Finite Group Databasebeta

← C4×#19127577 #35325549

Subgroups — C4×#19127577 #35325549

Order 21248.

3366 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D83C211yesmaximal, characteristic
2C22×C42×D83C211yesmaximal, characteristic, complemented
3C2×#19127577C212yesmaximal
4C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
6#24905700C212yesmaximal, complemented
7#24905694C212yesmaximal, complemented
8(C2×D83)⋊#95C212yesmaximal, complemented
9C4×C83⋊#95C211yesmaximal, characteristic, complemented
10C4×C83⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×C22⋊D83C2211yescharacteristic
13C23×C4×D83C2212yes—
14C23×C4×D83C2211yescharacteristic
15C2×C4×C22⋊D83—24no—
16C2×C4×C22⋊D83—24no—
17C2×C4×C22⋊D83C418yescomplemented
18C22×Dic83⋊C4C2211yescharacteristic
19C22×C22⋊Dic83C2212yes—
20C22×C22⋊Dic83C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2212yes—
23C22×C4×Dic83C2212yes—
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C2×C42×D83—24no—
28C2×C42×D83—24no—
29C2×C42×D83—24no—
30#19127577C4116yesdirect product factor
31C4×(C2×D83)⋊C4—24no—
32C4×C22⋊Dic83—24no—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C2×C83⋊#95C2212yes—
37C2×C83⋊#95C2212yes—
38C2×C83⋊#95C2212yes—
39C24×C4×C83C2211yescharacteristic
40C22×C22⋊C4×C83C2212yes—
41C22×C42×C83C2211yescharacteristic
42C22×C42×C83C2211yescharacteristic
43C4×C22⋊C4×C83—24no—
44C2×#95×C83C2212yes—
45C24×D83C2311yescharacteristic
46C22×C22⋊D83—22no—
47C22×C22⋊D83—22no—
48C22×C22⋊D83—24no—
49C22×C22⋊D83C2×C418yes—
50C22×C22⋊D83C2×C414yes—
51C23×Dic83C2312yes—
52C23×Dic83C2311yescharacteristic
53C23×Dic83C2311yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2312yes—
56C22×C4×D83—24no—
57C22×C4×D83—24no—
58C22×C4×D83—24no—
59C22×C4×D83—24no—
60C22×C4×D83—22no—
61C22×C4×D83—24no—
62C22×C4×D83—22no—
63C22×C4×D83—22no—
64C22×C4×D83—24no—
65C22×C4×D83—22no—
66C22×C4×D83C2×C414yes—
67C22×C4×D83C2×C418yescomplemented
68C22×C4×D83D414yes—
69C22×C4×D83D414yes—
70C4×C22⋊D83—232no—
71C2×Dic83⋊C4—22no—
72C2×Dic83⋊C4—22no—
73C2×Dic83⋊C4C2×C414yescomplemented
74C2×C22⋊Dic83—22no—
75C2×C22⋊Dic83—22no—
76C2×C22⋊Dic83—24no—
77C2×C22⋊Dic83—24no—
78C2×C22⋊Dic83C2×C418yescomplemented
79C2×C22⋊Dic83C2×C414yescomplemented
80C2×(C2×D83)⋊C4—22no—
81C2×(C2×D83)⋊C4—22no—
82C2×(C2×D83)⋊C4—24no—
83C2×(C2×D83)⋊C4—24no—
84C2×(C2×D83)⋊C4C2×C414yes—
85C2×(C2×D83)⋊C4C2×C418yescomplemented
86C2×C4×Dic83—24no—
87C2×C4×Dic83—24no—
88C2×C4×Dic83—22no—
89C2×C4×Dic83—24no—
90C2×C4×Dic83—22no—
91C2×C4×Dic83—22no—
92C2×C4×Dic83—22no—
93C2×C4×Dic83—22no—
94C2×C4×Dic83—22no—
95C2×C4×Dic83—22no—
96C2×C4×Dic83C2×C414yescomplemented
97C2×C4×Dic83D414yescomplemented
98C42×D83—232no—
99C83⋊#95—24no—
100C83⋊#95—24no—
101C83⋊#95—24no—
102C83⋊#95—24no—
103C83⋊#95C2×C418yescomplemented
104C83⋊#95C2×C418yescomplemented
105C25×C83C2311yescharacteristic
106C23×C4×C83—22no—
107C23×C4×C83—22no—
108C23×C4×C83—22no—
109C23×C4×C83—22no—
110C23×C4×C83—22no—
111C23×C4×C83—22no—
112C23×C4×C83C2×C414yescomplemented
113C23×C4×C83C2312yes—
