Finite Group Databasebeta

← C2×#24912441 #35575740

Subgroups — C2×#24912441 #35575740

Order 21248.

3310 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic, complemented
2C22×#14581778C211yesmaximal, characteristic
3C22×#14581778C211yesmaximal, characteristic
4C22×C4×Dic166C211yesmaximal, characteristic, complemented
5#24912441C2116yesmaximal, direct product factor
6C2×#19127625C211yesmaximal, characteristic, complemented
7C2×#19127624C211yesmaximal, characteristic, complemented
8C2×#19127624C211yesmaximal, characteristic, complemented
9C2×#19127623C211yesmaximal, characteristic, complemented
10C2×#19127605C211yesmaximal, characteristic, complemented
11C2×#19127601C211yesmaximal, characteristic
12C2×#19127593C211yesmaximal, characteristic, complemented
13C2×#19127592C211yesmaximal, characteristic, complemented
14C2×#19127589C211yesmaximal, characteristic, complemented
15C2×#19127552C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C23×C22⋊D83C2211yescharacteristic
20C2×#14581791—28no—
21C2×#14581791C2218yescomplemented
22C2×#14581778—28no—
23C2×#14581778—28no—
24C2×#14581778C2218yes—
25C2×#14581778C2218yes—
26C2×C4×Dic166—28no—
27C2×C4×Dic166C2218yescomplemented
28C22×C4⋊Dic83C2211yescharacteristic
29C22×C4⋊Dic83C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×C22⋊Dic83C2211yescharacteristic
37C22×C22⋊Dic83C2211yescharacteristic
38C22×C22⋊Dic83C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×(C2×D83)⋊C4C2211yescharacteristic
45C22×C4×Dic83C2211yescharacteristic
46C22×C4×Dic83C2211yescharacteristic
47C22×C4×Dic83C2211yescharacteristic
48C22×C4×Dic83C2211yescharacteristic
49#19127625C2218yescomplemented
50#19127624C2218yescomplemented
51#19127624C2218yescomplemented
52#19127623C2218yescomplemented
53#19127605C2218yescomplemented
54#19127601C2218yes—
55#19127593C2218yescomplemented
56#19127592C2218yescomplemented
57#19127589C2218yescomplemented
58#19127552C2218yescomplemented
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C2×C83⋊#95C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C22⋊C4×C83C2211yescharacteristic
67C22×C42×C83C2211yescharacteristic
68#388×C83C2218yescomplemented
69C2×#95×C83C2211yescharacteristic
70C2×#95×C83C2211yescharacteristic
71C24×D83C2311yescharacteristic
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166—24no—
75C22×Dic166—24no—
76C22×Dic166—24no—
77C22×Dic166D418yes—
78C22×Dic166C2314yes—
79C22×Dic166C2314yes—
80C22×C22⋊D83—24no—
81C22×C22⋊D83—24no—
82C22×C22⋊D83—24no—
83C22×C22⋊D83C2314yes—
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91#14581791—232no—
92#14581778—232no—
93#14581778—232no—
94C4×Dic166—232no—
95C2×C4⋊Dic83—24no—
96C2×C4⋊Dic83—24no—
97C2×C4⋊Dic83C2314yes—
98C2×C4⋊Dic83C2314yes—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—24no—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4—24no—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×C22⋊Dic83—24no—
112C2×C22⋊Dic83—24no—
113C2×C22⋊Dic83—24no—
114C2×C22⋊Dic83C2314yes—
115C2×C22⋊Dic83C2314yes—
116C2×C22⋊Dic83C2314yes—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4—24no—
119C2×(C2×D83)⋊C4—24no—
120C2×(C2×D83)⋊C4—24no—
