Finite Group Databasebeta

← #2584×D83 #35575633

Subgroups — #2584×D83 #35575633

Order 21248.

2574 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D83C211yesmaximal, characteristic
2C2×C4×Q8×D83C211yesmaximal, characteristic
3#24912852C211yesmaximal, characteristic, complemented
4#24912851C211yesmaximal, characteristic, complemented
5#24912850C212yesmaximal, complemented
6#24912849C214yesmaximal, complemented
7#24912848C212yesmaximal, complemented
8#24912847C212yesmaximal, complemented
9#24912846C211yesmaximal, characteristic, complemented
10#24912845C212yesmaximal, complemented
11#398×D83C212yesmaximal
12#395×D83C212yesmaximal
13#389×D83C212yesmaximal
14#389×D83C212yesmaximal
15#389×D83C214yesmaximal
16C4×C4⋊C4×D83C211yesmaximal, characteristic
17C83×#2584C211yesmaximal, characteristic, complemented
18C22×Q8×D83C2211yescharacteristic
19C2×#14581784C2211yescharacteristic
20C2×#14581783C2211yescharacteristic
21C2×#14581783C2211yescharacteristic
22C2×#14581782C2212yes—
23C2×#14581782C2212yes—
24#125×D83—28no—
25C2×Q8×Dic83C2211yescharacteristic
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×Dic166C2212yes—
28C2×#14581757C2211yescharacteristic
29C2×#14581757C2212yes—
30C4×Q8×D83—28no—
31C2×C4⋊C4×D83C2212yes—
32C2×C4⋊C4×D83C2211yescharacteristic
33C2×C4⋊C4×D83C2214yes—
34C2×C4⋊C4×D83C2212yes—
35C2×C4⋊C4×D83C2212yes—
36C2×C4⋊C4×D83C2211yescharacteristic
37C2×C4⋊C4×D83C2211yescharacteristic
38C2×C4⋊C4×D83C2214yes—
39C2×C4⋊C4×D83C2212yes—
40C2×C42×D83C2212yes—
41C2×C42×D83C2212yes—
42C2×C42×D83C2211yescharacteristic
43#19127635C2214yes—
44#19127634C2214yes—
45#19127633C2212yes—
46#19127632C2212yes—
47#19127631C2212yes—
48#19127622C2212yes—
49#19127622C2214yes—
50#19127621C2212yes—
51#19127621C2214yes—
52#19127620C2212yes—
53#19127600C2214yes—
54#19127600C2212yes—
55#19127600C2212yes—
56#19127599C2214yes—
57#19127599C2212yes—
58#19127599C2212yes—
59#19127598C2214yes—
60#19127598C2214yes—
61#19127598C2214yes—
62#19127598C2214yes—
63#19127597C2214yes—
64#19127597C2212yes—
65#19127597C2212yes—
66#19127596C2214yes—
67#19127596C2214yes—
68#19127596C2214yes—
69#19127596C2214yes—
70C4⋊C4×Dic83C2212yes—
71C4×Dic83⋊C4C2212yes—
72C4×C4⋊Dic83C2211yescharacteristic
73#19127552C2212yes—
74#95×D83C2214yes—
75#95×D83C2212yes—
76#95×D83C2214yes—
77C2×#125×C83C2211yescharacteristic
78C2×C4×Q8×C83C2211yescharacteristic
79#398×C83C2212yes—
80#395×C83C2212yes—
81#389×C83C2212yes—
82#389×C83C2214yes—
83#389×C83C2212yes—
84C4×C4⋊C4×C83C2211yescharacteristic
85C22×Dic166C2311yescharacteristic
86C22×Dic166C2312yes—
87C2×Q8×D83—24no—
88C2×Q8×D83—28no—
89C22×C4×D83C2312yes—
90C22×C4×D83C2312yes—
91C22×C4×D83C2312yes—
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2311yescharacteristic
94C22×C4×D83C2314yes—
95C22×C4×D83C2312yes—
96C22×C4×D83C2311yescharacteristic
97#14581784—24no—
98#14581783—24no—
99#14581783—24no—
100#14581782—28no—
101#14581782—28no—
102Q8×Dic83—24no—
103C4×Dic166—28no—
104C4×Dic166—24no—
105#14581757—24no—
106#14581757—28no—
