Finite Group Databasebeta

← C2×#24913531 #35570902

Subgroups — C2×#24913531 #35570902

Order 21248.

2394 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913531C2116yesmaximal, direct product factor
2C2×#19127635C211yesmaximal, characteristic, complemented
3C2×#19127630C211yesmaximal, characteristic, complemented
4C2×#19127628C211yesmaximal, characteristic, complemented
5C2×#19127619C211yesmaximal, characteristic
6C2×#19127619C211yesmaximal, characteristic
7C2×#19127614C211yesmaximal, characteristic, complemented
8C2×#19127614C211yesmaximal, characteristic, complemented
9C2×#19127605C211yesmaximal, characteristic, complemented
10C2×#19127593C211yesmaximal, characteristic, complemented
11C2×#19127593C211yesmaximal, characteristic, complemented
12C2×#19127584C211yesmaximal, characteristic, complemented
13C2×#19127579C211yesmaximal, characteristic
14C2×#19127575C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×#401×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
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
38#19127635C2218yescomplemented
39#19127630C2218yescomplemented
40#19127628C2218yescomplemented
41#19127619C2218yes—
42#19127619C2218yes—
43#19127614C2218yescomplemented
44#19127614C2218yescomplemented
45#19127605C2218yescomplemented
46#19127593C2218yescomplemented
47#19127593C2218yescomplemented
48#19127584C2218yescomplemented
49#19127579C2218yes—
50#19127575C2218yescomplemented
51#19127548C2218yescomplemented
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59#401×C83C2218yescomplemented
60C2×#95×C83C2211yescharacteristic
61C2×#95×C83C2211yescharacteristic
62C2×#95×C83C2211yescharacteristic
63C2×#95×C83C2211yescharacteristic
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C24×D83C2311yescharacteristic
69C22×Dic166—24no—
70C22×Dic166—42no—
71C22×Dic166—42no—
72C22×Dic166C2314yes—
73C22×D332—24no—
74C22×D332—42no—
75C22×D332—42no—
76C22×D332C2314yes—
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C22×C4×D83—24no—
84C22×C4×D83—42no—
85C22×C4×D83—42no—
86C22×C4×D83C2314yes—
87C2×C4⋊Dic83—24no—
88C2×C4⋊Dic83—42no—
89C2×C4⋊Dic83C2314yes—
90C2×C4⋊Dic83C2314yes—
91C2×Dic83⋊C4—42no—
92C2×Dic83⋊C4—42no—
93C2×Dic83⋊C4—42no—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—24no—
101C2×(C2×D83)⋊C4—24no—
102C2×(C2×D83)⋊C4—42no—
103C2×(C2×D83)⋊C4—42no—
104C2×(C2×D83)⋊C4—42no—
105C2×(C2×D83)⋊C4—42no—
106C2×(C2×D83)⋊C4—42no—
107C2×(C2×D83)⋊C4—42no—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×C4×Dic83—42no—
120C2×C4×Dic83—42no—
121C2×C4×Dic83C2314yes—
122C2×C4×Dic83C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137#95×C83C2314yes—
138#95×C83C2314yes—
139#95×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—22no—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83#4114yes—
158C23×D83C2412yes—
159C23×D83C2412yes—
160C2×Dic166—28no—
161C2×Dic166—44no—
162C2×Dic166—44no—
163C2×Dic166—416no—
164C2×D332—28no—
165C2×D332—44no—
166C2×D332—44no—
167C2×D332—416no—
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#4114yes—
185C22×Dic83#4114yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C2×C4×D83—28no—
193C2×C4×D83—44no—
194C2×C4×D83—44no—
195C2×C4×D83—416no—
196C4⋊Dic83—28no—
197C4⋊Dic83—44no—
198Dic83⋊C4—44no—
199Dic83⋊C4—44no—
200Dic83⋊C4—44no—
201(C2×D83)⋊C4—28no—
202(C2×D83)⋊C4—28no—
203(C2×D83)⋊C4—28no—
204(C2×D83)⋊C4—28no—
205(C2×D83)⋊C4—28no—
206(C2×D83)⋊C4—44no—
207(C2×D83)⋊C4—44no—
208(C2×D83)⋊C4—44no—
209(C2×D83)⋊C4—44no—
210(C2×D83)⋊C4—44no—
211(C2×D83)⋊C4—44no—
212C4×Dic83—44no—
213C4×Dic83—44no—
214C24×C83C2411yescharacteristic
215C22×C4×C83—22no—
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×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C22×C4×C83C2412yes—
242C22×C4×C83C2412yes—
243C23×C83C2×#4112yes—
244C23×C83C2×#4112yes—
245C23×C83C2×#4112yes—
246C23×C83H(5,𝔽2)12yes—
247C23×C83H(5,𝔽2)12yes—
248C23×C83H(5,𝔽2)12yes—
249C23×C832−1+412yes—
250C23×C83C2511yescharacteristic
251C22×D83—28no—
252C22×D83—28no—
253C22×D83—28no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—44no—
