Finite Group Databasebeta

← C2×#24911247 #35572557

Subgroups — C2×#24911247 #35572557

Order 21248.

3070 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581778C211yesmaximal, characteristic
2C22×C4×C22⋊D83C211yesmaximal, characteristic
3#24911247C2116yesmaximal, direct product factor
4C2×#19127629C211yesmaximal, characteristic, complemented
5C2×#19127628C211yesmaximal, characteristic, complemented
6C2×#19127627C211yesmaximal, characteristic, complemented
7C2×#19127626C211yesmaximal, characteristic, complemented
8C2×#19127605C211yesmaximal, characteristic, complemented
9C2×#19127605C211yesmaximal, characteristic, complemented
10C2×#19127601C211yesmaximal, characteristic
11C2×#19127596C211yesmaximal, characteristic, complemented
12C2×#19127572C211yesmaximal, characteristic, complemented
13C2×#19127564C211yesmaximal, characteristic, complemented
14C2×#19127563C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
16C2×#385×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581778—28no—
21C2×#14581778C2218yes—
22C2×C4×C22⋊D83—28no—
23C2×C4×C22⋊D83C2218yes—
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127629C2218yescomplemented
40#19127628C2218yescomplemented
41#19127627C2218yescomplemented
42#19127626C2218yescomplemented
43#19127605C2218yescomplemented
44#19127605C2218yescomplemented
45#19127601C2218yes—
46#19127596C2218yescomplemented
47#19127572C2218yescomplemented
48#19127564C2218yescomplemented
49#19127563C2218yescomplemented
50C4⋊C4×Dic83C2218yescomplemented
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C24×C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66#385×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—24no—
73C22×Dic166C2314yes—
74C22×C22⋊D83—24no—
75C22×C22⋊D83—24no—
76C22×C22⋊D83D418yes—
77C22×C22⋊D83C2314yes—
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C22×C4×D83—24no—
86C22×C4×D83—24no—
87C22×C4×D83—42no—
88C22×C4×D83C2314yes—
89#14581778—232no—
90C4×C22⋊D83—232no—
91C2×C4⋊Dic83—24no—
92C2×C4⋊Dic83C2314yes—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—42no—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×C22⋊Dic83—24no—
100C2×C22⋊Dic83—24no—
101C2×C22⋊Dic83—42no—
102C2×C22⋊Dic83C2314yes—
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×(C2×D83)⋊C4—24no—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4—24no—
108C2×(C2×D83)⋊C4—24no—
109C2×(C2×D83)⋊C4—42no—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×C4×Dic83—24no—
116C2×C4×Dic83—24no—
117C2×C4×Dic83—24no—
118C2×C4×Dic83C2314yes—
119C2×C4×Dic83C2314yes—
120C2×C4×Dic83C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C25×C83C2311yescharacteristic
132C23×C4×C83—24no—
133C23×C4×C83—24no—
134C23×C4×C83—42no—
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2314yes—
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C2×C4⋊C4×C83—24no—
143C2×C4⋊C4×C83—42no—
144C2×C4⋊C4×C83C2314yes—
145C2×C4⋊C4×C83C2314yes—
146C2×C22⋊C4×C83—24no—
147C2×C22⋊C4×C83—24no—
148C2×C22⋊C4×C83C2314yes—
149C2×C22⋊C4×C83C2314yes—
150#95×C83C2314yes—
151#95×C83C2314yes—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83C2×D414yes—
159C23×D83C2412yes—
160C2×Dic166—28no—
161C2×Dic166—28no—
162C2×Dic166—28no—
163C2×Dic166—416no—
164C2×C22⋊D83—232no—
165C2×C22⋊D83—28no—
166C2×C22⋊D83—28no—
167C2×C22⋊D83C2×D4116yes—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83C2×D414yes—
187C22×Dic83#4114yes—
188C22×Dic83#4114yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C2×C4×D83—28no—
197C2×C4×D83—28no—
198C2×C4×D83—44no—
199C2×C4×D83—416no—
