Finite Group Databasebeta

← C2×#24913415 #35570852

Subgroups — C2×#24913415 #35570852

Order 21248.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913415C2116yesmaximal, direct product factor
2C2×C83⋊#401C211yesmaximal, characteristic, complemented
3C2×#19127643C211yesmaximal, characteristic, complemented
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127640C211yesmaximal, characteristic, complemented
6C2×#19127629C211yesmaximal, characteristic, complemented
7C2×#19127626C211yesmaximal, characteristic, complemented
8C2×#19127624C211yesmaximal, characteristic, complemented
9C2×#19127577C211yesmaximal, characteristic
10C2×#19127577C211yesmaximal, characteristic
11C2×#19127577C211yesmaximal, characteristic
12C2×#19127575C211yesmaximal, characteristic, complemented
13C2×#19127575C211yesmaximal, characteristic, complemented
14C2×#19127572C211yesmaximal, characteristic, complemented
15C2×#95×D83C211yesmaximal, characteristic, complemented
16C2×#397×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C83⋊#401C2218yescomplemented
33#19127643C2218yescomplemented
34#19127642C2218yescomplemented
35#19127640C2218yescomplemented
36#19127629C2218yescomplemented
37#19127626C2218yescomplemented
38#19127624C2218yescomplemented
39#19127577C2218yes—
40#19127577C2218yes—
41#19127577C2218yes—
42#19127575C2218yescomplemented
43#19127575C2218yescomplemented
44#19127572C2218yescomplemented
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58#95×D83C2218yescomplemented
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C22⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63#397×C83C2218yescomplemented
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C22×C22⋊D83—24no—
69C22×C22⋊D83—24no—
70C22×C22⋊D83—24no—
71C22×C22⋊D83C2314yes—
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C22×C4×D83—24no—
80C22×C4×D83—24no—
81C22×C4×D83—24no—
82C22×C4×D83—42no—
83C22×C4×D83—42no—
84C22×C4×D83—42no—
85C22×C4×D83—42no—
86C22×C4×D83—42no—
87C22×C4×D83—42no—
88C22×C4×D83C2314yes—
89C22×C4×D83C2314yes—
90C22×C4×D83C2314yes—
91C2×C4⋊Dic83—42no—
92C2×C4⋊Dic83—42no—
93C2×C4⋊Dic83C2314yes—
94C2×C4⋊Dic83C2314yes—
95C2×Dic83⋊C4—42no—
96C2×Dic83⋊C4—42no—
97C2×Dic83⋊C4—42no—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×C22⋊Dic83—42no—
102C2×C22⋊Dic83—42no—
103C2×C22⋊Dic83—42no—
104C2×C22⋊Dic83C2314yes—
105C2×C22⋊Dic83C2314yes—
106C2×C22⋊Dic83C2314yes—
107C2×(C2×D83)⋊C4—24no—
108C2×(C2×D83)⋊C4—24no—
109C2×(C2×D83)⋊C4—24no—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C25×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83C2314yes—
135C2×C22⋊C4×C83—42no—
136C2×C22⋊C4×C83—42no—
137C2×C22⋊C4×C83—42no—
138C2×C22⋊C4×C83C2314yes—
139C2×C22⋊C4×C83C2314yes—
140C2×C22⋊C4×C83C2314yes—
141#95×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83#4114yes—
149C23×D83#4114yes—
150C23×D83#4114yes—
151C23×D83C2412yes—
152C2×C22⋊D83—28no—
153C2×C22⋊D83—28no—
154C2×C22⋊D83—28no—
155C2×C22⋊D83—416no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—22no—
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×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C2×C4×D83—28no—
185C2×C4×D83—28no—
186C2×C4×D83—28no—
187C2×C4×D83—44no—
188C2×C4×D83—44no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C2×C4×D83—44no—
