Finite Group Databasebeta

← #35425293

Subgroups — #35425293

Order 21248.

980 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic
2C2×#19127751C211yesmaximal, characteristic, complemented
3C4×#14581776C211yesmaximal, characteristic
4#24908181C211yesmaximal, characteristic, complemented
5#24908070C211yesmaximal, characteristic, complemented
6#24908069C211yesmaximal, characteristic, complemented
7#24908021C211yesmaximal, characteristic, complemented
8#24908021C211yesmaximal, characteristic, complemented
9#24907755C211yesmaximal, characteristic
10#24907643C211yesmaximal, characteristic, complemented
11#24907642C211yesmaximal, characteristic, complemented
12C8×C4⋊Dic83C211yesmaximal, characteristic, complemented
13C8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
14C2×#19127455C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C83C211yesmaximal, characteristic, complemented
16C23×C83⋊C8C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×#14581776C411yescharacteristic
19C2×C4×C22⋊D83C2211yescharacteristic
20C22×C4×Dic83C2211yescharacteristic
21(C22⋊D83)⋊C8—24no—
22#19127751—24no—
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×C4⋊(C83⋊C8)C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×C22⋊(C83⋊C8)C2211yescharacteristic
29C2×(C2×D83)⋊C8C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×C8×Dic83C2211yescharacteristic
33C2×C8×Dic83C2211yescharacteristic
34C2×C8×Dic83C2211yescharacteristic
35#19127593C411yescharacteristic
36#19127593C411yescharacteristic
37#19127586C411yescharacteristic
38#19127586C411yescharacteristic
39#19127578C411yescharacteristic
40#19127576C411yescharacteristic
41#19127562C411yescharacteristic
42C4×C4⋊Dic83C2211yescharacteristic
43C4×C4⋊Dic83C2211yescharacteristic
44C4×(C2×D83)⋊C4C2211yescharacteristic
45C4×(C2×D83)⋊C4C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C23×C8×C83C2211yescharacteristic
55C2×C22⋊C8×C83C2211yescharacteristic
56C2×C4×C8×C83C2211yescharacteristic
57C2×C4×C8×C83C2211yescharacteristic
58C4×C22⋊C4×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×C22⋊D83C2×C411yescharacteristic
62C23×Dic83C2×C411yescharacteristic
63C23×Dic83C2×C411yescharacteristic
64C22×C4×D83C2311yescharacteristic
65C22×C83⋊C8—22no—
66C22×C83⋊C8—22no—
67C22×C83⋊C8—41no—
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C2×C8×D83—22no—
73C2×C8×D83—22no—
74C2×C8×D83—41no—
75#14581776C818yescomplemented
76C4×C22⋊D83—22no—
77C4×C22⋊D83—22no—
78C2×C4⋊Dic83C2×C411yescharacteristic
79C2×C4⋊Dic83C2×C411yescharacteristic
80C2×C4⋊Dic83C2×C411yescharacteristic
81C2×C4⋊Dic83C2×C411yescharacteristic
82C2×Dic83⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic83C2×C411yescharacteristic
84C2×(C2×D83)⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×(C2×D83)⋊C4C2×C411yescharacteristic
87C2×(C2×D83)⋊C4C2×C411yescharacteristic
88C2×(C2×D83)⋊C4C2×C411yescharacteristic
89C2×C4×Dic83—22no—
90C2×C4×Dic83—22no—
91C2×C4×Dic83C2×C411yescharacteristic
92C2×C4×Dic83C2×C411yescharacteristic
93C2×C4×Dic83C2311yescharacteristic
94C2×C4×Dic83C2311yescharacteristic
95C2×C4×Dic83C2311yescharacteristic