200C4⋊Dic83—28no—
201Dic83⋊C4—28no—
202Dic83⋊C4—28no—
203Dic83⋊C4—44no—
204C22⋊Dic83—28no—
205C22⋊Dic83—28no—
206C22⋊Dic83—44no—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—28no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—28no—
211(C2×D83)⋊C4—44no—
212C4×Dic83—28no—
213C4×Dic83—28no—
214C4×Dic83—28no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83—22no—
219C24×C83—22no—
220C24×C83—22no—
221C24×C83C2×D414yes—
222C24×C83C2412yes—
223C24×C83C2411yescharacteristic
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—28no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—28no—
242C22×C4×C83—44no—
243C22×C4×C83—416no—
244C22×C4×C83#4114yes—
245C22×C4×C83#4114yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C4⋊C4×C83—28no—
253C4⋊C4×C83—44no—
254C22⋊C4×C83—28no—
255C22⋊C4×C83—28no—
256C23×C83—28no—
257C23×C83—28no—
258C23×C83—28no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—44no—
266C23×C83—44no—
267C23×C83—44no—
268C23×C83—44no—
269C23×C83C22×D414yes—
270C23×C83C22×D412yes—
271C23×C83C2×#4112yes—
272C23×C83C2×#4112yes—
273C23×C83C2×#4112yes—
274C23×C83C2×#4112yes—
275C23×C83H(5,𝔽2)12yes—
276C23×C832−1+412yes—
277C23×C83C2511yescharacteristic
278C22×D83—28no—
279C22×D83—28no—
280C22×D83—28no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—22no—
286C22×D83—22no—
287C22×D83—44no—
288C22×D83—44no—
289C22×D83—44no—
290C22×D83—44no—
291C22×D83C22×D414yes—
292C2×C4×C83—28no—
293C2×C4×C83—28no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—416no—
311C2×C4×C83—44no—
312C2×C4×C83—44no—
313C2×C4×C83—44no—
314C2×C4×C83—44no—
315C2×C4×C83C2×#4114yes—
316C2×C4×C83C2×#4114yes—
317C22⋊D83—232no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—44no—
337C2×Dic83—44no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83—44no—
341C2×Dic83—44no—
342C2×Dic83#123116yes—
343C2×Dic83C22×D414yes—
344C2×Dic83C2×#4114yes—
345C2×Dic83C2×#4114yes—
346C4×D83—416no—
347Dic166—416no—
348C22×C83—24no—
349C22×C83—24no—
350C22×C83—24no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—416no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83C2×#12314yes—
357C22×C83#52914yes—
358C22×C83#54214yes—
359C22×C83#54614yes—
360C22×C83#54714yes—
361C22×C83#55614yes—
362C22×C83#55914yes—
363C22×C83C23×D411yescharacteristic
364C22×C83C22×#4111yescharacteristic
365C22×C83C22×#4111yescharacteristic
366C22×C83C22×#4111yescharacteristic
367C22×C83C22×#4111yescharacteristic
368C22×C83C2×H(5,𝔽2)11yescharacteristic
369C22×C83C2×2−1+411yescharacteristic
370C2×D83—24no—
371C2×D83—24no—
372C2×D83—24no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—416no—
376C2×D83—42no—
377C2×D83—42no—
378C4×C83—24no—
379C4×C83—24no—
380C4×C83—42no—
381C4×C83—42no—
382C4×C83—42no—
383C4×C83—42no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389Dic83—42no—
390Dic83C2×#12318yes—
391C2×#2447—831nomaximal, Sylow
392C2×C83—44no—
393C2×C83#244718yescomplemented
394C2×C83C22×#12311yescharacteristic
395C2×C83C2×#52911yescharacteristic
396C2×C83C2×#54211yescharacteristic
397C2×C83C2×#54611yescharacteristic
398C2×C83C2×#54711yescharacteristic
399C2×C83C2×#55611yescharacteristic
400C2×C83C2×#55911yescharacteristic
401D83—44no—
402C22×#124—831no—
403C22×C4×D4—831no—
404#2447—8316no—
405C2×#397—831no—
406C2×#397—831no—
407C2×#397—831no—
408C2×#397—831no—
409C2×#391—831no—
410C2×#391—831no—
411C2×#390—831no—
412C2×#389—831no—
413C2×#385—831no—
414C2×#385D8311yescharacteristic, complemented
415C2×#381—831no—
416C2×#381—831no—
417C2×C4×C4⋊C4—831no—
418C83C2×#244711yescharacteristic, complemented, Sylow
