Finite Group Databasebeta

← C2×#24910476 #35563930

Subgroups — C2×#24910476 #35563930

Order 21248.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581765C211yesmaximal, characteristic
2C22×C4×D332C211yesmaximal, characteristic, complemented
3C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
6#24910476C2116yesmaximal, direct product factor
7C2×#19127601C211yesmaximal, characteristic, complemented
8C2×#19127598C211yesmaximal, characteristic, complemented
9C2×#19127593C211yesmaximal, characteristic, complemented
10C2×#19127579C211yesmaximal, characteristic, complemented
11C2×#19127577C211yesmaximal, characteristic, complemented
12C2×#19127576C211yesmaximal, characteristic, complemented
13C2×#19127572C211yesmaximal, characteristic, complemented
14C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C22⋊D83C2211yescharacteristic
20C24×Dic83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C23×C4×D83C2211yescharacteristic
23C23×C4×D83C2211yescharacteristic
24C23×C4×D83C2211yescharacteristic
25C2×#14581765C4116yescomplemented
26C2×#14581765C2218yes—
27C2×C4×D332—28no—
28C2×C4×D332C2218yescomplemented
29C2×(C22⋊D83)⋊C4—28no—
30C2×(C22⋊D83)⋊C4—28no—
31C2×(C22⋊D83)⋊C4C2218yescomplemented
32C2×(C22⋊D83)⋊C4C2218yescomplemented
33C22×C4⋊Dic83C2211yescharacteristic
34C22×C4⋊Dic83C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×Dic83⋊C4C2211yescharacteristic
37C22×Dic83⋊C4C2211yescharacteristic
38C22×Dic83⋊C4C2211yescharacteristic
39C2×C4⋊C4×D83—28no—
40C2×C4⋊C4×D83C2218yescomplemented
41C22×C22⋊Dic83C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×(C2×D83)⋊C4C2211yescharacteristic
45C22×(C2×D83)⋊C4C2211yescharacteristic
46C22×(C2×D83)⋊C4C2211yescharacteristic
47C22×(C2×D83)⋊C4C2211yescharacteristic
48C22×C4×Dic83C2211yescharacteristic
49C22×C4×Dic83C2211yescharacteristic
50C22×C4×Dic83C2211yescharacteristic
51#19127601C2218yescomplemented
52#19127598C2218yescomplemented
53#19127593C2218yescomplemented
54#19127579C2218yescomplemented
55#19127577C2218yescomplemented
56#19127576C2218yescomplemented
57#19127572C2218yescomplemented
58C4×Dic83⋊C4C2218yescomplemented
59#19127548C2218yescomplemented
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C2×C83⋊#95C2211yescharacteristic
63C2×C83⋊#95C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C22⋊C4×C83C2211yescharacteristic
67C22×C22⋊C4×C83C2211yescharacteristic
68C22×C42×C83C2211yescharacteristic
69#388×C83C2218yescomplemented
70C2×#95×C83C2211yescharacteristic
71C2×#95×C83C2211yescharacteristic
72C24×D83C2311yescharacteristic
73C24×D83C2311yescharacteristic
74C22×D332—24no—
75C22×D332—24no—
