Finite Group Databasebeta

← #2857×D83 #35610334

Subgroups — #2857×D83 #35610334

Order 21248.

3790 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D83C212yesmaximal
3C22×C42×D83C211yesmaximal, characteristic
4#24915816C211yesmaximal, characteristic, complemented
5#24915815C211yesmaximal, characteristic, complemented
6#24915814C214yesmaximal, complemented
7#24915813C214yesmaximal, complemented
8#24915812C212yesmaximal, complemented
9#24915811C212yesmaximal, complemented
10#24915810C211yesmaximal, characteristic, complemented
11#391×D83C212yesmaximal, complemented
12#389×D83C214yesmaximal, complemented
13#384×D83C211yesmaximal, characteristic, complemented
14#380×D83C214yesmaximal
15C83×#2857C211yesmaximal, characteristic, complemented
16C22×Q8×D83C2212yes—
17C23×C4×D83C2211yescharacteristic
18C23×C4×D83C2212yes—
19C2×#14581792C2211yescharacteristic, complemented
20C2×#14581791C2214yescomplemented
21C2×#14581790C2212yescomplemented
22C4⋊Q8×D83—28no—
23C2×#14581772C2212yes—
24C2×#14581771C2212yes—
25C2×#14581770C2214yes—
26C2×#14581769C2214yes—
27C2×#14581768C2212yes—
28C22⋊Q8×D83—216no—
29C2×C4⋊C4×D83C2214yes—
30C2×C4⋊C4×D83C2214yes—
31C2×C4⋊C4×D83C2212yes—
32C2×C4⋊C4×D83C2214yes—
33C2×C22⋊C4×D83C2214yes—
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2212yes—
36C2×C42×D83—28no—
37C2×C42×D83C2212yes—
38C2×C42×D83C2211yescharacteristic
39C2×C42×D83C2211yescharacteristic
40C2×C42×D83C2212yes—
41C2×C42×D83C2211yescharacteristic
42C2×C42×D83C2211yescharacteristic
43#19127608C2212yescomplemented
44#19127607C2212yescomplemented
45#19127606C2212yescomplemented
46#19127605C2218yescomplemented
47#19127600C2214yescomplemented
48#19127599C2214yescomplemented
49#19127598C2218yescomplemented
50#19127597C2214yescomplemented
51#19127596C2218yescomplemented
52#19127571C2211yescharacteristic, complemented
53#19127570C2212yescomplemented
54#19127570C2214yescomplemented
55#19127561C2214yes—
56#19127560C2218yes—
57#19127559C2218yes—
58#19127558C2214yes—
59#19127558C2214yes—
60#95×D83C2218yes—
61C2×C4⋊Q8×C83C2211yescharacteristic, complemented
62C2×C22⋊Q8×C83C2212yes—
63C22×C42×C83C2211yescharacteristic
64#391×C83C2212yescomplemented
65#389×C83C2214yescomplemented
66#384×C83C2211yescharacteristic, complemented
67#380×C83C2214yes—
68C24×D83C2311yescharacteristic
69C22×Dic166C2314yes—
70C22×Dic166C2312yes—
71C2×Q8×D83—28no—
72C2×Q8×D83—28no—
73C2×Q8×D83—28no—
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2312yes—
76C22×C4×D83—24no—
77C22×C4×D83—28no—
78C22×C4×D83—24no—
79C22×C4×D83—28no—
80C22×C4×D83D418yes—
81C22×C4×D83Q8116yescomplemented
82C22×C4×D83C2314yes—
83C22×C4×D83C2314yes—
84C22×C4×D83C2311yescharacteristic
85C22×C4×D83C2311yescharacteristic
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2312yes—
88C22×C4×D83C2312yes—
89C22×C4×D83C2312yes—
90C22×C4×D83C2311yescharacteristic
91C22×C4×D83C2312yes—
92#14581792—24no—
93#14581791—216no—
