Finite Group Databasebeta

← C2×#24913137 #35575238

Subgroups — C2×#24913137 #35575238

Order 21248.

3070 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×#14581751C211yesmaximal, characteristic, complemented
2C22×#14581748C211yesmaximal, characteristic, complemented
3#24913137C2116yesmaximal, direct product factor
4C2×#19127635C211yesmaximal, characteristic, complemented
5C2×#19127624C211yesmaximal, characteristic, complemented
6C2×#19127624C211yesmaximal, characteristic, complemented
7C2×#19127615C211yesmaximal, characteristic
8C2×#19127595C211yesmaximal, characteristic, complemented
9C2×#19127589C211yesmaximal, characteristic, complemented
10C2×#19127588C211yesmaximal, characteristic, complemented
11C2×#19127586C211yesmaximal, characteristic, complemented
12C2×#19127581C211yesmaximal, characteristic
13C2×#19127576C211yesmaximal, characteristic, complemented
14C2×#19127574C211yesmaximal, characteristic, complemented
15C2×#19127565C211yesmaximal, characteristic, complemented
16C2×#386×C83C211yesmaximal, characteristic
17C24×Dic83C2211yescharacteristic
18C2×#14581751—28no—
19C2×#14581751C2218yescomplemented
20C2×#14581748—28no—
21C2×#14581748C2218yescomplemented
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×C22⋊Dic83C2211yescharacteristic
36C22×C22⋊Dic83C2211yescharacteristic
37C22×C22⋊Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127635C2218yescomplemented
42#19127624C2218yescomplemented
43#19127624C2218yescomplemented
44#19127615C2218yes—
45#19127595C2218yescomplemented
46#19127589C2218yescomplemented
47#19127588C2218yescomplemented
48#19127586C2218yescomplemented
49#19127581C2218yes—
50#19127576C2218yescomplemented
51#19127574C2218yescomplemented
52#19127565C2218yescomplemented
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C23×D4×C83C2211yescharacteristic
62C24×C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66#386×C83C2218yes—
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C23×Dic83—24no—
70C23×Dic83—24no—
71C23×Dic83—24no—
72C23×Dic83C2314yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81#14581751—232no—
82#14581748—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83—24no—
85C2×C4⋊Dic83—24no—
86C2×C4⋊Dic83C2314yes—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—42no—
93C2×Dic83⋊C4—42no—
94C2×Dic83⋊C4—42no—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×C22⋊Dic83—24no—
102C2×C22⋊Dic83—24no—
103C2×C22⋊Dic83—24no—
104C2×C22⋊Dic83—24no—
105C2×C22⋊Dic83—24no—
106C2×C22⋊Dic83—24no—
107C2×C22⋊Dic83—42no—
108C2×C22⋊Dic83C2314yes—
109C2×C22⋊Dic83C2314yes—
110C2×C22⋊Dic83C2314yes—
111C2×C22⋊Dic83C2314yes—
112C2×C22⋊Dic83C2314yes—
113C2×C22⋊Dic83C2314yes—
114C2×C22⋊Dic83C2314yes—
115C2×C4×Dic83—24no—
116C2×C4×Dic83—24no—
117C2×C4×Dic83D418yescomplemented
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—
129C25×C83C2311yescharacteristic
130C25×C83C2311yescharacteristic
131C22×D4×C83—24no—
132C22×D4×C83—24no—
133C22×D4×C83—42no—
134C22×D4×C83C2314yes—
135C23×C4×C83—24no—
136C23×C4×C83—24no—
137C23×C4×C83—24no—
138C23×C4×C83C2314yes—
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C2×C22⋊C4×C83—24no—
145C2×C22⋊C4×C83—24no—
146C2×C22⋊C4×C83—42no—
147C2×C22⋊C4×C83C2314yes—
148C2×C22⋊C4×C83C2314yes—
149C2×C22⋊C4×C83C2314yes—
150#95×C83C2314yes—
151#95×C83C2314yes—
152C22×Dic83—232no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—28no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—28no—
161C22×Dic83—28no—
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×Dic83C2×D414yes—
178C22×Dic83C2×D414yes—
179C22×Dic83#4114yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C4⋊Dic83—28no—
189C4⋊Dic83—28no—
190C4⋊Dic83—28no—
191Dic83⋊C4—28no—
192Dic83⋊C4—28no—
193Dic83⋊C4—28no—
194Dic83⋊C4—44no—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197C22⋊Dic83—28no—
198C22⋊Dic83—28no—
199C22⋊Dic83—28no—
200C22⋊Dic83—28no—
201C22⋊Dic83—28no—
202C22⋊Dic83—28no—
203C22⋊Dic83—44no—
204C4×Dic83—28no—
205C4×Dic83—28no—
206C4×Dic83C2×D4116yescomplemented
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83—22no—
212C24×C83—22no—
213C24×C83—22no—
214C24×C83—22no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83—22no—
219C24×C83#4114yes—
220C24×C83#4114yes—
221C24×C83C2412yes—
222C24×C83C2412yes—
223C24×C83C2411yescharacteristic
224C2×D4×C83—28no—
225C2×D4×C83—28no—
226C2×D4×C83—44no—
227C2×D4×C83—416no—
228C22×C4×C83—232no—
229C22×C4×C83—22no—
230C22×C4×C83—28no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—28no—
