Finite Group Databasebeta

← #35564224

Subgroups — #35564224

Order 21248.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128363C211yesmaximal, characteristic
2C2×C4×#13050591C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
4#24910532C213yesmaximal, complemented
5#24910489C213yesmaximal, complemented
6#24910478C213yesmaximal, complemented
7#24910389C213yesmaximal, complemented
8#24910301C211yesmaximal, characteristic, complemented
9Q8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
10#24910002C213yesmaximal, complemented
11#24909993C213yesmaximal, complemented
12#24909971C213yesmaximal, complemented
13C4×Q8×Dic83C211yesmaximal, characteristic, complemented
14C4×#14581754C213yesmaximal, complemented
15C83×#2351C211yesmaximal, characteristic, complemented
16C22×#13050591C2211yescharacteristic
17C22×Q8×D83C2211yescharacteristic
18#19128363C4116yescomplemented
19C2×#14581780C2213yes—
20C2×#14581772C2213yes—
21C2×#14581767C2213yes—
22C4×#13050591—28no—
23C2×Q8×Dic83C2211yescharacteristic
24C2×Q8×Dic83C2211yescharacteristic
25C2×C4×Dic166C2213yes—
26C2×#14581757C2213yes—
27C4×Q8×D83—28no—
28C2×C4×D332C2213yes—
29C2×C4×D332C2213yes—
30C2×#14581754C2213yes—
31C2×#14581754C2213yes—
32C2×#14581754C2213yes—
33C2×#14581750C2213yes—
34C2×C4⋊C4×D83C2213yes—
35C2×C42×D83C2213yes—
36C2×C42×D83C2213yes—
37#19127607C2213yes—
38#19127606C2213yes—
39#19127603C2213yes—
40#19127602C2213yes—
41#19127591C2216yes—
42#19127590C2216yes—
43#19127590C2216yes—
44#19127584C2216yes—
45#19127579C2216yes—
46#19127572C2216yes—
47#19127558C2213yes—
48#19127558C2213yes—
49C4⋊C4×Dic83C2213yes—
50C4⋊C4×Dic83C2213yes—
51C4⋊C4×Dic83C2213yes—
52C4⋊C4×Dic83C2213yes—
53C4×C4⋊Dic83C2213yes—
54C4×(C2×D83)⋊C4C2213yes—
55C4×(C2×D83)⋊C4C2213yes—
56#19127548C2213yes—
57#19127548C2216yes—
58#19127548C2213yes—
59#19127548C2213yes—
60#19127548C2211yescharacteristic
61C42×Dic83C2213yes—
62C2×C4×Q8×C83C2211yescharacteristic
63C2×C4×Q8×C83C2211yescharacteristic
64C2×C4×Q8×C83C2211yescharacteristic
65#389×C83C2213yes—
66#389×C83C2213yes—
67#382×C83C2213yes—
68C4×C4⋊C4×C83C2213yes—
69C2×#13050591—24no—
70C2×#13050591—24no—
71C2×#13050591C2×C418yescomplemented
72C22×Dic166C2313yes—
73C2×Q8×D83—24no—
74C2×Q8×D83—24no—
75C2×Q8×D83C2×C418yescomplemented
76C22×D332C2313yes—
77C22×D332C2313yes—
78C22×C4×D83C2313yes—
79C22×C4×D83C2313yes—
80C22×C4×D83C2313yes—
81C22×C4×D83C2313yes—
82C22×C4×D83C2313yes—
83C22×C4×D83C2311yescharacteristic
84#14581780C2×C4124yescomplemented
85#14581772C2×C4124yescomplemented
86#14581767C2×C4124yescomplemented
87Q8×Dic83—24no—
