Finite Group Databasebeta

← C2×#24913520 #35570899

Subgroups — C2×#24913520 #35570899

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#24913520C2116yesmaximal, direct product factor
2C2×C83⋊#401C211yesmaximal, characteristic, complemented
3C2×#19127635C211yesmaximal, characteristic, complemented
4C2×#19127630C211yesmaximal, characteristic, complemented
5C2×#19127629C211yesmaximal, characteristic, complemented
6C2×#19127617C211yesmaximal, characteristic
7C2×#19127616C211yesmaximal, characteristic
8C2×#19127614C211yesmaximal, characteristic, complemented
9C2×#19127613C211yesmaximal, characteristic, complemented
10C2×#19127607C211yesmaximal, characteristic, complemented
11C2×#19127592C211yesmaximal, characteristic, complemented
12C2×#19127592C211yesmaximal, characteristic, complemented
13C2×#19127585C211yesmaximal, characteristic, complemented
14C2×#19127580C211yesmaximal, characteristic
15C2×#19127574C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C83⋊#401C2218yescomplemented
34#19127635C2218yescomplemented
35#19127630C2218yescomplemented
36#19127629C2218yescomplemented
37#19127617C2218yes—
38#19127616C2218yes—
39#19127614C2218yescomplemented
40#19127613C2218yescomplemented
41#19127607C2218yescomplemented
42#19127592C2218yescomplemented
43#19127592C2218yescomplemented
44#19127585C2218yescomplemented
45#19127580C2218yes—
46#19127574C2218yescomplemented
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
58C2×C83⋊#95C2211yescharacteristic
59C24×C4×C83C2211yescharacteristic
60C22×C22⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C42×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64C4×C22⋊C4×C83C2218yescomplemented
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C22×Dic166—24no—
69C22×Dic166—42no—
70C22×Dic166—42no—
71C22×Dic166C2314yes—
72C22×C22⋊D83—24no—
73C22×C22⋊D83—42no—
74C22×C22⋊D83—42no—
75C22×C22⋊D83C2314yes—
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C2×C4⋊Dic83—42no—
84C2×C4⋊Dic83C2314yes—
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—42no—
87C2×Dic83⋊C4—42no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4C2314yes—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×C22⋊Dic83—24no—
94C2×C22⋊Dic83—42no—
95C2×C22⋊Dic83—42no—
96C2×C22⋊Dic83C2314yes—
97C2×C22⋊Dic83C2314yes—
98C2×C22⋊Dic83C2314yes—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—24no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4—42no—
103C2×(C2×D83)⋊C4—42no—
104C2×(C2×D83)⋊C4—42no—
105C2×(C2×D83)⋊C4C2314yes—
106C2×(C2×D83)⋊C4C2314yes—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C25×C83C2311yescharacteristic
124C23×C4×C83—24no—
125C23×C4×C83—42no—
126C23×C4×C83—42no—
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2314yes—
134C2×C22⋊C4×C83—24no—
135C2×C22⋊C4×C83—24no—
136C2×C22⋊C4×C83C2314yes—
137C2×C22⋊C4×C83C2314yes—
138C2×C42×C83—42no—
139C2×C42×C83—42no—
140C2×C42×C83C2314yes—
141C2×C42×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×D83C2412yes—
152C2×Dic166—28no—
153C2×Dic166—44no—
154C2×Dic166—44no—
155C2×Dic166—416no—
156C2×C22⋊D83—28no—
157C2×C22⋊D83—44no—
158C2×C22⋊D83—44no—
159C2×C22⋊D83—416no—
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×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C4⋊Dic83—44no—
189Dic83⋊C4—28no—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192Dic83⋊C4—44no—
193C22⋊Dic83—28no—
194C22⋊Dic83—44no—
195C22⋊Dic83—44no—
196(C2×D83)⋊C4—28no—
197(C2×D83)⋊C4—28no—
198(C2×D83)⋊C4—44no—
199(C2×D83)⋊C4—44no—
200(C2×D83)⋊C4—44no—
201(C2×D83)⋊C4—44no—
202C24×C83—22no—
203C24×C83—22no—
204C24×C83—22no—
205C24×C83—22no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83#4114yes—
209C24×C83C2412yes—
210C24×C83C2411yescharacteristic
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
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—28no—
228C22×C4×C83—44no—
229C22×C4×C83—44no—
230C22×C4×C83—416no—
231C22×C4×C83#4114yes—
232C22×C4×C83#4114yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22⋊C4×C83—28no—
240C22⋊C4×C83—28no—