76C22×D332C2×C418yescomplemented
77C22×D332C2314yes—
78C22×C22⋊D83—24no—
79C22×C22⋊D83—24no—
80C22×C22⋊D83—24no—
81C22×C22⋊D83—24no—
82C22×C22⋊D83C2×C418yescomplemented
83C22×C22⋊D83C2×C418yescomplemented
84C22×C22⋊D83C2314yes—
85C22×C22⋊D83C2314yes—
86C23×Dic83—24no—
87C23×Dic83—24no—
88C23×Dic83—42no—
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91C23×Dic83C2314yes—
92C23×Dic83C2311yescharacteristic
93C23×Dic83C2311yescharacteristic
94C23×Dic83C2311yescharacteristic
95C23×Dic83C2311yescharacteristic
96C22×C4×D83—24no—
97C22×C4×D83—24no—
98C22×C4×D83—24no—
99C22×C4×D83—24no—
100C22×C4×D83—24no—
101C22×C4×D83—24no—
102C22×C4×D83—24no—
103C22×C4×D83—24no—
104C22×C4×D83—42no—
105C22×C4×D83—42no—
106C22×C4×D83—42no—
107C22×C4×D83C2×C418yescomplemented
108C22×C4×D83C2314yes—
109C22×C4×D83C2314yes—
110C22×C4×D83C2314yes—
111C22×C4×D83C2314yes—
112#14581765C2×C4164yescomplemented
113C4×D332—232no—
114(C22⋊D83)⋊C4—232no—
115(C22⋊D83)⋊C4—232no—
116C2×C4⋊Dic83—24no—
117C2×C4⋊Dic83—24no—
118C2×C4⋊Dic83C2314yes—
119C2×C4⋊Dic83C2314yes—
120C2×Dic83⋊C4—24no—
121C2×Dic83⋊C4—24no—
122C2×Dic83⋊C4C2×C418yescomplemented
123C2×Dic83⋊C4D418yescomplemented
124C2×Dic83⋊C4C2314yes—
125C2×Dic83⋊C4C2314yes—
126C2×Dic83⋊C4C2314yes—
127C2×Dic83⋊C4C2314yes—
128C4⋊C4×D83—232no—
129C2×C22⋊Dic83—42no—
130C2×C22⋊Dic83C2314yes—
131C2×(C2×D83)⋊C4—24no—
132C2×(C2×D83)⋊C4—24no—
133C2×(C2×D83)⋊C4—24no—
134C2×(C2×D83)⋊C4—42no—
135C2×(C2×D83)⋊C4C2×C418yescomplemented
136C2×(C2×D83)⋊C4D418yescomplemented
137C2×(C2×D83)⋊C4C2314yes—
138C2×(C2×D83)⋊C4C2314yes—
139C2×(C2×D83)⋊C4C2314yes—
140C2×(C2×D83)⋊C4C2314yes—
141C2×(C2×D83)⋊C4C2314yes—
142C2×(C2×D83)⋊C4C2314yes—
143C2×C4×Dic83—24no—
144C2×C4×Dic83—24no—
145C2×C4×Dic83—24no—
146C2×C4×Dic83C2314yes—
147C2×C4×Dic83C2314yes—
148C2×C4×Dic83C2314yes—
149C83⋊#95C2314yes—
150C83⋊#95C2314yes—
151C83⋊#95C2314yes—
152C83⋊#95C2314yes—
153C25×C83C2311yescharacteristic
154C23×C4×C83C2311yescharacteristic
155C23×C4×C83C2311yescharacteristic
156C23×C4×C83C2311yescharacteristic
157C23×C4×C83C2311yescharacteristic
158C23×C4×C83C2311yescharacteristic
159C23×C4×C83C2311yescharacteristic
160C2×C4⋊C4×C83—24no—
161C2×C4⋊C4×C83C2314yes—
162C2×C22⋊C4×C83—24no—
163C2×C22⋊C4×C83—24no—
164C2×C22⋊C4×C83C2×C418yescomplemented
165C2×C22⋊C4×C83C2314yes—
166C2×C22⋊C4×C83C2314yes—
167C2×C22⋊C4×C83C2314yes—
168C2×C42×C83—24no—
169C2×C42×C83C2314yes—
170#95×C83C2314yes—
171#95×C83C2314yes—
172C23×D83—22no—
173C23×D83—22no—
174C23×D83—22no—
175C23×D83—22no—
176C23×D83—22no—
177C23×D83—22no—
178C23×D83—22no—
179C23×D83—22no—
180C23×D83—22no—
181C23×D83—22no—
182C23×D83C22×C414yes—
183C23×D83C22×C414yes—
