Finite Group Databasebeta

← C2×#24910451 #35563903

Subgroups — C2×#24910451 #35563903

Order 21248.

3830 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×#14581775C211yesmaximal, characteristic
2C22×C4×C22⋊D83C211yesmaximal, characteristic
3C22×#14581751C211yesmaximal, characteristic, complemented
4#24910451C2116yesmaximal, direct product factor
5C2×#19127598C211yesmaximal, characteristic, complemented
6C2×#19127593C211yesmaximal, characteristic, complemented
7C2×#19127590C211yesmaximal, characteristic, complemented
8C2×#19127588C211yesmaximal, characteristic, complemented
9C2×#19127583C211yesmaximal, characteristic, complemented
10C2×#19127580C211yesmaximal, characteristic
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127574C211yesmaximal, characteristic, complemented
13C2×#19127552C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C22×#95×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C2×#14581775C4116yescomplemented
20C2×#14581775C2218yes—
21C2×C4×C22⋊D83—28no—
22C2×C4×C22⋊D83C2218yes—
23C2×#14581751—28no—
24C2×#14581751C2218yescomplemented
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
41C22×C4×Dic83C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic
44C22×C4×Dic83C2211yescharacteristic
45#19127598C2218yescomplemented
46#19127593C2218yescomplemented
47#19127590C2218yescomplemented
48#19127588C2218yescomplemented
49#19127583C2218yescomplemented
50#19127580C2218yes—
51#19127575C2218yescomplemented
52#19127574C2218yescomplemented
53#19127552C2218yescomplemented
54C4×C22⋊Dic83C2218yescomplemented
55#19127548C2218yescomplemented
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C24×C4×C83C2211yescharacteristic
63C24×C4×C83C2211yescharacteristic
64C24×C4×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C2×#95×C83C2218yescomplemented
70C24×D83C2311yescharacteristic
71C22×C22⋊D83—24no—
72C22×C22⋊D83—24no—
73C22×C22⋊D83C2×C418yes—
74C22×C22⋊D83C2314yes—
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83—42no—
85C22×C4×D83C2314yes—
86#14581775C2×C4164yescomplemented
87C4×C22⋊D83—232no—
88#14581751—232no—
89C2×C4⋊Dic83—24no—
90C2×C4⋊Dic83—24no—
91C2×C4⋊Dic83C2314yes—
92C2×C4⋊Dic83C2314yes—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—42no—
96C2×Dic83⋊C4C2×C418yescomplemented
97C2×Dic83⋊C4C2×C418yescomplemented
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×C22⋊Dic83—24no—
104C2×C22⋊Dic83C2×C418yescomplemented
105C2×C22⋊Dic83D418yes—
106C2×C22⋊Dic83C2314yes—
107C2×C22⋊Dic83C2314yes—
108C2×C22⋊Dic83C2314yes—
109C2×(C2×D83)⋊C4—24no—
110C2×(C2×D83)⋊C4—24no—
111C2×(C2×D83)⋊C4—42no—
112C2×(C2×D83)⋊C4C2×C418yescomplemented
113C2×(C2×D83)⋊C4C2×C418yescomplemented
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×C4×Dic83—24no—
120C2×C4×Dic83—24no—
121C2×C4×Dic83—24no—
122C2×C4×Dic83—24no—
123C2×C4×Dic83—42no—
124C2×C4×Dic83C2314yes—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2314yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C25×C83C2311yescharacteristic
136C23×C4×C83—24no—
137C23×C4×C83—24no—
138C23×C4×C83—24no—
139C23×C4×C83—24no—
140C23×C4×C83—24no—
141C23×C4×C83—24no—
142C23×C4×C83—42no—
143C23×C4×C83—42no—
144C23×C4×C83C2×C418yescomplemented
