Finite Group Databasebeta

← #35416747

Subgroups — #35416747

Order 21248.

1010 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D83C211yesmaximal, characteristic, complemented
2C2×#19127753C211yesmaximal, characteristic, complemented
3C4×#14581765C211yesmaximal, characteristic
4#24908256C211yesmaximal, characteristic, complemented
5#24908255C211yesmaximal, characteristic, complemented
6#24908255C211yesmaximal, characteristic, complemented
7#24908178C211yesmaximal, characteristic, complemented
8#24908071C211yesmaximal, characteristic, complemented
9#24908070C211yesmaximal, characteristic, complemented
10#24907755C211yesmaximal, characteristic, complemented
11#24907754C211yesmaximal, characteristic, complemented
12#24907639C211yesmaximal, characteristic, complemented
13#24907442C211yesmaximal, characteristic, complemented
14#24907324C211yesmaximal, characteristic, complemented
15C83×#1850C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C2×#14581765C411yescharacteristic
18C2×C4×D332C2211yescharacteristic
19C2×C4×C22⋊D83C2211yescharacteristic
20C2×C4×C22⋊D83C2211yescharacteristic
21C2×C42×D83C2211yescharacteristic
22C8×C22⋊D83—24no—
23#19127753—24no—
24C2×C4⋊(C83⋊C8)C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×C22⋊(C83⋊C8)C2211yescharacteristic
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36C2×(C2×D83)⋊C8C2211yescharacteristic
37C2×C4×C83⋊C8C2211yescharacteristic
38C2×C8×Dic83C2211yescharacteristic
39C2×C8×Dic83C2211yescharacteristic
40C2×C8×Dic83C2211yescharacteristic
41#19127601C411yescharacteristic
42#19127598C411yescharacteristic
43#19127594C411yescharacteristic
44#19127590C411yescharacteristic
45#19127579C411yescharacteristic
46#19127577C411yescharacteristic
47#19127560C411yescharacteristic
48C4×Dic83⋊C4C2211yescharacteristic
49C4×(C2×D83)⋊C4C2211yescharacteristic
50#19127456C2211yescharacteristic
51#19127456C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C23×C8×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C4×C22⋊C4×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×D332C2×C411yescharacteristic
62C22×C22⋊D83C2×C411yescharacteristic
63C22×C22⋊D83C2×C411yescharacteristic
64C22×C4×D83C2×C411yescharacteristic
65C22×C4×D83C2×C411yescharacteristic
66C22×C4×D83C2311yescharacteristic
67C22×C4×D83C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C2×C8×D83—22no—
73C2×C8×D83—41no—
74C2×C8×D83—41no—
75#14581765C818yescomplemented
76C4×D332—41no—
77C4×D332—41no—
78C4×C22⋊D83—22no—
79C4×C22⋊D83—22no—
80C4×C22⋊D83—41no—
81C4×C22⋊D83—41no—
82C2×C4⋊Dic83C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×Dic83⋊C4C2×C411yescharacteristic
85C2×Dic83⋊C4C2×C411yescharacteristic
86C2×Dic83⋊C4C2×C411yescharacteristic
87C2×C22⋊Dic83C2×C411yescharacteristic
88C2×C22⋊Dic83C2×C411yescharacteristic
89C2×(C2×D83)⋊C4C2×C411yescharacteristic
90C2×(C2×D83)⋊C4C2×C411yescharacteristic
91C2×(C2×D83)⋊C4C2×C411yescharacteristic
92C2×(C2×D83)⋊C4C2×C411yescharacteristic
93C2×(C2×D83)⋊C4C2×C411yescharacteristic
94C2×(C2×D83)⋊C4C2×C411yescharacteristic
95C2×C4×Dic83C2×C411yescharacteristic
96C2×C4×Dic83C2×C411yescharacteristic
97C2×C4×Dic83C2311yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99C42×D83—22no—
100C42×D83—22no—
101C4⋊(C83⋊C8)—22no—
102Dic83⋊C8—22no—
103Dic83⋊C8—22no—
104Dic83⋊C8—41no—