107C2×C4⋊Dic83C2314yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×C4⋊Dic83C2312yes—
113C2×C4⋊Dic83C2311yescharacteristic
114C2×C4⋊Dic83C2314yes—
115C2×C4⋊Dic83C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C2×Dic83⋊C4C2314yes—
119C2×Dic83⋊C4C2312yes—
120C2×Dic83⋊C4C2312yes—
121C2×Dic83⋊C4C2314yes—
122C2×Dic83⋊C4C2312yes—
123C2×Dic83⋊C4C2312yes—
124C2×Dic83⋊C4C2312yes—
125C2×Dic83⋊C4C2312yes—
126C2×Dic83⋊C4C2312yes—
127C2×Dic83⋊C4C2314yes—
128C2×Dic83⋊C4C2314yes—
129C2×Dic83⋊C4C2314yes—
130C4⋊C4×D83—28no—
131C4⋊C4×D83—24no—
132C4⋊C4×D83—28no—
133C4⋊C4×D83—28no—
134C4⋊C4×D83—24no—
135C4⋊C4×D83—24no—
136C4⋊C4×D83—216no—
137C4⋊C4×D83—48no—
138C4⋊C4×D83Q8116yescomplemented
139C2×C4×Dic83C2312yes—
140C2×C4×Dic83C2312yes—
141C2×C4×Dic83C2312yes—
142C2×C4×Dic83C2314yes—
143C2×C4×Dic83C2312yes—
144C2×C4×Dic83C2311yescharacteristic
145C2×C4×Dic83C2311yescharacteristic
146C2×C4×Dic83C2311yescharacteristic
147C42×D83—28no—
148C42×D83—44no—
149C42×D83D418yes—
150C83⋊#95C2312yes—
151C83⋊#95C2314yes—
152C83⋊#95C2314yes—
153C83⋊#95C2314yes—
154C83⋊#95C2314yes—
155C83⋊#95C2314yes—
156C83⋊#95C2314yes—
157C83⋊#95C2314yes—
158C22×Q8×C83C2311yescharacteristic
159#125×C83—24no—
160C4×Q8×C83—24no—
161C2×C4⋊C4×C83C2312yes—
162C2×C4⋊C4×C83C2312yes—
163C2×C4⋊C4×C83C2314yes—
164C2×C4⋊C4×C83C2311yescharacteristic
165C2×C4⋊C4×C83C2311yescharacteristic
166C2×C4⋊C4×C83C2311yescharacteristic
167C2×C4⋊C4×C83C2312yes—
168C2×C4⋊C4×C83C2314yes—
169C2×C4⋊C4×C83C2312yes—
170C2×C42×C83C2312yes—
171C2×C42×C83C2312yes—
172C2×C42×C83C2311yescharacteristic
173#95×C83C2312yes—
174#95×C83C2314yes—
175#95×C83C2314yes—
176C23×D83C2411yescharacteristic
177C2×Dic166—22no—
178C2×Dic166—24no—
179C2×Dic166—24no—
180C2×Dic166—24no—
181C2×Dic166—24no—
182Q8×D83—232no—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2411yescharacteristic
187C22×Dic83C2411yescharacteristic
188C22×Dic83C2414yes—
189C22×Dic83C2412yes—
190C22×Dic83C2411yescharacteristic
191C2×C4×D83—24no—
192C2×C4×D83—24no—
193C2×C4×D83—24no—
194C2×C4×D83—28no—
195C2×C4×D83—22no—
196C2×C4×D83—28no—
197C2×C4×D83—22no—
198C2×C4×D83—24no—
199C2×C4×D83—24no—
200C2×C4×D83—24no—
201C2×C4×D83—28no—
202C2×C4×D83—24no—
203C2×C4×D83—24no—
204C2×C4×D83—24no—
205C2×C4×D83—24no—
206C2×C4×D83C2×D414yes—
207C2×C4×D83C2×D414yes—
208C2×C4×D83C2×D414yes—
209C2×C4×D83C2×Q8116yes—
210C2×C4×D83C2×Q818yes—
211C2×C4×D83#4118yes—
212C4⋊Dic83—22no—
213C4⋊Dic83—22no—
214C4⋊Dic83—22no—
215C4⋊Dic83—24no—
216C4⋊Dic83—24no—
217C4⋊Dic83—24no—
218C4⋊Dic83—28no—
219C4⋊Dic83—44no—
220C4⋊Dic83C2×Q818yescomplemented
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—28no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4—24no—
231Dic83⋊C4—28no—
232Dic83⋊C4—44no—
233Dic83⋊C4—44no—
234Dic83⋊C4C2×Q8116yescomplemented
235C4×Dic83—24no—
236C4×Dic83—24no—
237C4×Dic83—24no—
238C4×Dic83—44no—
239C4×Dic83—42no—
240C4×Dic83C2×D414yes—
241C4×Dic83C2×D414yes—
242C4×Dic83C2×D414yes—
243C2×Q8×C83—22no—
244C2×Q8×C83—24no—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2411yescharacteristic
249C22×C4×C83C2411yescharacteristic