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2314yes—
148C23×C4×C83C2314yes—
149C23×C4×C83C2311yescharacteristic
150C23×C4×C83C2311yescharacteristic
151C23×C4×C83C2314yes—
152C23×C4×C83C2311yescharacteristic
153C23×C4×C83C2311yescharacteristic
154#95×C83C2314yes—
155#95×C83C2314yes—
156#95×C83C2314yes—
157#95×C83C2314yes—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83C22×C414yes—
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×Dic83C22×C414yes—
187C22×Dic83C22×C414yes—
188C22×Dic83C22×C414yes—
189C22×Dic83C2×D414yes—
190C22×Dic83C2×D414yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C2×C4×D83—28no—
199C2×C4×D83—28no—
200C2×C4×D83—44no—
201C2×C4×D83—416no—
202C4⋊Dic83—28no—
203C4⋊Dic83—28no—
204Dic83⋊C4—28no—
205Dic83⋊C4—28no—
206Dic83⋊C4—44no—
207Dic83⋊C4C22×C4116yescomplemented
208Dic83⋊C4C22×C4116yescomplemented
209C22⋊Dic83—28no—
210C22⋊Dic83C22×C4116yescomplemented
211C22⋊Dic83C2×D4116yes—
212(C2×D83)⋊C4—28no—
213(C2×D83)⋊C4—28no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4C22×C4116yescomplemented
216(C2×D83)⋊C4C22×C4116yescomplemented
217C4×Dic83—28no—
218C4×Dic83—28no—
219C4×Dic83—28no—
220C4×Dic83—28no—
221C4×Dic83—44no—
222C24×C83—22no—
223C24×C83—22no—
224C24×C83—22no—
225C24×C83—22no—
226C24×C83C22×C414yes—
227C24×C83C2×D414yes—
228C24×C83#4114yes—
229C24×C83C2412yes—
230C24×C83C2411yescharacteristic
231C22×C4×C83—232no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—28no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—28no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—28no—
244C22×C4×C83—28no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—28no—
251C22×C4×C83—28no—
252C22×C4×C83—44no—
253C22×C4×C83—44no—
254C22×C4×C83—416no—
255C22×C4×C83—416no—
256C22×C4×C83C22×C414yes—
257C22×C4×C83C22×C414yes—
258C22×C4×C83C22×C4116yescomplemented
259C22×C4×C83#4114yes—
260C22×C4×C83#4114yes—
261C22×C4×C83C2412yes—
262C22×C4×C83C2412yes—
263C22×C4×C83C2412yes—
264C22×C4×C83C2412yes—
265C22×C4×C83C2412yes—
266C22×C4×C83C2412yes—
267C23×C83—28no—
268C23×C83—28no—
269C23×C83—28no—
270C23×C83—28no—
271C23×C83—28no—
272C23×C83—28no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83C4×D4116yes—
278C23×C83C23×C414yes—
279C23×C83C23×C412yes—
280C23×C83C22×D414yes—
281C23×C83C22×D412yes—
282C23×C83C2×#4114yes—
283C23×C83C2×#4112yes—
284C23×C83C2×#4112yes—
285C23×C83C2×#4112yes—
286C23×C83H(5,𝔽2)12yes—
287C23×C832−1+412yes—
288C23×C83C2511yescharacteristic
289C22×D83—28no—
290C22×D83—28no—
291C22×D83—28no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—44no—
299C22×D83—44no—
300C22×D83—44no—
301C22×D83—44no—
302C22×D83C23×C414yes—
303C2×C4×C83—28no—
304C2×C4×C83—28no—
305C2×C4×C83—232no—
306C2×C4×C83—28no—
307C2×C4×C83—28no—
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—22no—
322C2×C4×C83—416no—
323C2×C4×C83—416no—
324C2×C4×C83—44no—
325C2×C4×C83—44no—
326C2×C4×C83C23×C414yes—
327C2×C4×C83C23×C414yes—
328C2×C4×C83C2×#4114yes—
329C2×C4×C83C2×#4114yes—
330C22⋊D83—232no—
331C2×Dic83—28no—
332C2×Dic83—28no—
333C2×Dic83—28no—
334C2×Dic83—28no—
335C2×Dic83—28no—
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—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—44no—
353C2×Dic83—44no—
354C2×Dic83C23×C414yes—