88Q8×Dic83D418yescomplemented
89C4×Dic166—212no—
90#14581757—212no—
91C4×D332—212no—
92C4×D332C2×C4124yescomplemented
93#14581754—212no—
94#14581754—212no—
95#14581754—212no—
96#14581750—212no—
97C2×C4⋊Dic83C2313yes—
98C2×C4⋊Dic83C2313yes—
99C2×C4⋊Dic83C2313yes—
100C2×Dic83⋊C4C2316yes—
101C4⋊C4×D83—212no—
102C2×(C2×D83)⋊C4C2313yes—
103C2×(C2×D83)⋊C4C2316yes—
104C2×(C2×D83)⋊C4C2313yes—
105C2×(C2×D83)⋊C4C2313yes—
106C2×(C2×D83)⋊C4C2316yes—
107C2×(C2×D83)⋊C4C2316yes—
108C2×(C2×D83)⋊C4C2313yes—
109C2×(C2×D83)⋊C4C2311yescharacteristic
110C2×(C2×D83)⋊C4C2311yescharacteristic
111C2×C4×Dic83C2313yes—
112C2×C4×Dic83C2311yescharacteristic
113C2×C4×Dic83C2313yes—
114C2×C4×Dic83C2313yes—
115C2×C4×Dic83C2313yes—
116C2×C4×Dic83C2313yes—
117C2×C4×Dic83C2313yes—
118C2×C4×Dic83C2311yescharacteristic
119C2×C4×Dic83C2313yes—
120C2×C4×Dic83C2313yes—
121C42×D83—212no—
122C42×D83—212no—
123C83⋊#95C2316yes—
124C83⋊#95C2311yescharacteristic
125C83⋊#95C2313yes—
126C83⋊#95C2313yes—
127C83⋊#95C2313yes—
128C83⋊#95C2316yes—
129C22×Q8×C83C2311yescharacteristic
130C4×Q8×C83—24no—
131C4×Q8×C83—24no—
132C4×Q8×C83C2×C418yescomplemented
133C2×C4⋊C4×C83C2313yes—
134C2×C4⋊C4×C83C2313yes—
135C2×C4⋊C4×C83C2313yes—
136C2×C4⋊C4×C83C2313yes—
137C2×C4⋊C4×C83C2313yes—
138C2×C42×C83C2313yes—
139C2×C42×C83C2313yes—
140C2×C42×C83C2313yes—
141#95×C83C2316yes—
142#95×C83C2313yes—
143#95×C83C2311yescharacteristic
144C23×D83C2413yes—
145C23×D83C2411yescharacteristic
146#13050591—232no—
147C2×Dic166—26no—
148C2×Dic166—26no—
149C2×Dic166C22×C4112yes—
150Q8×D83—232no—
151C2×D332—26no—
152C2×D332—26no—
153C2×D332—26no—
154C2×D332—26no—
155C2×D332C22×C4112yes—
156C2×D332C22×C4112yes—
157C22×Dic83C2413yes—
158C22×Dic83C2411yescharacteristic
159C22×Dic83C2413yes—
160C22×Dic83C2413yes—
161C22×Dic83C2411yescharacteristic
162C22×Dic83C2411yescharacteristic
163C2×C4×D83—26no—
164C2×C4×D83—26no—
165C2×C4×D83—26no—
166C2×C4×D83—26no—
167C2×C4×D83—22no—
168C2×C4×D83—22no—
169C2×C4×D83—26no—
170C2×C4×D83—26no—
171C2×C4×D83—26no—
172C2×C4×D83—26no—
173C2×C4×D83—26no—
174C2×C4×D83—26no—
175C2×C4×D83—26no—
176C2×C4×D83—43no—
177C2×C4×D83—43no—
178C2×C4×D83C22×C4112yes—
179C2×C4×D83C22×C4112yes—
180C2×C4×D83#4114yescomplemented
181C4⋊Dic83—26no—
182C4⋊Dic83C22×C4112yes—
183C4⋊Dic83C2×D4112yes—
184Dic83⋊C4—212no—
185(C2×D83)⋊C4—26no—
186(C2×D83)⋊C4—26no—
187(C2×D83)⋊C4—212no—
188(C2×D83)⋊C4—26no—
189(C2×D83)⋊C4—46no—
190(C2×D83)⋊C4C22×C4124yes—
191(C2×D83)⋊C4C22×C4112yes—
192(C2×D83)⋊C4C22×C414yes—
193(C2×D83)⋊C4#4114yescomplemented
194C4×Dic83—26no—
195C4×Dic83—22no—
196C4×Dic83—26no—
