Finite Group Databasebeta

← #35415050

Subgroups — #35415050

Order 21248.

930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic
2#24908071C211yesmaximal, characteristic, complemented
3#24908020C211yesmaximal, characteristic, complemented
4#24908018C211yesmaximal, characteristic, complemented
5#24907752C211yesmaximal, characteristic
6#24907752C211yesmaximal, characteristic
7#24907642C211yesmaximal, characteristic, complemented
8#24907639C211yesmaximal, characteristic, complemented
9#24907605C211yesmaximal, characteristic, complemented
10#24907579C211yesmaximal, characteristic, complemented
11#24907529C211yesmaximal, characteristic, complemented
12#24907441C211yesmaximal, characteristic, complemented
13C4×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
14#336×D83C211yesmaximal, characteristic, complemented
15C83×#1923C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×C4×C22⋊D83C2211yescharacteristic
19C2×(C22⋊D83)⋊C4C411yescharacteristic
20C2×(C22⋊D83)⋊C4C411yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C2×C42×D83C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×Dic83⋊C8C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×C22⋊(C83⋊C8)C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×(C2×D83)⋊C8C2211yescharacteristic
30C2×C4×C83⋊C8C2211yescharacteristic
31C4×Dic83⋊C4C2211yescharacteristic
32#19127552C411yescharacteristic
33#19127552C411yescharacteristic
34C22⋊C4×Dic83C411yescharacteristic
35C22⋊C4×Dic83C411yescharacteristic
36C4×(C2×D83)⋊C4C2211yescharacteristic
37#19127548C411yescharacteristic
38#19127548C411yescharacteristic
39C42×Dic83C2211yescharacteristic
40#19127456C2211yescharacteristic
41#19127456C2211yescharacteristic
42#19127455C2211yescharacteristic
43#19127455C2211yescharacteristic
44#19127455C2211yescharacteristic
45#19127455C2211yescharacteristic
46#19127455C2211yescharacteristic
47#19127455C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52C2×C4⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54C2×C22⋊C8×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C4×C22⋊C4×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×C22⋊D83C2×C411yescharacteristic
60C23×Dic83C2×C411yescharacteristic
61C23×Dic83C2×C411yescharacteristic
62C22×C4×D83C2×C411yescharacteristic
63C22×C4×D83C2×C411yescharacteristic
64C22×C4×D83C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C2×C8×D83—22no—
70C2×C8×D83—22no—
71C2×C8×D83—41no—
72C2×C8×D83—41no—
73C2×C8×D83—41no—
74C2×C8×D83—41no—
75C4×C22⋊D83—22no—
76C4×C22⋊D83—22no—
77(C22⋊D83)⋊C4—24no—
78(C22⋊D83)⋊C4C818yescomplemented
79C2×Dic83⋊C4C2×C411yescharacteristic
80C2×Dic83⋊C4C2×C411yescharacteristic
81C2×Dic83⋊C4C2×C411yescharacteristic
82C2×C22⋊Dic83C2×C411yescharacteristic
83C2×(C2×D83)⋊C4C2×C411yescharacteristic
84C2×(C2×D83)⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×C4×Dic83—41no—
87C2×C4×Dic83—41no—
88C2×C4×Dic83C2×C411yescharacteristic
89C2×C4×Dic83C2×C411yescharacteristic
90C2×C4×Dic83C2×C411yescharacteristic
91C2×C4×Dic83C2×C411yescharacteristic
92C2×C4×Dic83C2×C411yescharacteristic
93C2×C4×Dic83C2×C411yescharacteristic
94C2×C4×Dic83C2×C411yescharacteristic
95C2×C4×Dic83C2×C411yescharacteristic
96C2×C4×Dic83C2311yescharacteristic
97C2×C4×Dic83C2311yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99C42×D83—41no—
100C42×D83—41no—
101C4⋊(C83⋊C8)—41no—
102Dic83⋊C8—41no—
103Dic83⋊C8—41no—
104C22⋊(C83⋊C8)—41no—
105C22⋊(C83⋊C8)—41no—
106(C2×D83)⋊C8—22no—
107(C2×D83)⋊C8—22no—
108C4×C83⋊C8—41no—
109C83⋊#95C2×C411yescharacteristic
110C83⋊#95C2×C411yescharacteristic
