Finite Group Databasebeta

← C2×#24910133 #35563133

Subgroups — C2×#24910133 #35563133

Order 21248.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581774C211yesmaximal, characteristic
2C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic
3C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
4#24910133C2116yesmaximal, direct product factor
5C2×#19127599C211yesmaximal, characteristic, complemented
6C2×#19127596C211yesmaximal, characteristic, complemented
7C2×#19127595C211yesmaximal, characteristic, complemented
8C2×#19127588C211yesmaximal, characteristic, complemented
9C2×#19127584C211yesmaximal, characteristic, complemented
10C2×#19127577C211yesmaximal, characteristic
11C2×#19127576C211yesmaximal, characteristic, complemented
12C2×#19127575C211yesmaximal, characteristic, complemented
13C2×#19127573C211yesmaximal, characteristic, complemented
14C2×#19127563C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C2×#14581774C4116yescomplemented
23C2×#14581774C2218yes—
24C2×(C22⋊D83)⋊C4—28no—
25C2×(C22⋊D83)⋊C4C2218yes—
26C22×C4⋊Dic83C2211yescharacteristic
27C22×C4⋊Dic83C2211yescharacteristic
28C22×C4⋊Dic83C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C2×C4⋊C4×D83—28no—
35C2×C4⋊C4×D83C2218yescomplemented
36C22×C22⋊Dic83C2211yescharacteristic
37C22×C22⋊Dic83C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×C4×Dic83C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43#19127599C2218yescomplemented
44#19127596C2218yescomplemented
45#19127595C2218yescomplemented
46#19127588C2218yescomplemented
47#19127584C2218yescomplemented
48#19127577C2218yes—
49#19127576C2218yescomplemented
50#19127575C2218yescomplemented
51#19127573C2218yescomplemented
52#19127563C2218yescomplemented
53C4×(C2×D83)⋊C4C2218yescomplemented
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C42×C83C2211yescharacteristic
67#388×C83C2218yescomplemented
68C2×#95×C83C2211yescharacteristic
69C2×#95×C83C2211yescharacteristic
70C24×D83C2311yescharacteristic
71C22×C22⋊D83—24no—
72C22×C22⋊D83—24no—
73C22×C22⋊D83C2×C418yes—
74C22×C22⋊D83C2314yes—
75C23×Dic83—24no—
76C23×Dic83—42no—
77C23×Dic83—42no—
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2314yes—
86C22×C4×D83—24no—
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83—42no—
90C22×C4×D83—42no—
91C22×C4×D83—42no—
92C22×C4×D83—42no—
93C22×C4×D83C2×C418yescomplemented
94C22×C4×D83D418yes—
95C22×C4×D83C2314yes—
96C22×C4×D83C2314yes—
97C22×C4×D83C2314yes—
98#14581774C2×C4164yescomplemented
99(C22⋊D83)⋊C4—232no—
100C2×C4⋊Dic83—24no—
101C2×C4⋊Dic83—42no—
102C2×C4⋊Dic83C2×C418yescomplemented
103C2×C4⋊Dic83C2314yes—
104C2×C4⋊Dic83C2314yes—
105C2×C4⋊Dic83C2314yes—
106C2×Dic83⋊C4—24no—
107C2×Dic83⋊C4—24no—
108C2×Dic83⋊C4—24no—
109C2×Dic83⋊C4—42no—
110C2×Dic83⋊C4C2×C418yescomplemented
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C4⋊C4×D83—232no—
117C2×C22⋊Dic83—42no—
118C2×C22⋊Dic83C2×C418yescomplemented
119C2×C22⋊Dic83C2314yes—
120C2×C22⋊Dic83C2314yes—
121C2×(C2×D83)⋊C4—24no—
122C2×(C2×D83)⋊C4—24no—
123C2×(C2×D83)⋊C4C2×C418yescomplemented
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×C4×Dic83—24no—