94#14581790—28no—
95#14581772—28no—
96#14581771—28no—
97#14581770—216no—
98#14581769—216no—
99#14581768—28no—
100C2×C4⋊Dic83C2314yes—
101C2×C4⋊Dic83C2314yes—
102C2×C4⋊Dic83C2312yes—
103C2×C4⋊Dic83C2314yes—
104C2×Dic83⋊C4C2318yes—
105C2×Dic83⋊C4C2318yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C4⋊C4×D83—216no—
110C4⋊C4×D83—28no—
111C4⋊C4×D83—216no—
112C4⋊C4×D83—216no—
113C2×C22⋊Dic83C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C22⋊C4×D83—216no—
117C2×C4×Dic83—24no—
118C2×C4×Dic83—28no—
119C2×C4×Dic83C2312yes—
120C2×C4×Dic83C2312yes—
121C2×C4×Dic83C2312yes—
122C2×C4×Dic83C2312yes—
123C2×C4×Dic83C2311yescharacteristic
124C2×C4×Dic83C2311yescharacteristic
125C2×C4×Dic83C2312yes—
126C42×D83—24no—
127C42×D83—28no—
128C42×D83—24no—
129C42×D83—28no—
130C42×D83—24no—
131C42×D83D418yes—
132C83⋊#95C2318yes—
133C83⋊#95C2318yes—
134C83⋊#95C2318yes—
135C22×Q8×C83C2312yes—
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2312yes—
138C4⋊Q8×C83—24no—
139C22⋊Q8×C83—28no—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C4⋊C4×C83C2312yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C22⋊C4×C83C2314yes—
145C2×C42×C83—24no—
146C2×C42×C83C2312yes—
147C2×C42×C83C2311yescharacteristic
148C2×C42×C83C2311yescharacteristic
149#95×C83C2318yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—24no—
153C23×D83C2×D414yes—
154C23×D83C2×Q818yes—
155C23×D83C2411yescharacteristic
156C23×D83C2411yescharacteristic
157C2×Dic166—24no—
158C2×Dic166—24no—
159C2×Dic166—24no—
160C2×Dic166—28no—
161C2×Dic166—28no—
162C2×Dic166—28no—
163Q8×D83—432no—
164C22×Dic83—22no—
165C22×Dic83—24no—
166C22×Dic83—22no—
167C22×Dic83—24no—
168C22×Dic83C2×D414yes—
169C22×Dic83C2×Q818yescomplemented
170C22×Dic83C2414yes—
171C22×Dic83C2414yes—
172C22×Dic83C2411yescharacteristic
173C22×Dic83C2412yes—
174C22×Dic83C2411yescharacteristic
175C22×Dic83C2412yes—
176C2×C4×D83—22no—
177C2×C4×D83—24no—
178C2×C4×D83—22no—
179C2×C4×D83—24no—
180C2×C4×D83—22no—
181C2×C4×D83—24no—
182C2×C4×D83—22no—
183C2×C4×D83—24no—
184C2×C4×D83—22no—
185C2×C4×D83—24no—
186C2×C4×D83—22no—
187C2×C4×D83—24no—
188C2×C4×D83—232no—
189C2×C4×D83—264no—
190C2×C4×D83—28no—
191C2×C4×D83—28no—
192C2×C4×D83—28no—
193C2×C4×D83—28no—
194C2×C4×D83—216no—
195C2×C4×D83C2×D414yes—
196C2×C4×D83C2×D414yes—
197C2×C4×D83C2×D414yes—
198C2×C4×D83C2×D414yes—
199C2×C4×D83C2×D414yes—
200C2×C4×D83C2×D418yes—
201C2×C4×D83C2×Q818yes—
202C2×C4×D83C2×Q818yes—
203C2×C4×D83C2×Q818yescomplemented
204C2×C4×D83C2×Q818yescomplemented
205C2×C4×D83#4114yes—
206C2×C4×D83#4118yes—
207C4⋊Dic83—24no—
208C4⋊Dic83—28no—
209C4⋊Dic83—28no—
210C4⋊Dic83—28no—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—216no—
215Dic83⋊C4—216no—
216C22⋊Dic83—28no—
217(C2×D83)⋊C4—28no—
218(C2×D83)⋊C4—28no—
219C4×Dic83—22no—
220C4×Dic83—24no—
221C4×Dic83—24no—
222C4×Dic83—24no—
223C4×Dic83—24no—
224C4×Dic83C2×D414yes—
225C4×Dic83C2×D418yes—
