Finite Group Databasebeta

← #35564576

Subgroups — #35564576

Order 21248.

2470 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic83C211yesmaximal, characteristic
2#24910419C212yesmaximal, complemented
3#24910390C214yesmaximal, complemented
4D4×Dic83⋊C4C212yesmaximal, complemented
5#24910350C211yesmaximal, characteristic, complemented
6#24910346C211yesmaximal, characteristic, complemented
7#24910325C212yesmaximal, complemented
8#24910319C212yesmaximal, complemented
9#24910293C211yesmaximal, characteristic
10#24910108C212yesmaximal, complemented
11#24910089C214yesmaximal, complemented
12#24909865C211yesmaximal, characteristic, complemented
13#24909857C211yesmaximal, characteristic, complemented
14#24909854C212yesmaximal, complemented
15C2×#19127565C212yesmaximal, complemented
16#24909824C212yesmaximal, complemented
17C83×#2339C211yesmaximal, characteristic
18#41×Dic83C4116yescomplemented
19C2×Q8×Dic83C2211yescharacteristic
20C2×Q8×Dic83C2211yescharacteristic
21C2×D4×Dic83C2212yes—
22C2×D4×Dic83C2211yescharacteristic
23C2×D4×Dic83C2211yescharacteristic
24C2×D4×Dic83C2212yes—
25C2×D4×Dic83C2212yes—
26C2×#14581751C2211yescharacteristic
27C2×#14581751C2212yes—
28C2×#14581748C2212yes—
29C22×Dic83⋊C4C2214yes—
30C22×C4×Dic83C2212yes—
31C22×C4×Dic83C2211yescharacteristic
32#19127608C2212yes—
33#19127599C2212yes—
34#19127597C2212yes—
35#19127595C2214yes—
36#19127589C2214yes—
37#19127586C2214yes—
38#19127586C2214yes—
39#19127584C2214yes—
40#19127584C2214yes—
41#19127581C2214yes—
42#19127574C2214yes—
43#19127573C2214yes—
44#19127570C2212yes—
45#19127568C2214yes—
46#19127568C2211yescharacteristic
47#19127568C2211yescharacteristic
48#19127565C2214yes—
49#19127565C2212yes—
50#19127565C2212yes—
51#19127565C2211yescharacteristic
52#19127565C2212yes—
53#19127565C2214yes—
54#19127565C2211yescharacteristic
55#19127564C2212yes—
56#19127562C2212yes—
57#19127561C2211yescharacteristic
58#19127559C2212yes—
59#19127559C2214yes—
60#19127559C2212yes—
61C4⋊C4×Dic83C2212yes—
62C4⋊C4×Dic83C2212yes—
63C4×Dic83⋊C4C2212yes—
64C4×C4⋊Dic83C2212yes—
65#19127552C2214yes—
66#19127552C2212yes—
67C22⋊C4×Dic83C2214yes—
68C22⋊C4×Dic83C2214yes—
69C4×C22⋊Dic83C2214yes—
70C4×C22⋊Dic83C2211yescharacteristic
71#19127547C2212yes—
72#19127546C2212yes—
73#19127546C2212yes—
74C2×C83⋊#95C2214yes—
75C2×C83⋊#95C2212yes—
76C22×#41×C83C2211yescharacteristic
77C2×C4×D4×C83C2212yes—
78#391×C83C2212yes—
79#386×C83C2214yes—
80#381×C83C2212yes—
81#380×C83C2211yescharacteristic
82C4×C22⋊C4×C83C2211yescharacteristic
83C2×#95×C83C2212yes—
84C23×Dic83C2312yes—
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2314yes—
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2312yes—
89Q8×Dic83C2×C418yescomplemented
90Q8×Dic83C2×C418yescomplemented
91D4×Dic83—28no—
92D4×Dic83C2×C418yes—
93D4×Dic83C2×C418yes—
94D4×Dic83C2×C4116yescomplemented
95D4×Dic83C2×C4116yescomplemented
96#14581751C2×C4116yescomplemented
97#14581751C2×C418yescomplemented
98#14581748—44no—
99C2×C4⋊Dic83C2312yes—
100C2×C4⋊Dic83C2311yescharacteristic
101C2×C4⋊Dic83C2312yes—
102C2×C4⋊Dic83C2312yes—
103C2×C4⋊Dic83C2311yescharacteristic