128C2×C4×Dic83—42no—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C25×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C2×C4⋊C4×C83—24no—
147C2×C4⋊C4×C83C2314yes—
148C2×C22⋊C4×C83—24no—
149C2×C22⋊C4×C83—42no—
150C2×C22⋊C4×C83C2×C418yescomplemented
151C2×C22⋊C4×C83C2314yes—
152C2×C22⋊C4×C83C2314yes—
153C2×C22⋊C4×C83C2314yes—
154C2×C42×C83—42no—
155C2×C42×C83C2314yes—
156#95×C83C2314yes—
157#95×C83C2314yes—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83C22×C414yes—
163C23×D83C2×D414yes—
164C23×D83#4114yes—
165C23×D83C2412yes—
166C2×C22⋊D83—232no—
167C2×C22⋊D83—28no—
168C2×C22⋊D83—28no—
169C2×C22⋊D83C22×C4116yes—
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×Dic83—28no—
188C22×Dic83—44no—
189C22×Dic83—44no—
190C22×Dic83—416no—
191C22×Dic83C22×C414yes—
192C22×Dic83C22×C414yes—
193C22×Dic83C22×C414yes—
194C22×Dic83C2×D414yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2412yes—
199C22×Dic83C2412yes—
200C22×Dic83C2412yes—
201C22×Dic83C2412yes—
202C2×C4×D83—232no—
203C2×C4×D83—28no—
204C2×C4×D83—28no—
205C2×C4×D83—28no—
206C2×C4×D83—416no—
207C2×C4×D83—44no—
208C2×C4×D83—44no—
209C2×C4×D83—44no—
210C2×C4×D83—44no—
211C2×C4×D83—416no—
212C2×C4×D83C22×C4116yescomplemented
213C2×C4×D83C2×D4116yes—
214C4⋊Dic83—28no—
215C4⋊Dic83—44no—
216C4⋊Dic83C22×C4116yescomplemented
217Dic83⋊C4—28no—
218Dic83⋊C4—28no—
219Dic83⋊C4—28no—
220Dic83⋊C4—44no—
221Dic83⋊C4C22×C4116yescomplemented
222C22⋊Dic83—44no—
223C22⋊Dic83C22×C4116yescomplemented
224(C2×D83)⋊C4—28no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4C22×C4116yescomplemented
227C4×Dic83—28no—
228C4×Dic83—44no—
229C24×C83—22no—
230C24×C83—22no—
231C24×C83—22no—
232C24×C83—22no—
233C24×C83—22no—
234C24×C83—22no—
235C24×C83C22×C414yes—
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×C83C22×C414yes—
254C22×C4×C83C22×C414yes—
255C22×C4×C83C2×D414yes—
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—44no—
265C22⋊C4×C83C22×C4116yescomplemented
266C42×C83—44no—
267C23×C83—28no—
268C23×C83—28no—
269C23×C83—28no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—44no—
277C23×C83—44no—
278C23×C83—44no—
279C23×C83—44no—
280C23×C83C23×C414yes—
281C23×C83C23×C412yes—
282C23×C83C22×D412yes—
283C23×C83C2×#4112yes—
284C23×C83H(5,𝔽2)12yes—
285C23×C83H(5,𝔽2)12yes—
286C23×C832−1+412yes—
287C23×C832−1+412yes—
288C23×C83C2511yescharacteristic
289C22×D83—28no—
290C22×D83—28no—
291C22×D83—28no—
292C22×D83—28no—
293C22×D83—28no—
294C22×D83—28no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—22no—
299C22×D83C4×D4116yes—
300C22×D83C23×C414yes—
301C22×D83C22×D414yes—
302C22×D83C2×#4114yes—
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×C83C23×C414yes—
325C2×C4×C83C23×C414yes—
326C2×C4×C83C22×D414yes—
327C22⋊D83—232no—
328C2×Dic83—28no—
329C2×Dic83—28no—
330C2×Dic83—28no—
331C2×Dic83—28no—
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—22no—
349C2×Dic83—416no—
350C2×Dic83—44no—
351C2×Dic83—44no—
352C2×Dic83—44no—
353C2×Dic83C23×C414yes—
354C2×Dic83C23×C414yes—
355C2×Dic83C23×C414yes—
356C2×Dic83C22×D414yes—
357C4×D83—232no—
358C4×D83—416no—
359C4×D83—416no—
360C22×C83—24no—
361C22×C83—24no—
362C22×C83—24no—
363C22×C83—416no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—42no—
368C22×C83C2×C4×D414yes—