226C24×C83C2411yescharacteristic
227C2×Q8×C83—24no—
228C2×Q8×C83—24no—
229C2×Q8×C83—24no—
230C22×C4×C83—22no—
231C22×C4×C83—24no—
232C22×C4×C83—22no—
233C22×C4×C83—24no—
234C22×C4×C83C2×D414yes—
235C22×C4×C83C2×Q818yescomplemented
236C22×C4×C83C2414yes—
237C22×C4×C83C2414yes—
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2412yes—
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2412yes—
242C4⋊C4×C83—28no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—28no—
245C4⋊C4×C83—28no—
246C22⋊C4×C83—28no—
247C42×C83—22no—
248C42×C83—24no—
249C42×C83C2×D414yes—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—22no—
253C23×C83C22×D412yes—
254C23×C83C22×Q814yes—
255C23×C83C2511yescharacteristic
256C22×D83—21no—
257C22×D83—21no—
258C22×D83—22no—
259C22×D83—28no—
260C22×D83—216no—
261C22×D83—28no—
262C22×D83—216no—
263C22×D83C4⋊Q8116yescomplemented
264C22×D83C22×D412yes—
265C22×D83C22×D412yes—
266C22×D83C22×D412yes—
267C22×D83C22×Q814yes—
268C22×D83C22×Q814yes—
269C22×D83C2×#4112yes—
270C22×D83C2×#4114yes—
271Q8×C83—48no—
272C2×C4×C83—21no—
273C2×C4×C83—22no—
274C2×C4×C83—21no—
275C2×C4×C83—22no—
276C2×C4×C83—28no—
277C2×C4×C83—216no—
278C2×C4×C83—24no—
279C2×C4×C83—24no—
280C2×C4×C83—24no—
281C2×C4×C83—28no—
282C2×C4×C83—24no—
283C2×C4×C83C22×D412yes—
284C2×C4×C83C22×D412yes—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D414yes—
287C2×C4×C83C22×Q814yes—
288C2×C4×C83C22×Q814yes—
289C2×C4×C83C2×#4112yes—
290C2×C4×C83C2×#4114yes—
291C2×Dic83—21no—
292C2×Dic83—22no—
293C2×Dic83—21no—
294C2×Dic83—22no—
295C2×Dic83—28no—
296C2×Dic83—216no—
297C2×Dic83—24no—
298C2×Dic83—24no—
299C2×Dic83—24no—
300C2×Dic83—28no—
301C2×Dic83—24no—
302C2×Dic83C22×D412yes—
303C2×Dic83C22×D412yes—
304C2×Dic83C22×D412yes—
305C2×Dic83C22×D414yes—
306C2×Dic83C22×Q814yes—
307C2×Dic83C22×Q814yes—
308C2×Dic83C2×#4112yes—
309C2×Dic83C2×#4114yes—
310C4×D83—28no—
311C4×D83—216no—
312C4×D83—28no—
313C4×D83—216no—
314C4×D83—28no—
315C4×D83—216no—
316C4×D83—416no—
317C4×D83—416no—
318C4×D83#121116yes—
319C4×D83C22⋊Q8132yescomplemented
320Dic166—48no—
321Dic166—416no—
322C22×C83—22no—
323C22×C83—24no—
324C22×C83—22no—
325C22×C83—24no—
326C22×C83C2×C4⋊Q814yescomplemented
327C22×C83C23×D411yescharacteristic
328C22×C83C23×D411yescharacteristic
329C22×C83C23×Q812yes—
330C22×C83C22×#4111yescharacteristic
331C22×C83C22×#4112yes—
332C2×D83—22no—
333C2×D83—24no—
334C2×D83—22no—
335C2×D83—24no—
336C2×D83—232no—
337C2×D83C2×#12114yes—
338C2×D83C2×C22⋊Q818yes—
339C2×D83C2×C4⋊Q814yes—
340C2×D83C2×C4⋊Q814yescomplemented
341C2×D83#53214yes—
342C2×D83#53318yes—
343C4×C83—22no—
344C4×C83—24no—
345C4×C83—44no—
346C4×C83—44no—
347C4×C83C2×#12114yes—
348C4×C83C2×C22⋊Q818yescomplemented
349Dic83—22no—
350Dic83—24no—
351Dic83—44no—
352Dic83—44no—
353Dic83C2×#12114yes—
354Dic83C2×C22⋊Q818yescomplemented
355C2×#2857—831nomaximal, Sylow
356C2×C83—24no—
357C2×C83C22×#12111yescharacteristic