268C22×D83—44no—
269C22×D83—44no—
270C22×D83—44no—
271C22×D83—44no—
272C22×D83—44no—
273C22×D83—44no—
274C22×D83—44no—
275C22×D83—44no—
276C22×D83—44no—
277C22×D83—44no—
278C22×D83C2×#4114yes—
279C2×C4×C83—22no—
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—22no—
299C2×C4×C83—22no—
300C2×C4×C83—44no—
301C2×C4×C83—44no—
302C2×C4×C83—44no—
303C2×C4×C83—44no—
304C2×C4×C83—44no—
305C2×C4×C83—44no—
306C2×C4×C83—44no—
307C2×Dic83—28no—
308C2×Dic83—28no—
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—44no—
326C2×Dic83—44no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83C2×#4114yes—
330C2×Dic83C2×#4114yes—
331D332—416no—
332C4×D83—416no—
333Dic166—416no—
334C22×C83#52914yes—
335C22×C83#53814yes—
336C22×C83#53814yes—
337C22×C83#53814yes—
338C22×C83#53914yes—
339C22×C83#54214yes—
340C22×C83#54214yes—
341C22×C83C22×#4111yescharacteristic
342C22×C83C22×#4111yescharacteristic
343C22×C83C22×#4111yescharacteristic
344C22×C83C2×H(5,𝔽2)11yescharacteristic
345C22×C83C2×H(5,𝔽2)11yescharacteristic
346C22×C83C2×H(5,𝔽2)11yescharacteristic
347C22×C83C2×2−1+411yescharacteristic
348C2×D83—24no—
349C2×D83—24no—
350C2×D83—24no—
351C2×D83—416no—
352C2×D83—42no—
353C2×D83—42no—
354C2×D83—42no—
355C2×D83—42no—
356C2×D83—42no—
357C2×D83—42no—
358C2×D83—42no—
359C2×D83—42no—
360C2×D83—42no—
361C2×D83—42no—
362C2×D83—42no—
363C2×D83—88no—
364C4×C83—42no—
365C4×C83—42no—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371Dic83—24no—
372Dic83—24no—
373Dic83—42no—
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377C2×#2653—831nomaximal, Sylow
378C2×C83#265318yescomplemented
379C2×C83C2×#52911yescharacteristic
380C2×C83C2×#53811yescharacteristic
381C2×C83C2×#53811yescharacteristic
382C2×C83C2×#53811yescharacteristic
383C2×C83C2×#53911yescharacteristic
384C2×C83C2×#54211yescharacteristic
385C2×C83C2×#54211yescharacteristic
386D83—44no—
387D83—82no—
388#2653—8316no—
389C2×#401D8311yescharacteristic, complemented
390C2×#398—831no—
391C2×#397—831no—
392C2×#397—831no—
393C2×#394—831no—
394C2×#394—831no—
395C2×#393—831no—
396C2×#393—831no—
397C2×#391—831no—
398C2×#388—831no—
399C2×#388—831no—
400C2×#387—831no—
401C2×#386—831no—
402C2×#385—831no—
403C2×C4×C22⋊C4—831no—
404C83C2×#265311yescharacteristic, complemented, Sylow
405C23×Q8—831no—
406C23×D4—831no—
407C24×C4—831no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4—831no—
411C22×C4⋊C4—831no—
412C22×C4⋊C4—831no—
413C22×C22⋊C4—831no—
414C22×C22⋊C4—831no—
415C22×C22⋊C4—831no—
416C22×C22⋊C4—831no—
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⋊C4—831no—
424C22×C42—831no—
425C22×C42—831no—
426#401C2×D8318yescomplemented
427#398—838no—
428#397—838no—
429#397—838no—
430#394—838no—
431#394—838no—
432#393—838no—
433#393—838no—
434#391—838no—
435#388—838no—
436#388—838no—
437#387—838no—
438#386—838no—
439#385—838no—
440C4×C22⋊C4—838no—
441C2×#95—831no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95C2×D8311yescharacteristic
449C2×#95C2×D8311yescharacteristic
450C2×#95C2×D8311yescharacteristic
451C2×#95C2×D8311yescharacteristic
452C2×#95C2×D8311yescharacteristic
453C2×#95C2×D8311yescharacteristic
454C2×#95C2×D8311yescharacteristic
455C25—831no—
456C25—831no—
457C22×Q8—3322no—
458C22×Q8—3322no—
459C22×Q8—834no—
460C22×Q8—1664no—
461C22×D4—3322no—
462C22×D4—3322no—
463C22×D4—834no—
464C22×D4—1664no—
465C23×C4—3322no—
466C23×C4—3322no—
467C23×C4—834no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4—831no—
471C23×C4—831no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—1664no—
475C23×C4C22×D8311yescharacteristic
476C23×C4C22×D8311yescharacteristic
477C23×C4C22×D8311yescharacteristic
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C23×C4C22×D8311yescharacteristic
481C23×C4C22×D8311yescharacteristic
482C2×C4⋊C4—3322no—
483C2×C4⋊C4—3322no—
484C2×C4⋊C4—3322no—
485C2×C4⋊C4—3322no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—834no—
489C2×C4⋊C4—834no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—1664no—
492C2×C22⋊C4—3322no—
493C2×C22⋊C4—3322no—
