Finite Group Databasebeta

← C2×#24912808 #35574607

Subgroups — C2×#24912808 #35574607

Order 21248.

3374 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×C4×C22⋊D83C211yesmaximal, characteristic
2C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
3#24912808C2116yesmaximal, direct product factor
4C2×#19127635C211yesmaximal, characteristic, complemented
5C2×#19127632C211yesmaximal, characteristic, complemented
6C2×#19127624C211yesmaximal, characteristic, complemented
7C2×#19127624C211yesmaximal, characteristic, complemented
8C2×#19127586C211yesmaximal, characteristic, complemented
9C2×#19127582C211yesmaximal, characteristic, complemented
10C2×#19127577C211yesmaximal, characteristic
11C2×#19127577C211yesmaximal, characteristic
12C2×#19127575C211yesmaximal, characteristic, complemented
13C2×#19127574C211yesmaximal, characteristic, complemented
14C2×#19127572C211yesmaximal, characteristic, complemented
15C2×#19127560C211yesmaximal, characteristic, complemented
16C2×#385×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C2×C4×C22⋊D83—28no—
22C2×C4×C22⋊D83C2218yes—
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×Dic83⋊C4C2211yescharacteristic
32C2×C4⋊C4×D83—28no—
33C2×C4⋊C4×D83C2218yescomplemented
34C22×C22⋊Dic83C2211yescharacteristic
35C22×C22⋊Dic83C2211yescharacteristic
36C22×C22⋊Dic83C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127635C2218yescomplemented
42#19127632C2218yescomplemented
43#19127624C2218yescomplemented
44#19127624C2218yescomplemented
45#19127586C2218yescomplemented
46#19127582C2218yescomplemented
47#19127577C2218yes—
48#19127577C2218yes—
49#19127575C2218yescomplemented
50#19127574C2218yescomplemented
51#19127572C2218yescomplemented
52#19127560C2218yescomplemented
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C24×C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66#385×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×C22⋊D83—24no—
71C22×C22⋊D83—24no—
72C22×C22⋊D83Q818yes—
73C22×C22⋊D83C2314yes—
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C22×C4×D83—24no—
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83—24no—
85C22×C4×D83—42no—
86C22×C4×D83—42no—
87C22×C4×D83—42no—
88C22×C4×D83—42no—
89C22×C4×D83D418yes—
90C22×C4×D83C2314yes—
91C22×C4×D83C2314yes—
92C22×C4×D83C2314yes—
93C4×C22⋊D83—232no—
94C2×C4⋊Dic83—24no—
95C2×C4⋊Dic83—24no—
96C2×C4⋊Dic83C2314yes—
97C2×C4⋊Dic83C2314yes—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—42no—
103C2×Dic83⋊C4—42no—
104C2×Dic83⋊C4—42no—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C4⋊C4×D83—232no—
113C2×C22⋊Dic83—24no—
114C2×C22⋊Dic83—24no—
115C2×C22⋊Dic83—42no—
116C2×C22⋊Dic83C2314yes—
117C2×C22⋊Dic83C2314yes—
118C2×C22⋊Dic83C2314yes—
119C2×(C2×D83)⋊C4—24no—
120C2×(C2×D83)⋊C4—24no—
121C2×(C2×D83)⋊C4—24no—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×C4×Dic83—24no—
126C2×C4×Dic83C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C25×C83C2311yescharacteristic
136C23×C4×C83—24no—
137C23×C4×C83—42no—
138C23×C4×C83—42no—
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2314yes—
146C2×C4⋊C4×C83—24no—
147C2×C4⋊C4×C83—42no—
148C2×C4⋊C4×C83C2314yes—
149C2×C4⋊C4×C83C2314yes—
150C2×C22⋊C4×C83—24no—
151C2×C22⋊C4×C83—42no—
152C2×C22⋊C4×C83C2314yes—
153C2×C22⋊C4×C83C2314yes—
154#95×C83C2314yes—
155#95×C83C2314yes—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83C2×D414yes—
161C23×D83C2×Q814yes—
162C23×D83#4114yes—
163C23×D83C2412yes—
164C2×C22⋊D83—232no—
165C2×C22⋊D83—28no—
166C2×C22⋊D83—28no—
167C2×C22⋊D83C2×Q8116yes—
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×Dic83C2×D414yes—
187C22×Dic83C2×Q814yes—
188C22×Dic83#4114yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C2×C4×D83—232no—