358C2×C83C22×C22⋊Q812yes—
359C2×C83C22×C4⋊Q811yescharacteristic
360C2×C83C2×#53211yescharacteristic
361C2×C83C2×#53312yes—
362D83—24no—
363D83#285718yesdirect product factor
364C22×C4⋊Q8—831no—
365C22×C22⋊Q8—832no—
366C23×C42—831no—
367#2857—831no—
368#2857—832no—
369#2857—834no—
370#2857—831no—
371#2857—834no—
372#2857—831no—
373#2857—832no—
374#2857D8311yescharacteristic, direct product factor
375C2×#391—832no—
376C2×#389—834no—
377C2×#384—831no—
378C2×#380—834no—
379C83C2×#285711yescharacteristic, complemented, Sylow
380C23×Q8—832no—
381C24×C4—831no—
382C24×C4—832no—
383C2×C4⋊Q8—832no—
384C2×C4⋊Q8—834no—
385C2×C4⋊Q8—831no—
386C2×C4⋊Q8—1668no—
387C2×C4⋊Q8C2×D8311yescharacteristic, complemented
388C2×C22⋊Q8—832no—
389C2×C22⋊Q8—832no—
390C2×C22⋊Q8—834no—
391C2×C22⋊Q8—832no—
392C2×C22⋊Q8—834no—
393C2×C22⋊Q8—16616no—
394C2×C22⋊Q8C2×D8312yes—
395C22×C4⋊C4—832no—
396C22×C4⋊C4—834no—
397C22×C4⋊C4—834no—
398C22×C4⋊C4—834no—
399C22×C22⋊C4—834no—
400C22×C42—831no—
401C22×C42—832no—
402C22×C42—831no—
403C22×C42—831no—
404C22×C42—832no—
405C22×C42—831no—
406C22×C42—832no—
407C22×C42—831no—
408C22×C42—1668no—
409C22×C42C2×D8311yescharacteristic
410#391—832no—
411#391—832no—
412#391—832no—
413#391—838no—
414#391C2×D8312yescomplemented
415#389—838no—
416#389—834no—
417#389—834no—
418#389—834no—
419#389—838no—
420#389C2×D8314yescomplemented
421#384—834no—
422#384—832no—
423#384—831no—
424#384C2×D8311yescharacteristic, complemented
425#380—834no—
426#380—834no—
427#380—834no—
428#380—838no—
429#380—838no—
430#380C2×D8314yes—
431C2×#95—838no—
432C25—831no—
433C22×Q8—834no—
434C22×Q8—832no—
435C22×Q8—1668no—
436C22×Q8—1668no—
437C22×Q8—1668no—
438C22×Q8C22×D8312yes—
439C23×C4—832no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—832no—
443C23×C4—838no—
444C23×C4—8316no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—832no—
449C23×C4—832no—
450C23×C4—832no—
451C23×C4—834no—
452C23×C4—834no—
453C23×C4—1668no—
454C23×C4—1664no—
455C23×C4—1668no—
456C23×C4—1664no—
457C23×C4C22×D8311yescharacteristic
458C23×C4C22×D8312yes—
459C4⋊Q8—24no—
460C4⋊Q8—16616no—
461C4⋊Q8—1668no—
462C4⋊Q8—1664no—
463C22⋊Q8—28no—
464C22⋊Q8—16616no—
465C22⋊Q8—16616no—
466C22⋊Q8—1668no—
467C22⋊Q8—1668no—
468C22⋊Q8—1668no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—832no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—838no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—838no—
477C2×C4⋊C4—834no—
478C2×C4⋊C4—1668no—
479C2×C4⋊C4—16616no—
480C2×C4⋊C4—16616no—
481C2×C4⋊C4—16616no—
482C2×C4⋊C4C22×D8312yes—
483C2×C4⋊C4C22×D8314yes—
484C2×C4⋊C4C22×D8314yes—
485C2×C4⋊C4C22×D8314yes—
486C2×C22⋊C4—834no—
487C2×C22⋊C4—834no—
488C2×C22⋊C4—834no—
489C2×C22⋊C4—16616no—
490C2×C22⋊C4C22×D8314yes—
491C2×C42—24no—
492C2×C42—831no—
493C2×C42—832no—
494C2×C42—838no—
495C2×C42—832no—
496C2×C42—832no—
497C2×C42—832no—
498C2×C42—832no—
499C2×C42—831no—
500C2×C42—1664no—
501C2×C42—1668no—
