Finite Group Databasebeta

← C2×#24913615 #35570974

Subgroups — C2×#24913615 #35570974

Order 21248.

2786 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581774C211yesmaximal, characteristic
2C22×#14581770C211yesmaximal, characteristic, complemented
3#24913615C2116yesmaximal, direct product factor
4C2×#19127643C211yesmaximal, characteristic, complemented
5C2×#19127637C211yesmaximal, characteristic, complemented
6C2×#19127630C211yesmaximal, characteristic, complemented
7C2×#19127628C211yesmaximal, characteristic, complemented
8C2×#19127622C211yesmaximal, characteristic, complemented
9C2×#19127617C211yesmaximal, characteristic
10C2×#19127616C211yesmaximal, characteristic
11C2×#19127613C211yesmaximal, characteristic, complemented
12C2×#19127599C211yesmaximal, characteristic, complemented
13C2×#19127596C211yesmaximal, characteristic, complemented
14C2×#19127595C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581774—28no—
21C2×#14581774C2218yes—
22C2×#14581770—28no—
23C2×#14581770C2218yescomplemented
24C22×C4⋊Dic83C2211yescharacteristic
25C22×C4⋊Dic83C2211yescharacteristic
26C22×C4⋊Dic83C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127643C2218yescomplemented
42#19127637C2218yescomplemented
43#19127630C2218yescomplemented
44#19127628C2218yescomplemented
45#19127622C2218yescomplemented
46#19127617C2218yes—
47#19127616C2218yes—
48#19127613C2218yescomplemented
49#19127599C2218yescomplemented
50#19127596C2218yescomplemented
51#19127595C2218yescomplemented
52C4×(C2×D83)⋊C4C2218yescomplemented
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66#388×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—42no—
72C22×Dic166—42no—
73C22×Dic166C2314yes—
74C22×C22⋊D83—24no—
75C22×C22⋊D83—42no—
76C22×C22⋊D83—42no—
77C22×C22⋊D83C2314yes—
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C22×C4×D83—42no—
86C22×C4×D83—42no—
87C22×C4×D83D418yes—
88C22×C4×D83C2314yes—
89#14581774—232no—
90#14581770—232no—
91C2×C4⋊Dic83—24no—
92C2×C4⋊Dic83—24no—
93C2×C4⋊Dic83—42no—
94C2×C4⋊Dic83C2314yes—
95C2×C4⋊Dic83C2314yes—
96C2×C4⋊Dic83C2314yes—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—42no—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×C22⋊Dic83—24no—
108C2×C22⋊Dic83—24no—
109C2×C22⋊Dic83—42no—
110C2×C22⋊Dic83C2314yes—
111C2×C22⋊Dic83C2314yes—
112C2×C22⋊Dic83C2314yes—
113C2×(C2×D83)⋊C4—24no—
114C2×(C2×D83)⋊C4—24no—
115C2×(C2×D83)⋊C4—24no—
116C2×(C2×D83)⋊C4—24no—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×C4×Dic83—42no—
124C2×C4×Dic83C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C25×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C2×C4⋊C4×C83—24no—
141C2×C4⋊C4×C83C2314yes—
142C2×C22⋊C4×C83—24no—
143C2×C22⋊C4×C83—24no—
144C2×C22⋊C4×C83—42no—
145C2×C22⋊C4×C83C2314yes—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148C2×C42×C83—42no—
149C2×C42×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—44no—
162C2×Dic166—44no—
163C2×Dic166—416no—
164C2×C22⋊D83—28no—
165C2×C22⋊D83—44no—
166C2×C22⋊D83—44no—
167C2×C22⋊D83—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—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83C2×D414yes—
188C22×Dic83#4114yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C2×C4×D83—416no—
197C2×C4×D83—44no—
198C2×C4×D83—44no—
199C2×C4×D83C2×D4116yes—