369C22×C83#52014yes—
370C22×C83#52014yes—
371C22×C83#53414yes—
372C22×C83#53614yes—
373C22×C83#53914yes—
374C22×C83#53914yes—
375C22×C83C24×C411yescharacteristic
376C22×C83C23×D411yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C2×H(5,𝔽2)11yescharacteristic
379C22×C83C2×H(5,𝔽2)11yescharacteristic
380C22×C83C2×2−1+411yescharacteristic
381C22×C83C2×2−1+411yescharacteristic
382C2×D83—232no—
383C2×D83—24no—
384C2×D83—24no—
385C2×D83—24no—
386C2×D83—24no—
387C2×D83—24no—
388C2×D83—24no—
389C2×D83C2×C4×D418yes—
390C4×C83—24no—
391C4×C83—24no—
392C4×C83—24no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396Dic83—24no—
397Dic83—24no—
398Dic83—24no—
399Dic83—24no—
400Dic83—42no—
401Dic83—42no—
402Dic83—42no—
403C2×#2322—831nomaximal, Sylow
404C2×C83—44no—
405C2×C83#232218yescomplemented
406C2×C83C22×C4×D411yescharacteristic
407C2×C83C2×#52011yescharacteristic
408C2×C83C2×#52011yescharacteristic
409C2×C83C2×#53411yescharacteristic
410C2×C83C2×#53611yescharacteristic
411C2×C83C2×#53911yescharacteristic
412C2×C83C2×#53911yescharacteristic
413D83—28no—
414C22×#123—831no—
415C22×C4×D4—831no—
416C23×C4⋊C4—831no—
417#2322—8316no—
418C2×#389—831no—
419C2×#389—831no—
420C2×#388—831no—
421C2×#388D8311yescharacteristic, complemented
422C2×#387—831no—
423C2×#387—831no—
424C2×#386—831no—
425C2×#385—831no—
426C2×#385—831no—
427C2×#385—831no—
428C2×#381—831no—
429C2×C4×C22⋊C4—831no—
430C83C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—831no—
432C24×C4—831no—
433C24×C4—831no—
434C24×C4—831no—
435C24×C4—831no—
436C2×#123—8316no—
437C2×#123—838no—
438C2×C4×D4—838no—
439C2×C4×D4—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⋊C4—838no—
449C22×C4⋊C4—1668no—
450C22×C4⋊C4C2×D8311yescharacteristic
451C22×C22⋊C4—831no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4—831no—
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4C2×D8311yescharacteristic
457C22×C22⋊C4C2×D8311yescharacteristic
458C22×C22⋊C4C2×D8311yescharacteristic
459C22×C42—831no—
460C22×C42—831no—
461C22×C42C2×D8311yescharacteristic
462#389—838no—
463#389—838no—
464#388—838no—
465#388C2×D8318yescomplemented
466#387—838no—
467#387—838no—
468#386—838no—
469#385—838no—
470#385—838no—
471#385—838no—
472#381—838no—
473C4×C22⋊C4—838no—
474C2×#95—831no—
475C2×#95—831no—
476C2×#95—831no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95—831no—
480C2×#95—831no—
481C2×#95—831no—
482C2×#95C2×D8311yescharacteristic
483C2×#95C2×D8311yescharacteristic
484C25—831no—
485C25C22×D8311yescharacteristic
486C22×D4—838no—
487C22×D4—834no—
488C22×D4—1664no—
489C22×D4—1664no—
490C23×C4—3322no—
491C23×C4—3322no—
492C23×C4—3322no—
493C23×C4—3322no—
494C23×C4—3322no—
495C23×C4—3322no—
496C23×C4—838no—
497C23×C4—834no—
498C23×C4—834no—
499C23×C4—834no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4—838no—
505C23×C4—834no—
506C23×C4—831no—
507C23×C4—831no—
508C23×C4—831no—
509C23×C4—1664no—
510C23×C4—1664no—
511C23×C4—1664no—
512C23×C4—1664no—
513C23×C4C22×D8311yescharacteristic
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8311yescharacteristic
516C23×C4C22×D8311yescharacteristic
517C23×C4C22×D8311yescharacteristic
518C23×C4C22×D8311yescharacteristic