96C4⋊(C83⋊C8)—22no—
97C4⋊(C83⋊C8)—41no—
98Dic83⋊C8—22no—
99Dic83⋊C8—22no—
100Dic83⋊C8—22no—
101C22⋊(C83⋊C8)—22no—
102(C2×D83)⋊C8—22no—
103(C2×D83)⋊C8—22no—
104(C2×D83)⋊C8—41no—
105C8×Dic83—22no—
106C8×Dic83—22no—
107C8×Dic83—22no—
108C83⋊#95C2×C411yescharacteristic
109C83⋊#95C2×C411yescharacteristic
110C83⋊#95C2×C411yescharacteristic
111C83⋊#95C2×C411yescharacteristic
112C83⋊#95C2×C411yescharacteristic
113C83⋊#95C2×C411yescharacteristic
114C83⋊#95C2×C411yescharacteristic
115C83⋊#95C2×C411yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C22×C8×C83—22no—
118C22×C8×C83—22no—
119C22×C8×C83—41no—
120C22×C8×C83C2311yescharacteristic
121C22×C8×C83C2311yescharacteristic
122C22×C8×C83C2311yescharacteristic
123C22×C8×C83C2311yescharacteristic
124C2×C22⋊C4×C83C2×C411yescharacteristic
125C2×C22⋊C4×C83C2×C411yescharacteristic
126C2×C42×C83C2311yescharacteristic
127C2×C42×C83C2311yescharacteristic
128C22⋊C8×C83D414yes—
129C4×C8×C83—22no—
130C4×C8×C83—41no—
131#95×C83C2×C411yescharacteristic
132#95×C83C2×C411yescharacteristic
133C23×D83C22×C411yescharacteristic
134C2×C22⋊D83—22no—
135C2×C22⋊D83—22no—
136C2×C22⋊D83C2×C814yes—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—41no—
142C22×Dic83C2×C814yescomplemented
143C22×Dic83C22×C411yescharacteristic
144C22×Dic83C22×C411yescharacteristic
145C22×Dic83C22×C411yescharacteristic
146C22×Dic83C22×C411yescharacteristic
147C22×Dic83C22×C411yescharacteristic
148C22×Dic83C22×C411yescharacteristic
149C22×Dic83C22×C411yescharacteristic
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—44no—
168C2×C83⋊C8#4112yes—
169C8×D83—44no—
170C4⋊Dic83—22no—
171C4⋊Dic83—41no—
172C4⋊Dic83C2×C814yescomplemented
173C4⋊Dic83C2×C814yescomplemented
174Dic83⋊C4—22no—
175C22⋊Dic83—22no—
176(C2×D83)⋊C4—22no—
177(C2×D83)⋊C4—22no—
178(C2×D83)⋊C4—41no—
179(C2×D83)⋊C4C2×C814yescomplemented
180(C2×D83)⋊C4C2×C814yescomplemented
181C4×Dic83—22no—
182C4×Dic83—22no—
183C4×Dic83—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C24×C83C22×C411yescharacteristic
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83C22×C411yescharacteristic
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C22×C411yescharacteristic
199C22×C4×C83C2×D412yes—
200C22×C4×C83#4112yes—
201C22×C4×C83C2411yescharacteristic
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—21no—
211C2×C8×C83—44no—
212C2×C8×C83C2×D412yes—
213C2×C8×C83C2×D412yes—
214C2×C8×C83#4112yes—
215C22⋊C4×C83—22no—
216C22⋊C4×C83C2×C814yescomplemented
217C42×C83—21no—
218C42×C83—21no—
219C42×C83—21no—
220C42×C83—21no—
221C23×C83—21no—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83C4×D412yes—
226C23×C83C22×C812yes—
227C23×C83#13112yes—
228C23×C83C23×C411yescharacteristic
229C22×D83—21no—
230C22×D83—21no—
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83—21no—
235C22×D83C22×C812yes—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—22no—
243C2×C4×C83—22no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83C4×D412yes—
253C2×C4×C83C22×C812yes—
254C2×C4×C83C22×C812yes—
255C2×C4×C83C22×D411yescharacteristic
256C2×C4×C83C2×#4111yescharacteristic