121C2×(C2×D83)⋊C4—24no—
122C2×(C2×D83)⋊C4—24no—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2314yes—
129C2×C4×Dic83—24no—
130C2×C4×Dic83—24no—
131C2×C4×Dic83—24no—
132C2×C4×Dic83D418yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2314yes—
136C2×C4×Dic83C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C25×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148C2×C4⋊C4×C83—24no—
149C2×C4⋊C4×C83C2314yes—
150C2×C22⋊C4×C83—24no—
151C2×C22⋊C4×C83—24no—
152C2×C22⋊C4×C83—24no—
153C2×C22⋊C4×C83C2314yes—
154C2×C22⋊C4×C83C2314yes—
155C2×C22⋊C4×C83C2314yes—
156C2×C42×C83—24no—
157C2×C42×C83C2314yes—
158#95×C83C2314yes—
159#95×C83C2314yes—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83—22no—
167C23×D83C2412yes—
168C2×Dic166—232no—
169C2×Dic166—28no—
170C2×Dic166—28no—
171C2×Dic166—28no—
172C2×Dic166—28no—
173C2×Dic166—28no—
174C2×Dic166—416no—
175C2×Dic166C2×D4116yes—
176C2×C22⋊D83—28no—
177C2×C22⋊D83—28no—
178C2×C22⋊D83—28no—
179C2×C22⋊D83—416no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83—22no—
188C22×Dic83—22no—
189C22×Dic83—22no—
190C22×Dic83—22no—
191C22×Dic83—22no—
192C22×Dic83—22no—
193C22×Dic83—22no—
194C22×Dic83—22no—
195C22×Dic83C2×D414yes—
196C22×Dic83C2×D414yes—
197C22×Dic83C2×D414yes—
198C22×Dic83C2×D414yes—
199C22×Dic83#4114yes—
200C22×Dic83#4114yes—
201C22×Dic83C2412yes—
202C22×Dic83C2412yes—
203C22×Dic83C2412yes—
204C22×Dic83C2412yes—
205C22×Dic83C2412yes—
206C22×Dic83C2412yes—
207C22×Dic83C2412yes—
208C4⋊Dic83—28no—
209C4⋊Dic83—28no—
210Dic83⋊C4—28no—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—28no—
216C22⋊Dic83—28no—
217C22⋊Dic83—28no—
218C22⋊Dic83—28no—
219(C2×D83)⋊C4—28no—
220(C2×D83)⋊C4—28no—
221(C2×D83)⋊C4—28no—
222(C2×D83)⋊C4—28no—
223(C2×D83)⋊C4—28no—
224(C2×D83)⋊C4—28no—
225C4×Dic83—28no—
226C4×Dic83—28no—
227C4×Dic83—28no—
228C4×Dic83C2×D4116yes—
229C24×C83—22no—
230C24×C83—22no—
231C24×C83—22no—
232C24×C83—22no—
233C24×C83—22no—
234C24×C83—22no—
235C24×C83—22no—
236C24×C83C2412yes—
237C24×C83C2411yescharacteristic
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×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83C2×D414yes—
254C22×C4×C83C2×D414yes—
255C22×C4×C83#4114yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C22×C4×C83C2412yes—
262C4⋊C4×C83—28no—
263C22⋊C4×C83—28no—
264C22⋊C4×C83—28no—
265C22⋊C4×C83—28no—
266C42×C83—28no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
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×C83C22×D412yes—
283C23×C83C2×#4112yes—
284C23×C83C2×#4112yes—
285C23×C83C2×#4112yes—
286C23×C832−1+412yes—
287C23×C832−1+412yes—
288C23×C83C2511yescharacteristic
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—44no—
297C22×D83—44no—
298C22×D83—44no—
299C22×D83—44no—
300C22×D83—44no—
301C22×D83—44no—
302C22×D83—44no—
303C2×C4×C83—28no—
304C2×C4×C83—28no—
305C2×C4×C83—28no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—44no—
322C2×C4×C83—44no—
323C2×C4×C83—44no—
324C2×C4×C83C22×D414yes—
325C2×C4×C83C22×D414yes—
326C2×C4×C83C2×#4114yes—
327C22⋊D83—416no—
328C2×Dic83—28no—
329C2×Dic83—28no—
330C2×Dic83—28no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—44no—