355C2×Dic83C23×C414yes—
356C2×Dic83C23×C414yes—
357C2×Dic83C22×D414yes—
358C2×Dic83C22×D414yes—
359C4×D83—416no—
360C22×C83—232no—
361C22×C83—24no—
362C22×C83—24no—
363C22×C83—24no—
364C22×C83—24no—
365C22×C83—24no—
366C22×C83—24no—
367C22×C83C2×C4×D418yes—
368C22×C83C2×C4×D414yes—
369C22×C83C4×#4114yes—
370C22×C83#52014yes—
371C22×C83#54614yes—
372C22×C83#54714yes—
373C22×C83#55114yes—
374C22×C83#55214yes—
375C22×C83C24×C411yescharacteristic
376C22×C83C23×D411yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C22×#4111yescharacteristic
379C22×C83C22×#4111yescharacteristic
380C22×C83C2×H(5,𝔽2)11yescharacteristic
381C22×C83C2×2−1+411yescharacteristic
382C2×D83—24no—
383C2×D83—24no—
384C2×D83—24no—
385C2×D83—416no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—42no—
389C2×D83—42no—
390C4×C83—24no—
391C4×C83—24no—
392C4×C83—24no—
393C4×C83—24no—
394C4×C83—42no—
395C4×C83—42no—
396Dic83—24no—
397Dic83—24no—
398Dic83—24no—
399Dic83—24no—
400Dic83—24no—
401Dic83—42no—
402Dic83—42no—
403C2×#2359—831nomaximal, Sylow
404C2×C83—28no—
405C2×C83#235918yescomplemented
406C2×C83C22×C4×D411yescharacteristic
407C2×C83C2×C4×#4111yescharacteristic
408C2×C83C2×#52011yescharacteristic
409C2×C83C2×#54611yescharacteristic
410C2×C83C2×#54711yescharacteristic
411C2×C83C2×#55111yescharacteristic
412C2×C83C2×#55211yescharacteristic
413D83—44no—
414C22×#123—831no—
415C22×C4×D4—831no—
416C22×#117—831no—
417#2359—8316no—
418C2×#389—831no—
419C2×#388—831no—
420C2×#388—831no—
421C2×#387—831no—
422C2×#387—831no—
423C2×#386—831no—
424C2×#385—831no—
425C2×#385—831no—
426C2×C4×C4⋊C4—831no—
427C2×C4×C22⋊C4—831no—
428C2×C4×C22⋊C4—831no—
429C22×#95D8311yescharacteristic, complemented
430C83C2×#235911yescharacteristic, complemented, Sylow
431C23×D4—831no—
432C24×C4—831no—
433C24×C4C2×D8311yescharacteristic
434C24×C4C2×D8311yescharacteristic
435C24×C4C2×D8311yescharacteristic
436C2×#123—8316no—
437C2×#123—838no—
438C2×C4×D4—838no—
439C2×C4×D4—1668no—
440C2×#117—838no—
441C2×#117—1668no—
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—831no—
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×C42—831no—
458C22×C42—831no—
459C22×C42—831no—
460C22×C42—831no—
461C22×C42—831no—
462#389—838no—
463#388—838no—
464#388—838no—
465#387—838no—
466#387—838no—
467#386—838no—
468#385—838no—
469#385—838no—
470C4×C4⋊C4—838no—
471C4×C22⋊C4—838no—
472C4×C22⋊C4—838no—
473C2×#95—831no—
474C2×#95—831no—
475C2×#95—831no—
476C2×#95—831no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95C2×D8311yescharacteristic
480C2×#95C2×D8311yescharacteristic
481C2×#95C2×D8311yescharacteristic
482C2×#95C2×D8311yescharacteristic
483C2×#95C2×D8318yescomplemented
484C25—831no—
485C25C22×D8311yescharacteristic
486C22×D4—838no—
487C22×D4—834no—
488C22×D4—1664no—
489C22×D4—1664no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—24no—
496C23×C4—42no—
497C23×C4—42no—
498C23×C4—3322no—
499C23×C4—834no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4—831no—
505C23×C4—831no—
506C23×C4—831no—
507C23×C4—1664no—
508C23×C4—1664no—
509C23×C4C4×D8318yescomplemented
510C23×C4C22×D8311yescharacteristic
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8314yes—
513C23×C4C22×D8314yes—