184C23×D83C2×D414yes—
185C23×D83#4114yes—
186C23×D83C2412yes—
187C23×D83C2412yes—
188C2×D332—232no—
189C2×D332—28no—
190C2×D332—28no—
191C2×D332C22×C4116yescomplemented
192C2×C22⋊D83—232no—
193C2×C22⋊D83—28no—
194C2×C22⋊D83—28no—
195C2×C22⋊D83—232no—
196C2×C22⋊D83—28no—
197C2×C22⋊D83—28no—
198C2×C22⋊D83C22×C4116yescomplemented
199C2×C22⋊D83C22×C4116yescomplemented
200C22×Dic83—22no—
201C22×Dic83—22no—
202C22×Dic83—22no—
203C22×Dic83—22no—
204C22×Dic83—22no—
205C22×Dic83—22no—
206C22×Dic83—22no—
207C22×Dic83—22no—
208C22×Dic83—22no—
209C22×Dic83—22no—
210C22×Dic83—22no—
211C22×Dic83—22no—
212C22×Dic83—28no—
213C22×Dic83—28no—
214C22×Dic83—44no—
215C22×Dic83—416no—
216C22×Dic83C22×C414yes—
217C22×Dic83C22×C414yes—
218C22×Dic83C2×D414yes—
219C22×Dic83C2×D414yes—
220C22×Dic83C2×D414yes—
221C22×Dic83#4114yes—
222C22×Dic83C2412yes—
223C22×Dic83C2412yes—
224C22×Dic83C2412yes—
225C22×Dic83C2412yes—
226C22×Dic83C2412yes—
227C22×Dic83C2412yes—
228C2×C4×D83—232no—
229C2×C4×D83—28no—
230C2×C4×D83—28no—
231C2×C4×D83—28no—
232C2×C4×D83—28no—
233C2×C4×D83—28no—
234C2×C4×D83—28no—
235C2×C4×D83—28no—
236C2×C4×D83—28no—
237C2×C4×D83—44no—
238C2×C4×D83—44no—
239C2×C4×D83—44no—
240C2×C4×D83—416no—
241C2×C4×D83—416no—
242C2×C4×D83—416no—
243C2×C4×D83C22×C4116yescomplemented
244C4⋊Dic83—28no—
245C4⋊Dic83—28no—
246Dic83⋊C4—28no—
247Dic83⋊C4—28no—
248Dic83⋊C4C22×C4116yescomplemented
249Dic83⋊C4C2×D4116yescomplemented
250C22⋊Dic83—44no—
251(C2×D83)⋊C4—28no—
252(C2×D83)⋊C4—28no—
253(C2×D83)⋊C4—28no—
254(C2×D83)⋊C4—44no—
255(C2×D83)⋊C4C22×C4116yescomplemented
256(C2×D83)⋊C4C2×D4116yescomplemented
257C4×Dic83—28no—
258C4×Dic83—28no—
259C4×Dic83—28no—
260C24×C83—22no—
261C24×C83—22no—
262C24×C83—22no—
263C24×C83—22no—
264C24×C83—22no—
265C24×C83—22no—
266C24×C83C22×C414yes—
267C24×C83C2412yes—
268C24×C83C2411yescharacteristic
269C22×C4×C83—22no—
270C22×C4×C83—22no—
271C22×C4×C83—22no—
272C22×C4×C83—22no—
273C22×C4×C83—22no—
274C22×C4×C83—22no—
275C22×C4×C83—22no—
276C22×C4×C83—22no—
277C22×C4×C83—22no—
278C22×C4×C83—22no—
279C22×C4×C83—22no—
280C22×C4×C83—22no—
281C22×C4×C83—22no—
282C22×C4×C83—22no—
283C22×C4×C83C22×C414yes—
284C22×C4×C83C22×C414yes—
285C22×C4×C83C2×D414yes—
286C22×C4×C83C2×D414yes—
287C22×C4×C83C2412yes—
288C22×C4×C83C2412yes—
289C22×C4×C83C2412yes—
290C22×C4×C83C2412yes—
291C22×C4×C83C2412yes—
292C22×C4×C83C2412yes—
293C4⋊C4×C83—28no—
294C22⋊C4×C83—28no—
295C22⋊C4×C83—28no—
296C22⋊C4×C83C22×C4116yescomplemented
297C42×C83—28no—
298C23×C83—28no—
299C23×C83—28no—
300C23×C83—28no—
301C23×C83—22no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—44no—
308C23×C83—44no—
309C23×C83—44no—