257C2×C4×C83C2×#4111yescharacteristic
258C2×C4×C83C2×#4111yescharacteristic
259C2×C4×C83H(5,𝔽2)11yescharacteristic
260C2×C4×C832−1+411yescharacteristic
261C22⋊D83—28no—
262C2×Dic83—21no—
263C2×Dic83—21no—
264C2×Dic83—21no—
265C2×Dic83—21no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—21no—
269C2×Dic83—21no—
270C2×Dic83—28no—
271C2×Dic83—21no—
272C2×Dic83—21no—
273C2×Dic83—21no—
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—21no—
277C2×Dic83—21no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—44no—
281C2×Dic83C22×C812yes—
282C2×Dic83C22×C812yes—
283C2×Dic83C22×C812yes—
284C2×Dic83#13112yes—
285C4×D83—41no—
286C4×D83—41no—
287C4×D83—41no—
288C4×D83—41no—
289C8×C83—22no—
290C8×C83—22no—
291C8×C83—22no—
292C8×C83—41no—
293C83⋊C8—22no—
294C83⋊C8—41no—
295C83⋊C8—41no—
296C83⋊C8—41no—
297C22×C83—22no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—22no—
301C22×C83—22no—
302C22×C83—22no—
303C22×C83C8×D414yes—
304C22×C83C2×C4×D411yescharacteristic
305C22×C83C4×#4111yescharacteristic
306C22×C83#52011yescharacteristic
307C22×C83C23×C811yescharacteristic
308C22×C83C2×#13111yescharacteristic
309C22×C83C2×#13111yescharacteristic
310C22×C83#56811yescharacteristic
311C2×D83—22no—
312C2×D83—22no—
313C2×D83—22no—
314C2×D83—41no—
315C2×D83—41no—
316C2×D83—41no—
317C2×D83—41no—
318C4×C83—22no—
319C4×C83—22no—
320C4×C83—22no—
321C4×C83—41no—
322C4×C83—41no—
323C4×C83#54611yescharacteristic
324C4×C83#54711yescharacteristic
325C4×C83#55111yescharacteristic
326C4×C83#55211yescharacteristic
327Dic83—22no—
328Dic83—22no—
329Dic83—22no—
330Dic83—22no—
331Dic83—41no—
332Dic83—41no—
333Dic83—41no—
334#22900—831nomaximal, Sylow
335C2×C83—24no—
336C2×C83#235911yescharacteristic
337C2×C83C2×C8×D411yescharacteristic
338C2×C83#293311yescharacteristic
339C2×C83C8×#4111yescharacteristic
340C2×C83#296811yescharacteristic
341C2×C83#298811yescharacteristic
342C2×C83#299411yescharacteristic
343D83—42no—
344C2×C8×D4—831no—
345C2×#431—831no—
346C4×#123—831no—
347#1939—831no—
348#1923—831no—
349#1923—831no—
350#1916—831no—
351#1916—831no—
352#1869—831no—
353#1850—831no—
354#1850—831no—
355C8×C4⋊C4—831no—
356C8×C22⋊C4—831no—
357C8×C22⋊C4D8311yescharacteristic, complemented
358C2×#336—831no—
359C83#2290011yescharacteristic, complemented, Sylow
360C23×C8—831no—
361C23×C8—831no—
362C23×C8C2×D8311yescharacteristic
363C2×#123—831no—
364C2×C4×D4—831no—
365C22×C42—831no—
366C8×D4—1664no—
367#431—1664no—
368C2×C4⋊C8—831no—
369C2×C4⋊C8—831no—
370C2×C4⋊C8—831no—
371C2×C4⋊C8—831no—
372C2×C4⋊C8—831no—
373C2×C22⋊C8—831no—
374C2×C22⋊C8—831no—
375C2×C22⋊C8—831no—
376C2×C22⋊C8—831no—
377C2×C22⋊C8C2×D8311yescharacteristic
378C2×C4×C8—831no—
379C2×C4×C8—831no—
380C2×C4×C8—831no—
381C2×C4×C8C2×D8311yescharacteristic
382C2×C4×C8C2×D8311yescharacteristic
383#388—831no—
384#388—831no—
385#387—831no—
386#387—831no—
387#386—831no—
388#385—831no—
389#381—831no—
390C4×C4⋊C4—831no—
391C4×C4⋊C4—831no—
392C4×C22⋊C4—831no—
393C4×C22⋊C4—831no—
394C4×C22⋊C4C2×D8311yescharacteristic
395#336—831no—
396#336—831no—
397#336—831no—
398#336—831no—
399#336—831no—
400#336—831no—
401#336—831no—