105C22⋊(C83⋊C8)—22no—
106C22⋊(C83⋊C8)—41no—
107(C2×D83)⋊C8—22no—
108(C2×D83)⋊C8—22no—
109(C2×D83)⋊C8—22no—
110(C2×D83)⋊C8—41no—
111(C2×D83)⋊C8—41no—
112(C2×D83)⋊C8—41no—
113(C2×D83)⋊C8—41no—
114C4×C83⋊C8—41no—
115C8×Dic83—22no—
116C8×Dic83—41no—
117C8×Dic83D414yescomplemented
118C83⋊#95C2×C411yescharacteristic
119C83⋊#95C2×C411yescharacteristic
120C83⋊#95C2×C411yescharacteristic
121C83⋊#95C2×C411yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C22×C8×C83—22no—
124C22×C8×C83—41no—
125C22×C8×C83—41no—
126C22×C8×C83C2311yescharacteristic
127C22×C8×C83C2311yescharacteristic
128C22×C8×C83C2311yescharacteristic
129C22×C8×C83C2311yescharacteristic
130C2×C22⋊C4×C83C2×C411yescharacteristic
131C2×C22⋊C4×C83C2×C411yescharacteristic
132C2×C42×C83C2311yescharacteristic
133C2×C42×C83C2311yescharacteristic
134C4⋊C8×C83—22no—
135C4⋊C8×C83—41no—
136C22⋊C8×C83—41no—
137#95×C83C2×C411yescharacteristic
138#95×C83C2×C411yescharacteristic
139C23×D83C22×C411yescharacteristic
140C23×D83C22×C411yescharacteristic
141C2×D332—41no—
142C2×D332—41no—
143C2×D332C2×C814yescomplemented
144C2×C22⋊D83—22no—
145C2×C22⋊D83—22no—
146C2×C22⋊D83—41no—
147C2×C22⋊D83—41no—
148C2×C22⋊D83C2×C814yes—
149C2×C22⋊D83C2×C814yescomplemented
150C22×Dic83C22×C411yescharacteristic
151C22×Dic83C22×C411yescharacteristic
152C22×Dic83C22×C411yescharacteristic
153C22×Dic83C22×C411yescharacteristic
154C22×Dic83C22×C411yescharacteristic
155C22×Dic83C22×C411yescharacteristic
156C2×C4×D83—22no—
157C2×C4×D83—22no—
158C2×C4×D83—21no—
159C2×C4×D83—21no—
160C2×C4×D83—21no—
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164C2×C4×D83—21no—
165C2×C4×D83—21no—
166C2×C4×D83—21no—
167C2×C4×D83—21no—
168C2×C4×D83—21no—
169C2×C4×D83—21no—
170C2×C4×D83—22no—
171C2×C4×D83—41no—
172C2×C4×D83—41no—
173C2×C4×D83C2×C814yescomplemented
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C2×C83⋊C8—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—21no—
185C2×C83⋊C8C2×D412yes—
186C8×D83—44no—
187C4⋊Dic83—41no—
188Dic83⋊C4—22no—
189Dic83⋊C4—22no—
190Dic83⋊C4—41no—
191Dic83⋊C4C2×C814yescomplemented
192C22⋊Dic83—22no—
193C22⋊Dic83—41no—
194(C2×D83)⋊C4—22no—
195(C2×D83)⋊C4—41no—
196(C2×D83)⋊C4—41no—
197(C2×D83)⋊C4—41no—
198(C2×D83)⋊C4—41no—
199(C2×D83)⋊C4C2×C814yescomplemented
200C4×Dic83—21no—
201C4×Dic83—21no—
202C4×Dic83—22no—
203C4×Dic83—22no—
204C4×Dic83C2×D412yes—
205C4×Dic83#4112yes—
206C24×C83C22×C411yescharacteristic
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83C22×C411yescharacteristic
214C22×C4×C83C22×C411yescharacteristic
215C22×C4×C83C22×C411yescharacteristic
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C2411yescharacteristic
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—44no—
231C2×C8×C83C2×D412yes—
232C22⋊C4×C83—41no—
233C22⋊C4×C83C2×C814yescomplemented
234C42×C83—21no—
235C42×C83—21no—
236C42×C83—21no—
237C42×C83—21no—
238C23×C83—21no—
239C23×C83—21no—
240C23×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83C22×C812yes—
245C23×C83C23×C411yescharacteristic
246C22×D83—21no—
247C22×D83—21no—
248C22×D83—21no—
249C22×D83—21no—
250C22×D83—21no—
251C22×D83—21no—
252C22×D83—21no—
253C22×D83—21no—
254C22×D83—21no—
255C22×D83—21no—
256C22×D83—21no—
257C22×D83—21no—
258C22×D83C22×C812yes—
259C22×D83C22×C812yes—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83C22×C812yes—