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8311yescharacteristic
516C23×C4C22×D8314yes—
517C23×C4C22×D8311yescharacteristic
518C23×C4C22×D8311yescharacteristic
519#123—8364no—
520C4×D4—16632no—
521#117—16632no—
522C2×C4⋊C4—3322no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—838no—
525C2×C4⋊C4—838no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—834no—
531C2×C4⋊C4—834no—
532C2×C4⋊C4—1664no—
533C2×C4⋊C4—1664no—
534C2×C4⋊C4—1664no—
535C2×C4⋊C4—1664no—
536C2×C22⋊C4—3322no—
537C2×C22⋊C4—834no—
538C2×C22⋊C4—838no—
539C2×C22⋊C4—838no—
540C2×C22⋊C4—834no—
541C2×C22⋊C4—834no—
542C2×C22⋊C4—838no—
543C2×C22⋊C4—838no—
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×C42—3322no—
553C2×C42—834no—
554C2×C42—834no—
555C2×C42—834no—
556C2×C42—834no—
557C2×C42—834no—
558C2×C42—1664no—
559C2×C42—1664no—
560C2×C42—1664no—
561C2×C42—1664no—
562#95—834no—
563#95—834no—
564#95—834no—
565#95—834no—
566#95—834no—
567#95—834no—
568#95C22×D8314yes—
569#95C22×D8314yes—
570#95C22×D8314yes—
571#95C22×D8314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—834no—
577C24—832no—
578C24—1662no—
579C24—1662no—
580C24—1662no—
581C24—1662no—
582C24—1662no—
583C24—1662no—
584C24C2×C4×D8314yes—
585C24D4×D8314yes—
586C24#1305058914yes—
587C24C23×D8312yes—
588C24C23×D8311yescharacteristic
589C2×D4—8316no—
590C2×D4—1668no—
591C2×D4—1668no—
592C2×D4—16632no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—232no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—416no—
617C22×C4—416no—
618C22×C4—33216no—
619C22×C4—3324no—
620C22×C4—834no—
621C22×C4—834no—
622C22×C4—834no—
623C22×C4—834no—
624C22×C4—834no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—832no—
630C22×C4—832no—
631C22×C4—832no—
632C22×C4—1668no—
633C22×C4—1662no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1662no—
638C22×C4—1662no—
639C22×C4—1668no—
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×C4C2×C4×D8314yes—
651C22×C4C2×C4×D8314yes—
652C22×C4C2×C4×D83116yescomplemented
653C22×C4#1305059014yes—
654C22×C4#1305059014yes—
655C22×C4C23×D8312yes—
656C22×C4C23×D8312yes—
657C22×C4C23×D8312yes—
658C22×C4C23×D8312yes—
659C22×C4C23×D8312yes—
660C22×C4C23×D8312yes—
661C4⋊C4—3324no—
662C4⋊C4—8316no—
663C4⋊C4—8316no—
664C4⋊C4—1668no—
665C4⋊C4—1668no—
666C4⋊C4—1668no—
667C4⋊C4—1668no—
668C22⋊C4—3324no—
669C22⋊C4—8316no—
670C22⋊C4—8316no—
671C22⋊C4—8316no—
672C22⋊C4—8316no—
673C22⋊C4—1668no—
674C22⋊C4—1668no—
675C22⋊C4—1668no—
676C42—3324no—
677C42—1668no—
678C42—1668no—
679C42—1668no—
680C42—1668no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—3324no—
692C23—3324no—
693C23—3324no—
694C23—3324no—
695C23—834no—
696C23—1668no—
697C23—1668no—
698C23—1668no—
699C23—1662no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23(C22⋊D83)⋊C4116yes—
706C23C22×C4×D8314yes—
707C23C22×C4×D8312yes—
708C23C2×D4×D8314yes—
709C23C2×D4×D8312yes—
710C23C2×#1305058914yes—
711C23C2×#1305058912yes—
712C23C2×#1305059012yes—
713C23C2×#1305059012yes—
714C23#1458183712yes—
715C23#1458184012yes—
716C23C24×D8311yescharacteristic
717D4—16632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—232no—
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—22no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—33216no—