402#336—831no—
403#336C2×D8311yescharacteristic
404#336C2×D8311yescharacteristic
405C22×D4—831no—
406C23×C4—831no—
407C23×C4—831no—
408C23×C4—831no—
409C23×C4C22×D8311yescharacteristic
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—41no—
413C22×C8—3321no—
414C22×C8—3321no—
415C22×C8—831no—
416C22×C8—831no—
417C22×C8—831no—
418C22×C8—831no—
419C22×C8—1662no—
420C22×C8—1662no—
421C22×C8—1662no—
422C22×C8—1662no—
423C22×C8C22×D8311yescharacteristic
424C22×C8C22×D8311yescharacteristic
425C22×C8C22×D8311yescharacteristic
426C22×C8C22×D8311yescharacteristic
427#123—838no—
428C4×D4—1662no—
429C4×D4—1662no—
430C2×C4⋊C4—831no—
431C2×C4⋊C4—831no—
432C2×C4⋊C4—831no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—831no—
435C2×C22⋊C4—831no—
436C2×C22⋊C4—831no—
437C2×C22⋊C4—831no—
438C2×C22⋊C4—831no—
439C2×C22⋊C4—831no—
440C2×C22⋊C4—831no—
441C2×C22⋊C4C4×D8311yescharacteristic
442C2×C22⋊C4C4×D8311yescharacteristic
443C2×C42—831no—
444C2×C42—831no—
445C2×C42—831no—
446C2×C42—831no—
447C2×C42—831no—
448C2×C42—1662no—
449C2×C42—1662no—
450C2×C42C22×D8311yescharacteristic
451C2×C42C22×D8311yescharacteristic
452C4⋊C8—3321no—
453C4⋊C8—1662no—
454C4⋊C8—1662no—
455C4⋊C8—1662no—
456C4⋊C8—1662no—
457C22⋊C8—3321no—
458C22⋊C8—1662no—
459C22⋊C8—1662no—
460C22⋊C8—1662no—
461C22⋊C8D33214yes—
462C4×C8—22no—
463C4×C8—41no—
464C4×C8—1662no—
465C4×C8—1662no—
466C4×C8—1662no—
467#95—831no—
468#95—831no—
469#95—831no—
470#95—831no—
471#95—831no—
472#95—831no—
473#95—831no—
474#95—831no—
475#95C4×D8311yescharacteristic
476#95C4×D8311yescharacteristic
477C24—831no—
478C24C2×C4×D8311yescharacteristic
479C2×D4—834no—
480C2×D4—1662no—
481C2×D4—1662no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—3321no—
487C22×C4—834no—
488C22×C4—831no—
489C22×C4—831no—
490C22×C4—831no—
491C22×C4—831no—
492C22×C4—831no—
493C22×C4—831no—
494C22×C4—831no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1661no—
498C22×C4—1661no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4C2×C4×D8311yescharacteristic
506C22×C4C2×C4×D8311yescharacteristic
507C22×C4C2×C4×D8311yescharacteristic
508C22×C4C2×C4×D8311yescharacteristic
509C22×C4C2×C4×D8311yescharacteristic
510C22×C4C2×D33212yes—
511C22×C4#1305059012yes—
512C22×C4C23×D8311yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—44no—
523C2×C8—3324no—
524C2×C8—3324no—
525C2×C8—832no—
526C2×C8—1661no—
527C2×C8—1661no—
528C2×C8—1661no—
529C2×C8—1661no—
530C2×C8—1661no—
531C2×C8—1661no—
532C2×C8—1661no—
533C2×C8—1661no—
534C2×C8—1661no—
535C2×C8—1661no—
536C2×C8—1661no—
537C2×C8C2×D33212yes—
538C2×C8C2×D33212yes—
539C2×C8#1305058912yes—
540C4⋊C4—3321no—
541C4⋊C4—834no—
542C4⋊C4—834no—
543C4⋊C4—1662no—
544C4⋊C4—1662no—
545C22⋊C4—22no—
546C22⋊C4—3321no—
547C22⋊C4—834no—
548C22⋊C4—834no—
549C22⋊C4—1662no—
550C22⋊C4—1662no—
551C22⋊C4—1662no—
552C22⋊C4C8×D8314yescomplemented
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—1661no—
558C42—1661no—
559C42—1661no—
560C42—1661no—
561C42—1661no—
562C42—1661no—
563C42—1662no—
564C42—1662no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—832no—
570C23—1661no—
571C23—1661no—