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2312yes—
116C23×C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—24no—
118C2×C22⋊C4×C83—24no—
119C2×C22⋊C4×C83C2×C418yescomplemented
120C2×C42×C83—22no—
121C2×C42×C83—22no—
122C2×C42×C83—22no—
123C2×C42×C83—22no—
124C2×C42×C83—22no—
125C2×C42×C83D414yescomplemented
126#95×C83—24no—
127C23×D83—21no—
128C23×D83—21no—
129C23×D83—22no—
130C23×D83—21no—
131C23×D83—21no—
132C23×D83—22no—
133C23×D83C22×C412yes—
134C23×D83C22×C414yes—
135C23×D83C2×D412yes—
136C23×D83C2×D412yes—
137C23×D83#4114yes—
138C2×C22⋊D83—28no—
139C2×C22⋊D83—28no—
140C2×C22⋊D83—216no—
141C2×C22⋊D83—216no—
142C2×C22⋊D83C42116yescomplemented
143C22×Dic83—21no—
144C22×Dic83—22no—
145C22×Dic83—21no—
146C22×Dic83—22no—
147C22×Dic83—21no—
148C22×Dic83—21no—
149C22×Dic83—22no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83C22×C414yes—
165C22×Dic83C22×C412yes—
166C22×Dic83C22×C414yes—
167C22×Dic83C22×C412yes—
168C22×Dic83C22×C412yes—
169C22×Dic83C22×C414yes—
170C22×Dic83C2×D412yes—
171C22×Dic83C2×D412yes—
172C22×Dic83C2×D414yes—
173C22×Dic83#4114yes—
174C2×C4×D83—216no—
175C2×C4×D83—216no—
176C2×C4×D83—216no—
177C2×C4×D83—216no—
178C2×C4×D83—216no—
179C2×C4×D83—28no—
180C2×C4×D83—28no—
181C2×C4×D83—216no—
182C2×C4×D83—28no—
183C2×C4×D83—28no—
184C2×C4×D83—28no—
185C2×C4×D83—28no—
186C2×C4×D83—216no—
187C2×C4×D83C22⋊C4116yescomplemented
188Dic83⋊C4—28no—
189C22⋊Dic83—28no—
190C22⋊Dic83—216no—
191(C2×D83)⋊C4—28no—
192(C2×D83)⋊C4—216no—
193C4×Dic83—216no—
194C4×Dic83—28no—
195C4×Dic83—28no—
196C4×Dic83—44no—
197C24×C83—21no—
198C24×C83—21no—
199C24×C83—21no—
200C24×C83—21no—
201C24×C83—22no—
202C24×C83—22no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—22no—
206C24×C83C22×C414yes—
207C24×C83C22×C412yes—
208C24×C83C2411yescharacteristic
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—21no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—28no—
226C22×C4×C83—28no—
227C22×C4×C83—28no—
228C22×C4×C83—44no—
229C22×C4×C83—44no—
230C22×C4×C83—44no—
231C22×C4×C83—44no—
232C22×C4×C83C22×C414yes—
233C22×C4×C83C22×C412yes—
234C22×C4×C83C22×C414yes—
235C22×C4×C83C22×C412yes—
236C22×C4×C83C2×D412yes—
237C22×C4×C83C2×D412yes—
238C22×C4×C83C2×D412yes—
239C22×C4×C83C2×D414yes—
240C22×C4×C83C2×D412yes—
241C22×C4×C83#4112yes—
242C22×C4×C83#4114yes—
243C22×C4×C83#4112yes—
244C22⋊C4×C83—216no—
245C42×C83—28no—
246C42×C83—44no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—24no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—24no—
253C23×C83—24no—
254C23×C83—24no—
255C23×C83—24no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—24no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—42no—
264C23×C83—42no—
265C23×C83—42no—
266C23×C83—42no—
267C23×C83—42no—
268C23×C83—42no—
269C23×C83C2×C4214yescomplemented
270C23×C83C23×C411yescharacteristic
271C23×C83C23×C412yes—
272C23×C83C22×D411yescharacteristic
273C23×C83C22×D411yescharacteristic
274C23×C83C22×D411yescharacteristic
275C23×C83C22×D411yescharacteristic
276C23×C83C2×#4112yes—
277C23×C83C2×#4112yes—
278C23×C83C2×#4111yescharacteristic