241C42×C83—44no—
242C42×C83—44no—
243C23×C83—28no—
244C23×C83—28no—
245C23×C83—28no—
246C23×C83—22no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—44no—
253C23×C83—44no—
254C23×C83—44no—
255C23×C83—44no—
256C23×C83C2×#4114yes—
257C23×C83C2×#4112yes—
258C23×C83C2×#4112yes—
259C23×C83C2×#4112yes—
260C23×C83H(5,𝔽2)12yes—
261C23×C83H(5,𝔽2)12yes—
262C23×C83H(5,𝔽2)12yes—
263C23×C832−1+412yes—
264C23×C83C2511yescharacteristic
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—44no—
273C22×D83—44no—
274C22×D83—44no—
275C22×D83—44no—
276C22×D83—44no—
277C22×D83—44no—
278C22×D83—44no—
279C2×C4×C83—28no—
280C2×C4×C83—28no—
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—416no—
298C2×C4×C83—44no—
299C2×C4×C83—44no—
300C2×C4×C83—44no—
301C2×C4×C83—44no—
302C2×C4×C83C2×#4114yes—
303C2×C4×C83C2×#4114yes—
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—
333Dic166—416no—
334C22×C83—24no—
335C22×C83—24no—
336C22×C83—24no—
337C22×C83—416no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83#52914yes—
343C22×C83#53814yes—
344C22×C83#53814yes—
345C22×C83#53814yes—
346C22×C83#53914yes—
347C22×C83#54214yes—
348C22×C83#54214yes—
349C22×C83C22×#4111yescharacteristic
350C22×C83C22×#4111yescharacteristic
351C22×C83C22×#4111yescharacteristic
352C22×C83C2×H(5,𝔽2)11yescharacteristic
353C22×C83C2×H(5,𝔽2)11yescharacteristic
354C22×C83C2×H(5,𝔽2)11yescharacteristic
355C22×C83C2×2−1+411yescharacteristic
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—24no—
365C4×C83—24no—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369C4×C83—42no—
370Dic83—42no—
371Dic83—42no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377C2×#2653—831nomaximal, Sylow
378C2×C83—44no—
379C2×C83#265318yescomplemented
380C2×C83C2×#52911yescharacteristic
381C2×C83C2×#53811yescharacteristic
382C2×C83C2×#53811yescharacteristic
383C2×C83C2×#53811yescharacteristic
384C2×C83C2×#53911yescharacteristic
385C2×C83C2×#54211yescharacteristic
386C2×C83C2×#54211yescharacteristic
387D83—82no—
388#2653—8316no—
389C2×#401—831no—
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⋊C4D8311yescharacteristic, complemented
404C83C2×#265311yescharacteristic, complemented, Sylow
405C23×Q8—831no—
406C23×D4—831no—
407C24×C4C2×D8311yescharacteristic
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⋊C4C2×D8311yescharacteristic
423C22×C22⋊C4C2×D8311yescharacteristic
424C22×C42C2×D8311yescharacteristic
425C22×C42C2×D8311yescharacteristic
426#401—838no—
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⋊C4C2×D8318yescomplemented
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×#95C2×D8311yescharacteristic
454C2×#95C2×D8311yescharacteristic
455C25—831no—
456C25C22×D8311yescharacteristic
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—24no—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4—831no—
471C23×C4—831no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—831no—
475C23×C4C22×D8311yescharacteristic
476C23×C4C22×D8311yescharacteristic
477C23×C4C22×D8311yescharacteristic
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C23×C4C22×D8311yescharacteristic
481C23×C4C22×D8314yes—
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—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—3322no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—3322no—
498C2×C22⋊C4—3322no—
499C2×C22⋊C4—3322no—
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⋊C4C22×D8314yes—
513C2×C22⋊C4C22×D8314yes—
514C2×C42—42no—
515C2×C42—42no—
516C2×C42C22×D8314yes—
517C2×C42C22×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#95C22×D8314yes—
531#95C22×D8314yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—832no—
539C24—1662no—
540C24—1662no—
541C24—1662no—
542C24—1662no—
543C24—1662no—
544C24—1662no—
545C24—1662no—
546C24#1305059014yes—
547C24C23×D8312yes—
548C24C23×D8311yescharacteristic
549C2×Q8—33216no—
550C2×Q8—3324no—
551C2×Q8—3324no—
552C2×Q8—1668no—
553C2×D4—33216no—
554C2×D4—3324no—
555C2×D4—3324no—