104C2×Dic83⋊C4—48no—
105C2×Dic83⋊C4C2312yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2312yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×C22⋊Dic83C2314yes—
112C2×C22⋊Dic83C2312yes—
113C2×C22⋊Dic83C2312yes—
114C2×C22⋊Dic83C2312yes—
115C2×C22⋊Dic83C2312yes—
116C2×C22⋊Dic83C2312yes—
117C2×C4×Dic83C2×C418yescomplemented
118C2×C4×Dic83C2×C4116yescomplemented
119C2×C4×Dic83C2312yes—
120C2×C4×Dic83C2314yes—
121C2×C4×Dic83C2314yes—
122C2×C4×Dic83C2314yes—
123C2×C4×Dic83C2312yes—
124C2×C4×Dic83C2311yescharacteristic
125C2×C4×Dic83C2311yescharacteristic
126C2×C4×Dic83C2311yescharacteristic
127C2×C4×Dic83C2311yescharacteristic
128C2×C4×Dic83C2312yes—
129C2×C4×Dic83C2312yes—
130C83⋊#95C2312yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2312yes—
134C83⋊#95C2312yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2312yes—
140C83⋊#95C2312yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2311yescharacteristic
144C83⋊#95C2311yescharacteristic
145C83⋊#95C2314yes—
146C2×#41×C83—28no—
147C2×#41×C83C2×C418yes—
148C22×Q8×C83C2311yescharacteristic
149C22×D4×C83C2312yes—
150C22×D4×C83C2311yescharacteristic
151C23×C4×C83C2311yescharacteristic
152C23×C4×C83C2312yes—
153C23×C4×C83C2314yes—
154C4×D4×C83—28no—
155C2×C4⋊C4×C83C2312yes—
156C2×C22⋊C4×C83C2314yes—
157C2×C22⋊C4×C83C2312yes—
158C2×C22⋊C4×C83C2312yes—
159C2×C42×C83C2312yes—
160#95×C83C2312yes—
161#95×C83C2314yes—
162#95×C83C2311yescharacteristic
163#95×C83C2314yes—
164#95×C83C2311yescharacteristic
165C22×Dic83—24no—
166C22×Dic83—22no—
167C22×Dic83—24no—
168C22×Dic83—22no—
169C22×Dic83—28no—
170C22×Dic83—44no—
171C22×Dic83—42no—
172C22×Dic83—44no—
173C22×Dic83—44no—
174C22×Dic83C22×C418yes—
175C22×Dic83C22×C414yes—
176C22×Dic83C22×C418yes—
177C22×Dic83C22×C414yes—
178C22×Dic83C2412yes—
179C22×Dic83C2414yes—
180C22×Dic83C2412yes—
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2411yescharacteristic
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2411yescharacteristic
186C22×Dic83C2411yescharacteristic
187C4⋊Dic83—24no—
188C4⋊Dic83C22×C414yes—
189C4⋊Dic83C22×C414yes—
190C4⋊Dic83C22×C418yes—
191C4⋊Dic83C22×C418yes—
192Dic83⋊C4—24no—
193Dic83⋊C4—28no—
194Dic83⋊C4—24no—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197Dic83⋊C4—44no—
198C22⋊Dic83—28no—
199C22⋊Dic83—42no—
200C22⋊Dic83—42no—
201C22⋊Dic83C22×C418yes—
202C22⋊Dic83C22×C418yes—
203C22⋊Dic83C22×C418yes—
204C4×Dic83—24no—
205C4×Dic83—44no—
206C4×Dic83—44no—
207C4×Dic83—44no—
208C4×Dic83C22×C414yes—
209C4×Dic83C22×C414yes—
210C4×Dic83C22×C418yes—
211C4×Dic83C22×C414yes—
212C4×Dic83C22×C414yes—
213C4×Dic83C22×C418yes—
214C4×Dic83C22×C418yes—
215C24×C83C2411yescharacteristic
216C24×C83C2412yes—
217#41×C83—232no—
218C2×Q8×C83—24no—
219C2×Q8×C83C22×C414yes—
220C2×D4×C83—28no—
221C2×D4×C83C22×C418yes—
222C2×D4×C83C22×C414yes—
223C2×D4×C83#4118yes—
224C22×C4×C83—28no—
225C22×C4×C83—24no—
226C22×C4×C83—28no—
227C22×C4×C83—44no—
228C22×C4×C83—44no—
229C22×C4×C83C22×C418yes—
230C22×C4×C83C22×C414yes—
231C22×C4×C83C2412yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2414yes—
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2412yes—