419C23×Q8—831no—
420C23×D4—831no—
421C24×C4—831no—
422C24×C4C2×D8311yescharacteristic
423C2×#124—838no—
424C2×#124—1668no—
425C2×C4×D4—838no—
426C2×C4×D4—1668no—
427C22×C4⋊C4—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4C2×D8311yescharacteristic
432C22×C4⋊C4C2×D8311yescharacteristic
433C22×C22⋊C4—831no—
434C22×C22⋊C4—831no—
435C22×C22⋊C4—831no—
436C22×C22⋊C4—831no—
437C22×C22⋊C4—831no—
438C22×C22⋊C4—831no—
439C22×C22⋊C4—831no—
440C22×C22⋊C4—831no—
441C22×C22⋊C4C2×D8311yescharacteristic
442C22×C22⋊C4C2×D8311yescharacteristic
443C22×C42—831no—
444C22×C42—831no—
445C22×C42—831no—
446#397—838no—
447#397—838no—
448#397—838no—
449#397—838no—
450#391—838no—
451#391—838no—
452#390—838no—
453#389—838no—
454#385—838no—
455#385C2×D8318yescomplemented
456#381—838no—
457#381—838no—
458C4×C4⋊C4—838no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95—831no—
468C2×#95—831no—
469C2×#95C2×D8311yescharacteristic
470C2×#95C2×D8311yescharacteristic
471C25—831no—
472C25C22×D8311yescharacteristic
473C22×Q8—834no—
474C22×Q8—1664no—
475C22×Q8—1664no—
476C22×Q8—1664no—
477C22×D4—838no—
478C22×D4—834no—
479C22×D4—1664no—
480C22×D4—1664no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—42no—
484C23×C4—3322no—
485C23×C4—834no—
486C23×C4—831no—
487C23×C4—831no—
488C23×C4—831no—
489C23×C4—831no—
490C23×C4—831no—
491C23×C4—831no—
492C23×C4—831no—
493C23×C4—1664no—
494C23×C4—1664no—
495C23×C4C22×D8311yescharacteristic
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C23×C4C22×D8311yescharacteristic
499C23×C4C22×D8314yes—
500C23×C4C22×D8311yescharacteristic
501C23×C4C22×D8311yescharacteristic
502#124—16632no—
503C4×D4—16632no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—3322no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—834no—
511C2×C4⋊C4—1664no—
512C2×C4⋊C4—1664no—
513C2×C4⋊C4—1664no—
514C2×C4⋊C4C22×D8314yes—
515C2×C4⋊C4C22×D8314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—3322no—
519C2×C22⋊C4—3322no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—834no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—834no—
527C2×C22⋊C4—834no—
528C2×C22⋊C4—1664no—
529C2×C22⋊C4—1664no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4C22×D8314yes—
535C2×C22⋊C4C22×D8314yes—
536C2×C42—834no—
537C2×C42—834no—
538C2×C42—834no—
539C2×C42—1664no—
540C2×C42—1664no—
541C2×C42—1664no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548#95—834no—
549#95—834no—
550#95—834no—
551#95—834no—
552#95C22×D8314yes—
553#95C22×D8314yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—834no—
561C24—832no—
562C24—1662no—
563C24—1662no—
564C24—1662no—
565C24—1662no—
566C24—1662no—
567C24—1662no—
568C24D4×D8314yes—
569C24C23×D8312yes—
570C24C23×D8311yescharacteristic
571C2×Q8—33216no—
572C2×Q8—1668no—
573C2×Q8—1668no—
574C2×Q8—1668no—
575C2×D4—8316no—
576C2×D4—16632no—
577C2×D4—1668no—
578C2×D4—1668no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—416no—
599C22×C4—33216no—
600C22×C4—3324no—
601C22×C4—834no—
602C22×C4—834no—
603C22×C4—834no—
604C22×C4—832no—
605C22×C4—832no—
606C22×C4—832no—
607C22×C4—832no—
608C22×C4—832no—
609C22×C4—832no—
610C22×C4—832no—
611C22×C4—1668no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1662no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1662no—
626C22×C4—1662no—
627C22×C4—1662no—
628C22×C4—1662no—
629C22×C4—1662no—
630C22×C4—1668no—
631C22×C4#1305058914yes—
632C22×C4#1305059014yes—
633C22×C4C23×D8312yes—
634C22×C4C23×D8312yes—
635C22×C4C23×D8312yes—
636C22×C4C23×D8312yes—
637C22×C4C23×D8312yes—