250C22×C4×C83C2414yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2411yescharacteristic
253C4⋊C4×C83—24no—
254C4⋊C4×C83—24no—
255C4⋊C4×C83—22no—
256C4⋊C4×C83—22no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—22no—
259C4⋊C4×C83—28no—
260C4⋊C4×C83—44no—
261C4⋊C4×C83C2×Q818yescomplemented
262C42×C83—24no—
263C42×C83—42no—
264C42×C83C2×D414yes—
265C23×C83C2511yescharacteristic
266C22×D83C22×D412yes—
267C22×D83C22×Q814yes—
268C22×D83C2×#4114yes—
269C22×D83H(5,𝔽2)12yes—
270C22×D832−1+412yes—
271Q8×C83—28no—
272C2×C4×C83—22no—
273C2×C4×C83—24no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—21no—
277C2×C4×C83—24no—
278C2×C4×C83—21no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×Q818yes—
291C2×C4×C83C22×Q814yes—
292C2×C4×C83C2×#4114yes—
293C2×Dic83—22no—
294C2×Dic83—24no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—21no—
298C2×Dic83—24no—
299C2×Dic83—21no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—24no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83C22×D412yes—
309C2×Dic83C22×D412yes—
310C2×Dic83C22×D412yes—
311C2×Dic83C22×Q818yes—
312C2×Dic83C22×Q814yes—
313C2×Dic83C2×#4114yes—
314C4×D83—28no—
315C4×D83—216no—
316C4×D83—28no—
317C4×D83—232no—
318C4×D83—48no—
319C4×D83—48no—
320C4×D83—48no—
321C4×D83C4⋊Q8116yes—
322Dic166—216no—
323Dic166—28no—
324C22×C83C23×D411yescharacteristic
325C22×C83C23×Q812yes—
326C22×C83C22×#4112yes—
327C22×C83C2×H(5,𝔽2)11yescharacteristic
328C22×C83C2×2−1+411yescharacteristic
329C2×D83#52514yes—
330C2×D83C2×C4⋊Q814yes—
331C2×D83#53714yes—
332C2×D83#55418yes—
333C2×D83#55718yes—
334C4×C83—22no—
335C4×C83—24no—
336C4×C83—22no—
337C4×C83—28no—
338C4×C83—42no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83C2×C4⋊Q814yes—
342Dic83—22no—
343Dic83—24no—
344Dic83—22no—
345Dic83—28no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83C2×C4⋊Q814yes—
350C2×#2584—831nomaximal, Sylow
351C2×C83C2×#52511yescharacteristic
352C2×C83C22×C4⋊Q811yescharacteristic
353C2×C83C2×#53711yescharacteristic
354C2×C83C2×#55412yes—
355C2×C83C2×#55712yes—
356D83#258418yesdirect product factor
357C22×#125—831no—
358C22×C4×Q8—831no—
359#2584—832no—
360#2584—832no—
361#2584—832no—
362#2584—834no—
363#2584—832no—
364#2584—831no—
365#2584—831no—
366#2584—831no—
367#2584D8311yescharacteristic, direct product factor
368C2×#398—832no—
369C2×#395—832no—
370C2×#389—832no—
371C2×#389—834no—
372C2×#389—832no—
373C2×C4×C4⋊C4—831no—
374C83C2×#258411yescharacteristic, complemented, Sylow
375C23×Q8—831no—
376C2×#125—832no—
377C2×#125—832no—
378C2×#125—831no—
379C2×#125—831no—
380C2×#125—831no—
381C2×#125—1668no—
382C2×#125C2×D8311yescharacteristic
383C2×C4×Q8—831no—
384C2×C4×Q8—831no—
385C2×C4×Q8—832no—
386C2×C4×Q8—832no—
387C2×C4×Q8—831no—
388C2×C4×Q8—1668no—
389C2×C4×Q8C2×D8311yescharacteristic
390C22×C4⋊C4—834no—
391C22×C4⋊C4—832no—
392C22×C4⋊C4—832no—
393C22×C4⋊C4—834no—
394C22×C4⋊C4—831no—
395C22×C4⋊C4—832no—
396C22×C4⋊C4—831no—
397C22×C4⋊C4—831no—
398C22×C4⋊C4—832no—
399C22×C42—832no—
400C22×C42—831no—
401C22×C42—832no—
402#398—832no—