236C22×C4×C83C2411yescharacteristic
237C4⋊C4×C83—24no—
238C22⋊C4×C83—28no—
239C22⋊C4×C83—42no—
240C22⋊C4×C83—42no—
241C42×C83—24no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—24no—
245C23×C83—22no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83—22no—
249C23×C83C23×C412yes—
250C23×C83C23×C414yes—
251C23×C83C2×#4118yes—
252C23×C83C2511yescharacteristic
253Q8×C83—28no—
254D4×C83—216no—
255D4×C83#117116yescomplemented
256C2×C4×C83—216no—
257C2×C4×C83—22no—
258C2×C4×C83—24no—
259C2×C4×C83—28no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—24no—
263C2×C4×C83—24no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—24no—
269C2×C4×C83—88no—
270C2×C4×C83C23×C412yes—
271C2×C4×C83C23×C414yes—
272C2×C4×C83C23×C412yes—
273C2×C4×C83C2×#4114yes—
274C2×Dic83—21no—
275C2×Dic83—22no—
276C2×Dic83—21no—
277C2×Dic83—22no—
278C2×Dic83—24no—
279C2×Dic83—22no—
280C2×Dic83—22no—
281C2×Dic83—216no—
282C2×Dic83—28no—
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—24no—
286C2×Dic83—24no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—24no—
291C2×Dic83—22no—
292C2×Dic83—48no—
293C2×Dic83—44no—
294C2×Dic83—88no—
295C2×Dic83C23×C412yes—
296C2×Dic83C23×C412yes—
297C2×Dic83C23×C414yes—
298C2×Dic83C23×C412yes—
299C2×Dic83C23×C414yes—
300C2×Dic83C23×C412yes—
301C2×Dic83H(5,𝔽2)12yes—
302C2×Dic832−1+412yes—
303C22×C83—24no—
304C22×C83—24no—
305C22×C83—28no—
306C22×C83—28no—
307C22×C83—22no—
308C22×C83—22no—
309C22×C83—22no—
310C22×C83—42no—
311C22×C83—42no—
312C22×C83C2×#11718yes—
313C22×C83C24×C411yescharacteristic
314C22×C83C22×#4112yes—
315C22×C83C2×H(5,𝔽2)11yescharacteristic
316C22×C83C2×2−1+411yescharacteristic
317C22×C83#58512yes—
318C4×C83—22no—
319C4×C83—24no—
320C4×C83—44no—
321C4×C83—42no—
322C4×C83—42no—
323C4×C83C2×#11714yes—
324Dic83—22no—
325Dic83—24no—
326Dic83—22no—
327Dic83—24no—
328Dic83—22no—
329Dic83—44no—
330Dic83—42no—
331Dic83—42no—
332Dic83#52014yes—
333#34191—831nomaximal, Sylow
334C2×C83—28no—
335C2×C83—42no—
336C2×C83C22×#11711yescharacteristic
337C2×C83C2×#52011yescharacteristic
338C2×C83#342811yescharacteristic
339C2×C83#351412yes—
340C2×C83#351512yes—
341C2×C4×#41—831no—
342#2355—832no—
343#2352—834no—
344D4×C4⋊C4—832no—
345#2346—831no—
346#2346—831no—
347#2343—832no—
348#2343—832no—
349#2339—831no—
350#2339D8311yescharacteristic
351#2320—832no—
352#2318—834no—
353#2285—831no—
354#2283—832no—
355#2283—831no—
356C2×#382—832no—
357#2275—832no—
358C83#3419111yescharacteristic, complemented, Sylow
359C22×#41C2×D8311yescharacteristic
360C4×#41—8316no—
361C2×C4×Q8—831no—
362C2×C4×Q8—831no—
363C2×C4×D4—832no—
364C2×C4×D4—831no—
365C2×C4×D4—832no—
366C2×C4×D4—831no—
367C2×C4×D4—832no—
368C2×C4×D4C2×D8312yes—
369C2×#117—832no—
370C2×#117—831no—
371C2×#117—832no—
372C22×C4⋊C4—834no—
373C22×C42—832no—
374C22×C42—831no—
375#391—832no—
376#391C2×D8312yes—
377#389—832no—
378#389—832no—
379#388—834no—
380#388—834no—
381#387—834no—
382#387—834no—
383#387—834no—
384#387—834no—
385#386—834no—
386#386C2×D8314yes—
387#385—834no—
388#385—834no—
389#384—832no—
390#383—834no—
391#383—831no—
392#383—831no—
393#382—834no—
394#382—832no—
395#382—832no—