310C23×C83—44no—
311C23×C83C23×C414yes—
312C23×C83C23×C412yes—
313C23×C83C22×D412yes—
314C23×C83C22×D412yes—
315C23×C83C2×#4112yes—
316C23×C83C2×#4112yes—
317C23×C83H(5,𝔽2)12yes—
318C23×C832−1+412yes—
319C23×C83C2511yescharacteristic
320C22×D83—28no—
321C22×D83—28no—
322C22×D83—28no—
323C22×D83—28no—
324C22×D83—28no—
325C22×D83—28no—
326C22×D83—22no—
327C22×D83—22no—
328C22×D83—22no—
329C22×D83—22no—
330C22×D83—28no—
331C22×D83—28no—
332C22×D83—28no—
333C22×D83—22no—
334C22×D83—22no—
335C22×D83—22no—
336C22×D83—22no—
337C22×D83—22no—
338C22×D83—22no—
339C22×D83—44no—
340C22×D83—44no—
341C22×D83—44no—
342C22×D83—44no—
343C22×D83C4×D4116yescomplemented
344C22×D83C23×C414yes—
345C22×D83C23×C414yes—
346C22×D83C22×D414yes—
347C22×D83C2×#4114yes—
348C2×C4×C83—28no—
349C2×C4×C83—28no—
350C2×C4×C83—28no—
351C2×C4×C83—28no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—44no—
367C2×C4×C83—44no—
368C2×C4×C83C23×C414yes—
369C2×C4×C83C23×C414yes—
370C2×C4×C83C22×D414yes—
371C2×C4×C83C22×D414yes—
372C22⋊D83—232no—
373C22⋊D83—232no—
374C2×Dic83—28no—
375C2×Dic83—28no—
376C2×Dic83—28no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—416no—
390C2×Dic83—44no—
391C2×Dic83—44no—
392C2×Dic83C4×D4116yescomplemented
393C2×Dic83C23×C414yes—
394C2×Dic83C23×C414yes—
395C2×Dic83C22×D414yes—
396C2×Dic83C22×D414yes—
397C2×Dic83C22×D414yes—
398C2×Dic83C2×#4114yes—
399D332—232no—
400C4×D83—232no—
401C4×D83—416no—
402C4×D83—416no—
403C4×D83—416no—
404C22×C83—24no—
405C22×C83—24no—
406C22×C83—24no—
407C22×C83—416no—
408C22×C83—42no—
409C22×C83—42no—
410C22×C83—42no—
411C22×C83—42no—
412C22×C83C2×C4×D414yes—
413C22×C83C2×C4×D414yes—
414C22×C83#52014yes—
415C22×C83D4214yes—
416C22×C83#54714yes—
417C22×C83#54814yes—
418C22×C83#55314yes—
419C22×C83C24×C411yescharacteristic
420C22×C83C23×D411yescharacteristic
421C22×C83C23×D411yescharacteristic
422C22×C83C22×#4111yescharacteristic
423C22×C83C22×#4111yescharacteristic
424C22×C83C2×H(5,𝔽2)11yescharacteristic
425C22×C83C2×2−1+411yescharacteristic
426C2×D83—232no—
427C2×D83—24no—
428C2×D83—24no—
429C2×D83—24no—
430C2×D83—24no—
431C2×D83—24no—
432C2×D83—24no—
433C2×D83—24no—
434C2×D83—24no—
435C2×D83—24no—
436C2×D83—416no—
437C2×D83—42no—
438C2×D83—42no—
439C2×D83—42no—
440C2×D83—42no—
441C2×D83C2×C4×D418yescomplemented
442C4×C83—24no—
443C4×C83—24no—
444C4×C83—24no—
445C4×C83—24no—
446C4×C83—42no—
447C4×C83—42no—
448Dic83—24no—
449Dic83—24no—
450Dic83—24no—
451Dic83—42no—
452Dic83—42no—
453Dic83C2×C4×D418yescomplemented
454C2×#2361—831nomaximal, Sylow
455C2×C83—44no—
456C2×C83#236118yescomplemented
457C2×C83C22×C4×D411yescharacteristic