197C4×Dic83—26no—
198C4×Dic83—26no—
199C4×Dic83—26no—
200C4×Dic83—26no—
201C4×Dic83—22no—
202C4×Dic83—43no—
203C4×Dic83C2×D4112yes—
204C2×Q8×C83C22×C414yes—
205C2×Q8×C83C2×D414yes—
206C2×Q8×C83#4114yes—
207C22×C4×C83C2413yes—
208C22×C4×C83C2413yes—
209C22×C4×C83C2413yes—
210C22×C4×C83C2411yescharacteristic
211C22×C4×C83C2411yescharacteristic
212C22×C4×C83C2411yescharacteristic
213C22×C4×C83C2413yes—
214C4⋊C4×C83—26no—
215C4⋊C4×C83—26no—
216C4⋊C4×C83—26no—
217C4⋊C4×C83—26no—
218C4⋊C4×C83C22×C4112yes—
219C42×C83—26no—
220C42×C83—26no—
221C42×C83C22×C4112yes—
222C23×C83C2511yescharacteristic
223C22×D83—21no—
224C22×D83—21no—
225C22×D83—21no—
226C22×D83—21no—
227C22×D83—23no—
228C22×D83—23no—
229C22×D83—23no—
230C22×D83—23no—
231C22×D83—23no—
232C22×D83—23no—
233C22×D83C23×C416yes—
234C22×D83C23×C412yes—
235C22×D83C2×#4112yes—
236C22×D83C2×#4112yes—
237Q8×C83C4×D4116yescomplemented
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—23no—
241C2×C4×C83—23no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—23no—
247C2×C4×C83—23no—
248C2×C4×C83—23no—
249C2×C4×C83—23no—
250C2×C4×C83—23no—
251C2×C4×C83—23no—
252C2×C4×C83C23×C412yes—
253C2×C4×C83C23×C416yes—
254C2×C4×C83C23×C416yes—
255C2×C4×C83C22×D416yes—
256C2×C4×C83C2×#4112yes—
257C2×C4×C83C2×#4112yes—
258C2×C4×C83C2×#4116yes—
259C2×Dic83—21no—
260C2×Dic83—23no—
261C2×Dic83—21no—
262C2×Dic83—23no—
263C2×Dic83—21no—
264C2×Dic83—23no—
265C2×Dic83—21no—
266C2×Dic83—23no—
267C2×Dic83—23no—
268C2×Dic83—23no—
269C2×Dic83—23no—
270C2×Dic83C23×C416yes—
271C2×Dic83C23×C412yes—
272C2×Dic83C22×D416yes—
273C2×Dic83C22×D412yes—
274C2×Dic83C2×#4112yes—
275C2×Dic83C2×#4112yes—
276C2×Dic832−1+412yes—
277D332—224no—
278D332—224no—
279C4×D83—224no—
280C4×D83—224no—
281C4×D83—28no—
282C4×D83—412no—
283C4×D83—412no—
284C4×D83—412no—
285Dic166—224no—
286C22×C83C24×C411yescharacteristic
287C22×C83C23×D411yescharacteristic
288C22×C83C22×#4111yescharacteristic
289C22×C83C22×#4111yescharacteristic
290C22×C83C22×#4111yescharacteristic
291C22×C83C2×2−1+411yescharacteristic
292C22×C83#58511yescharacteristic
293C2×D83—22no—
294C2×D83—22no—
295C2×D83—22no—
296C2×D83—22no—
297C2×D83—22no—
298C2×D83—22no—
299C2×D83—26no—
300C2×D83—26no—
301C2×D83—26no—
302C2×D83—43no—
303C2×D83—43no—
304C2×D83—43no—
305C2×D83—43no—
306C2×D83C4×#4114yescomplemented
307C4×C83—26no—
308C4×C83—22no—
309C4×C83—22no—
310C4×C83—22no—
311C4×C83—43no—
312C4×C83—43no—
313C4×C83C2×C4×D4112yes—
314Dic83—26no—
315Dic83—22no—
316Dic83—26no—
317Dic83—22no—
318Dic83—43no—
319Dic83#54814yescomplemented
320C4×#548—831nomaximal, Sylow