197C2×C4×D83—28no—
198C2×C4×D83—28no—
199C2×C4×D83—28no—
200C2×C4×D83—28no—
201C2×C4×D83—416no—
202C2×C4×D83—44no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205C2×C4×D83—44no—
206C2×C4×D83—416no—
207C2×C4×D83C2×D4116yes—
208C4⋊Dic83—28no—
209C4⋊Dic83—28no—
210Dic83⋊C4—28no—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—44no—
215Dic83⋊C4—44no—
216Dic83⋊C4—44no—
217C22⋊Dic83—28no—
218C22⋊Dic83—28no—
219C22⋊Dic83—44no—
220(C2×D83)⋊C4—28no—
221(C2×D83)⋊C4—28no—
222(C2×D83)⋊C4—28no—
223C4×Dic83—28no—
224C24×C83—22no—
225C24×C83—22no—
226C24×C83—22no—
227C24×C83—22no—
228C24×C83—22no—
229C24×C83—22no—
230C24×C83C2×Q814yes—
231C24×C83C2412yes—
232C24×C83C2411yescharacteristic
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×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—28no—
250C22×C4×C83—44no—
251C22×C4×C83—44no—
252C22×C4×C83—416no—
253C22×C4×C83C2×D414yes—
254C22×C4×C83#4114yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C4⋊C4×C83—28no—
262C4⋊C4×C83—44no—
263C22⋊C4×C83—28no—
264C22⋊C4×C83—44no—
265C23×C83—28no—
266C23×C83—28no—
267C23×C83—28no—
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×C83C22×D412yes—
279C23×C83C22×Q814yes—
280C23×C83C22×Q812yes—
281C23×C83C2×#4112yes—
282C23×C83C2×#4112yes—
283C23×C83C2×#4112yes—
284C23×C83H(5,𝔽2)12yes—
285C23×C83H(5,𝔽2)12yes—
286C23×C83C2511yescharacteristic
287C22×D83—28no—
288C22×D83—28no—
289C22×D83—28no—
290C22×D83—28no—
291C22×D83—28no—
292C22×D83—28no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83C22⋊Q8116yes—
298C22×D83C22×D414yes—
299C22×D83C22×Q814yes—
300C22×D83C2×#4114yes—
301C2×C4×C83—28no—
302C2×C4×C83—28no—
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—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—416no—
320C2×C4×C83—44no—
321C2×C4×C83—44no—
322C2×C4×C83—44no—
323C2×C4×C83—44no—
324C2×C4×C83C22×D414yes—
325C2×C4×C83C2×#4114yes—
326C22⋊D83—232no—
327C2×Dic83—28no—
328C2×Dic83—28no—
329C2×Dic83—28no—
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—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—44no—
349C2×Dic83—44no—
350C2×Dic83—44no—
351C2×Dic83—44no—
352C2×Dic83C22×D414yes—
353C2×Dic83C22×Q814yes—
354C2×Dic83C2×#4114yes—
355C4×D83—232no—
356C4×D83—416no—
357C4×D83—416no—
358C22×C83—24no—
359C22×C83—24no—
360C22×C83—24no—
361C22×C83—416no—
362C22×C83—42no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83C2×C22⋊Q814yes—
367C22×C83#52514yes—
368C22×C83#53414yes—
369C22×C83#55314yes—
370C22×C83#55314yes—
371C22×C83#55414yes—
372C22×C83#55414yes—
373C22×C83C23×D411yescharacteristic
374C22×C83C23×Q811yescharacteristic
375C22×C83C22×#4111yescharacteristic
376C22×C83C22×#4111yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C2×H(5,𝔽2)11yescharacteristic
379C22×C83C2×H(5,𝔽2)11yescharacteristic
380C2×D83—232no—
381C2×D83—24no—
382C2×D83—24no—
383C2×D83—24no—
384C2×D83—24no—
385C2×D83—24no—
386C2×D83—24no—
387C2×D83C2×C22⋊Q818yes—
388C4×C83—24no—
389C4×C83—24no—
390C4×C83—42no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394Dic83—24no—
395Dic83—24no—
396Dic83—24no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83—42no—
401C2×#2579—831nomaximal, Sylow
402C2×C83—44no—
403C2×C83#257918yescomplemented
404C2×C83C22×C22⋊Q811yescharacteristic
405C2×C83C2×#52511yescharacteristic
406C2×C83C2×#53411yescharacteristic
407C2×C83C2×#55311yescharacteristic
408C2×C83C2×#55311yescharacteristic
409C2×C83C2×#55411yescharacteristic
410C2×C83C2×#55411yescharacteristic
411D83—28no—
412C22×C4×D4—831no—
413C23×C4⋊C4—831no—
414#2579—8316no—
415C2×#398—831no—
416C2×#398—831no—
417C2×#396—831no—
418C2×#396—831no—
419C2×#387—831no—
420C2×#387—831no—