458C2×C83C22×C4×D411yescharacteristic
459C2×C83C2×#52011yescharacteristic
460C2×C83C2×D4211yescharacteristic
461C2×C83C2×#54711yescharacteristic
462C2×C83C2×#54811yescharacteristic
463C2×C83C2×#55311yescharacteristic
464D83—28no—
465D83—44no—
466C22×#121—831no—
467C22×C4×D4—831no—
468C22×C4×D4—831no—
469C22×C4×D4—831no—
470C23×C4⋊C4—831no—
471#2361—8316no—
472C2×#390—831no—
473C2×#389—831no—
474C2×#388—831no—
475C2×#388D8311yescharacteristic, complemented
476C2×#386—831no—
477C2×#386—831no—
478C2×#385—831no—
479C2×#385—831no—
480C2×C4×C4⋊C4—831no—
481C2×C4×C22⋊C4—831no—
482C83C2×#236111yescharacteristic, complemented, Sylow
483C23×D4—831no—
484C23×D4—831no—
485C23×D4—831no—
486C24×C4—831no—
487C24×C4—831no—
488C24×C4—831no—
489C24×C4—831no—
490C24×C4—831no—
491C2×#121—8316no—
492C2×#121—838no—
493C2×C4×D4—838no—
494C2×C4×D4—838no—
495C2×C4×D4—838no—
496C2×C4×D4—1668no—
497C2×C4×D4—1668no—
498C2×C4×D4—1668no—
499C22×C4⋊C4—831no—
500C22×C4⋊C4—831no—
501C22×C4⋊C4—831no—
502C22×C4⋊C4—831no—
503C22×C4⋊C4—831no—
504C22×C4⋊C4—831no—
505C22×C4⋊C4—838no—
506C22×C4⋊C4—1668no—
507C22×C4⋊C4C2×D8311yescharacteristic
508C22×C22⋊C4—831no—
509C22×C22⋊C4—831no—
510C22×C22⋊C4—831no—
511C22×C22⋊C4—831no—
512C22×C22⋊C4—831no—
513C22×C22⋊C4—831no—
514C22×C22⋊C4—831no—
515C22×C22⋊C4C2×D8311yescharacteristic
516C22×C22⋊C4C2×D8311yescharacteristic
517C22×C22⋊C4C2×D8311yescharacteristic
518C22×C42—831no—
519C22×C42—831no—
520C22×C42—831no—
521C22×C42C2×D8311yescharacteristic
522#390—838no—
523#389—838no—
524#388—838no—
525#388C2×D8318yescomplemented
526#386—838no—
527#386—838no—
528#385—838no—
529#385—838no—
530C4×C4⋊C4—838no—
531C4×C22⋊C4—838no—
532C2×#95—831no—
533C2×#95—831no—
534C2×#95—831no—
535C2×#95—831no—
536C2×#95C2×D8311yescharacteristic
537C2×#95C2×D8311yescharacteristic
538C25—831no—
539C25—831no—
540C25C22×D8311yescharacteristic
541C22×D4—838no—
542C22×D4—838no—
543C22×D4—834no—
544C22×D4—834no—
545C22×D4—838no—
546C22×D4—834no—
547C22×D4—1664no—
548C22×D4—1664no—
549C22×D4—1664no—
550C22×D4—1664no—
551C22×D4—1664no—
552C22×D4—1664no—
553C23×C4—3322no—
554C23×C4—3322no—
555C23×C4—3322no—
556C23×C4—3322no—
557C23×C4—834no—
558C23×C4—834no—
559C23×C4—834no—
560C23×C4—834no—
561C23×C4—831no—
562C23×C4—831no—
563C23×C4—831no—
564C23×C4—831no—
565C23×C4—838no—
566C23×C4—834no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—1664no—
570C23×C4—1664no—
571C23×C4—1664no—
572C23×C4—1664no—
573C23×C4—1664no—
574C23×C4—1664no—
575C23×C4—1664no—
576C23×C4—1664no—
577C23×C4—1664no—
578C23×C4—1664no—
579C23×C4C22×D8311yescharacteristic
580C23×C4C22×D8311yescharacteristic
581C23×C4C22×D8311yescharacteristic