279C23×C83C2×#4111yescharacteristic
280C23×C83C2×#4112yes—
281C22×D83—24no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—24no—
285C22×D83—24no—
286C22×D83—22no—
287C22×D83—22no—
288C22×D83—24no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—24no—
294C22×D83—24no—
295C22×D83—24no—
296C22×D83—24no—
297C22×D83—24no—
298C22×D83—24no—
299C22×D83C2×C4214yes—
300C22×D83C2×C22⋊C414yes—
301C22×D83#11714yes—
302C22×D83C4×D418yes—
303C22×D83C4×D418yes—
304C2×C4×C83—24no—
305C2×C4×C83—24no—
306C2×C4×C83—24no—
307C2×C4×C83—24no—
308C2×C4×C83—24no—
309C2×C4×C83—24no—
310C2×C4×C83—22no—
311C2×C4×C83—24no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—24no—
315C2×C4×C83—24no—
316C2×C4×C83—41no—
317C2×C4×C83—42no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83—42no—
322C2×C4×C83—42no—
323C2×C4×C83—42no—
324C2×C4×C83—416no—
325C2×C4×C83C2×C22⋊C414yes—
326C2×C4×C83C4×D414yes—
327C2×C4×C83C4×D414yes—
328C2×C4×C83C4×D418yescomplemented
329C2×C4×C83#12014yes—
330C2×C4×C83#12114yes—
331C2×C4×C83#12114yes—
332C2×C4×C83#12314yes—
333C22⋊D83—232no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—24no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—24no—
340C2×Dic83—24no—
341C2×Dic83—24no—
342C2×Dic83—22no—
343C2×Dic83—24no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—24no—
348C2×Dic83—24no—
349C2×Dic83—24no—
350C2×Dic83—22no—
351C2×Dic83—24no—
352C2×Dic83—24no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—24no—
356C2×Dic83—42no—
357C2×Dic83—42no—
358C2×Dic83—42no—
359C2×Dic83—42no—
360C2×Dic83—42no—
361C2×Dic83—42no—
362C2×Dic83C2×C4214yescomplemented
363C2×Dic83C2×C22⋊C414yes—
364C2×Dic83C4×D418yescomplemented
365C4×D83—264no—
366C4×D83—232no—
367C22×C83—24no—
368C22×C83—24no—
369C22×C83—24no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—44no—
375C22×C83—44no—
376C22×C83—44no—
377C22×C83—44no—
378C22×C83C22×C4211yescharacteristic
379C22×C83C22×C22⋊C411yescharacteristic
380C22×C83C2×#11711yescharacteristic
381C22×C83C2×C4×D412yes—
382C22×C83C2×C4×D412yes—
383C22×C83C2×C4×D412yes—
384C22×C83C2×C4×D411yescharacteristic
385C22×C83C2×C4×D411yescharacteristic
386C22×C83C2×C4×D412yes—
387C22×C83C4×#4112yes—
388C22×C83C4×#4111yescharacteristic
389C22×C83C4×#4111yescharacteristic
390C22×C83C4×#4112yes—
391C22×C83C2×#12011yescharacteristic
392C22×C83C2×#12111yescharacteristic
393C22×C83C2×#12111yescharacteristic
394C22×C83C2×#12311yescharacteristic
395C22×C83#52512yes—
396C22×C83#52512yes—
397C22×C83#52512yes—
398C22×C83#52912yes—
399C22×C83#52912yes—
400C22×C83#53212yes—
401C2×D83—24no—
402C2×D83—24no—
403C2×D83—24no—
404C2×D83—24no—
405C2×D83—24no—
406C2×D83—24no—
407C2×D83—28no—
408C2×D83—28no—
409C2×D83—28no—
410C2×D83—28no—
411C2×D83C4×C22⋊C418yescomplemented
412C4×C83—28no—
413C4×C83—42no—
414C4×C83—44no—
415C4×C83#38618yescomplemented
416Dic83—24no—
417Dic83—24no—
418Dic83—28no—
419Dic83—42no—
420Dic83—44no—
421C4×#386—831nomaximal, Sylow
422C2×C83—44no—
423C2×C83C2×C4×C22⋊C411yescharacteristic
424C2×C83C42×D411yescharacteristic