396#382—834no—
397#382—831no—
398#382—832no—
399#382—831no—
400#381—832no—
401#381—832no—
402#381C2×D8312yes—
403#380—831no—
404#380—832no—
405#380—834no—
406#380—832no—
407#380C2×D8311yescharacteristic
408C4×C4⋊C4—832no—
409C4×C4⋊C4—832no—
410C4×C4⋊C4—832no—
411C4×C4⋊C4—832no—
412C4×C4⋊C4—832no—
413C4×C4⋊C4—834no—
414C4×C22⋊C4—831no—
415C4×C22⋊C4—834no—
416C4×C22⋊C4—834no—
417C4×C22⋊C4—834no—
418C4×C22⋊C4C2×D8311yescharacteristic
419#376—832no—
420#376—832no—
421#376—832no—
422C2×#95—834no—
423C2×#95—832no—
424C2×#95C2×D8312yes—
425C2×#41—28no—
426C2×#41C4×D8318yes—
427C22×Q8C22×D8311yescharacteristic
428C22×D4C22×D8312yes—
429C22×D4C22×D8311yescharacteristic
430C23×C4—832no—
431C23×C4—831no—
432C23×C4—834no—
433C23×C4—832no—
434C23×C4—831no—
435C23×C4C22×D8312yes—
436C23×C4C22×D8311yescharacteristic
437C23×C4C22×D8314yes—
438C4×Q8—838no—
439C4×Q8—838no—
440C4×D4—28no—
441C4×D4—838no—
442C4×D4—838no—
443C4×D4—8316no—
444C4×D4—8316no—
445C4×D4—1668no—
446#117—3324no—
447#117—8316no—
448#117—838no—
449C2×C4⋊C4—3328no—
450C2×C4⋊C4—834no—
451C2×C4⋊C4—834no—
452C2×C4⋊C4—834no—
453C2×C4⋊C4—831no—
454C2×C4⋊C4—832no—
455C2×C4⋊C4—832no—
456C2×C4⋊C4—831no—
457C2×C4⋊C4—832no—
458C2×C4⋊C4—834no—
459C2×C4⋊C4—832no—
460C2×C4⋊C4—832no—
461C2×C4⋊C4C22×D8312yes—
462C2×C22⋊C4—832no—
463C2×C22⋊C4—832no—
464C2×C22⋊C4—832no—
465C2×C22⋊C4—832no—
466C2×C22⋊C4—832no—
467C2×C22⋊C4—834no—
468C2×C22⋊C4C22×D8314yes—
469C2×C22⋊C4C22×D8312yes—
470C2×C22⋊C4C22×D8312yes—
471C2×C42—834no—
472C2×C42—834no—
473C2×C42—834no—
474C2×C42—8316no—
475C2×C42—838no—
476C2×C42—832no—
477C2×C42—831no—
478C2×C42—831no—
479C2×C42—832no—
480C2×C42—831no—
481C2×C42—832no—
482C2×C42—831no—
483C2×C42—832no—
484C2×C42C22×D8312yes—
485#95—832no—
486#95—831no—
487#95—832no—
488#95—834no—
489#95—834no—
490#95—834no—
491#95—834no—
492#95—831no—
493#95—832no—
494#95—832no—
495#95—832no—
496#95—834no—
497#95—834no—
498#95—832no—
499#95—832no—
500#95—834no—
501#95C22×D8311yescharacteristic
502#95C22×D8312yes—
503#95C22×D8314yes—
504#95C22×D8311yescharacteristic
505#95C22×D8314yes—
506C24C23×D8311yescharacteristic
507C24C23×D8312yes—
508#41—232no—
509C2×Q8—24no—
510C2×Q8C2×C4×D8314yes—
511C2×D4—28no—
512C2×D4C2×C4×D8318yes—
513C2×D4C2×C4×D8314yes—
514C2×D4#1305058918yes—
515C22×C4—28no—
516C22×C4—24no—
517C22×C4—28no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—3324no—
521C22×C4—3322no—
522C22×C4—3324no—
523C22×C4—3324no—
524C22×C4—834no—
525C22×C4—838no—
526C22×C4—831no—
527C22×C4—834no—
528C22×C4—838no—
529C22×C4—831no—
530C22×C4—831no—
531C22×C4—832no—
532C22×C4—832no—
533C22×C4—831no—
534C22×C4—832no—
535C22×C4—832no—
536C22×C4—834no—
537C22×C4—1664no—
538C22×C4—1662no—
539C22×C4—1664no—
540C22×C4—1662no—
541C22×C4—1668no—
542C22×C4C2×C4×D8318yes—
543C22×C4C2×C4×D8314yes—
544C22×C4C23×D8312yes—
545C22×C4C23×D8312yes—
546C22×C4C23×D8314yes—
547C22×C4C23×D8311yescharacteristic
548C22×C4C23×D8312yes—
549C22×C4C23×D8311yescharacteristic
550C4⋊C4—24no—
551C4⋊C4—3324no—
552C4⋊C4—3324no—
553C4⋊C4—3324no—
554C4⋊C4—838no—
555C4⋊C4—838no—
556C4⋊C4—834no—
557C4⋊C4—834no—
558C4⋊C4—1664no—
559C4⋊C4—1668no—
