C22#348611yescharacteristic
732C22#348711yescharacteristic
733C22#348912yes—
734C22#348912yes—
735C22#348912yes—
736C22#349712yes—
737C22#349911yescharacteristic
738C22#350011yescharacteristic
739C22#355212yes—
740C22#355512yes—
741C22#355512yes—
742C22#355512yes—
743C22#355612yes—
744C22#355712yes—
745C22#356212yes—
746C22#356312yes—
747C4—24no—
748C4—24no—
749C4—44no—
750C4—42no—
751C4—44no—
752C4—44no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—42no—
757C4—44no—
758C4—82no—
759C4—84no—
760C4—82no—
761C4—84no—
762C4#261618yes—
763C2—82no—
764C2C2×#261611yescharacteristic
765C2#3565911yescharacteristic
766C2#3566011yescharacteristic
767C2#3737712yes—
768C2#3737812yes—
769C2#4279111yescharacteristic
770C2#4279311yescharacteristic
771C2#4280112yes—
772C2#4280212yes—
773C2#4287711yescharacteristic
774C2#4287911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2582C2semidirect
3. C2×#2581C2semidirect
8. #16634C2semidirect
9. #16608C2semidirect
10. #16605C2semidirect
11. #15218C2semidirect
12. #15180C2semidirect
16. #13942C2semidirect
17. #13926C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5412
C2×#25822
C2×#25812
C2×#23962
#166742
#166592
#166562
#166342
#166082
#166052
#152182
#151802
#151792
#143402
#139422
#139262