582C23×C4C22×D8311yescharacteristic
583C23×C4C22×D8311yescharacteristic
584C23×C4C22×D8311yescharacteristic
585#121—8364no—
586C4×D4—16632no—
587C4×D4—16632no—
588C4×D4—16632no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—838no—
591C2×C4⋊C4—838no—
592C2×C4⋊C4—834no—
593C2×C4⋊C4—834no—
594C2×C4⋊C4—834no—
595C2×C4⋊C4—834no—
596C2×C4⋊C4—834no—
597C2×C4⋊C4—834no—
598C2×C4⋊C4—16632no—
599C2×C4⋊C4—1664no—
600C2×C4⋊C4—1664no—
601C2×C4⋊C4—1664no—
602C2×C4⋊C4—1664no—
603C2×C4⋊C4C22×D8314yes—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—3322no—
607C2×C22⋊C4—3322no—
608C2×C22⋊C4—834no—
609C2×C22⋊C4—834no—
610C2×C22⋊C4—838no—
611C2×C22⋊C4—838no—
612C2×C22⋊C4—834no—
613C2×C22⋊C4—834no—
614C2×C22⋊C4—834no—
615C2×C22⋊C4—834no—
616C2×C22⋊C4—834no—
617C2×C22⋊C4—1664no—
618C2×C22⋊C4—1664no—
619C2×C22⋊C4—1664no—
620C2×C22⋊C4C4×D8318yescomplemented
621C2×C22⋊C4C22×D8314yes—
622C2×C22⋊C4C22×D8314yes—
623C2×C22⋊C4C22×D8314yes—
624C2×C42—24no—
625C2×C42—834no—
626C2×C42—834no—
627C2×C42—834no—
628C2×C42—1664no—
629C2×C42—1664no—
630C2×C42—1664no—
631C2×C42C22×D8314yes—
632#95—834no—
633#95—834no—
634#95—834no—
635#95—834no—
636#95C22×D8314yes—
637#95C22×D8314yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—834no—
645C24—834no—
646C24—834no—
647C24—832no—
648C24—834no—
649C24—832no—
650C24—1662no—
651C24—1662no—
652C24—1662no—
653C24—1662no—
654C24—1662no—
655C24—1662no—
656C24—1662no—
657C24—1662no—
658C24—1662no—
659C24—1662no—
660C24C2×C4×D8314yes—
661C24C23×D8312yes—
662C24C23×D8311yescharacteristic
663C2×D4—8316no—
664C2×D4—8316no—
665C2×D4—8316no—
666C2×D4—1668no—
667C2×D4—16632no—
668C2×D4—1668no—
669C2×D4—1668no—
670C2×D4—16632no—
671C2×D4—1668no—
672C2×D4—1668no—
673C2×D4—16632no—
674C2×D4—1668no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—33216no—
690C22×C4—33216no—
691C22×C4—3324no—
692C22×C4—3324no—
693C22×C4—3324no—
694C22×C4—33216no—
695C22×C4—3324no—
696C22×C4—33216no—
697C22×C4—834no—
698C22×C4—834no—
699C22×C4—834no—
700C22×C4—832no—
701C22×C4—834no—
702C22×C4—834no—
703C22×C4—834no—
704C22×C4—832no—
705C22×C4—832no—
706C22×C4—832no—
707C22×C4—8316no—
708C22×C4—832no—
709C22×C4—832no—
710C22×C4—1668no—
711C22×C4—1668no—
712C22×C4—1668no—
713C22×C4—1668no—
714C22×C4—1668no—
715C22×C4—16632no—
716C22×C4—1668no—
717C22×C4—1668no—
718C22×C4—1668no—
719C22×C4—1662no—
720C22×C4—1662no—
721C22×C4—1662no—
722C22×C4—1662no—
723C22×C4—1662no—
724C22×C4—1662no—
725C22×C4—1668no—
726C22×C4—1668no—
727C22×C4—1662no—
728C22×C4—1662no—
729C22×C4—1662no—
730C22×C4—1662no—
731C22×C4—1662no—
732C22×C4—1662no—
733C22×C4C2×C4×D8314yes—
734C22×C4C2×C4×D8314yes—