200C4⋊Dic83—28no—
201C4⋊Dic83—28no—
202C4⋊Dic83—44no—
203Dic83⋊C4—28no—
204Dic83⋊C4—28no—
205Dic83⋊C4—28no—
206Dic83⋊C4—28no—
207Dic83⋊C4—44no—
208C22⋊Dic83—28no—
209C22⋊Dic83—28no—
210C22⋊Dic83—44no—
211(C2×D83)⋊C4—28no—
212(C2×D83)⋊C4—28no—
213(C2×D83)⋊C4—28no—
214(C2×D83)⋊C4—28no—
215(C2×D83)⋊C4—28no—
216C4×Dic83—44no—
217C24×C83—22no—
218C24×C83—22no—
219C24×C83—22no—
220C24×C83—22no—
221C24×C83—22no—
222C24×C83—22no—
223C24×C83—22no—
224C24×C83C2412yes—
225C24×C83C2411yescharacteristic
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×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83C2×D414yes—
243C22×C4×C83#4114yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C4⋊C4×C83—28no—
251C22⋊C4×C83—28no—
252C22⋊C4×C83—28no—
253C22⋊C4×C83—44no—
254C42×C83—44no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—44no—
263C23×C83—44no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83—44no—
267C23×C83—44no—
268C23×C83—44no—
269C23×C83C22×D412yes—
270C23×C83C2×#4112yes—
271C23×C83C2×#4112yes—
272C23×C83H(5,𝔽2)12yes—
273C23×C83H(5,𝔽2)12yes—
274C23×C832−1+412yes—
275C23×C832−1+412yes—
276C23×C83C2511yescharacteristic
277C22×D83—28no—
278C22×D83—28no—
279C22×D83—28no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—22no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83—44no—
289C22×D83—44no—
290C22×D83C22×D414yes—
291C2×C4×C83—28no—
292C2×C4×C83—28no—
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—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—44no—
310C2×C4×C83—44no—
311C2×C4×C83—44no—
312C2×C4×C83—44no—
313C2×C4×C83C22×D414yes—
314C2×C4×C83C2×#4114yes—
315C22⋊D83—416no—
316C2×Dic83—28no—
317C2×Dic83—28no—
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—22no—
337C2×Dic83—44no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83—44no—
341C2×Dic83—44no—
342C2×Dic83C22×D414yes—
343C2×Dic83C2×#4114yes—
344C4×D83—416no—
345Dic166—416no—
346C22×C83—42no—
347C22×C83—42no—
348C22×C83—42no—
349C22×C83—42no—
350C22×C83—42no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—88no—
354C22×C83#53214yes—
355C22×C83#53414yes—
356C22×C83#53614yes—
357C22×C83#53914yes—
358C22×C83#53914yes—
359C22×C83#54214yes—
360C22×C83#54214yes—
361C22×C83C23×D411yescharacteristic
362C22×C83C22×#4111yescharacteristic
363C22×C83C22×#4111yescharacteristic
364C22×C83C2×H(5,𝔽2)11yescharacteristic
365C22×C83C2×H(5,𝔽2)11yescharacteristic
366C22×C83C2×2−1+411yescharacteristic
367C22×C83C2×2−1+411yescharacteristic
368C2×D83—24no—
369C2×D83—24no—
370C2×D83—24no—
371C2×D83—416no—
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C4×C83—24no—
377C4×C83—24no—
378C4×C83—42no—
379C4×C83—42no—
380C4×C83—42no—
381C4×C83—42no—
382Dic83—24no—
383Dic83—24no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389C2×#2663—831nomaximal, Sylow
390C2×C83—82no—
391C2×C83#266318yescomplemented
392C2×C83C2×#53211yescharacteristic
393C2×C83C2×#53411yescharacteristic
394C2×C83C2×#53611yescharacteristic
395C2×C83C2×#53911yescharacteristic
396C2×C83C2×#53911yescharacteristic
397C2×C83C2×#54211yescharacteristic
398C2×C83C2×#54211yescharacteristic
399D83—44no—
400C22×#123—831no—
401C22×C22⋊Q8—831no—
402#2663—8316no—
403C2×#400—831no—
404C2×#399—831no—
405C2×#397—831no—
406C2×#397—831no—
407C2×#395—831no—
408C2×#394—831no—
409C2×#394—831no—