278C2×C4×C83C22×C812yes—
279C2×C4×C83C22×D411yescharacteristic
280C2×C4×C83C2×#4111yescharacteristic
281C2×C4×C83H(5,𝔽2)11yescharacteristic
282C2×C4×C83H(5,𝔽2)11yescharacteristic
283C2×C4×C83H(5,𝔽2)11yescharacteristic
284C2×C4×C832−1+411yescharacteristic
285C22⋊D83—28no—
286C22⋊D83—44no—
287C2×Dic83—21no—
288C2×Dic83—21no—
289C2×Dic83—21no—
290C2×Dic83—21no—
291C2×Dic83—21no—
292C2×Dic83—21no—
293C2×Dic83—21no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83C4×D412yes—
301C2×Dic83C4×D412yes—
302C2×Dic83C22×C812yes—
303C2×Dic83C22×C812yes—
304C2×Dic83#13112yes—
305D332—44no—
306C4×D83—28no—
307C4×D83—44no—
308C4×D83—41no—
309C4×D83—41no—
310C4×D83—41no—
311C4×D83—41no—
312C4×D83—41no—
313C4×D83—41no—
314C4×D83—41no—
315C4×D83—41no—
316C8×C83—22no—
317C8×C83—41no—
318C8×C83—41no—
319C8×C83—41no—
320C83⋊C8—22no—
321C83⋊C8—41no—
322C83⋊C8—41no—
323C83⋊C8—41no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—41no—
328C22×C83—41no—
329C22×C83—41no—
330C22×C83—41no—
331C22×C83C2×C4×D411yescharacteristic
332C22×C83#51811yescharacteristic
333C22×C83#52011yescharacteristic
334C22×C83C23×C811yescharacteristic
335C22×C83C2×#13111yescharacteristic
336C22×C83#56811yescharacteristic
337C22×C83#56811yescharacteristic
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—22no—
342C2×D83—22no—
343C2×D83—22no—
344C2×D83—41no—
345C2×D83—41no—
346C2×D83—41no—
347C2×D83—41no—
348C2×D83—41no—
349C2×D83—41no—
350C2×D83—41no—
351C2×D83—41no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—41no—
355C4×C83—41no—
356C4×C83—41no—
357C4×C83#53511yescharacteristic
358C4×C83#53711yescharacteristic
359C4×C83#54011yescharacteristic
360C4×C83#54211yescharacteristic
361Dic83—22no—
362Dic83—22no—
363Dic83—41no—
364Dic83—41no—
365Dic83—41no—
366Dic83C8×D414yes—
367#22133—831nomaximal, Sylow
368C2×C83—42no—
369C2×C83#232411yescharacteristic
370C2×C83C2×C8×D411yescharacteristic
371C2×C83#293011yescharacteristic
372C2×C83#297211yescharacteristic
373C2×C83#298111yescharacteristic
374C2×C83#298811yescharacteristic
375C2×C83#299311yescharacteristic
376D83—42no—
377D83—42no—
378C2×C8×D4—831no—
379C2×#431—831no—
380C4×#121—831no—
381#1954—831no—
382#1954—831no—
383#1954—831no—
384#1939—831no—
385#1923—831no—
386#1923—831no—
387#1869—831no—
388#1869—831no—
389#1850—831no—
390#1850D8311yescharacteristic, complemented
391#1797—831no—
392C8×C4⋊C4—831no—
393C83#2213311yescharacteristic, complemented, Sylow
394C23×C8—831no—
395C23×C8C2×D8311yescharacteristic
396C2×#121—831no—
397C2×C4×D4—831no—
398C2×C4×D4—831no—
399C2×C4×D4—831no—
400C22×C42—831no—
401C8×D4—1664no—
402#431—1664no—
403C2×C4⋊C8—831no—
404C2×C4⋊C8—831no—
405C2×C4⋊C8—831no—
406C2×C4⋊C8—831no—
407C2×C4⋊C8C2×D8311yescharacteristic
408C2×C4⋊C8C2×D8311yescharacteristic
409C2×C22⋊C8—831no—
410C2×C22⋊C8—831no—
411C2×C22⋊C8—831no—
412C2×C22⋊C8—831no—
413C2×C22⋊C8—831no—
414C2×C22⋊C8—831no—
415C2×C22⋊C8—831no—
416C2×C22⋊C8—831no—
417C2×C22⋊C8—831no—
418C2×C22⋊C8C2×D8311yescharacteristic
419C2×C4×C8—831no—
420C2×C4×C8—831no—
421C2×C4×C8—831no—
422C2×C4×C8—831no—
423#390—831no—
424#389—831no—
425#388—831no—
426#388—831no—
427#386—831no—
428#386—831no—
429#380—831no—
430C4×C4⋊C4—831no—
431C4×C22⋊C4—831no—
432C4×C22⋊C4C2×D8311yescharacteristic
433#336—831no—
434#336—831no—
435#336—831no—
436#336—831no—