502C2×C42—1668no—
503C2×C42—1664no—
504C2×C42—1664no—
505C2×C42—1668no—
506C2×C42—1664no—
507C2×C42C22×D8312yes—
508C2×C42C22×D8311yescharacteristic
509C2×C42C22×D8311yescharacteristic
510#95—838no—
511#95—838no—
512#95—838no—
513#95C22×D8318yes—
514C24—831no—
515C24—834no—
516C24—838no—
517C24—831no—
518C24—1662no—
519C24—1662no—
520C24—1664no—
521C24C23×D8311yescharacteristic
522C2×Q8—24no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—33232no—
526C2×Q8—1668no—
527C2×Q8—1668no—
528C2×Q8—1668no—
529C2×Q8—1664no—
530C2×Q8—1664no—
531C2×Q8—1664no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—832no—
537C22×C4—831no—
538C22×C4—838no—
539C22×C4—834no—
540C22×C4—834no—
541C22×C4—838no—
542C22×C4—838no—
543C22×C4—834no—
544C22×C4—834no—
545C22×C4—838no—
546C22×C4—832no—
547C22×C4—831no—
548C22×C4—834no—
549C22×C4—834no—
550C22×C4—834no—
551C22×C4—838no—
552C22×C4—838no—
553C22×C4—838no—
554C22×C4—834no—
555C22×C4—834no—
556C22×C4—1668no—
557C22×C4—1668no—
558C22×C4—1668no—
559C22×C4—16616no—
560C22×C4—1668no—
561C22×C4—1664no—
562C22×C4—1662no—
563C22×C4—1664no—
564C22×C4—1662no—
565C22×C4—16632no—
566C22×C4—16664no—
567C22×C4—1662no—
568C22×C4—1664no—
569C22×C4—1662no—
570C22×C4—1664no—
571C22×C4—1664no—
572C22×C4—1662no—
573C22×C4—1664no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4—1664no—
577C22×C4—1662no—
578C22×C4—1664no—
579C22×C4D4×D8314yes—
580C22×C4Q8×D8318yescomplemented
581C22×C4C23×D8314yes—
582C22×C4C23×D8314yes—
583C22×C4C23×D8311yescharacteristic
584C22×C4C23×D8312yes—
585C22×C4C23×D8311yescharacteristic
586C22×C4C23×D8312yes—
587C4⋊C4—24no—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—1668no—
592C4⋊C4—1668no—
593C4⋊C4—1668no—
594C4⋊C4—16616no—
595C4⋊C4—16616no—
596C4⋊C4—1668no—
597C4⋊C4—1664no—
598C4⋊C4—1668no—
599C4⋊C4—1668no—
600C22⋊C4—28no—
601C22⋊C4—1668no—
602C22⋊C4—1668no—
603C22⋊C4—1668no—
604C42—22no—
605C42—24no—
606C42—834no—
607C42—838no—
608C42—1664no—
609C42—1664no—
610C42—1664no—
611C42—1662no—
612C42—1664no—
613C42D4×D8314yes—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—832no—
618C23—832no—
619C23—834no—
620C23—832no—
621C23—834no—
622C23—8316no—
623C23—832no—
624C23—834no—
625C23—1668no—
626C23—16616no—
627C23—1668no—
628C23—16616no—
629C23—1661no—
630C23—1661no—
631C23—1662no—
632C23C2×D4×D8312yes—
633C23C2×Q8×D8314yes—
634C23C24×D8311yescharacteristic
635Q8—48no—
636Q8—33216no—
637Q8—3328no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—28no—
643C2×C4—216no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—33216no—
650C2×C4—33216no—
651C2×C4—834no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—834no—
655C2×C4—834no—
656C2×C4—832no—
657C2×C4—8316no—
658C2×C4—8332no—
659C2×C4—832no—
660C2×C4—834no—
661C2×C4—1668no—
662C2×C4—16616no—
663C2×C4—1668no—
664C2×C4—16616no—
665C2×C4—1664no—
666C2×C4—1664no—
667C2×C4—1664no—
668C2×C4—1668no—
669C2×C4—1664no—
670C2×C4—1668no—