235C22×C4×C83—28no—
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×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83C2×D414yes—
246C22×C4×C83#4114yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C22⋊C4×C83—28no—
253C22⋊C4×C83—28no—
254C22⋊C4×C83—44no—
255C23×C83—28no—
256C23×C83—28no—
257C23×C83—28no—
258C23×C83—28no—
259C23×C83—28no—
260C23×C83—28no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—44no—
274C23×C83—44no—
275C23×C83—44no—
276C23×C83—44no—
277C23×C83—44no—
278C23×C83—44no—
279C23×C83—44no—
280C23×C83—44no—
281C23×C83C22×D412yes—
282C23×C83C2×#4112yes—
283C23×C83C2×#4114yes—
284C23×C83C2×#4112yes—
285C23×C83C2×#4112yes—
286C23×C83C2×#4114yes—
287C23×C83C2×#4112yes—
288C23×C83H(5,𝔽2)12yes—
289C23×C832−1+412yes—
290C23×C83C2511yescharacteristic
291D4×C83—416no—
292C2×C4×C83—232no—
293C2×C4×C83—28no—
294C2×C4×C83—28no—
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—44no—
309C2×C4×C83—44no—
310C2×C4×C83—44no—
311C2×C4×C83C22×D414yes—
312C2×C4×C83C2×#4114yes—
313C2×Dic83—232no—
314C2×Dic83—28no—
315C2×Dic83—28no—
316C2×Dic83—28no—
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—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—22no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83—44no—
341C2×Dic83—44no—
342C2×Dic83—44no—
343C2×Dic83C22×D414yes—
344C2×Dic83C22×D414yes—
345C2×Dic83C2×#4114yes—
346C22×C83—24no—
347C22×C83—24no—
348C22×C83—24no—
349C22×C83—24no—
350C22×C83—24no—
351C22×C83—24no—
352C22×C83—416no—
353C22×C83—416no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—42no—
357C22×C83—42no—
358C22×C83—42no—
359C22×C83—42no—
360C22×C83—42no—
361C22×C83—42no—
362C22×C83#52514yes—
363C22×C83#52514yes—
364C22×C83#53714yes—
365C22×C83#55114yes—
366C22×C83#55214yes—
367C22×C83#55214yes—
368C22×C83#55514yes—
369C22×C83C23×D411yescharacteristic
370C22×C83C22×#4111yescharacteristic
371C22×C83C22×#4111yescharacteristic
372C22×C83C22×#4111yescharacteristic
373C22×C83C22×#4111yescharacteristic
374C22×C83C2×H(5,𝔽2)11yescharacteristic
375C22×C83C2×2−1+411yescharacteristic
376C4×C83—24no—
377C4×C83—24no—
378C4×C83—42no—
379C4×C83—42no—
380C4×C83—42no—
381Dic83—24no—
382Dic83—24no—
383Dic83—24no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389C2×#2609—831nomaximal, Sylow
390C2×C83—44no—
391C2×C83—44no—
392C2×C83#260918yescomplemented
393C2×C83C2×#52511yescharacteristic
394C2×C83C2×#52511yescharacteristic
395C2×C83C2×#53711yescharacteristic
396C2×C83C2×#55111yescharacteristic
397C2×C83C2×#55211yescharacteristic
398C2×C83C2×#55211yescharacteristic
399C2×C83C2×#55511yescharacteristic
400C22×#117—831no—
401C22×#117—831no—
402#2609—8316no—
403C2×#398—831no—
404C2×#396—831no—
405C2×#396—831no—
406C2×#394—831no—
407C2×#388—831no—
408C2×#388—831no—
409C2×#387—831no—
410C2×#387—831no—
411C2×#386—831no—
412C2×#386D8311yescharacteristic
413C2×#385—831no—
414C2×#385—831no—
415C2×#382—831no—
416C83C2×#260911yescharacteristic, complemented, Sylow
417C23×D4C2×D8311yescharacteristic
418C24×C4—831no—
419C24×C4C2×D8311yescharacteristic
420C2×#117—838no—
421C2×#117—838no—
422C2×#117—1668no—
423C2×#117—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⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
441C22×C22⋊C4C2×D8311yescharacteristic
442C22×C22⋊C4C2×D8311yescharacteristic
443C22×C42—831no—
444C22×C42—831no—
445C22×C42—831no—
446#398—838no—
447#396—838no—
448#396—838no—
449#394—838no—
450#388—838no—
451#388—838no—
452#387—838no—
453#387—838no—
454#386—838no—
455#386C2×D8318yes—
456#385—838no—
457#385—838no—
458#382—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
469C25C22×D8311yescharacteristic
470C25C22×D8311yescharacteristic
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—42no—
474C22×D4C22×D8314yes—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—831no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—834no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—1664no—
488C23×C4—1664no—
489C23×C4—1664no—
490C23×C4C22×D8314yes—
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C23×C4C22×D8311yescharacteristic
496#117—16632no—
497#117—16632no—
498C2×C4⋊C4—3322no—
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—834no—
510C2×C4⋊C4—1664no—
511C2×C4⋊C4—1664no—
512C2×C4⋊C4—1664no—
513C2×C4⋊C4—1664no—
514C2×C4⋊C4—1664no—
515C2×C4⋊C4—1664no—
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—1664no—
528C2×C22⋊C4—1664no—
529C2×C22⋊C4—1664no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4C22×D8314yes—