735C22×C4D4×D8314yes—
736C22×C4D4×D8314yes—
737C22×C4C23×D8312yes—
738C22×C4C23×D8312yes—
739C22×C4C23×D8312yes—
740C22×C4C23×D8312yes—
741C22×C4C23×D8312yes—
742C22×C4C23×D8312yes—
743C4⋊C4—28no—
744C4⋊C4—8316no—
745C4⋊C4—8316no—
746C4⋊C4—1668no—
747C4⋊C4—1668no—
748C4⋊C4—1668no—
749C4⋊C4—1668no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—3324no—
753C22⋊C4—3324no—
754C22⋊C4—8316no—
755C22⋊C4—8316no—
756C22⋊C4—1668no—
757C22⋊C4—1668no—
758C22⋊C4—1668no—
759C22⋊C4C2×C4×D83116yescomplemented
760C42—28no—
761C42—1668no—
762C42—1668no—
763C42—1668no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—3324no—
778C23—3324no—
779C23—3324no—
780C23—3324no—
781C23—8316no—
782C23—834no—
783C23—834no—
784C23—834no—
785C23—834no—
786C23—1668no—
787C23—1668no—
788C23—1668no—
789C23—1662no—
790C23—1662no—
791C23—1662no—
792C23—1662no—
793C23—1662no—
794C23—1662no—
795C23—1668no—
796C23—1668no—
797C23—1668no—
798C23—1668no—
799C23—1668no—
800C23—1668no—
801C23—1662no—
802C23—1662no—
803C23—1662no—
804C23—1662no—
805C23C22×C4×D8314yes—
806C23C22×C4×D8312yes—
807C23C2×D4×D8312yes—
808C23C2×D4×D8312yes—
809C23#41×D8312yes—
810C23#41×D8312yes—
811C23#1458183812yes—
812C23#1458183912yes—
813C23C24×D8311yescharacteristic
814D4—16632no—
815D4—16632no—
816D4—16632no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—33216no—
838C2×C4—33216no—
839C2×C4—33216no—
840C2×C4—3324no—
841C2×C4—3324no—
842C2×C4—33216no—
843C2×C4—8316no—
844C2×C4—834no—
845C2×C4—834no—
846C2×C4—834no—
847C2×C4—834no—
848C2×C4—834no—
849C2×C4—834no—
850C2×C4—16632no—
851C2×C4—1662no—
852C2×C4—1662no—
853C2×C4—1662no—
854C2×C4—1662no—
855C2×C4—1662no—
856C2×C4—1662no—
857C2×C4—1668no—
858C2×C4—1668no—
859C2×C4—1668no—
860C2×C4—1662no—
861C2×C4—1662no—
862C2×C4—1662no—
863C2×C4—1662no—
864C2×C4—1662no—
865C2×C4—1662no—
866C2×C4C22×C4×D8314yes—
867C2×C4C22×C4×D8314yes—
868C2×C4C2×D4×D8314yes—
869C2×C4C2×D4×D8314yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—3322no—
879C22—3322no—
880C22—3322no—
881C22—33216no—
882C22—3322no—
883C22—838no—
884C22—1664no—
885C22—1664no—
886C22—1664no—
887C22—1664no—
888C22—1664no—
889C22—1664no—
890C22—1664no—
891C22—1664no—
892C22—16632no—
893C22—1664no—
894C22C4×D4×D8314yes—
895C22C4×D4×D8314yes—
896C22#1912818114yes—
897C22#1912833514yes—
898C22#1912834914yes—
899C22#1912835914yes—
900C22#1912840214yes—
901C22C23×C4×D8311yescharacteristic
902C22C22×D4×D8311yescharacteristic
903C22C22×D4×D8311yescharacteristic
904C22C2×#41×D8311yescharacteristic
905C22C2×#41×D8311yescharacteristic
906C22C2×#1458183811yescharacteristic
907C22C2×#1458183911yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—3322no—