494C2×C22⋊C4—3322no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—3322no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—834no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—1664no—
510C2×C22⋊C4—1664no—
511C2×C22⋊C4—1664no—
512C2×C22⋊C4—1664no—
513C2×C22⋊C4—1664no—
514C2×C42—3322no—
515C2×C42—3322no—
516C2×C42—834no—
517C2×C42—834no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95C22×D8314yes—
526#95C22×D8314yes—
527#95C22×D8314yes—
528#95C22×D8314yes—
529#95C22×D8314yes—
530#95C22×D8314yes—
531#95C22×D8314yes—
532C24—834no—
533C24—832no—
534C24—832no—
535C24—1662no—
536C24—1662no—
537C24—1662no—
538C24—1662no—
539C24—1662no—
540C24—1662no—
541C24—1662no—
542C24—1662no—
543C24—1662no—
544C24—1662no—
545C24—1662no—
546C24—1662no—
547C24—1662no—
548C24C23×D8311yescharacteristic
549C2×Q8—3324no—
550C2×Q8—3324no—
551C2×Q8—33216no—
552C2×Q8—1668no—
553C2×D4—3324no—
554C2×D4—3324no—
555C2×D4—33216no—
556C2×D4—1668no—
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—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—3324no—
579C22×C4—3324no—
580C22×C4—33216no—
581C22×C4—834no—
582C22×C4—834no—
583C22×C4—832no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—832no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—1668no—
590C22×C4—1662no—
591C22×C4—1662no—
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×C4C23×D8312yes—
607C22×C4C23×D8312yes—
608C22×C4C23×D8312yes—
609C22×C4C23×D8312yes—
610C22×C4C23×D8312yes—
611C22×C4C23×D8312yes—
612C22×C4C23×D8312yes—
613C4⋊C4—3324no—
614C4⋊C4—3324no—
615C4⋊C4—3324no—
616C4⋊C4—3324no—
617C4⋊C4—1668no—
618C22⋊C4—3324no—
619C22⋊C4—3324no—
620C22⋊C4—3324no—
621C22⋊C4—3324no—
622C22⋊C4—3324no—
623C22⋊C4—3324no—
624C22⋊C4—1668no—
625C22⋊C4—1668no—
626C22⋊C4—1668no—
627C22⋊C4—1668no—
628C22⋊C4—1668no—
629C42—3324no—
630C42—3324no—
631C23—3324no—
632C23—3324no—
633C23—3324no—
634C23—3324no—
635C23—3324no—
636C23—3324no—
637C23—3324no—
638C23—3324no—
639C23—3324no—
640C23—3324no—
641C23—3324no—
642C23—834no—
643C23—1662no—
644C23—1662no—
645C23—1662no—
646C23—1662no—
647C23—1662no—
648C23—1662no—
649C23—1662no—
650C23—1668no—
651C23—1662no—
652C23—1662no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23—1668no—
658C23—1668no—
659C23#41×D8312yes—
660C23#41×D8312yes—
661C23#41×D8312yes—
662C23#1458183812yes—
663C23#1458183812yes—
664C23#1458183812yes—
665C23#1458183912yes—
666C23C24×D8311yescharacteristic
667Q8—33216no—
668D4—33216no—
669C2×C4—22no—
670C2×C4—22no—
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—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—33216no—
698C2×C4—3324no—
699C2×C4—3324no—
700C2×C4—3324no—
701C2×C4—3324no—
702C2×C4—834no—
703C2×C4—834no—
704C2×C4—1662no—
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—1668no—
721C2×C4—1668no—
722C22—3322no—
723C22—3322no—
724C22—33216no—
725C22—3322no—
726C22—3322no—
727C22—3322no—
728C22—3322no—
729C22—3322no—
730C22—3322no—
731C22—3322no—
732C22—3322no—
733C22—3322no—
734C22—6648no—
735C22—1664no—
736C22—1664no—
737C22—1664no—
738C22#1912823414yes—
739C22#1912829014yes—
740C22#1912829014yes—
741C22#1912829014yes—
742C22#1912829214yes—
743C22#1912831714yes—
744C22#1912831714yes—
745C22C2×#41×D8311yescharacteristic
746C22C2×#41×D8311yescharacteristic
747C22C2×#41×D8311yescharacteristic
748C22C2×#1458183811yescharacteristic
749C22C2×#1458183811yescharacteristic
750C22C2×#1458183811yescharacteristic
751C22C2×#1458183911yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—3322no—
760C4—3322no—
761C4—3322no—
762C4—3322no—
763C4—1664no—
764C4—1664no—
765C2—3324no—
766C2—6642no—
767C2#2491353118yesdirect product factor
768C2C2×#1912823411yescharacteristic
769C2C2×#1912829011yescharacteristic
770C2C2×#1912829011yescharacteristic
771C2C2×#1912829011yescharacteristic
772C2C2×#1912829211yescharacteristic
773C2C2×#1912831711yescharacteristic
774C2C2×#1912831711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#401×C83C2
socleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×#401D83
hypocenterC83C2×#2653
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#401