519#123—8364no—
520C4×D4—16632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—3322no—
523C2×C4⋊C4—3322no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—838no—
527C2×C4⋊C4—838no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—834no—
531C2×C4⋊C4—834no—
532C2×C4⋊C4—834no—
533C2×C4⋊C4—834no—
534C2×C4⋊C4—16632no—
535C2×C4⋊C4—1664no—
536C2×C4⋊C4—1664no—
537C2×C4⋊C4—1664no—
538C2×C4⋊C4—1664no—
539C2×C4⋊C4C22×D8314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—3322no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—838no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—838no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—834no—
550C2×C22⋊C4—1664no—
551C2×C22⋊C4—1664no—
552C2×C22⋊C4C4×D8318yescomplemented
553C2×C22⋊C4C22×D8314yes—
554C2×C22⋊C4C22×D8314yes—
555C2×C22⋊C4C22×D8314yes—
556C2×C42—42no—
557C2×C42—3322no—
558C2×C42—834no—
559C2×C42—834no—
560C2×C42—1664no—
561C2×C42C22×D8314yes—
562#95—834no—
563#95—834no—
564#95—834no—
565#95—834no—
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—834no—
579C24—834no—
580C24—834no—
581C24—832no—
582C24—1662no—
583C24—1662no—
584C24—1662no—
585C24—1662no—
586C24C2×C4×D8314yes—
587C24C23×D8312yes—
588C24C23×D8311yescharacteristic
589C2×D4—8316no—
590C2×D4—1668no—
591C2×D4—16632no—
592C2×D4—1668no—
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—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—33216no—
609C22×C4—3324no—
610C22×C4—3324no—
611C22×C4—3324no—
612C22×C4—3324no—
613C22×C4—33216no—
614C22×C4—33216no—
615C22×C4—3324no—
616C22×C4—3324no—
617C22×C4—8316no—
618C22×C4—834no—
619C22×C4—834no—
620C22×C4—834no—
621C22×C4—834no—
622C22×C4—832no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—8316no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—832no—
630C22×C4—1668no—
631C22×C4—1668no—
632C22×C4—16632no—
633C22×C4—1668no—
634C22×C4—1668no—
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—1662no—
649C22×C4—1662no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4C2×C4×D8314yes—
653C22×C4C2×C4×D8314yes—
654C22×C4D4×D8314yes—
655C22×C4C23×D8312yes—
656C22×C4C23×D8312yes—
657C22×C4C23×D8312yes—
658C22×C4C23×D8312yes—
659C22×C4C23×D8312yes—
660C22×C4C23×D8312yes—
661C4⋊C4—28no—
662C4⋊C4—3324no—
663C4⋊C4—3324no—
664C4⋊C4—8316no—
665C4⋊C4—8316no—
666C4⋊C4—1668no—
667C4⋊C4—1668no—
668C4⋊C4—1668no—
669C4⋊C4—1668no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—3324no—
673C22⋊C4—8316no—
674C22⋊C4—8316no—
675C22⋊C4—1668no—
676C22⋊C4—1668no—
677C22⋊C4C2×C4×D83116yescomplemented
678C42—44no—
679C42—3324no—
680C42—1668no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—8316no—
695C23—834no—
696C23—834no—
697C23—834no—
698C23—1668no—
699C23—1668no—
700C23—1668no—
701C23—1668no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1668no—
707C23—1668no—
708C23C22×C4×D8314yes—
709C23C22×C4×D8312yes—
710C23C2×D4×D8312yes—
711C23#41×D8312yes—
712C23#1458183712yes—
713C23#1458183812yes—
714C23#1458183912yes—
715C23#1458183912yes—
716C23C24×D8311yescharacteristic
717D4—16632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
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—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—33216no—