638C22×C4C23×D8312yes—
639C4⋊C4—28no—
640C4⋊C4—44no—
641C4⋊C4—3324no—
642C4⋊C4—1668no—
643C4⋊C4—1668no—
644C4⋊C4—1668no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—3324no—
648C22⋊C4—3324no—
649C22⋊C4—1668no—
650C22⋊C4—1668no—
651C22⋊C4—1668no—
652C22⋊C4—1668no—
653C22⋊C4—1668no—
654C22⋊C4—1668no—
655C42—1668no—
656C42—1668no—
657C42—1668no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—3324no—
672C23—3324no—
673C23—3324no—
674C23—3324no—
675C23—834no—
676C23—1668no—
677C23—1668no—
678C23—1668no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23C2×D4×D8314yes—
686C23C2×D4×D8312yes—
687C23#41×D8312yes—
688C23#41×D8312yes—
689C23C2×#1305058912yes—
690C23C2×#1305059012yes—
691C23#1458183712yes—
692C23#1458184012yes—
693C23C24×D8311yescharacteristic
694Q8—33216no—
695D4—16632no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—33216no—
720C2×C4—3324no—
721C2×C4—3324no—
722C2×C4—3324no—
723C2×C4—3324no—
724C2×C4—3324no—
725C2×C4—3324no—
726C2×C4—8316no—
727C2×C4—834no—
728C2×C4—834no—
729C2×C4—834no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1662no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—1662no—
746C2×C4—1662no—
747C2×C4—1662no—
748C2×C4C2×#1305058914yes—
749C2×C4C2×#1305059014yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—416no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—3322no—
759C22—33216no—
760C22—3322no—
761C22—3322no—
762C22—3322no—
763C22—1664no—
764C22—1664no—
765C22—1664no—
766C22#123×D8314yes—
767C22#1912823114yes—
768C22#1912832114yes—
769C22#1912833814yes—
770C22#1912835214yes—
771C22#1912842214yes—
772C22#1912843414yes—
773C22C22×D4×D8311yescharacteristic
774C22C2×#41×D8311yescharacteristic
775C22C2×#41×D8311yescharacteristic
776C22C22×#1305058911yescharacteristic
777C22C22×#1305059011yescharacteristic
778C22C2×#1458183711yescharacteristic
779C22C2×#1458184011yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—3322no—
787C4—3322no—
788C4—3322no—
789C4—3322no—
790C4—3322no—
791C4—3322no—
792C4—838no—
793C2—44no—
794C2—3324no—
795C2#2491124718yesdirect product factor
796C2C2×#123×D8311yescharacteristic
797C2C2×#1912823111yescharacteristic
798C2C2×#1912832111yescharacteristic
799C2C2×#1912833811yescharacteristic
800C2C2×#1912835211yescharacteristic
801C2C2×#1912842211yescharacteristic
802C2C2×#1912843411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#385D83
hypocenterC83C2×#2447
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #24911247C2direct (N × H)
4. C2×#19127629C2semidirect
5. C2×#19127628C2semidirect
6. C2×#19127627C2semidirect
7. C2×#19127626C2semidirect
8. C2×#19127605C2semidirect
9. C2×#19127605C2semidirect
11. C2×#19127596C2semidirect
12. C2×#19127572C2semidirect
13. C2×#19127564C2semidirect
14. C2×#19127563C2semidirect
15. C2×C4⋊C4×Dic83C2semidirect
16. C2×#385×C83C2semidirect
39. #19127629C22semidirect
40. #19127628C22semidirect
41. #19127627C22semidirect
42. #19127626C22semidirect
43. #19127605C22semidirect
44. #19127605C22semidirect
46. #19127596C22semidirect
47. #19127572C22semidirect
48. #19127564C22semidirect
49. #19127563C22semidirect
50. C4⋊C4×Dic83C22semidirect
66. #385×C83C22semidirect
393. C2×C83#2447semidirect
414. C2×#385D83semidirect
418. C83C2×#2447semidirect
455. #385C2×D83semidirect
795. C2#24911247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817782
C22×C4×C22⋊D832
#249112472
C2×#191276292
C2×#191276282
C2×#191276272
C2×#191276262
C2×#191276052
C2×#191276012
C2×#191275962
C2×#191275722
C2×#191275642
C2×#191275632
C2×C4⋊C4×Dic832
C2×#385×C832
C2×#244783