915C4—3322no—
916C4—838no—
917C4—1664no—
918C4—1664no—
919C4—1664no—
920C2—44no—
921C2—3324no—
922C2—1668no—
923C2#2491047618yesdirect product factor
924C2C2×C4×D4×D8311yescharacteristic
925C2C2×C4×D4×D8311yescharacteristic
926C2C2×#1912818111yescharacteristic
927C2C2×#1912833511yescharacteristic
928C2C2×#1912834911yescharacteristic
929C2C2×#1912835911yescharacteristic
930C2C2×#1912840211yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC22×#14581765C2
cosocleC23×C83C25
hypercenterC2×#388D83
hypocenterC83C2×#2361
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D332C2semidirect
3. C22×(C22⋊D83)⋊C4C2semidirect
4. C22×(C22⋊D83)⋊C4C2semidirect
5. C22×C4⋊C4×D83C2semidirect
6. #24910476C2direct (N × H)
7. C2×#19127601C2semidirect
8. C2×#19127598C2semidirect
9. C2×#19127593C2semidirect
10. C2×#19127579C2semidirect
11. C2×#19127577C2semidirect
12. C2×#19127576C2semidirect
13. C2×#19127572C2semidirect
14. C2×C4×Dic83⋊C4C2semidirect
15. C2×#19127548C2semidirect
16. C2×#388×C83C2semidirect
25. C2×#14581765C4semidirect
28. C2×C4×D332C22semidirect
31. C2×(C22⋊D83)⋊C4C22semidirect
32. C2×(C22⋊D83)⋊C4C22semidirect
40. C2×C4⋊C4×D83C22semidirect
51. #19127601C22semidirect
52. #19127598C22semidirect
53. #19127593C22semidirect
54. #19127579C22semidirect
55. #19127577C22semidirect
56. #19127576C22semidirect
57. #19127572C22semidirect
58. C4×Dic83⋊C4C22semidirect
59. #19127548C22semidirect
69. #388×C83C22semidirect
76. C22×D332C2×C4semidirect
82. C22×C22⋊D83C2×C4semidirect
83. C22×C22⋊D83C2×C4semidirect
107. C22×C4×D83C2×C4semidirect
112. #14581765C2×C4semidirect
122. C2×Dic83⋊C4C2×C4semidirect
123. C2×Dic83⋊C4D4semidirect
135. C2×(C2×D83)⋊C4C2×C4semidirect
136. C2×(C2×D83)⋊C4D4semidirect
164. C2×C22⋊C4×C83C2×C4semidirect
191. C2×D332C22×C4semidirect
198. C2×C22⋊D83C22×C4semidirect
199. C2×C22⋊D83C22×C4semidirect
243. C2×C4×D83C22×C4semidirect
248. Dic83⋊C4C22×C4semidirect
249. Dic83⋊C4C2×D4semidirect
255. (C2×D83)⋊C4C22×C4semidirect
256. (C2×D83)⋊C4C2×D4semidirect
296. C22⋊C4×C83C22×C4semidirect
343. C22×D83C4×D4semidirect
392. C2×Dic83C4×D4semidirect
441. C2×D83C2×C4×D4semidirect
453. Dic83C2×C4×D4semidirect
456. C2×C83#2361semidirect
475. C2×#388D83semidirect
482. C83C2×#2361semidirect
525. #388C2×D83semidirect
620. C2×C22⋊C4C4×D83semidirect
759. C22⋊C4C2×C4×D83semidirect
923. C2#24910476direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817652
C22×C4×D3322
C22×(C22⋊D83)⋊C42
C22×C4⋊C4×D832
#249104762
C2×#191276012
C2×#191275982
C2×#191275932
C2×#191275792
C2×#191275772
C2×#191275762
C2×#191275722
C2×C4×Dic83⋊C42
C2×#191275482
C2×#388×C832
C2×#236183