437#336C2×D8311yescharacteristic
438#336C2×D8311yescharacteristic
439C22×D4—831no—
440C22×D4—831no—
441C22×D4—831no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C23×C4—831no—
446C23×C4C22×D8311yescharacteristic
447C22×C8—22no—
448C22×C8—41no—
449C22×C8—41no—
450C22×C8—3321no—
451C22×C8—3321no—
452C22×C8—831no—
453C22×C8—831no—
454C22×C8—831no—
455C22×C8—831no—
456C22×C8—1662no—
457C22×C8C22×D8311yescharacteristic
458C22×C8C22×D8311yescharacteristic
459C22×C8C22×D8311yescharacteristic
460C22×C8C22×D8311yescharacteristic
461#121—838no—
462C4×D4—3321no—
463C4×D4—3321no—
464C4×D4—3321no—
465C4×D4—3321no—
466C4×D4—1662no—
467C4×D4—1662no—
468C2×C4⋊C4—831no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—831no—
471C2×C4⋊C4—831no—
472C2×C4⋊C4—831no—
473C2×C22⋊C4—831no—
474C2×C22⋊C4—831no—
475C2×C22⋊C4—831no—
476C2×C22⋊C4—831no—
477C2×C22⋊C4—831no—
478C2×C22⋊C4—831no—
479C2×C22⋊C4—831no—
480C2×C22⋊C4—831no—
481C2×C22⋊C4C4×D8311yescharacteristic
482C2×C22⋊C4C4×D8311yescharacteristic
483C2×C42—831no—
484C2×C42—831no—
485C2×C42—831no—
486C2×C42—831no—
487C2×C42—1662no—
488C2×C42—1662no—
489C2×C42C22×D8311yescharacteristic
490C2×C42C22×D8311yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—41no—
493C4⋊C8—3321no—
494C4⋊C8—1662no—
495C4⋊C8—1662no—
496C4⋊C8—1662no—
497C22⋊C8—41no—
498C22⋊C8—3321no—
499C22⋊C8—3321no—
500C22⋊C8—3321no—
501C22⋊C8—3321no—
502C22⋊C8—3321no—
503C22⋊C8—1662no—
504C22⋊C8—1662no—
505C22⋊C8—1662no—
506C22⋊C8—1662no—
507C4×C8—3321no—
508C4×C8—3321no—
509C4×C8—834no—
510C4×C8—1662no—
511#95—831no—
512#95—831no—
513#95—831no—
514#95—831no—
515#95C4×D8311yescharacteristic
516#95C4×D8311yescharacteristic
517C24—831no—
518C24—831no—
519C24C2×C4×D8311yescharacteristic
520C2×D4—3321no—
521C2×D4—3321no—
522C2×D4—3321no—
523C2×D4—3321no—
524C2×D4—834no—
525C2×D4—834no—
526C2×D4—834no—
527C2×D4—1662no—
528C2×D4—1662no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—3321no—
536C22×C4—3321no—
537C22×C4—831no—
538C22×C4—831no—
539C22×C4—831no—
540C22×C4—834no—
541C22×C4—831no—
542C22×C4—831no—
543C22×C4—831no—
544C22×C4—1662no—
545C22×C4—1662no—
546C22×C4—1662no—
547C22×C4—1661no—
548C22×C4—1661no—
549C22×C4—1661no—
550C22×C4—1661no—
551C22×C4—1661no—
552C22×C4—1661no—
553C22×C4—1661no—
554C22×C4—1661no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1661no—
558C22×C4—1661no—
559C22×C4C2×C4×D8311yescharacteristic
560C22×C4C2×C4×D8311yescharacteristic
561C22×C4C2×C4×D8311yescharacteristic
562C22×C4C2×C4×D8311yescharacteristic
563C22×C4C2×C4×D8311yescharacteristic
564C22×C4C23×D8311yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8—3324no—
578C2×C8—832no—
579C2×C8—1661no—
580C2×C8—1661no—
581C2×C8—1661no—
582C2×C8—1661no—
583C2×C8—1661no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8—1661no—
590C2×C8D4×D8312yes—
591C4⋊C4—3321no—
592C4⋊C4—3321no—
593C4⋊C4—834no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C22⋊C4—41no—
597C22⋊C4—3321no—
598C22⋊C4—3321no—
599C22⋊C4—3321no—
600C22⋊C4—3321no—
601C22⋊C4—3321no—
602C22⋊C4—834no—
603C22⋊C4—1662no—
604C22⋊C4—1662no—
605C22⋊C4C8×D8314yescomplemented
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—832no—
611C42—832no—
612C42—1662no—
613C42—1662no—
614C42—1661no—
615C42—1661no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—832no—