425C2×C83C42×D411yescharacteristic
426C2×C83C2×#38611yescharacteristic
427C2×C83#229011yescharacteristic
428C2×C83#229011yescharacteristic
429C2×C83#229711yescharacteristic
430C2×C83C4×#12012yes—
431C2×C83C4×#12112yes—
432C2×C83C4×#12112yes—
433C2×C83C4×#12312yes—
434D83—28no—
435C22×C4×D4—831no—
436C23×C42—831no—
437C2×#386—832no—
438C2×C4×C22⋊C4—831no—
439C2×C4×C22⋊C4—831no—
440C2×C4×C22⋊C4D8311yescharacteristic, complemented
441#1437—832no—
442#1436—832no—
443C22⋊#95—832no—
444C4×#95—831no—
445C4×#95—831no—
446C83C4×#38611yescharacteristic, complemented, Sylow
447C23×D4—831no—
448C24×C4—831no—
449C24×C4—832no—
450C24×C4C2×D8311yescharacteristic
451C2×C4×D4—838no—
452C2×C4×D4—1664no—
453C2×C4×D4—1664no—
454C22×C4⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—832no—
457C22×C22⋊C4—831no—
458C22×C22⋊C4—832no—
459C22×C22⋊C4C2×D8312yes—
460C22×C42—831no—
461C22×C42—831no—
462C22×C42—832no—
463C22×C42—831no—
464C22×C42—1664no—
465C22×C42—1664no—
466C22×C42—1664no—
467C22×C42C2×D8311yescharacteristic
468C22×C42C2×D8311yescharacteristic
469#386—8316no—
470C4×C22⋊C4—24no—
471C4×C22⋊C4—1664no—
472C4×C22⋊C4—1664no—
473C2×#95—832no—
474C2×#95—832no—
475C2×#95—832no—
476C2×#95—832no—
477C2×#95—832no—
478C2×#95—832no—
479C2×#95C2×D8312yes—
480C25—831no—
481C25C22×D8311yescharacteristic
482C22×D4—834no—
483C22×D4—838no—
484C22×D4—1662no—
485C22×D4—1662no—
486C22×D4—1664no—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—831no—
494C23×C4—832no—
495C23×C4—831no—
496C23×C4—834no—
497C23×C4—834no—
498C23×C4—834no—
499C23×C4—832no—
500C23×C4—831no—
501C23×C4—838no—
502C23×C4—1664no—
503C23×C4—1664no—
504C23×C4—1664no—
505C23×C4—1664no—
506C23×C4—1662no—
507C23×C4—1664no—
508C23×C4—1662no—
509C23×C4—1662no—
510C23×C4—1664no—
511C23×C4—1662no—
512C23×C4C4×D8314yescomplemented
513C23×C4C22×D8312yes—
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8312yes—
516C23×C4C22×D8311yescharacteristic
517C4×D4—16632no—
518C2×C4⋊C4—834no—
519C2×C4⋊C4—1662no—
520C2×C4⋊C4—1662no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—838no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—838no—
527C2×C22⋊C4—1662no—
528C2×C22⋊C4—1662no—
529C2×C22⋊C4—1664no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1662no—
532C2×C22⋊C4—1662no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4—1664no—
535C2×C22⋊C4C4×D8318yescomplemented
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—834no—
542C2×C42—834no—
543C2×C42—16632no—
544C2×C42—1662no—
545C2×C42—1662no—
546C2×C42—1662no—
547C2×C42—1664no—
548C2×C42—1664no—
549C2×C42—1662no—
550C2×C42—1662no—
551C2×C42—1662no—
552C2×C42—1664no—
553C2×C42—1662no—
554C2×C42C22⋊D8314yescomplemented
555#95—24no—
556#95—838no—
557#95—838no—
558#95—1664no—
559#95—1664no—
560#95—1664no—
561#95—1664no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—22no—
567C24—22no—
568C24—21no—
569C24—22no—
570C24—21no—
571C24—832no—
572C24—834no—
573C24—832no—
574C24—832no—
575C24—834no—
576C24—1661no—
577C24—1661no—
578C24—1662no—
579C24—1661no—
580C24—1661no—
581C24—1662no—