572C23—1661no—
573C23—1661no—
574C23—1661no—
575C23—1661no—
576C23C4×D33212yes—
577C23C2×C8×D8312yes—
578C23#1458179812yes—
579C23C22×C4×D8311yescharacteristic
580D4—1668no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—3324no—
598C2×C4—3321no—
599C2×C4—3321no—
600C2×C4—3321no—
601C2×C4—3321no—
602C2×C4—832no—
603C2×C4—832no—
604C2×C4—832no—
605C2×C4—832no—
606C2×C4—1661no—
607C2×C4—1661no—
608C2×C4—1661no—
609C2×C4—1661no—
610C2×C4—1661no—
611C2×C4—1661no—
612C2×C4—1661no—
613C2×C4—1661no—
614C2×C4—1661no—
615C2×C4—1661no—
616C2×C4—1661no—
617C2×C4—1661no—
618C2×C4—1661no—
619C2×C4—1661no—
620C2×C4—1661no—
621C2×C4—1661no—
622C2×C4—1661no—
623C2×C4—1668no—
624C2×C4C4×D33212yes—
625C2×C4C2×C8×D8312yes—
626C2×C4C2×C8×D8312yes—
627C2×C4C22×D33211yescharacteristic
628C2×C4#41×D8311yescharacteristic
629C2×C4C2×#1305058911yescharacteristic
630C2×C4C2×#1305059011yescharacteristic
631C2×C4#1458183711yescharacteristic
632C2×C4#1458183911yescharacteristic
633C8—22no—
634C8—22no—
635C8—22no—
636C8—41no—
637C8—3321no—
638C8—3321no—
639C8—3321no—
640C8—1662no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—3321no—
648C22—3321no—
649C22—3321no—
650C22—3321no—
651C22—1662no—
652C22—1662no—
653C22—1662no—
654C22C8×D33214yes—
655C22C2×C4×D33211yescharacteristic
656C22C4×#1305058911yescharacteristic
657C22#1912818011yescharacteristic
658C22C22×C8×D8311yescharacteristic
659C22#131×D8311yescharacteristic
660C22C2×#1458179811yescharacteristic
661C22#1912846611yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—3321no—
668C4—3321no—
669C4—3321no—
670C4—1662no—
671C4—1662no—
672C4—1662no—
673C4—1662no—
674C4#1912834611yescharacteristic
675C4#1912835511yescharacteristic
676C4#1912837711yescharacteristic
677C4#1912838411yescharacteristic
678C2—24no—
679C2—3322no—
680C2#2491045711yescharacteristic
681C2C2×C8×D33211yescharacteristic
682C2#2491619111yescharacteristic
683C2C8×#1305058911yescharacteristic
684C2#2491645111yescharacteristic
685C2#2491657011yescharacteristic
686C2#2491662011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C23×C8
FittingC8×C22⋊C4×C83C2
socleC23×C83C23×C4
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenterC8×C22⋊C4D83
hypocenterC83#22900
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19127751C2semidirect
4. #24908181C2semidirect
5. #24908070C2semidirect
6. #24908069C2semidirect
7. #24908021C2semidirect
8. #24908021C2semidirect
10. #24907643C2semidirect
11. #24907642C2semidirect
12. C8×C4⋊Dic83C2semidirect
13. C8×(C2×D83)⋊C4C2semidirect
14. C2×#19127455C2semidirect
15. C8×C22⋊C4×C83C2semidirect
75. #14581776C8semidirect
142. C22×Dic83C2×C8semidirect
172. C4⋊Dic83C2×C8semidirect
173. C4⋊Dic83C2×C8semidirect
179. (C2×D83)⋊C4C2×C8semidirect
180. (C2×D83)⋊C4C2×C8semidirect
216. C22⋊C4×C83C2×C8semidirect
357. C8×C22⋊C4D83semidirect
359. C83#22900semidirect
552. C22⋊C4C8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D83)⋊C82
C2×#191277512
C4×#145817762
#249081812
#249080702
#249080692
#249080212
#249077552
#249076432
#249076422
C8×C4⋊Dic832
C8×(C2×D83)⋊C42
C2×#191274552
C8×C22⋊C4×C832
#2290083