534C2×C22⋊C4C22×D8314yes—
535C2×C22⋊C4C22×D8314yes—
536C2×C42—838no—
537C2×C42—834no—
538C2×C42—834no—
539C2×C42—834no—
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#95C22×D8314yes—
551#95C22×D8314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24#1305058914yes—
565C24#1305059014yes—
566C24C23×D8312yes—
567C24C23×D8312yes—
568C24C23×D8311yescharacteristic
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—44no—
572C2×D4—416no—
573C22×C4—232no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—28no—
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—834no—
591C22×C4—834no—
592C22×C4—834no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—832no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—832no—
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×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1668no—
617C22×C4—1668no—
618C22×C4—16632no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1668no—
622C22×C4—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1662no—
626C22×C4D4×D8314yes—
627C22×C4#1305058914yes—
628C22×C4C23×D8312yes—
629C22×C4C23×D8312yes—
630C22×C4C23×D8312yes—
631C22×C4C23×D8312yes—
632C22×C4C23×D8312yes—
633C4⋊C4—3324no—
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—
652C42—8316no—
653C42—1668no—
654C42—1668no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23C2×D4×D8312yes—
682C23#41×D8312yes—
683C23C2×#1305058914yes—
684C23C2×#1305058912yes—
685C23C2×#1305058912yes—
686C23C2×#1305059014yes—
687C23C2×#1305059012yes—
688C23#1458183712yes—
689C23#1458183912yes—
690C23C24×D8311yescharacteristic
691D4—416no—
692C2×C4—232no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
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—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—3324no—
712C2×C4—3324no—
713C2×C4—3324no—
714C2×C4—3324no—
715C2×C4—3324no—
716C2×C4—834no—
717C2×C4—834no—
718C2×C4—834no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
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—16632no—
735C2×C4—1668no—
736C2×C4—1668no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1662no—
743C2×C4—1668no—
744C2×C4C2×D4×D8314yes—
745C2×C4C2×#1305058914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—416no—
761C22—416no—
762C22#1912820714yes—
763C22#1912821014yes—
764C22#1912828014yes—
765C22#1912837714yes—
766C22#1912838814yes—
767C22#1912839114yes—
768C22#1912841514yes—
769C22C22×D4×D8311yescharacteristic
770C22C2×#41×D8311yescharacteristic
771C22C22×#1305058911yescharacteristic
772C22C22×#1305058911yescharacteristic
773C22C22×#1305059011yescharacteristic
774C22C2×#1458183711yescharacteristic
775C22C2×#1458183911yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—3322no—
782C4—3322no—
783C4—3322no—
784C4—3322no—
785C4—3322no—
786C4—1664no—
787C4—1664no—
788C4—1664no—
789C2—44no—
790C2—44no—
791C2#2491313718yesdirect product factor
792C2C2×#1912820711yescharacteristic
793C2C2×#1912821011yescharacteristic
794C2C2×#1912828011yescharacteristic
795C2C2×#1912837711yescharacteristic
796C2C2×#1912838811yescharacteristic
797C2C2×#1912839111yescharacteristic
798C2C2×#1912841511yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#386×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC2×#386D83
hypocenterC83C2×#2609
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#14581751C2semidirect
2. C22×#14581748C2semidirect
3. #24913137C2direct (N × H)
4. C2×#19127635C2semidirect
5. C2×#19127624C2semidirect
6. C2×#19127624C2semidirect
8. C2×#19127595C2semidirect
9. C2×#19127589C2semidirect
10. C2×#19127588C2semidirect
11. C2×#19127586C2semidirect
13. C2×#19127576C2semidirect
14. C2×#19127574C2semidirect
15. C2×#19127565C2semidirect
19. C2×#14581751C22semidirect
21. C2×#14581748C22semidirect
41. #19127635C22semidirect
42. #19127624C22semidirect
43. #19127624C22semidirect
45. #19127595C22semidirect
46. #19127589C22semidirect
47. #19127588C22semidirect
48. #19127586C22semidirect
50. #19127576C22semidirect
51. #19127574C22semidirect
52. #19127565C22semidirect
117. C2×C4×Dic83D4semidirect
206. C4×Dic83C2×D4semidirect
392. C2×C83#2609semidirect
416. C83C2×#2609semidirect
791. C2#24913137direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817512
C22×#145817482
#249131372
C2×#191276352
C2×#191276242
C2×#191276152
C2×#191275952
C2×#191275892
C2×#191275882
C2×#191275862
C2×#191275812
C2×#191275762
C2×#191275742
C2×#191275652
C2×#386×C832
C2×#260983