321C2×C83C22×C4×D411yescharacteristic
322C2×C83C2×C4×#4111yescharacteristic
323C2×C83C4×2−1+411yescharacteristic
324C2×C83C2×#54811yescharacteristic
325C2×C83D4×#4111yescharacteristic
326C2×C83#348011yescharacteristic
327C2×C83#348211yescharacteristic
328D83—24no—
329D83—46no—
330C2×#548—831no—
331C2×C4×#41—831no—
332C22×C4×Q8—831no—
333#2367—833no—
334#2362—833no—
335#2361—833no—
336#2352—833no—
337#2351D8311yescharacteristic, complemented
338#2341—831no—
339Q8×C22⋊C4—831no—
340C4×#124—833no—
341C4×C22⋊Q8—833no—
342C4×#121—833no—
343C42×Q8—831no—
344C42×D4—833no—
345C83C4×#54811yescharacteristic, complemented, Sylow
346C22×#41—831no—
347C23×Q8—831no—
348#548—8316no—
349C2×#124—833no—
350C2×C22⋊Q8—833no—
351C2×#121—833no—
352C4×#41—1668no—
353C2×C4×Q8—831no—
354C2×C4×Q8—831no—
355C2×C4×Q8—833no—
356C2×C4×Q8—833no—
357C2×C4×Q8—1668no—
358C2×C4×Q8C2×D8311yescharacteristic
359C2×C4×Q8C2×D8311yescharacteristic
360C2×C4×Q8C2×D8311yescharacteristic
361C2×C4×D4—833no—
362C2×C4×D4—833no—
363C2×C4×D4—833no—
364C2×C4×D4—833no—
365C2×C4×D4—833no—
366C2×#117—833no—
367C22×C4⋊C4—833no—
368C22×C42—833no—
369C22×C42—833no—
370#391—833no—
371#391—833no—
372#390—833no—
373#390—833no—
374#389C2×D8313yes—
375#389C2×D8313yes—
376#388—836no—
377#388—836no—
378#388—836no—
379#387—836no—
380#386—836no—
381#385—836no—
382#382C2×D8313yes—
383#380—833no—
384#380—833no—
385C4×C4⋊C4—833no—
386C4×C4⋊C4—833no—
387C4×C4⋊C4—833no—
388C4×C4⋊C4—833no—
389C4×C4⋊C4—833no—
390C4×C4⋊C4C2×D8313yes—
391C4×C22⋊C4—833no—
392C4×C22⋊C4—833no—
393C4×C22⋊C4—833no—
394C4×C22⋊C4—833no—
395C4×C22⋊C4—831no—
396C4×C22⋊C4—833no—
397C4×C22⋊C4—836no—
398C43—833no—
399C2×#41—838no—
400C2×#41—1664no—
401C2×#41—1664no—
402C22×Q8—838no—
403C22×Q8—833no—
404C22×Q8—1664no—
405C22×Q8—1664no—
406C22×Q8C22×D8311yescharacteristic
407C22×D4—833no—
408C22×D4—833no—
409C23×C4—833no—
410C23×C4—833no—
411C23×C4—833no—
412C23×C4—833no—
413C23×C4—831no—
414C23×C4—833no—
415#124—8324no—
416C22⋊Q8—8324no—
417#121—8324no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—838no—
421C4×Q8—16612no—
422C4×Q8—16612no—
423C4×Q8—1664no—
424C4×Q8C4×D8318yescomplemented
425C4×D4—8324no—
426C4×D4—16612no—
427C4×D4—16612no—
428C4×D4—16612no—
429C4×D4—16612no—
430#117—16612no—
431C2×C4⋊C4—833no—
432C2×C4⋊C4—833no—
433C2×C4⋊C4—836no—
434C2×C4⋊C4—833no—
435C2×C4⋊C4—16612no—
436C2×C4⋊C4C22×D8313yes—
437C2×C4⋊C4C22×D8313yes—
438C2×C4⋊C4C22×D8313yes—
439C2×C4⋊C4C22×D8313yes—
440C2×C4⋊C4C22×D8313yes—
441C2×C22⋊C4—836no—
442C2×C22⋊C4—831no—
443C2×C22⋊C4—831no—
444C2×C22⋊C4—833no—
445C2×C22⋊C4—836no—