192C2×C4×D83—44no—
193C2×C4×D83—416no—
194C2×C4×D83—416no—
195C2×C4×D83—416no—
196C4⋊Dic83—44no—
197C4⋊Dic83—44no—
198Dic83⋊C4—44no—
199Dic83⋊C4—44no—
200Dic83⋊C4—44no—
201C22⋊Dic83—44no—
202C22⋊Dic83—44no—
203C22⋊Dic83—44no—
204(C2×D83)⋊C4—28no—
205(C2×D83)⋊C4—28no—
206(C2×D83)⋊C4—28no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83—22no—
212C24×C83—22no—
213C24×C83—22no—
214C24×C83C2412yes—
215C24×C83C2411yescharacteristic
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
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—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C4⋊C4×C83—44no—
241C22⋊C4×C83—44no—
242C22⋊C4×C83—44no—
243C22⋊C4×C83—44no—
244C23×C83—22no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—44no—
252C23×C83—44no—
253C23×C83—44no—
254C23×C83—44no—
255C23×C83—44no—
256C23×C83—44no—
257C23×C83—44no—
258C23×C83C2×#4112yes—
259C23×C83C2×#4112yes—
260C23×C83C2×#4112yes—
261C23×C83H(5,𝔽2)12yes—
262C23×C83H(5,𝔽2)12yes—
263C23×C83H(5,𝔽2)12yes—
264C23×C832−1+412yes—
265C23×C83C2511yescharacteristic
266C22×D83—28no—
267C22×D83—28no—
268C22×D83—28no—
269C22×D83—28no—
270C22×D83—28no—
271C22×D83—28no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83#126116yes—
277C22×D83C2×#4114yes—
278C22×D83C2×#4114yes—
279C22×D83C2×#4114yes—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—44no—
299C2×C4×C83—44no—
300C2×C4×C83—44no—
301C2×C4×C83—44no—
302C2×C4×C83—44no—
303C2×C4×C83—44no—
304C22⋊D83—416no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
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—44no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83—44no—
331C2×Dic83—44no—
332C2×Dic83—44no—
333C4×D83—416no—
334C4×D83—416no—
335C4×D83—416no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—88no—
344C22×C83C2×#12614yes—
345C22×C83#53814yes—
346C22×C83#53814yes—
347C22×C83#53814yes—
348C22×C83#53914yes—
349C22×C83#53914yes—
350C22×C83#53914yes—
351C22×C83C22×#4111yescharacteristic
352C22×C83C22×#4111yescharacteristic
353C22×C83C22×#4111yescharacteristic
354C22×C83C2×H(5,𝔽2)11yescharacteristic
355C22×C83C2×H(5,𝔽2)11yescharacteristic
356C22×C83C2×H(5,𝔽2)11yescharacteristic
357C22×C83C2×2−1+411yescharacteristic
358C2×D83—232no—
359C2×D83—24no—
360C2×D83—24no—
361C2×D83—24no—
362C2×D83—24no—
363C2×D83—24no—
364C2×D83—24no—
365C2×D83C2×#12618yes—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371C4×C83—42no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377Dic83—42no—
378Dic83—42no—
379C2×#2643—831nomaximal, Sylow
380C2×C83—82no—
381C2×C83#264318yescomplemented
382C2×C83C22×#12611yescharacteristic
383C2×C83C2×#53811yescharacteristic
384C2×C83C2×#53811yescharacteristic
385C2×C83C2×#53811yescharacteristic
386C2×C83C2×#53911yescharacteristic
387C2×C83C2×#53911yescharacteristic
388C2×C83C2×#53911yescharacteristic
389D83—28no—
390#2643—8316no—
391C2×#401—831no—
392C2×#400—831no—
393C2×#400—831no—
394C2×#400—831no—
395C2×#397—831no—
396C2×#397—831no—
397C2×#397D8311yescharacteristic, complemented
398C2×#396—831no—
399C2×#386—831no—
400C2×#386—831no—
401C2×#386—831no—
402C2×#385—831no—
403C2×#385—831no—
404C2×#385—831no—
405C22×#95—831no—
406C83C2×#264311yescharacteristic, complemented, Sylow