421C2×#386—831no—
422C2×#386—831no—
423C2×#385—831no—
424C2×#385—831no—
425C2×#385—831no—
426C2×#385D8311yescharacteristic, complemented
427C2×#380—831no—
428C83C2×#257911yescharacteristic, complemented, Sylow
429C23×D4—831no—
430C24×C4—831no—
431C24×C4—831no—
432C24×C4—831no—
433C24×C4C2×D8311yescharacteristic
434C2×C4×D4—838no—
435C2×C4×D4—1668no—
436C22×C4⋊C4—831no—
437C22×C4⋊C4—831no—
438C22×C4⋊C4—831no—
439C22×C4⋊C4—831no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4—831no—
442C22×C4⋊C4—831no—
443C22×C4⋊C4—831no—
444C22×C4⋊C4—831no—
445C22×C4⋊C4—838no—
446C22×C4⋊C4—1668no—
447C22×C4⋊C4C2×D8311yescharacteristic
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⋊C4C2×D8311yescharacteristic
456C22×C22⋊C4C2×D8311yescharacteristic
457C22×C42—831no—
458#398—838no—
459#398—838no—
460#396—838no—
461#396—838no—
462#387—838no—
463#387—838no—
464#386—838no—
465#386—838no—
466#385—838no—
467#385—838no—
468#385—838no—
469#385C2×D8318yescomplemented
470#380—838no—
471C2×#95—831no—
472C2×#95—831no—
473C2×#95—831no—
474C2×#95—831no—
475C2×#95—831no—
476C2×#95—831no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95C2×D8311yescharacteristic
480C2×#95C2×D8311yescharacteristic
481C25—831no—
482C25C22×D8311yescharacteristic
483C22×D4—838no—
484C22×D4—834no—
485C22×D4—1664no—
486C22×D4—1664no—
487C23×C4—24no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4—3322no—
491C23×C4—3322no—
492C23×C4—3322no—
493C23×C4—3322no—
494C23×C4—838no—
495C23×C4—834no—
496C23×C4—834no—
497C23×C4—831no—
498C23×C4—831no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4—834no—
505C23×C4—1664no—
506C23×C4—1664no—
507C23×C4—1664no—
508C23×C4—1664no—
509C23×C4C22×D8311yescharacteristic
510C23×C4C22×D8311yescharacteristic
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8311yescharacteristic
513C23×C4C22×D8311yescharacteristic
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8314yes—
516C4×D4—16632no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—3322no—
520C2×C4⋊C4—3322no—
521C2×C4⋊C4—3322no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—834no—
531C2×C4⋊C4—16632no—
532C2×C4⋊C4—1664no—
533C2×C4⋊C4—1664no—
534C2×C4⋊C4—1664no—
535C2×C4⋊C4—1664no—
536C2×C4⋊C4—1664no—
537C2×C4⋊C4—1664no—
538C2×C4⋊C4C22×D8314yes—
539C2×C4⋊C4C22×D8314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—3322no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—1664no—
550C2×C22⋊C4—1664no—
551C2×C22⋊C4—1664no—
552C2×C22⋊C4—1664no—
553C2×C22⋊C4—1664no—
554C2×C22⋊C4C22×D8314yes—
555C2×C22⋊C4C22×D8314yes—
556C2×C42—834no—
557C2×C42—1664no—
558#95—834no—
559#95—834no—
560#95—834no—
561#95—834no—
562#95—834no—
563#95—834no—
564#95—834no—
565#95—834no—
566#95C22×D8314yes—
567#95C22×D8314yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—834no—
575C24—834no—
576C24—834no—
577C24—832no—
578C24—1662no—
579C24—1662no—
580C24—1662no—
581C24—1662no—
582C24Q8×D8314yes—
583C24C23×D8312yes—
584C24C23×D8311yescharacteristic
585C2×D4—8316no—
586C2×D4—1668no—
587C2×D4—16632no—
588C2×D4—1668no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—416no—
609C22×C4—33216no—
610C22×C4—3324no—
611C22×C4—3324no—
612C22×C4—3324no—
613C22×C4—3324no—
614C22×C4—33216no—
615C22×C4—8316no—
616C22×C4—834no—
617C22×C4—834no—
618C22×C4—834no—
619C22×C4—832no—
620C22×C4—832no—
621C22×C4—832no—
622C22×C4—832no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—1668no—
627C22×C4—1668no—
628C22×C4—1668no—
629C22×C4—16632no—
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×C4—1662no—
645C22×C4—1662no—
646C22×C4—1662no—
647C22×C4—1662no—
648C22×C4—1668no—
649C22×C4D4×D8314yes—
650C22×C4#1305059014yes—
651C22×C4C23×D8312yes—
652C22×C4C23×D8312yes—