347C2×Dic83—44no—
348C2×Dic83—44no—
349C2×Dic83#121116yes—
350C2×Dic83C22×D414yes—
351C2×Dic83C22×D414yes—
352C2×Dic83C22×D414yes—
353C2×Dic83C22×D414yes—
354C2×Dic83C2×#4114yes—
355C2×Dic83C2×#4114yes—
356Dic166—232no—
357Dic166—416no—
358C22×C83—42no—
359C22×C83—42no—
360C22×C83—42no—
361C22×C83—42no—
362C22×C83—42no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—88no—
366C22×C83C2×#12114yes—
367C22×C83#53214yes—
368C22×C83#53614yes—
369C22×C83#54814yes—
370C22×C83#54814yes—
371C22×C83#55614yes—
372C22×C83#55614yes—
373C22×C83C23×D411yescharacteristic
374C22×C83C23×D411yescharacteristic
375C22×C83C22×#4111yescharacteristic
376C22×C83C22×#4111yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C2×2−1+411yescharacteristic
379C22×C83C2×2−1+411yescharacteristic
380C2×D83—42no—
381C2×D83—42no—
382C2×D83—42no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—88no—
388C4×C83—24no—
389C4×C83—24no—
390C4×C83—24no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394Dic83—24no—
395Dic83—24no—
396Dic83—24no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83C2×#12118yes—
401C2×#2545—831nomaximal, Sylow
402C2×C83—82no—
403C2×C83#254518yescomplemented
404C2×C83C22×#12111yescharacteristic
405C2×C83C2×#53211yescharacteristic
406C2×C83C2×#53611yescharacteristic
407C2×C83C2×#54811yescharacteristic
408C2×C83C2×#54811yescharacteristic
409C2×C83C2×#55611yescharacteristic
410C2×C83C2×#55611yescharacteristic
411D83—82no—
412C22×C4⋊Q8—831no—
413C22×#124—831no—
414C22×#124—831no—
415C22×C4×Q8—831no—
416#2545—8316no—
417C2×#396—831no—
418C2×#396—831no—
419C2×#396—831no—
420C2×#396—831no—
421C2×#391—831no—
422C2×#390—831no—
423C2×#388—831no—
424C2×#388—831no—
425C2×#388—831no—
426C2×#388D8311yescharacteristic, complemented
427C2×C4×C4⋊C4—831no—
428C83C2×#254511yescharacteristic, complemented, Sylow
429C23×Q8—831no—
430C23×Q8—831no—
431C23×D4—831no—
432C2×C4⋊Q8—838no—
433C2×C4⋊Q8—1668no—
434C2×#124—838no—
435C2×#124—838no—
436C2×#124—1668no—
437C2×#124—1668no—
438C2×C4×Q8—838no—
439C2×C4×Q8—1668no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4—831no—
442C22×C4⋊C4—831no—
443C22×C4⋊C4—831no—
444C22×C4⋊C4—831no—
445C22×C4⋊C4—831no—
446C22×C4⋊C4—831no—
447C22×C4⋊C4—831no—
448C22×C4⋊C4C2×D8311yescharacteristic
449C22×C22⋊C4—831no—
450C22×C22⋊C4—831no—
451C22×C22⋊C4—831no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4—831no—
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—831no—
457C22×C22⋊C4—831no—
458C22×C22⋊C4C2×D8311yescharacteristic
459C22×C22⋊C4C2×D8311yescharacteristic
460C22×C22⋊C4C2×D8311yescharacteristic
461C22×C42—831no—
462C22×C42—831no—
463C22×C42—831no—
464C22×C42—831no—
465C22×C42C2×D8311yescharacteristic
466#396—838no—
467#396—838no—
468#396—838no—
469#396—838no—
470#391—838no—
471#390—838no—
472#388—838no—
473#388—838no—
474#388—838no—
475#388C2×D8318yescomplemented
476C4×C4⋊C4—838no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95—831no—
480C2×#95—831no—
481C2×#95C2×D8311yescharacteristic
482C2×#95C2×D8311yescharacteristic
483C25—831no—
484C25C22×D8311yescharacteristic
485C22×Q8—838no—
486C22×Q8—834no—
487C22×Q8—834no—