111C83⋊#95C2×C411yescharacteristic
112C83⋊#95C2×C411yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C22×C8×C83C2311yescharacteristic
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117C22×C8×C83C2311yescharacteristic
118C2×C22⋊C4×C83C2×C411yescharacteristic
119C2×C22⋊C4×C83C2×C411yescharacteristic
120C2×C42×C83C2311yescharacteristic
121C2×C42×C83C2311yescharacteristic
122C4⋊C8×C83—41no—
123C22⋊C8×C83—41no—
124C22⋊C8×C83—41no—
125C4×C8×C83—41no—
126#95×C83C2×C411yescharacteristic
127#95×C83C2×C411yescharacteristic
128C23×D83C22×C411yescharacteristic
129C2×C22⋊D83—22no—
130C2×C22⋊D83—22no—
131C2×C22⋊D83C2×C814yes—
132C22×Dic83—22no—
133C22×Dic83—41no—
134C22×Dic83—41no—
135C22×Dic83—41no—
136C22×Dic83—41no—
137C22×Dic83C2×C814yescomplemented
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C22×Dic83C22×C411yescharacteristic
143C22×Dic83C22×C411yescharacteristic
144C22×Dic83C22×C411yescharacteristic
145C2×C4×D83—21no—
146C2×C4×D83—21no—
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—41no—
150C2×C4×D83—41no—
151C2×C4×D83—41no—
152C2×C4×D83—41no—
153C2×C4×D83C2×C814yes—
154C2×C4×D83M1614yes—
155C2×C4×D83#4112yes—
156C2×C4×D83#4112yes—
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—21no—
168C2×C83⋊C8—21no—
169C8×D83—44no—
170C8×D83—44no—
171Dic83⋊C4—22no—
172Dic83⋊C4—22no—
173Dic83⋊C4C2×C814yescomplemented
174C22⋊Dic83—22no—
175(C2×D83)⋊C4—22no—
176(C2×D83)⋊C4—22no—
177(C2×D83)⋊C4C2×C814yes—
178C4×Dic83—21no—
179C4×Dic83—21no—
180C4×Dic83—21no—
181C4×Dic83—21no—
182C4×Dic83—21no—
183C4×Dic83—21no—
184C4×Dic83—22no—
185C4×Dic83—41no—
186C4×Dic83—41no—
187C4×Dic83—41no—
188C4×Dic83—41no—
189C4×Dic83—41no—
190C4×Dic83—41no—
191C4×Dic83C2×C814yescomplemented
192C24×C83C22×C411yescharacteristic
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83C22×C411yescharacteristic
200C22×C4×C83C22×C411yescharacteristic
201C22×C4×C83C22×C411yescharacteristic
202C22×C4×C83C22×C411yescharacteristic
203C22×C4×C83C22×C411yescharacteristic
204C22×C4×C83C2411yescharacteristic
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—21no—
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83—21no—
215C2×C8×C83—21no—
216C2×C8×C83—21no—
217C22⋊C4×C83—22no—
218C22⋊C4×C83C2×C814yescomplemented
219C42×C83—21no—
220C42×C83—21no—
221C42×C83—21no—
222C42×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83—21no—
228C23×C83—21no—
229C23×C83C22×C812yes—
230C23×C83C23×C411yescharacteristic
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83—21no—
235C22×D83#11712yes—
236C22×D83C22×C812yes—
237C22×D83C2×M1612yes—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—41no—
251C2×C4×C83—41no—
252C2×C4×C83—41no—
253C2×C4×C83—41no—
254C2×C4×C83C22×C812yes—
255C2×C4×C83C22×C812yes—
256C2×C4×C83C2×M1612yes—
257C2×C4×C83C2×#4111yescharacteristic
258C2×C4×C83C2×#4111yescharacteristic
259C2×C4×C83H(5,𝔽2)11yescharacteristic
260C2×C4×C83H(5,𝔽2)11yescharacteristic
261C2×C4×C83H(5,𝔽2)11yescharacteristic
262C2×C4×C832−1+411yescharacteristic
263C22⋊D83—28no—
264C2×Dic83—21no—
265C2×Dic83—21no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—21no—
269C2×Dic83—21no—
270C2×Dic83—21no—
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×Dic83—44no—
282C2×Dic83#11712yes—
283C2×Dic83C22×C812yes—
284C2×Dic83C22×C812yes—
285C2×Dic83C22×C812yes—
286C2×Dic83C2×M1612yes—
287C4×D83—22no—
288C4×D83—22no—
289C4×D83—22no—
290C4×D83—22no—
291C4×D83—44no—
292C4×D83—44no—
293C8×C83—41no—
294C8×C83—41no—
295C8×C83—41no—
296C8×C83—41no—
297C83⋊C8—41no—
298C83⋊C8—41no—