410C2×#393—831no—
411C2×#389—831no—
412C2×#389—831no—
413C2×#388—831no—
414C2×#388D8311yescharacteristic, complemented
415C2×C4×C22⋊C4—831no—
416C83C2×#266311yescharacteristic, complemented, Sylow
417C23×Q8—831no—
418C23×D4—831no—
419C24×C4—831no—
420C2×#123—838no—
421C2×#123—1668no—
422C2×C22⋊Q8—838no—
423C2×C22⋊Q8—1668no—
424C22×C4⋊C4—831no—
425C22×C4⋊C4—831no—
426C22×C4⋊C4—831no—
427C22×C4⋊C4—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4—831no—
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×C22⋊C4C2×D8311yescharacteristic
444C22×C42—831no—
445C22×C42C2×D8311yescharacteristic
446#400—838no—
447#399—838no—
448#397—838no—
449#397—838no—
450#395—838no—
451#394—838no—
452#394—838no—
453#393—838no—
454#389—838no—
455#389—838no—
456#388—838no—
457#388C2×D8318yescomplemented
458C4×C22⋊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×#95C2×D8311yescharacteristic
468C2×#95C2×D8311yescharacteristic
469C25—831no—
470C25C22×D8311yescharacteristic
471C22×Q8—3322no—
472C22×Q8—3322no—
473C22×Q8—834no—
474C22×Q8—1664no—
475C22×D4—3322no—
476C22×D4—3322no—
477C22×D4—834no—
478C22×D4—1664no—
479C23×C4—3322no—
480C23×C4—3322no—
481C23×C4—838no—
482C23×C4—834no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—831no—
488C23×C4—831no—
489C23×C4—831no—
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C23×C4C22×D8311yescharacteristic
496#123—16632no—
497C22⋊Q8—16632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—3322no—
500C2×C4⋊C4—3322no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—1664no—
510C2×C4⋊C4—1664no—
511C2×C4⋊C4—1664no—
512C2×C4⋊C4—1664no—
513C2×C4⋊C4—1664no—
514C2×C4⋊C4—1664no—
515C2×C4⋊C4C22×D8314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—42no—
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⋊C4—1664no—
535C2×C22⋊C4C22×D8314yes—
536C2×C22⋊C4C22×D8314yes—
537C2×C22⋊C4C22×D8314yes—
538C2×C42—42no—
539C2×C42—3322no—
540C2×C42—834no—
541C2×C42C22×D8314yes—
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#95C22×D8314yes—
551#95C22×D8314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—834no—
560C24—832no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24—1662no—
565C24—1662no—
566C24—1662no—
567C24C23×D8312yes—
568C24C23×D8311yescharacteristic
569C2×Q8—3324no—
570C2×Q8—3324no—
571C2×Q8—33216no—
572C2×Q8—1668no—
573C2×D4—33216no—
574C2×D4—3324no—
575C2×D4—3324no—
576C2×D4—1668no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—33216no—
594C22×C4—3324no—
595C22×C4—3324no—
596C22×C4—8316no—
597C22×C4—834no—
598C22×C4—834no—
599C22×C4—832no—
600C22×C4—832no—
601C22×C4—832no—
602C22×C4—832no—
603C22×C4—832no—
604C22×C4—832no—
605C22×C4—832no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
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×C4D4×D8314yes—
626C22×C4#1305059014yes—
627C22×C4C23×D8312yes—
628C22×C4C23×D8312yes—
629C22×C4C23×D8312yes—
630C22×C4C23×D8312yes—
631C22×C4C23×D8312yes—
632C22×C4C23×D8312yes—
633C4⋊C4—28no—
634C4⋊C4—3324no—
635C4⋊C4—3324no—
636C4⋊C4—1668no—
637C4⋊C4—1668no—
638C4⋊C4—1668no—
639C4⋊C4—1668no—
640C4⋊C4—1668no—
641C4⋊C4—1668no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—44no—
645C22⋊C4—3324no—
646C22⋊C4—1668no—
647C22⋊C4—1668no—
648C22⋊C4—1668no—
649C22⋊C4—1668no—
650C22⋊C4—1668no—
651C22⋊C4—1668no—