671C2×C4—16616no—
672C2×C4—1661no—
673C2×C4—1662no—
674C2×C4—1661no—
675C2×C4—1662no—
676C2×C4—1668no—
677C2×C4—16616no—
678C2×C4C2×D4×D8312yes—
679C2×C4C2×D4×D8312yes—
680C2×C4C2×D4×D8312yes—
681C2×C4C2×D4×D8314yes—
682C2×C4C2×Q8×D8314yes—
683C2×C4C2×Q8×D8314yes—
684C2×C4#41×D8312yes—
685C2×C4#41×D8314yes—
686C22—22no—
687C22—24no—
688C22—22no—
689C22—24no—
690C22—834no—
691C22—838no—
692C22—834no—
693C22—834no—
694C22—838no—
695C22—834no—
696C22—16632no—
697C22—1662no—
698C22—1664no—
699C22—1662no—
700C22—1664no—
701C22C4⋊Q8×D8314yescomplemented
702C22C22×D4×D8311yescharacteristic
703C22C22×D4×D8311yescharacteristic
704C22C22×Q8×D8312yes—
705C22C2×#41×D8311yescharacteristic
706C22C2×#41×D8312yes—
707C4—22no—
708C4—24no—
709C4—44no—
710C4—44no—
711C4—3324no—
712C4—3324no—
713C4—834no—
714C4—838no—
715C4—1662no—
716C4—1664no—
717C4#121×D8314yes—
718C4C22⋊Q8×D8318yescomplemented
719C2—24no—
720C2—838no—
721C2—1664no—
722C2C2×#121×D8311yescharacteristic
723C2C2×C22⋊Q8×D8312yes—
724C2C2×C4⋊Q8×D8311yescharacteristic
725C2#532×D8311yescharacteristic
726C2#533×D8312yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2857C2
prime radicalC24×D83C23
hypercenter#2857D83
hypocenterC83C2×#2857
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D83C2semidirect
4. #24915816C2semidirect
5. #24915815C2semidirect
6. #24915814C2semidirect
7. #24915813C2semidirect
8. #24915812C2semidirect
9. #24915811C2semidirect
10. #24915810C2semidirect
11. #391×D83C2semidirect
12. #389×D83C2semidirect
13. #384×D83C2semidirect
15. C83×#2857C2semidirect
19. C2×#14581792C22semidirect
20. C2×#14581791C22semidirect
21. C2×#14581790C22semidirect
43. #19127608C22semidirect
44. #19127607C22semidirect
45. #19127606C22semidirect
46. #19127605C22semidirect
47. #19127600C22semidirect
48. #19127599C22semidirect
49. #19127598C22semidirect
50. #19127597C22semidirect
51. #19127596C22semidirect
52. #19127571C22semidirect
53. #19127570C22semidirect
54. #19127570C22semidirect
61. C2×C4⋊Q8×C83C22semidirect
64. #391×C83C22semidirect
65. #389×C83C22semidirect
66. #384×C83C22semidirect
81. C22×C4×D83Q8semidirect
169. C22×Dic83C2×Q8semidirect
203. C2×C4×D83C2×Q8semidirect
204. C2×C4×D83C2×Q8semidirect
235. C22×C4×C83C2×Q8semidirect
263. C22×D83C4⋊Q8semidirect
319. C4×D83C22⋊Q8semidirect
326. C22×C83C2×C4⋊Q8semidirect
340. C2×D83C2×C4⋊Q8semidirect
348. C4×C83C2×C22⋊Q8semidirect
354. Dic83C2×C22⋊Q8semidirect
363. D83#2857direct (N × H)
374. #2857D83direct (N × H)
379. C83C2×#2857semidirect
387. C2×C4⋊Q8C2×D83semidirect
414. #391C2×D83semidirect
420. #389C2×D83semidirect
424. #384C2×D83semidirect
580. C22×C4Q8×D83semidirect
701. C22C4⋊Q8×D83semidirect
718. C4C22⋊Q8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D832
C2×C22⋊Q8×D832
C22×C42×D832
#249158162
#249158152
#249158142
#249158132
#249158122
#249158112
#249158102
#391×D832
#389×D832
#384×D832
#380×D832
C83×#28572
C2×#285783