740C2×C4—33216no—
741C2×C4—3324no—
742C2×C4—3324no—
743C2×C4—3324no—
744C2×C4—33216no—
745C2×C4—834no—
746C2×C4—834no—
747C2×C4—834no—
748C2×C4—834no—
749C2×C4—16632no—
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—1668no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1662no—
771C2×C4C22×C4×D8314yes—
772C2×C4C22×C4×D8314yes—
773C2×C4C2×D4×D8314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—838no—
783C22—16632no—
784C22—1664no—
785C22—1664no—
786C22—1664no—
787C22—1664no—
788C22—1664no—
789C22—1664no—
790C22C4×D4×D8314yes—
791C22#1912818014yes—
792C22#1912818114yes—
793C22#1912825914yes—
794C22#1912827114yes—
795C22#1912829214yes—
796C22#1912829414yes—
797C22C23×C4×D8311yescharacteristic
798C22C22×D4×D8311yescharacteristic
799C22C2×#41×D8311yescharacteristic
800C22C2×#1458183711yescharacteristic
801C22C2×#1458183811yescharacteristic
802C22C2×#1458183911yescharacteristic
803C22C2×#1458183911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—3322no—
811C4—3322no—
812C4—3322no—
813C4—1664no—
814C4—1664no—
815C4—1664no—
816C4—1664no—
817C2—44no—
818C2—1668no—
819C2#2491013318yesdirect product factor
820C2C2×C4×D4×D8311yescharacteristic
821C2C2×#1912818011yescharacteristic
822C2C2×#1912818111yescharacteristic
823C2C2×#1912825911yescharacteristic
824C2C2×#1912827111yescharacteristic
825C2C2×#1912829211yescharacteristic
826C2C2×#1912829411yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC2×#388D83
hypocenterC83C2×#2322
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D83C2semidirect
4. #24910133C2direct (N × H)
5. C2×#19127599C2semidirect
6. C2×#19127596C2semidirect
7. C2×#19127595C2semidirect
8. C2×#19127588C2semidirect
9. C2×#19127584C2semidirect
11. C2×#19127576C2semidirect
12. C2×#19127575C2semidirect
13. C2×#19127573C2semidirect
14. C2×#19127563C2semidirect
15. C2×C4×(C2×D83)⋊C4C2semidirect
16. C2×#388×C83C2semidirect
22. C2×#14581774C4semidirect
35. C2×C4⋊C4×D83C22semidirect
43. #19127599C22semidirect
44. #19127596C22semidirect
45. #19127595C22semidirect
46. #19127588C22semidirect
47. #19127584C22semidirect
49. #19127576C22semidirect
50. #19127575C22semidirect
51. #19127573C22semidirect
52. #19127563C22semidirect
53. C4×(C2×D83)⋊C4C22semidirect
67. #388×C83C22semidirect
93. C22×C4×D83C2×C4semidirect
98. #14581774C2×C4semidirect
102. C2×C4⋊Dic83C2×C4semidirect
110. C2×Dic83⋊C4C2×C4semidirect
118. C2×C22⋊Dic83C2×C4semidirect
123. C2×(C2×D83)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C83C2×C4semidirect
212. C2×C4×D83C22×C4semidirect
216. C4⋊Dic83C22×C4semidirect
221. Dic83⋊C4C22×C4semidirect
223. C22⋊Dic83C22×C4semidirect
226. (C2×D83)⋊C4C22×C4semidirect
265. C22⋊C4×C83C22×C4semidirect
405. C2×C83#2322semidirect
421. C2×#388D83semidirect
430. C83C2×#2322semidirect
465. #388C2×D83semidirect
552. C2×C22⋊C4C4×D83semidirect
677. C22⋊C4C2×C4×D83semidirect
819. C2#24910133direct (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×(C22⋊D83)⋊C42
C22×C4⋊C4×D832
#249101332
C2×#191275992
C2×#191275962
C2×#191275952
C2×#191275882
C2×#191275842
C2×#191275772
C2×#191275762
C2×#191275752
C2×#191275732
C2×#191275632
C2×C4×(C2×D83)⋊C42
C2×#388×C832
C2×#232283