652C22⋊C4—1668no—
653C42—44no—
654C42—3324no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—3324no—
670C23—3324no—
671C23—3324no—
672C23—3324no—
673C23—834no—
674C23—1668no—
675C23—1668no—
676C23—1662no—
677C23—1668no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23C2×D4×D8312yes—
684C23#41×D8312yes—
685C23C2×#1305059012yes—
686C23#1458183712yes—
687C23#1458183812yes—
688C23#1458183912yes—
689C23#1458183912yes—
690C23C24×D8311yescharacteristic
691Q8—33216no—
692D4—33216no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
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—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—33216no—
716C2×C4—3324no—
717C2×C4—3324no—
718C2×C4—3324no—
719C2×C4—3324no—
720C2×C4—3324no—
721C2×C4—834no—
722C2×C4—834no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
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—1668no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1662no—
743C2×C4—1668no—
744C2×C4C2×D4×D8314yes—
745C2×C4C2×#1305059014yes—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—3322no—
755C22—3322no—
756C22—33216no—
757C22—3322no—
758C22—3322no—
759C22—1664no—
760C22—1664no—
761C22—1664no—
762C22#1912824814yes—
763C22#1912825914yes—
764C22#1912827114yes—
765C22#1912829214yes—
766C22#1912829314yes—
767C22#1912831914yes—
768C22#1912832214yes—
769C22C22×D4×D8311yescharacteristic
770C22C2×#41×D8311yescharacteristic
771C22C22×#1305059011yescharacteristic
772C22C2×#1458183711yescharacteristic
773C22C2×#1458183811yescharacteristic
774C22C2×#1458183911yescharacteristic
775C22C2×#1458183911yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—3322no—
783C4—3322no—
784C4—3322no—
785C4—3322no—
786C4—3322no—
787C4—1664no—
788C4—1664no—
789C2—82no—
790C2—3324no—
791C2#2491361518yesdirect product factor
792C2C2×#1912824811yescharacteristic
793C2C2×#1912825911yescharacteristic
794C2C2×#1912827111yescharacteristic
795C2C2×#1912829211yescharacteristic
796C2C2×#1912829311yescharacteristic
797C2C2×#1912831911yescharacteristic
798C2C2×#1912832211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#388D83
hypocenterC83C2×#2663
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14581770C2semidirect
3. #24913615C2direct (N × H)
4. C2×#19127643C2semidirect
5. C2×#19127637C2semidirect
6. C2×#19127630C2semidirect
7. C2×#19127628C2semidirect
8. C2×#19127622C2semidirect
11. C2×#19127613C2semidirect
12. C2×#19127599C2semidirect
13. C2×#19127596C2semidirect
14. C2×#19127595C2semidirect
15. C2×C4×(C2×D83)⋊C4C2semidirect
16. C2×#388×C83C2semidirect
23. C2×#14581770C22semidirect
41. #19127643C22semidirect
42. #19127637C22semidirect
43. #19127630C22semidirect
44. #19127628C22semidirect
45. #19127622C22semidirect
48. #19127613C22semidirect
49. #19127599C22semidirect
50. #19127596C22semidirect
51. #19127595C22semidirect
52. C4×(C2×D83)⋊C4C22semidirect
66. #388×C83C22semidirect
391. C2×C83#2663semidirect
414. C2×#388D83semidirect
416. C83C2×#2663semidirect
457. #388C2×D83semidirect
791. C2#24913615direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817742
C22×#145817702
#249136152
C2×#191276432
C2×#191276372
C2×#191276302
C2×#191276282
C2×#191276222
C2×#191276172
C2×#191276162
C2×#191276132
C2×#191275992
C2×#191275962
C2×#191275952
C2×C4×(C2×D83)⋊C42
C2×#388×C832
C2×#266383