407C23×D4—831no—
408C24×C4—831no—
409C24×C4—831no—
410C24×C4—831no—
411C22×C4⋊C4—831no—
412C22×C4⋊C4—831no—
413C22×C4⋊C4—831no—
414C22×C4⋊C4—831no—
415C22×C4⋊C4—831no—
416C22×C4⋊C4C2×D8311yescharacteristic
417C22×C22⋊C4—831no—
418C22×C22⋊C4—831no—
419C22×C22⋊C4—831no—
420C22×C22⋊C4—831no—
421C22×C22⋊C4—831no—
422C22×C22⋊C4—831no—
423C22×C22⋊C4C2×D8311yescharacteristic
424C22×C22⋊C4C2×D8311yescharacteristic
425C22×C22⋊C4C2×D8311yescharacteristic
426#401—838no—
427#400—838no—
428#400—838no—
429#400—838no—
430#397—838no—
431#397—838no—
432#397C2×D8318yescomplemented
433#396—838no—
434#386—838no—
435#386—838no—
436#386—838no—
437#385—838no—
438#385—838no—
439#385—838no—
440C2×#95—831no—
441C2×#95—831no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—831no—
452C2×#95—831no—
453C2×#95—838no—
454C2×#95C2×D8311yescharacteristic
455C2×#95C2×D8311yescharacteristic
456C2×#95C2×D8311yescharacteristic
457C25—831no—
458C25C22×D8311yescharacteristic
459C22×D4—834no—
460C22×D4—1664no—
461C22×D4—1664no—
462C22×D4—1664no—
463C23×C4—3322no—
464C23×C4—3322no—
465C23×C4—3322no—
466C23×C4—3322no—
467C23×C4—3322no—
468C23×C4—3322no—
469C23×C4—834no—
470C23×C4—834no—
471C23×C4—834no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—831no—
475C23×C4—831no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—1664no—
480C23×C4—1664no—
481C23×C4—1664no—
482C23×C4C22×D8311yescharacteristic
483C23×C4C22×D8311yescharacteristic
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8311yescharacteristic
486C23×C4C22×D8311yescharacteristic
487C23×C4C22×D8311yescharacteristic
488C2×C4⋊C4—42no—
489C2×C4⋊C4—3322no—
490C2×C4⋊C4—3322no—
491C2×C4⋊C4—3322no—
492C2×C4⋊C4—3322no—
493C2×C4⋊C4—3322no—
494C2×C4⋊C4—834no—
495C2×C4⋊C4—834no—
496C2×C4⋊C4—834no—
497C2×C4⋊C4—834no—
498C2×C4⋊C4—834no—
499C2×C4⋊C4C22×D8314yes—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—3322no—
504C2×C22⋊C4—3322no—
505C2×C22⋊C4—3322no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4—834no—
512C2×C22⋊C4—1664no—
513C2×C22⋊C4—1664no—
514C2×C22⋊C4—1664no—
515C2×C22⋊C4C22×D8314yes—
516C2×C22⋊C4C22×D8314yes—
517C2×C22⋊C4C22×D8314yes—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95—834no—
531#95C22×D8314yes—
532#95C22×D8314yes—
533#95C22×D8314yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—834no—
542C24—834no—
543C24—834no—
544C24—832no—
545C24—1662no—
546C24—1662no—
547C24—1662no—
548C24—1662no—
549C24C23×D8312yes—
550C24C23×D8311yescharacteristic
551C2×D4—33216no—
552C2×D4—1668no—
553C2×D4—1668no—
554C2×D4—1668no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—3324no—
574C22×C4—3324no—
575C22×C4—3324no—
576C22×C4—3324no—
577C22×C4—3324no—
578C22×C4—3324no—
579C22×C4—33216no—
580C22×C4—33216no—
581C22×C4—33216no—
582C22×C4—832no—
583C22×C4—832no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—832no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—1668no—
590C22×C4—1668no—
591C22×C4—1668no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4—1662no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
612C22×C4—1662no—
613C22×C4C23×D8312yes—
614C22×C4C23×D8312yes—
615C22×C4C23×D8312yes—
616C22×C4C23×D8312yes—
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C4⋊C4—44no—
620C4⋊C4—3324no—
621C4⋊C4—3324no—