623C23—832no—
624C23—1661no—
625C23—1661no—
626C23—1661no—
627C23—1661no—
628C23—1661no—
629C23—1661no—
630C23—1661no—
631C23—1661no—
632C23—1661no—
633C23—1661no—
634C23—1661no—
635C23—1661no—
636C23C2×C8×D8312yes—
637C23C22×C4×D8311yescharacteristic
638D4—3324no—
639D4—3324no—
640D4—1668no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—3324no—
659C2×C4—3321no—
660C2×C4—3321no—
661C2×C4—3321no—
662C2×C4—3321no—
663C2×C4—3321no—
664C2×C4—3321no—
665C2×C4—3321no—
666C2×C4—3321no—
667C2×C4—832no—
668C2×C4—832no—
669C2×C4—832no—
670C2×C4—832no—
671C2×C4—832no—
672C2×C4—1668no—
673C2×C4—1661no—
674C2×C4—1661no—
675C2×C4—1661no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1661no—
679C2×C4—1661no—
680C2×C4—1661no—
681C2×C4—1661no—
682C2×C4—1661no—
683C2×C4—1661no—
684C2×C4—1661no—
685C2×C4—1661no—
686C2×C4C2×C8×D8312yes—
687C2×C4C2×C8×D8312yes—
688C2×C4C2×D4×D8311yescharacteristic
689C2×C4#41×D8311yescharacteristic
690C2×C4#1458183711yescharacteristic
691C2×C4#1458183711yescharacteristic
692C2×C4#1458183811yescharacteristic
693C2×C4#1458184011yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—3321no—
699C8—3321no—
700C8—3321no—
701C8—1662no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—3321no—
710C22—3321no—
711C22—3321no—
712C22—3321no—
713C22—3321no—
714C22—3321no—
715C22—3321no—
716C22—3321no—
717C22—1662no—
718C22—1662no—
719C22—1662no—
720C22—1662no—
721C22—1662no—
722C22—1662no—
723C22C4×D4×D8311yescharacteristic
724C22#1912817311yescharacteristic
725C22#1912818211yescharacteristic
726C22C22×C8×D8311yescharacteristic
727C22#131×D8311yescharacteristic
728C22#1912846611yescharacteristic
729C22#1912846711yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—3321no—
736C4—3321no—
737C4—3321no—
738C4—834no—
739C4—1662no—
740C4—1662no—
741C4#1912826611yescharacteristic
742C4#1912828111yescharacteristic
743C4#1912830311yescharacteristic
744C4#1912832111yescharacteristic
745C2—42no—
746C2—3322no—
747C2—3322no—
748C2#2491015511yescharacteristic
749C2C8×D4×D8311yescharacteristic
750C2#2491616111yescharacteristic
751C2#2491648411yescharacteristic
752C2#2491653511yescharacteristic
753C2#2491657211yescharacteristic
754C2#2491661011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C23×C8
FittingC83×#1850C2
socleC23×C83C23×C4
prime radicalC2×#14581765C4
cosocleC22×C4×C83C24
hypercenter#1850D83
hypocenterC83#22133
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×C8×C22⋊D83C2semidirect
2. C2×#19127753C2semidirect
4. #24908256C2semidirect
5. #24908255C2semidirect
6. #24908255C2semidirect
7. #24908178C2semidirect
8. #24908071C2semidirect
9. #24908070C2semidirect
10. #24907755C2semidirect
11. #24907754C2semidirect
12. #24907639C2semidirect
13. #24907442C2semidirect
14. #24907324C2semidirect
15. C83×#1850C2semidirect
75. #14581765C8semidirect
117. C8×Dic83D4semidirect
143. C2×D332C2×C8semidirect
149. C2×C22⋊D83C2×C8semidirect
173. C2×C4×D83C2×C8semidirect
191. Dic83⋊C4C2×C8semidirect
199. (C2×D83)⋊C4C2×C8semidirect
233. C22⋊C4×C83C2×C8semidirect
390. #1850D83semidirect
393. C83#22133semidirect
605. C22⋊C4C8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D832
C2×#191277532
C4×#145817652
#249082562
#249082552
#249081782
#249080712
#249080702
#249077552
#249077542
#249076392
#249074422
#249073242
C83×#18502
#2213383