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8312yes—
656C22×C4C23×D8312yes—
657C4⋊C4—28no—
658C4⋊C4—44no—
659C4⋊C4—3324no—
660C4⋊C4—3324no—
661C4⋊C4—3324no—
662C4⋊C4—1668no—
663C4⋊C4—1668no—
664C4⋊C4—1668no—
665C4⋊C4—1668no—
666C4⋊C4—1668no—
667C4⋊C4—1668no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—3324no—
671C22⋊C4—1668no—
672C22⋊C4—1668no—
673C22⋊C4—1668no—
674C22⋊C4—1668no—
675C22⋊C4—1668no—
676C42—1668no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—8316no—
691C23—834no—
692C23—834no—
693C23—834no—
694C23—1668no—
695C23—1668no—
696C23—1668no—
697C23—1668no—
698C23—1668no—
699C23—1668no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23C2×D4×D8312yes—
705C23C2×Q8×D8314yes—
706C23C2×Q8×D8312yes—
707C23#41×D8312yes—
708C23#41×D8312yes—
709C23C2×#1305059012yes—
710C23#1458183712yes—
711C23#1458183712yes—
712C23C24×D8311yescharacteristic
713D4—16632no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
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—416no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—33216no—
738C2×C4—33216no—
739C2×C4—3324no—
740C2×C4—3324no—
741C2×C4—3324no—
742C2×C4—3324no—
743C2×C4—834no—
744C2×C4—834no—
745C2×C4—834no—
746C2×C4—16632no—
747C2×C4—1662no—
748C2×C4—1662no—
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—1662no—
759C2×C4—1668no—
760C2×C4—1668no—
761C2×C4—1668no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4C2×D4×D8314yes—
769C2×C4C2×#1305059014yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—838no—
779C22—1664no—
780C22—1664no—
781C22—1664no—
782C22—1664no—
783C22—1664no—
784C22—16632no—
785C22—1664no—
786C22C22⋊Q8×D8314yes—
787C22#1912821014yes—
788C22#1912826114yes—
789C22#1912839614yes—
790C22#1912840114yes—
791C22#1912840514yes—
792C22#1912840614yes—
793C22C22×D4×D8311yescharacteristic
794C22C22×Q8×D8311yescharacteristic
795C22C2×#41×D8311yescharacteristic
796C22C2×#41×D8311yescharacteristic
797C22C22×#1305059011yescharacteristic
798C22C2×#1458183711yescharacteristic
799C22C2×#1458183711yescharacteristic
800C4—24no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—3322no—
810C4—1664no—
811C4—1664no—
812C4—1664no—
813C2—44no—
814C2—1668no—
815C2#2491280818yesdirect product factor
816C2C2×C22⋊Q8×D8311yescharacteristic
817C2C2×#1912821011yescharacteristic
818C2C2×#1912826111yescharacteristic
819C2C2×#1912839611yescharacteristic
820C2C2×#1912840111yescharacteristic
821C2C2×#1912840511yescharacteristic
822C2C2×#1912840611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#385D83
hypocenterC83C2×#2579
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D83C2semidirect
3. #24912808C2direct (N × H)
4. C2×#19127635C2semidirect
5. C2×#19127632C2semidirect
6. C2×#19127624C2semidirect
7. C2×#19127624C2semidirect
8. C2×#19127586C2semidirect
9. C2×#19127582C2semidirect
12. C2×#19127575C2semidirect
13. C2×#19127574C2semidirect
14. C2×#19127572C2semidirect
15. C2×#19127560C2semidirect
16. C2×#385×C83C2semidirect
33. C2×C4⋊C4×D83C22semidirect
41. #19127635C22semidirect
42. #19127632C22semidirect
43. #19127624C22semidirect
44. #19127624C22semidirect
45. #19127586C22semidirect
46. #19127582C22semidirect
49. #19127575C22semidirect
50. #19127574C22semidirect
51. #19127572C22semidirect
52. #19127560C22semidirect
66. #385×C83C22semidirect
403. C2×C83#2579semidirect
426. C2×#385D83semidirect
428. C83C2×#2579semidirect
469. #385C2×D83semidirect
815. C2#24912808direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C22×C4⋊C4×D832
#249128082
C2×#191276352
C2×#191276322
C2×#191276242
C2×#191275862
C2×#191275822
C2×#191275772
C2×#191275752
C2×#191275742
C2×#191275722
C2×#191275602
C2×#385×C832
C2×#257983