488C22×Q8—1664no—
489C22×Q8—1664no—
490C22×Q8—1664no—
491C22×Q8—1664no—
492C22×Q8—1664no—
493C22×D4—834no—
494C22×D4—1664no—
495C22×D4—1664no—
496C22×D4—1664no—
497C23×C4—831no—
498C23×C4—831no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4C22×D8311yescharacteristic
505C23×C4C22×D8311yescharacteristic
506C23×C4C22×D8311yescharacteristic
507C23×C4C22×D8311yescharacteristic
508C23×C4C22×D8311yescharacteristic
509C23×C4C22×D8311yescharacteristic
510C4⋊Q8—16632no—
511#124—16632no—
512#124—16632no—
513C4×Q8—16632no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—834no—
516C2×C4⋊C4—834no—
517C2×C4⋊C4—834no—
518C2×C4⋊C4—834no—
519C2×C4⋊C4—834no—
520C2×C4⋊C4—834no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—1664no—
524C2×C4⋊C4—1664no—
525C2×C4⋊C4—1664no—
526C2×C4⋊C4—1664no—
527C2×C4⋊C4—1664no—
528C2×C4⋊C4—1664no—
529C2×C4⋊C4—1664no—
530C2×C4⋊C4—1664no—
531C2×C4⋊C4C22×D8314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—834no—
536C2×C22⋊C4—834no—
537C2×C22⋊C4—834no—
538C2×C22⋊C4—834no—
539C2×C22⋊C4—834no—
540C2×C22⋊C4—834no—
541C2×C22⋊C4—834no—
542C2×C22⋊C4—834no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—1664no—
545C2×C22⋊C4—1664no—
546C2×C22⋊C4—1664no—
547C2×C22⋊C4—1664no—
548C2×C22⋊C4—1664no—
549C2×C22⋊C4—1664no—
550C2×C22⋊C4—1664no—
551C2×C22⋊C4—1664no—
552C2×C22⋊C4—1664no—
553C2×C22⋊C4C22×D8314yes—
554C2×C22⋊C4C22×D8314yes—
555C2×C22⋊C4C22×D8314yes—
556C2×C42—24no—
557C2×C42—838no—
558C2×C42—834no—
559C2×C42—834no—
560C2×C42—834no—
561C2×C42—834no—
562C2×C42—1664no—
563C2×C42—1664no—
564C2×C42—1664no—
565C2×C42C22×D8314yes—
566#95—834no—
567#95—834no—
568#95—834no—
569#95—834no—
570#95C22×D8314yes—
571#95C22×D8314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—832no—
580C24—1662no—
581C24—1662no—
582C24—1662no—
583C24—1662no—
584C24—1662no—
585C24—1662no—
586C24—1662no—
587C24C23×D8312yes—
588C24C23×D8311yescharacteristic
589C2×Q8—33216no—
590C2×Q8—8316no—
591C2×Q8—1668no—
592C2×Q8—1668no—
593C2×Q8—1668no—
594C2×Q8—1668no—
595C2×Q8—16632no—
596C2×Q8—1668no—
597C2×D4—33216no—
598C2×D4—1668no—
599C2×D4—1668no—
600C2×D4—1668no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—834no—
617C22×C4—834no—
618C22×C4—834no—
619C22×C4—832no—
620C22×C4—834no—
621C22×C4—834no—
622C22×C4—834no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—1662no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4—1662no—
633C22×C4—1662no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1662no—
638C22×C4—1662no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1662no—
642C22×C4—1662no—
643C22×C4—1662no—
644C22×C4D4×D8314yes—
645C22×C4D4×D8314yes—
646C22×C4#1305059014yes—
647C22×C4C23×D8312yes—
648C22×C4C23×D8312yes—
649C22×C4C23×D8312yes—
650C22×C4C23×D8312yes—
651C22×C4C23×D8312yes—
652C22×C4C23×D8312yes—
653C4⋊C4—28no—
654C4⋊C4—1668no—
655C4⋊C4—1668no—
656C4⋊C4—1668no—
657C4⋊C4—1668no—
658C4⋊C4—1668no—
659C4⋊C4—1668no—
660C4⋊C4—1668no—
661C4⋊C4—1668no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—1668no—
666C22⋊C4—1668no—
667C22⋊C4—1668no—
668C22⋊C4—1668no—
669C22⋊C4—1668no—
670C22⋊C4—1668no—
671C22⋊C4—1668no—
672C22⋊C4—1668no—