446C2×C22⋊C4—836no—
447C2×C22⋊C4—833no—
448C2×C22⋊C4—833no—
449C2×C22⋊C4—833no—
450C2×C42—833no—
451C2×C42—833no—
452C2×C42—833no—
453C2×C42—833no—
454C2×C42—833no—
455C2×C42—833no—
456C2×C42—833no—
457C2×C42—833no—
458C2×C42—831no—
459C2×C42—831no—
460C2×C42—16612no—
461C2×C42—16612no—
462C2×C42C22×D8313yes—
463C2×C42C22×D8313yes—
464C2×C42C22×D8313yes—
465#95—831no—
466#95—833no—
467#95—833no—
468#95—833no—
469#95—836no—
470#95—836no—
471#95C22×D8311yescharacteristic
472#95C22×D8313yes—
473#95C22×D8316yes—
474C24—831no—
475C24—833no—
476#41—16632no—
477C2×Q8—8312no—
478C2×Q8—16632no—
479C2×Q8—1666no—
480C2×Q8—1666no—
481C2×Q8C2×C4×D8314yes—
482C2×Q8D4×D8314yes—
483C2×Q8#1305059114yes—
484C2×D4—8312no—
485C2×D4—8312no—
486C2×D4—1666no—
487C2×D4—1666no—
488C2×D4—1666no—
489C2×D4—1666no—
490C22×C4—3323no—
491C22×C4—3323no—
492C22×C4—831no—
493C22×C4—831no—
494C22×C4—831no—
495C22×C4—833no—
496C22×C4—833no—
497C22×C4—8312no—
498C22×C4—8312no—
499C22×C4—834no—
500C22×C4—833no—
501C22×C4—1666no—
502C22×C4—1666no—
503C22×C4—1666no—
504C22×C4—1666no—
505C22×C4—1666no—
506C22×C4—1666no—
507C22×C4—1662no—
508C22×C4—1662no—
509C22×C4—1666no—
510C22×C4—1666no—
511C22×C4—1666no—
512C22×C4—1666no—
513C22×C4—1666no—
514C22×C4C23×D8313yes—
515C22×C4C23×D8313yes—
516C22×C4C23×D8313yes—
517C22×C4C23×D8311yescharacteristic
518C22×C4C23×D8311yescharacteristic
519C22×C4C23×D8311yescharacteristic
520C22×C4C23×D8313yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—26no—
524C4⋊C4—26no—
525C4⋊C4—8312no—
526C4⋊C4—8312no—
527C4⋊C4—16612no—
528C4⋊C4—1666no—
529C4⋊C4C2×C4×D83112yes—
530C22⋊C4—3326no—
531C22⋊C4—834no—
532C22⋊C4—8312no—
533C22⋊C4—8324no—
534C22⋊C4—834no—
535C22⋊C4—16612no—
536C22⋊C4—1666no—
537C22⋊C4—1666no—
538C22⋊C4—1666no—
539C42—26no—
540C42—26no—
541C42—3323no—
542C42—8312no—
543C42—1662no—
544C42—1666no—
545C42—1666no—
546C42—1666no—
547C42—1666no—
548C42—1666no—
549C42—1662no—
550C42—1666no—
551C42C2×C4×D83112yes—
552C23—832no—
553C23—832no—
554C23—832no—
555C23—836no—
556C23—1663no—
557C23—1663no—
558C23—1663no—
559C23—1663no—
560C23—1663no—
561C23—1663no—
562C23—1661no—
563C23—1661no—
564C23—1661no—
565C23—1661no—
566C23C24×D8311yescharacteristic
567Q8—16624no—
568Q8#14581754116yescomplemented
569D4—16624no—
570D4—16624no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—33212no—
586C2×C4—33212no—
587C2×C4—33212no—
588C2×C4—832no—
589C2×C4—832no—
590C2×C4—832no—
591C2×C4—836no—
592C2×C4—832no—
593C2×C4—836no—
594C2×C4—832no—
595C2×C4—1668no—
596C2×C4—1663no—
597C2×C4—1663no—
598C2×C4—1663no—
599C2×C4—1661no—