742C2×C4—3324no—
743C2×C4—3324no—
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—1668no—
756C2×C4—1668no—
757C2×C4—1668no—
758C2×C4—1668no—
759C2×C4—1668no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4C22×C4×D8314yes—
771C2×C4C22×C4×D8314yes—
772C2×C4C2×#1305059014yes—
773C2×C4C2×#1305059014yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—3322no—
782C22—3322no—
783C22—33216no—
784C22—3322no—
785C22—3322no—
786C22—1664no—
787C22—1664no—
788C22—1664no—
789C22C2×(C22⋊D83)⋊C418yes—
790C22C2×(C22⋊D83)⋊C414yes—
791C22C4×#1305059014yes—
792C22#1912818214yes—
793C22#1912834114yes—
794C22#1912835214yes—
795C22#1912837714yes—
796C22#1912838614yes—
797C22C23×C4×D8311yescharacteristic
798C22C22×D4×D8311yescharacteristic
799C22C22×#1305058911yescharacteristic
800C22C22×#1305059011yescharacteristic
801C22C22×#1305059011yescharacteristic
802C22C2×#1458183711yescharacteristic
803C22C2×#1458184011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—3322no—
811C4—3322no—
812C4—1664no—
813C4—1664no—
814C4—1664no—
815C4—1664no—
816C4—1664no—
817C2—28no—
818C2—3324no—
819C2#2491045118yesdirect product factor
820C2C22×(C22⋊D83)⋊C411yescharacteristic
821C2C2×C4×#1305059011yescharacteristic
822C2C2×#1912818211yescharacteristic
823C2C2×#1912834111yescharacteristic
824C2C2×#1912835211yescharacteristic
825C2C2×#1912837711yescharacteristic
826C2C2×#1912838611yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC22×#95×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC22×#95D83
hypocenterC83C2×#2359
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C22×#14581751C2semidirect
4. #24910451C2direct (N × H)
5. C2×#19127598C2semidirect
6. C2×#19127593C2semidirect
7. C2×#19127590C2semidirect
8. C2×#19127588C2semidirect
9. C2×#19127583C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127574C2semidirect
13. C2×#19127552C2semidirect
14. C2×C4×C22⋊Dic83C2semidirect
15. C2×#19127548C2semidirect
16. C22×#95×C83C2semidirect
19. C2×#14581775C4semidirect
24. C2×#14581751C22semidirect
45. #19127598C22semidirect
46. #19127593C22semidirect
47. #19127590C22semidirect
48. #19127588C22semidirect
49. #19127583C22semidirect
51. #19127575C22semidirect
52. #19127574C22semidirect
53. #19127552C22semidirect
54. C4×C22⋊Dic83C22semidirect
55. #19127548C22semidirect
69. C2×#95×C83C22semidirect
86. #14581775C2×C4semidirect
96. C2×Dic83⋊C4C2×C4semidirect
97. C2×Dic83⋊C4C2×C4semidirect
104. C2×C22⋊Dic83C2×C4semidirect
112. C2×(C2×D83)⋊C4C2×C4semidirect
113. C2×(C2×D83)⋊C4C2×C4semidirect
144. C23×C4×C83C2×C4semidirect
207. Dic83⋊C4C22×C4semidirect
208. Dic83⋊C4C22×C4semidirect
210. C22⋊Dic83C22×C4semidirect
215. (C2×D83)⋊C4C22×C4semidirect
216. (C2×D83)⋊C4C22×C4semidirect
258. C22×C4×C83C22×C4semidirect
405. C2×C83#2359semidirect
429. C22×#95D83semidirect
430. C83C2×#2359semidirect
483. C2×#95C2×D83semidirect
509. C23×C4C4×D83semidirect
652. C22×C4C2×C4×D83semidirect
819. C2#24910451direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817752
C22×C4×C22⋊D832
C22×#145817512
#249104512
C2×#191275982
C2×#191275932
C2×#191275902
C2×#191275882
C2×#191275832
C2×#191275802
C2×#191275752
C2×#191275742
C2×#191275522
C2×C4×C22⋊Dic832
C2×#191275482
C22×#95×C832
C2×#235983