560C4⋊C4—1664no—
561C4⋊C4—1664no—
562C22⋊C4—28no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—3322no—
566C22⋊C4—3322no—
567C22⋊C4—838no—
568C22⋊C4—838no—
569C22⋊C4—838no—
570C22⋊C4—1668no—
571C42—24no—
572C42—3324no—
573C42—3324no—
574C42—3324no—
575C42—834no—
576C42—838no—
577C42—834no—
578C42—838no—
579C42—834no—
580C42—838no—
581C42—834no—
582C42—1664no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—22no—
587C23—21no—
588C23—21no—
589C23—22no—
590C23C22×C4×D8312yes—
591C23C22×C4×D8314yes—
592C23C2×#1305058918yes—
593C23C24×D8311yescharacteristic
594Q8—28no—
595D4—216no—
596D4#14581748116yescomplemented
597C2×C4—216no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—88no—
611C2×C4—3328no—
612C2×C4—3324no—
613C2×C4—832no—
614C2×C4—832no—
615C2×C4—832no—
616C2×C4—832no—
617C2×C4—832no—
618C2×C4—834no—
619C2×C4—834no—
620C2×C4—832no—
621C2×C4—6648no—
622C2×C4—1662no—
623C2×C4—1662no—
624C2×C4—1664no—
625C2×C4—1664no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1664no—
630C2×C4—1662no—
631C2×C4—16616no—
632C2×C4—1668no—
633C2×C4—1661no—
634C2×C4—1662no—
635C2×C4—1661no—
636C2×C4—1662no—
637C2×C4—1664no—
638C2×C4—1662no—
639C2×C4—1662no—
640C2×C4C22×C4×D8312yes—
641C2×C4C22×C4×D8314yes—
642C2×C4C22×C4×D8312yes—
643C2×C4C2×#1305058914yes—
644C22—28no—
645C22—24no—
646C22—28no—
647C22—24no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—42no—
652C22—42no—
653C22C2×#1458174818yes—
654C22C23×C4×D8311yescharacteristic
655C22C22×#1305058912yes—
656C22H(5,𝔽2)×D8311yescharacteristic
657C222−1+4×D8311yescharacteristic
658C22#1912853712yes—
659C4—22no—
660C4—24no—
661C4—42no—
662C4—44no—
663C4—42no—
664C4—3322no—
665C4—3324no—
666C4—3322no—
667C4—834no—
668C4—1662no—
669C4—1664no—
670C4—1662no—
671C4—1664no—
672C4—1662no—
673C4C2×#1458174814yes—
674C2—28no—
675C2—42no—
676C2C22×#1458174811yescharacteristic
677C2#520×D8311yescharacteristic
678C2#2492066211yescharacteristic
679C2#2492141112yes—
680C2#2492142812yes—
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2339C2
socle, cosocleC23×C83C25
prime radicalC22×#41×C83C22
hypercenter#2339D83
hypocenterC83#34191
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #24910419C2semidirect
3. #24910390C2semidirect
4. D4×Dic83⋊C4C2semidirect
5. #24910350C2semidirect
6. #24910346C2semidirect
7. #24910325C2semidirect
8. #24910319C2semidirect
10. #24910108C2semidirect
11. #24910089C2semidirect
12. #24909865C2semidirect
13. #24909857C2semidirect
14. #24909854C2semidirect
15. C2×#19127565C2semidirect
16. #24909824C2semidirect
18. #41×Dic83C4semidirect
89. Q8×Dic83C2×C4semidirect
90. Q8×Dic83C2×C4semidirect
94. D4×Dic83C2×C4semidirect
95. D4×Dic83C2×C4semidirect
96. #14581751C2×C4semidirect
97. #14581751C2×C4semidirect
117. C2×C4×Dic83C2×C4semidirect
118. C2×C4×Dic83C2×C4semidirect
255. D4×C83#117semidirect
358. C83#34191semidirect
596. D4#14581748semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic832
#249104192
#249103902
D4×Dic83⋊C42
#249103502
#249103462
#249103252
#249103192
#249102932
#249101082
#249100892
#249098652
#249098572
#249098542
C2×#191275652
#249098242
C83×#23392
#3419183