600C2×C4—1663no—
601C2×C4—1663no—
602C2×C4—1661no—
603C2×C4—1661no—
604C2×C4—1663no—
605C2×C4—1661no—
606C2×C4—1663no—
607C2×C4—16624no—
608C2×C4—16624no—
609C2×C4C22×C4×D8312yes—
610C2×C4C22×C4×D8316yes—
611C2×C4C22×C4×D8316yes—
612C2×C4C2×D4×D8316yes—
613C2×C4#41×D8312yes—
614C2×C4#41×D8312yes—
615C2×C4C2×#1305059116yes—
616C22—3323no—
617C22—3323no—
618C22—3323no—
619C22—3323no—
620C22—834no—
621C22—1666no—
622C22—1666no—
623C22—1666no—
624C22—1662no—
625C22—1662no—
626C22—1662no—
627C22—1662no—
628C22—1662no—
629C22—1662no—
630C22C23×C4×D8311yescharacteristic
631C22C22×D4×D8311yescharacteristic
632C22C2×#41×D8311yescharacteristic
633C22C2×#41×D8311yescharacteristic
634C22C22×#1305059111yescharacteristic
635C222−1+4×D8311yescharacteristic
636C22#1912853811yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—43no—
642C4—43no—
643C4—3323no—
644C4—834no—
645C4—1662no—
646C4—1666no—
647C4—1666no—
648C4—1662no—
649C4C2×#14581754112yes—
650C2—3326no—
651C2—1664no—
652C2C22×#1458175411yescharacteristic
653C2C4×#41×D8311yescharacteristic
654C2#2492067211yescharacteristic
655C2#548×D8311yescharacteristic
656C2#2492095211yescharacteristic
657C2#2492106311yescharacteristic
658C2#2492108311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2351C2
socle, cosocleC23×C83C25
prime radicalC2×#19128363C2
hypercenter#2351D83
hypocenterC83C4×#548
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×C4×#13050591C2semidirect
3. C2×C4×Q8×D83C2semidirect
4. #24910532C2semidirect
5. #24910489C2semidirect
6. #24910478C2semidirect
7. #24910389C2semidirect
8. #24910301C2semidirect
9. Q8×(C2×D83)⋊C4C2semidirect
10. #24910002C2semidirect
11. #24909993C2semidirect
12. #24909971C2semidirect
13. C4×Q8×Dic83C2semidirect
14. C4×#14581754C2semidirect
15. C83×#2351C2semidirect
18. #19128363C4semidirect
71. C2×#13050591C2×C4semidirect
75. C2×Q8×D83C2×C4semidirect
84. #14581780C2×C4semidirect
85. #14581772C2×C4semidirect
86. #14581767C2×C4semidirect
88. Q8×Dic83D4semidirect
92. C4×D332C2×C4semidirect
132. C4×Q8×C83C2×C4semidirect
180. C2×C4×D83#41semidirect
193. (C2×D83)⋊C4#41semidirect
237. Q8×C83C4×D4semidirect
306. C2×D83C4×#41semidirect
319. Dic83#548semidirect
337. #2351D83semidirect
345. C83C4×#548semidirect
424. C4×Q8C4×D83semidirect
568. Q8#14581754semidirect

Maximal subgroups

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

subgroupindex
C2×#191283632
C2×C4×#130505912
C2×C4×Q8×D832
#249105322
#249104892
#249104782
#249103892
#249103012
Q8×(C2×D83)⋊C42
#249100022
#249099932
#249099712
C4×Q8×Dic832
C4×#145817542
C83×#23512
C4×#54883