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—28no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—416no—
577C22×C4—832no—
578C22×C4—832no—
579C22×C4—832no—
580C22×C4—832no—
581C22×C4—832no—
582C22×C4—832no—
583C22×C4—832no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
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#1305059014yes—
606C22×C4#1305059014yes—
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—28no—
619C22⋊C4—28no—
620C22⋊C4—3324no—
621C22⋊C4—3324no—
622C22⋊C4—3324no—
623C22⋊C4—3324no—
624C22⋊C4—3324no—
625C22⋊C4—3324no—
626C22⋊C4—1668no—
627C22⋊C4—1668no—
628C22⋊C4—1668no—
629C42—44no—
630C42—44no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—28no—
639C23—28no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—3324no—
645C23—3324no—
646C23—3324no—
647C23—3324no—
648C23—3324no—
649C23—3324no—
650C23—3324no—
651C23—1662no—
652C23—1662no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23—1662no—
658C23C2×#1305059014yes—
659C23C2×#1305059012yes—
660C23C2×#1305059012yes—
661C23C2×#1305059012yes—
662C23#1458183712yes—
663C23#1458183712yes—
664C23#1458183812yes—
665C23#1458183912yes—
666C23C24×D8311yescharacteristic
667Q8—33216no—
668D4—33216no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
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—416no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—3324no—
693C2×C4—3324no—
694C2×C4—3324no—
695C2×C4—3324no—
696C2×C4—3324no—
697C2×C4—3324no—
698C2×C4—3324no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
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×C4C2×#1305059014yes—
721C2×C4C2×#1305059014yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—416no—
728C22—42no—
729C22—42no—
730C22—3322no—
731C22—3322no—
732C22—3322no—
733C22—3322no—
734C22—3322no—
735C22—3322no—
736C22—3322no—
737C22—6648no—
738C22#1912823514yes—
739C22#1912828414yes—
740C22#1912828414yes—
741C22#1912828914yes—
742C22#1912829314yes—
743C22#1912831614yes—
744C22#1912832214yes—
745C22C22×#1305059011yescharacteristic
746C22C22×#1305059011yescharacteristic
747C22C22×#1305059011yescharacteristic
748C22C2×#1458183711yescharacteristic
749C22C2×#1458183711yescharacteristic
750C22C2×#1458183811yescharacteristic
751C22C2×#1458183911yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—3322no—
759C4—3322no—
760C4—3322no—
761C4—3322no—
762C4—3322no—
763C4—3322no—
764C4—3322no—
765C2—44no—
766C2—6642no—
767C2#2491352018yesdirect product factor
768C2C2×#1912823511yescharacteristic
769C2C2×#1912828411yescharacteristic
770C2C2×#1912828411yescharacteristic
771C2C2×#1912828911yescharacteristic
772C2C2×#1912829311yescharacteristic
773C2C2×#1912831611yescharacteristic
774C2C2×#1912832211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×C4×C22⋊C4×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C2×#2653
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #24913520C2direct (N × H)
2. C2×C83⋊#401C2semidirect
3. C2×#19127635C2semidirect
4. C2×#19127630C2semidirect
5. C2×#19127629C2semidirect
8. C2×#19127614C2semidirect
9. C2×#19127613C2semidirect
10. C2×#19127607C2semidirect
11. C2×#19127592C2semidirect
12. C2×#19127592C2semidirect
13. C2×#19127585C2semidirect
15. C2×#19127574C2semidirect
16. C2×C4×C22⋊C4×C83C2semidirect
33. C83⋊#401C22semidirect
34. #19127635C22semidirect
35. #19127630C22semidirect
36. #19127629C22semidirect
39. #19127614C22semidirect
40. #19127613C22semidirect
41. #19127607C22semidirect
42. #19127592C22semidirect
43. #19127592C22semidirect
44. #19127585C22semidirect
46. #19127574C22semidirect
64. C4×C22⋊C4×C83C22semidirect
379. C2×C83#2653semidirect
403. C2×C4×C22⋊C4D83semidirect
404. C83C2×#2653semidirect
440. C4×C22⋊C4C2×D83semidirect
767. C2#24913520direct (N × H)

Maximal subgroups

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

subgroupindex
#249135202
C2×C83⋊#4012
C2×#191276352
C2×#191276302
C2×#191276292
C2×#191276172
C2×#191276162
C2×#191276142
C2×#191276132
C2×#191276072
C2×#191275922
C2×#191275852
C2×#191275802
C2×#191275742
C2×C4×C22⋊C4×C832
C2×#265383