673C22⋊C4—1668no—
674C42—28no—
675C42—8316no—
676C42—1668no—
677C42—1668no—
678C42—1668no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—3324no—
694C23—3324no—
695C23—3324no—
696C23—3324no—
697C23—3324no—
698C23—3324no—
699C23—3324no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1662no—
707C23C2×D4×D8312yes—
708C23C2×D4×D8312yes—
709C23#41×D8312yes—
710C23#41×D8312yes—
711C23C2×#1305059012yes—
712C23#1458183912yes—
713C23#1458183912yes—
714C23C24×D8311yescharacteristic
715Q8—33216no—
716Q8—16632no—
717D4—33216no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—3324no—
740C2×C4—3324no—
741C2×C4—3324no—
742C2×C4—8316no—
743C2×C4—834no—
744C2×C4—834no—
745C2×C4—834no—
746C2×C4—834no—
747C2×C4—834no—
748C2×C4—834no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1668no—
759C2×C4—1668no—
760C2×C4—1668no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4C2×D4×D8314yes—
768C2×C4C2×D4×D8314yes—
769C2×C4C2×#1305059014yes—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22—3322no—
779C22—3322no—
780C22—3322no—
781C22—3322no—
782C22—3322no—
783C22—3322no—
784C22—3322no—
785C22—6648no—
786C22#121×D8314yes—
787C22#1912824814yes—
788C22#1912827314yes—
789C22#1912835914yes—
790C22#1912836014yes—
791C22#1912841814yes—
792C22#1912841914yes—
793C22C22×D4×D8311yescharacteristic
794C22C22×D4×D8311yescharacteristic
795C22C2×#41×D8311yescharacteristic
796C22C2×#41×D8311yescharacteristic
797C22C22×#1305059011yescharacteristic
798C22C2×#1458183911yescharacteristic
799C22C2×#1458183911yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—838no—
810C4—1664no—
811C4—1664no—
812C4—1664no—
813C2—82no—
814C2—6642no—
815C2#2491244118yesdirect product factor
816C2C2×#121×D8311yescharacteristic
817C2C2×#1912824811yescharacteristic
818C2C2×#1912827311yescharacteristic
819C2C2×#1912835911yescharacteristic
820C2C2×#1912836011yescharacteristic
821C2C2×#1912841811yescharacteristic
822C2C2×#1912841911yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#388D83
hypocenterC83C2×#2545
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#14581791C2semidirect
4. C22×C4×Dic166C2semidirect
5. #24912441C2direct (N × H)
6. C2×#19127625C2semidirect
7. C2×#19127624C2semidirect
8. C2×#19127624C2semidirect
9. C2×#19127623C2semidirect
10. C2×#19127605C2semidirect
12. C2×#19127593C2semidirect
13. C2×#19127592C2semidirect
14. C2×#19127589C2semidirect
15. C2×#19127552C2semidirect
16. C2×#388×C83C2semidirect
21. C2×#14581791C22semidirect
27. C2×C4×Dic166C22semidirect
49. #19127625C22semidirect
50. #19127624C22semidirect
51. #19127624C22semidirect
52. #19127623C22semidirect
53. #19127605C22semidirect
55. #19127593C22semidirect
56. #19127592C22semidirect
57. #19127589C22semidirect
58. #19127552C22semidirect
68. #388×C83C22semidirect
403. C2×C83#2545semidirect
426. C2×#388D83semidirect
428. C83C2×#2545semidirect
475. #388C2×D83semidirect
815. C2#24912441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817912
C22×#145817782
C22×C4×Dic1662
#249124412
C2×#191276252
C2×#191276242
C2×#191276232
C2×#191276052
C2×#191276012
C2×#191275932
C2×#191275922
C2×#191275892
C2×#191275522
C2×#388×C832
C2×#254583