582C24C2×C4×D8314yes—
583C24C2×C4×D8312yes—
584C24C23×D8311yescharacteristic
585C2×D4—8316no—
586C2×D4—1668no—
587C2×D4—1668no—
588C2×D4—16616no—
589C2×D4—16616no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—834no—
614C22×C4—834no—
615C22×C4—832no—
616C22×C4—832no—
617C22×C4—832no—
618C22×C4—834no—
619C22×C4—832no—
620C22×C4—834no—
621C22×C4—8316no—
622C22×C4—834no—
623C22×C4—832no—
624C22×C4—16616no—
625C22×C4—16616no—
626C22×C4—16616no—
627C22×C4—16616no—
628C22×C4—16616no—
629C22×C4—16616no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4—1661no—
633C22×C4—1661no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1662no—
638C22×C4—1662no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1661no—
642C22×C4—1661no—
643C22×C4—1661no—
644C22×C4—1661no—
645C22×C4—1662no—
646C22×C4—1662no—
647C22×C4—1662no—
648C22×C4—1661no—
649C22×C4—1661no—
650C22×C4—1662no—
651C22×C4—1668no—
652C22×C4—1668no—
653C22×C4—1668no—
654C22×C4—1668no—
655C22×C4—1668no—
656C22×C4—1668no—
657C22×C4—16616no—
658C22×C4C2×C4×D8314yes—
659C22×C4C2×C4×D8312yes—
660C22×C4C2×C4×D8314yes—
661C22×C4C2×C4×D8312yes—
662C22×C4D4×D8312yes—
663C22×C4D4×D8312yes—
664C22×C4D4×D8312yes—
665C22×C4C2×C22⋊D8314yes—
666C22×C4C2×C22⋊D8312yes—
667C22×C4#1305058912yes—
668C22×C4#1305059014yes—
669C22×C4#1305059012yes—
670C4⋊C4—1668no—
671C22⋊C4—216no—
672C22⋊C4—1668no—
673C22⋊C4—16616no—
674C22⋊C4—1668no—
675C22⋊C4—16616no—
676C42—28no—
677C42—44no—
678C42—3324no—
679C42—16616no—
680C42—1668no—
681C42—1668no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—24no—
689C23—22no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—834no—
705C23—834no—
706C23—834no—
707C23—838no—
708C23—838no—
709C23—1664no—
710C23—1662no—
711C23—1662no—
712C23—1664no—
713C23—1664no—
714C23—1662no—
715C23—1662no—
716C23—1664no—
717C23—1662no—
718C23—1662no—
719C23—1662no—
720C23—1662no—
721C23—1664no—
722C23—1664no—
723C23—1664no—
724C23—1664no—
725C23—1664no—
726C23—1664no—
727C23C42×D8314yescomplemented
728C23C22×C4×D8311yescharacteristic
729C23C22×C4×D8312yes—
730C23C2×D4×D8311yescharacteristic
731C23C2×D4×D8311yescharacteristic
732C23C2×D4×D8311yescharacteristic
733C23C22×C22⋊D8311yescharacteristic
734C23#41×D8312yes—
735C23#41×D8312yes—
736C23C2×#1305058911yescharacteristic
737C23C2×#1305059011yescharacteristic
738C23C2×#1305059012yes—
739D4—16632no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—416no—
761C2×C4—3322no—
762C2×C4—3322no—
763C2×C4—3322no—
764C2×C4—3322no—
765C2×C4—3322no—
766C2×C4—3322no—
767C2×C4—834no—
768C2×C4—834no—
769C2×C4—838no—
770C2×C4—16664no—
771C2×C4—1662no—
772C2×C4—1664no—
773C2×C4—1664no—
774C2×C4—1662no—
775C2×C4—1662no—
776C2×C4—1664no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1664no—
780C2×C4—1664no—
781C2×C4—1664no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4—1664no—
785C2×C4—1662no—
786C2×C4—1664no—
787C2×C4—1662no—
788C2×C4—1662no—
789C2×C4—1662no—
790C2×C4—1664no—
791C2×C4—1664no—
792C2×C4—1664no—
793C2×C4—16632no—
794C2×C4C22⋊C4×D8314yes—
795C2×C4(C22⋊D83)⋊C414yes—