403#398—832no—
404#398—834no—
405#398—832no—
406#398—834no—
407#398C2×D8312yes—
408#395—832no—
409#395—834no—
410#395—832no—
411#395—834no—
412#395—832no—
413#395C2×D8312yes—
414#389—834no—
415#389—834no—
416#389—834no—
417#389—834no—
418#389—832no—
419#389—834no—
420#389—832no—
421#389—832no—
422#389—834no—
423#389—832no—
424#389—832no—
425#389—834no—
426#389—832no—
427#389—834no—
428#389—834no—
429#389—834no—
430#389—834no—
431#389C2×D8312yes—
432#389C2×D8314yes—
433#389C2×D8312yes—
434C4×C4⋊C4—832no—
435C4×C4⋊C4—831no—
436C4×C4⋊C4—832no—
437C4×C4⋊C4—832no—
438C4×C4⋊C4C2×D8311yescharacteristic
439C2×#95—832no—
440C2×#95—834no—
441C2×#95—834no—
442C22×Q8—831no—
443C22×Q8—832no—
444C22×Q8—1664no—
445C22×Q8—1668no—
446C22×Q8C22×D8311yescharacteristic
447C23×C4—831no—
448C23×C4—831no—
449C23×C4—831no—
450C23×C4—832no—
451C23×C4—834no—
452C23×C4—832no—
453C23×C4—832no—
454C23×C4—832no—
455#125—24no—
456#125—1668no—
457#125—1668no—
458#125—1664no—
459#125—1664no—
460#125—1664no—
461C4×Q8—24no—
462C4×Q8—1668no—
463C4×Q8—1664no—
464C4×Q8—1668no—
465C4×Q8—1664no—
466C4×Q8—1664no—
467C2×C4⋊C4—3328no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—832no—
473C2×C4⋊C4—8316no—
474C2×C4⋊C4—832no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—832no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—832no—
483C2×C4⋊C4—832no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4—834no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—834no—
492C2×C4⋊C4—1664no—
493C2×C4⋊C4—1668no—
494C2×C4⋊C4—1664no—
495C2×C4⋊C4—1664no—
496C2×C4⋊C4—1668no—
497C2×C4⋊C4—1668no—
498C2×C4⋊C4—16616no—
499C2×C4⋊C4C22×D8312yes—
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C4⋊C4C22×D8312yes—
502C2×C4⋊C4C22×D8311yescharacteristic
503C2×C4⋊C4C22×D8311yescharacteristic
504C2×C4⋊C4C22×D8312yes—
505C2×C4⋊C4C22×D8314yes—
506C2×C4⋊C4C22×D8314yes—
507C2×C4⋊C4C22×D8312yes—
508C2×C42—3324no—
509C2×C42—832no—
510C2×C42—834no—
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—838no—
515C2×C42—832no—
516C2×C42—832no—
517C2×C42—832no—
518C2×C42—1668no—
519C2×C42C22×D8312yes—
520C2×C42C22×D8312yes—
521C2×C42C22×D8311yescharacteristic
522#95—832no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95C22×D8312yes—
531#95C22×D8314yes—
532#95C22×D8314yes—
533C24—831no—
534C2×Q8—22no—
535C2×Q8—24no—
536C2×Q8—1664no—
537C2×Q8—1664no—
538C2×Q8—1664no—
539C2×Q8—16632no—
540C2×Q8—1662no—
541C2×Q8—1664no—
542C22×C4—831no—
543C22×C4—834no—
544C22×C4—838no—
545C22×C4—834no—
546C22×C4—831no—
547C22×C4—832no—
548C22×C4—831no—
549C22×C4—834no—
550C22×C4—834no—
551C22×C4—8316no—
552C22×C4—838no—
553C22×C4—832no—
554C22×C4—832no—
555C22×C4—832no—
556C22×C4—1664no—
557C22×C4—1664no—
558C22×C4—1664no—
559C22×C4—1664no—
560C22×C4—1664no—
561C22×C4—1668no—
562C22×C4—1664no—
563C22×C4—1664no—
564C22×C4—1662no—
565C22×C4—1668no—
566C22×C4—1664no—
567C22×C4—1668no—
568C22×C4—1664no—
569C22×C4—1664no—
570C22×C4—1662no—
571C22×C4C23×D8312yes—
572C22×C4C23×D8312yes—
573C22×C4C23×D8312yes—
574C22×C4C23×D8311yescharacteristic