622C4⋊C4—3324no—
623C4⋊C4—3324no—
624C4⋊C4—3324no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—3324no—
629C22⋊C4—3324no—
630C22⋊C4—3324no—
631C22⋊C4—1668no—
632C22⋊C4—1668no—
633C22⋊C4—1668no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—8316no—
649C23—834no—
650C23—834no—
651C23—834no—
652C23—1662no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1668no—
657C23—1668no—
658C23—1668no—
659C23—1668no—
660C23—1668no—
661C23—1668no—
662C23#41×D8312yes—
663C23#41×D8312yes—
664C23#41×D8312yes—
665C23#1458183712yes—
666C23#1458183712yes—
667C23#1458183812yes—
668C23#1458183912yes—
669C23C24×D8311yescharacteristic
670D4—33216no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—33216no—
696C2×C4—33216no—
697C2×C4—33216no—
698C2×C4—3324no—
699C2×C4—3324no—
700C2×C4—3324no—
701C2×C4—3324no—
702C2×C4—3324no—
703C2×C4—3324no—
704C2×C4—3324no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4—1662no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22—838no—
735C22—16632no—
736C22—1664no—
737C22—1664no—
738C22—1664no—
739C22—1664no—
740C22—1664no—
741C22—1664no—
742C22#126×D8314yes—
743C22#1912828314yes—
744C22#1912828514yes—
745C22#1912828714yes—
746C22#1912829214yes—
747C22#1912829414yes—
748C22#1912829414yes—
749C22C2×#41×D8311yescharacteristic
750C22C2×#41×D8311yescharacteristic
751C22C2×#41×D8311yescharacteristic
752C22C2×#1458183711yescharacteristic
753C22C2×#1458183711yescharacteristic
754C22C2×#1458183811yescharacteristic
755C22C2×#1458183911yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—3322no—
763C4—3322no—
764C4—3322no—
765C4—3322no—
766C4—3322no—
767C4—3322no—
768C4—3322no—
769C2—82no—
770C2—1668no—
771C2#2491341518yesdirect product factor
772C2C2×#126×D8311yescharacteristic
773C2C2×#1912828311yescharacteristic
774C2C2×#1912828511yescharacteristic
775C2C2×#1912828711yescharacteristic
776C2C2×#1912829211yescharacteristic
777C2C2×#1912829411yescharacteristic
778C2C2×#1912829411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#397×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#397D83
hypocenterC83C2×#2643
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #24913415C2direct (N × H)
2. C2×C83⋊#401C2semidirect
3. C2×#19127643C2semidirect
4. C2×#19127642C2semidirect
5. C2×#19127640C2semidirect
6. C2×#19127629C2semidirect
7. C2×#19127626C2semidirect
8. C2×#19127624C2semidirect
12. C2×#19127575C2semidirect
13. C2×#19127575C2semidirect
14. C2×#19127572C2semidirect
15. C2×#95×D83C2semidirect
16. C2×#397×C83C2semidirect
32. C83⋊#401C22semidirect
33. #19127643C22semidirect
34. #19127642C22semidirect
35. #19127640C22semidirect
36. #19127629C22semidirect
37. #19127626C22semidirect
38. #19127624C22semidirect
42. #19127575C22semidirect
43. #19127575C22semidirect
44. #19127572C22semidirect
58. #95×D83C22semidirect
63. #397×C83C22semidirect
381. C2×C83#2643semidirect
397. C2×#397D83semidirect
406. C83C2×#2643semidirect
432. #397C2×D83semidirect
771. C2#24913415direct (N × H)

Maximal subgroups

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

subgroupindex
#249134152
C2×C83⋊#4012
C2×#191276432
C2×#191276422
C2×#191276402
C2×#191276292
C2×#191276262
C2×#191276242
C2×#191275772
C2×#191275752
C2×#191275722
C2×#95×D832
C2×#397×C832
C2×#264383