796C2×C4C4×C22⋊D8314yes—
797C2×C4C4×C22⋊D8318yescomplemented
798C2×C4#1458176014yes—
799C2×C4#1458176314yes—
800C2×C4#1458176514yes—
801C2×C4#1458177414yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—838no—
814C22—1664no—
815C22—1664no—
816C22—1664no—
817C22—1664no—
818C22—1668no—
819C22—1668no—
820C22—1668no—
821C22—1668no—
822C22—1664no—
823C22—1664no—
824C22C2×C42×D8311yescharacteristic
825C22C2×C22⋊C4×D8311yescharacteristic
826C22#117×D8311yescharacteristic
827C22C4×D4×D8312yes—
828C22C4×D4×D8312yes—
829C22C4×D4×D8312yes—
830C22C2×(C22⋊D83)⋊C411yescharacteristic
831C22C2×C4×C22⋊D8311yescharacteristic
832C22C2×C4×C22⋊D8312yes—
833C22C4×#1305058912yes—
834C22#1912816911yescharacteristic
835C22C4×#1305059011yescharacteristic
836C22C4×#1305059012yes—
837C22C2×#1458176011yescharacteristic
838C22C2×#1458176311yescharacteristic
839C22C2×#1458176511yescharacteristic
840C22C2×#1458177411yescharacteristic
841C22#1912820812yes—
842C22#1912821012yes—
843C22#1912821012yes—
844C22#1912822912yes—
845C22#1912823312yes—
846C22#1912824812yes—
847C4—28no—
848C4—42no—
849C4—44no—
850C4—3322no—
851C4—3324no—
852C4—1664no—
853C4—1668no—
854C4—1664no—
855C4#1912757718yesdirect product factor
856C2—44no—
857C2—1668no—
858C2C4×C22⋊C4×D8311yescharacteristic
859C2C4×(C22⋊D83)⋊C411yescharacteristic
860C2C42×C22⋊D8311yescharacteristic
861C2C2×#1912757711yescharacteristic
862C2#2490990011yescharacteristic
863C2#2490990911yescharacteristic
864C2#2490994911yescharacteristic
865C2C4×#1458176012yes—
866C2C4×#1458176312yes—
867C2C4×#1458176512yes—
868C2C4×#1458177412yes—
subgroupG/H
centerC23×C4C22×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C4×#386
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C42×D83C2semidirect
4. C2×C4×(C2×D83)⋊C4C2semidirect
5. C2×C4×C22⋊Dic83C2semidirect
6. #24905700C2semidirect
7. #24905694C2semidirect
8. (C2×D83)⋊#95C2semidirect
9. C4×C83⋊#95C2semidirect
10. C4×C83⋊#95C2semidirect
11. C2×C4×C22⋊C4×C83C2semidirect
17. C2×C4×C22⋊D83C4semidirect
30. #19127577C4direct (N × H)
67. C22×C4×D83C2×C4semidirect
73. C2×Dic83⋊C4C2×C4semidirect
78. C2×C22⋊Dic83C2×C4semidirect
79. C2×C22⋊Dic83C2×C4semidirect
85. C2×(C2×D83)⋊C4C2×C4semidirect
96. C2×C4×Dic83C2×C4semidirect
97. C2×C4×Dic83D4semidirect
103. C83⋊#95C2×C4semidirect
104. C83⋊#95C2×C4semidirect
112. C23×C4×C83C2×C4semidirect
119. C2×C22⋊C4×C83C2×C4semidirect
125. C2×C42×C83D4semidirect
142. C2×C22⋊D83C42semidirect
187. C2×C4×D83C22⋊C4semidirect
269. C23×C83C2×C42semidirect
328. C2×C4×C83C4×D4semidirect
362. C2×Dic83C2×C42semidirect
364. C2×Dic83C4×D4semidirect
411. C2×D83C4×C22⋊C4semidirect
415. C4×C83#386semidirect
440. C2×C4×C22⋊C4D83semidirect
446. C83C4×#386semidirect
512. C23×C4C4×D83semidirect
535. C2×C22⋊C4C4×D83semidirect
554. C2×C42C22⋊D83semidirect
727. C23C42×D83semidirect
797. C2×C4C4×C22⋊D83semidirect
855. C4#19127577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C22×C42×D832
C2×#191275772
C2×C4×(C2×D83)⋊C42
C2×C4×C22⋊Dic832
#249057002
#249056942
(C2×D83)⋊#952
C4×C83⋊#952
C2×C4×C22⋊C4×C832
C4×#38683