575C22×C4C23×D8311yescharacteristic
576C22×C4C23×D8314yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8311yescharacteristic
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—28no—
586C4⋊C4—44no—
587C4⋊C4—3324no—
588C4⋊C4—3324no—
589C4⋊C4—3324no—
590C4⋊C4—8316no—
591C4⋊C4—838no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1668no—
602C4⋊C4—1668no—
603C4⋊C4—1664no—
604C4⋊C4—1662no—
605C4⋊C4—1664no—
606C4⋊C4—1664no—
607C4⋊C4—1662no—
608C4⋊C4—1662no—
609C4⋊C4—1668no—
610C4⋊C4Q8×D8318yescomplemented
611C42—24no—
612C42—42no—
613C42—3322no—
614C42—3324no—
615C42—834no—
616C42—834no—
617C42—834no—
618C42—1664no—
619C42—1664no—
620C42—1664no—
621C42D4×D8314yes—
622C23—832no—
623C23—834no—
624C23—834no—
625C23—832no—
626C23—832no—
627C23C24×D8311yescharacteristic
628Q8—28no—
629Q8—1668no—
630Q8—16616no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—24no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—3328no—
647C2×C4—3328no—
648C2×C4—3328no—
649C2×C4—832no—
650C2×C4—834no—
651C2×C4—8316no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—838no—
655C2×C4—834no—
656C2×C4—1668no—
657C2×C4—16616no—
658C2×C4—16632no—
659C2×C4—1668no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1664no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1664no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1661no—
673C2×C4—1664no—
674C2×C4—1661no—
675C2×C4C2×D4×D8312yes—
676C2×C4C2×D4×D8312yes—
677C2×C4C2×D4×D8312yes—
678C2×C4C2×Q8×D8318yes—
679C2×C4C2×Q8×D8314yes—
680C2×C4#41×D8314yes—
681C22—834no—
682C22—838no—
683C22—834no—
684C22—838no—
685C22—834no—
686C22C22×D4×D8311yescharacteristic
687C22C22×Q8×D8312yes—
688C22C2×#41×D8312yes—
689C22H(5,𝔽2)×D8311yescharacteristic
690C222−1+4×D8311yescharacteristic
691C4—22no—
692C4—24no—
693C4—28no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—3322no—
699C4—3322no—
700C4—3322no—
701C4—834no—
702C4—1662no—
703C4—1664no—
704C4—1668no—
705C4—1662no—
706C4C4⋊Q8×D8314yes—
707C2—838no—
708C2#525×D8311yescharacteristic
709C2C2×C4⋊Q8×D8311yescharacteristic
710C2#537×D8311yescharacteristic
711C2#554×D8312yes—
712C2#557×D8312yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2584C2
prime radicalC23×D83C24
hypercenter#2584D83
hypocenterC83C2×#2584
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2584

Complements

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

NH ≅ G/Ntype
3. #24912852C2semidirect
4. #24912851C2semidirect
5. #24912850C2semidirect
6. #24912849C2semidirect
7. #24912848C2semidirect
8. #24912847C2semidirect
9. #24912846C2semidirect
10. #24912845C2semidirect
17. C83×#2584C2semidirect
138. C4⋊C4×D83Q8semidirect
220. C4⋊Dic83C2×Q8semidirect
234. Dic83⋊C4C2×Q8semidirect
261. C4⋊C4×C83C2×Q8semidirect
356. D83#2584direct (N × H)
367. #2584D83direct (N × H)
374. C83C2×#2584semidirect
610. C4⋊C4Q8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D832
C2×C4×Q8×D832
#249128522
#249128512
#249128502
#249128492
#249128482
#249128472
#249128462
#249128452
#398×D832
#395×D832
#389×D832
C4×C4⋊C4×D832
C83×#25842
C2×#258483