Complements

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

NH ≅ G/Ntype
1. #24913531C2direct (N × H)
2. C2×#19127635C2semidirect
3. C2×#19127630C2semidirect
4. C2×#19127628C2semidirect
7. C2×#19127614C2semidirect
8. C2×#19127614C2semidirect
9. C2×#19127605C2semidirect
10. C2×#19127593C2semidirect
11. C2×#19127593C2semidirect
12. C2×#19127584C2semidirect
14. C2×#19127575C2semidirect
15. C2×#19127548C2semidirect
16. C2×#401×C83C2semidirect
38. #19127635C22semidirect
39. #19127630C22semidirect
40. #19127628C22semidirect
43. #19127614C22semidirect
44. #19127614C22semidirect
45. #19127605C22semidirect
46. #19127593C22semidirect
47. #19127593C22semidirect
48. #19127584C22semidirect
50. #19127575C22semidirect
51. #19127548C22semidirect
59. #401×C83C22semidirect
378. C2×C83#2653semidirect
389. C2×#401D83semidirect
404. C83C2×#2653semidirect
426. #401C2×D83semidirect
767. C2#24913531direct (N × H)

Maximal subgroups

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

subgroupindex
#249135312
C2×#191276352
C2×#191276302
C2×#191276282
C2×#191276192
C2×#191276142
C2×#191276052
C2×#191275932
C2×#191275842
C2×#191275792
C2×#191275752
C2×#191275482
C2×#401×C832
C2×#265383