299C83⋊C8—41no—
300C83⋊C8—41no—
301C22×C83—22no—
302C22×C83—22no—
303C22×C83—22no—
304C22×C83—41no—
305C22×C83—41no—
306C22×C83—41no—
307C22×C83—41no—
308C22×C83C2×#11711yescharacteristic
309C22×C83#51811yescharacteristic
310C22×C83#52011yescharacteristic
311C22×C83C23×C811yescharacteristic
312C22×C83C22×M1611yescharacteristic
313C22×C83#56811yescharacteristic
314C22×C83#56811yescharacteristic
315C2×D83—22no—
316C2×D83—22no—
317C2×D83—22no—
318C2×D83—22no—
319C2×D83—22no—
320C2×D83—22no—
321C2×D83#43114yes—
322C4×C83—22no—
323C4×C83—22no—
324C4×C83—22no—
325C4×C83—41no—
326C4×C83—41no—
327C4×C83#53811yescharacteristic
328C4×C83#53811yescharacteristic
329C4×C83#53911yescharacteristic
330C4×C83#53911yescharacteristic
331Dic83—22no—
332Dic83—22no—
333Dic83—22no—
334Dic83—22no—
335Dic83—22no—
336Dic83—41no—
337Dic83—41no—
338#21996—831nomaximal, Sylow
339C2×C83—42no—
340C2×C83#231811yescharacteristic
341C2×C83C2×#43111yescharacteristic
342C2×C83#292311yescharacteristic
343C2×C83#297211yescharacteristic
344C2×C83#297311yescharacteristic
345C2×C83#298811yescharacteristic
346C2×C83#298911yescharacteristic
347D83—24no—
348C42×D4—831no—
349#1923—831no—
350#1923D8311yescharacteristic, complemented
351#1916—831no—
352#1916—831no—
353#1869—831no—
354#1869—831no—
355#1850—831no—
356#1850—831no—
357#1839—831no—
358#1831—831no—
359#1817—831no—
360#1797—831no—
361C4×C22⋊C8—831no—
362C2×#336—831no—
363C83#2199611yescharacteristic, complemented, Sylow
364C23×C8—831no—
365C23×C8—831no—
366C2×C4×D4—831no—
367C2×C4×D4—831no—
368C2×C4×D4—831no—
369C22×C42—831no—
370C22×C42—831no—
371C2×C4⋊C8—831no—
372C2×C4⋊C8—831no—
373C2×C4⋊C8—831no—
374C2×C4⋊C8C2×D8311yescharacteristic
375C2×C22⋊C8—831no—
376C2×C22⋊C8—831no—
377C2×C22⋊C8—831no—
378C2×C22⋊C8—831no—
379C2×C22⋊C8C2×D8311yescharacteristic
380C2×C22⋊C8C2×D8311yescharacteristic
381C2×C4×C8—831no—
382C2×C4×C8C2×D8311yescharacteristic
383C4×C4⋊C4—831no—
384C4×C4⋊C4—831no—
385C4×C4⋊C4—831no—
386C4×C22⋊C4—831no—
387C4×C22⋊C4—831no—
388C4×C22⋊C4—831no—
389C4×C22⋊C4—831no—
390C4×C22⋊C4—831no—
391C4×C22⋊C4C2×D8311yescharacteristic
392C43—831no—
393#336—831no—
394#336—831no—
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#336—831no—
404#336—831no—
405#336C2×D8311yescharacteristic
406#336C2×D8311yescharacteristic
407C22×D4—831no—
408C23×C4—831no—
409C23×C4—831no—
410C23×C4—831no—
411C23×C4—831no—
412C23×C4—831no—
413C23×C4C22×D8311yescharacteristic
414C22×C8—3321no—
415C22×C8—3321no—
416C22×C8—3321no—
417C22×C8—3321no—
418C22×C8—831no—
419C22×C8—831no—
420C22×C8—831no—
421C22×C8—831no—
422C22×C8—1662no—
423C22×C8—1662no—
424C22×C8C22×D8311yescharacteristic
425C22×C8C22×D8311yescharacteristic
426C22×C8C22×D8311yescharacteristic
427C22×C8C22×D8311yescharacteristic
428C4×D4—838no—
429C4×D4—1664no—
430C4×D4—1662no—
431C4×D4—1662no—
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⋊C4C4×D8311yescharacteristic
440C2×C22⋊C4C4×D8311yescharacteristic
441C2×C42—3321no—
442C2×C42—3321no—
443C2×C42—3321no—
444C2×C42—3321no—
445C2×C42—831no—
446C2×C42—831no—
447C2×C42—831no—
448C2×C42—831no—
449C2×C42—831no—
450C2×C42—831no—
451C2×C42—831no—
452C2×C42—831no—
453C2×C42—831no—
454C2×C42—831no—
455C2×C42—831no—
456C2×C42C22×D8311yescharacteristic
457C2×C42C22×D8311yescharacteristic
458C4⋊C8—41no—
459C4⋊C8—3321no—
460C4⋊C8—3321no—
461C4⋊C8—3321no—
462C22⋊C8—41no—
463C22⋊C8—41no—
464C22⋊C8—3321no—
465C22⋊C8—3321no—
466C22⋊C8—1662no—
467C22⋊C8—1662no—
468C4×C8—41no—
469C4×C8—3321no—
470#95—831no—
471#95—831no—
472#95—831no—
473#95—831no—
474#95C4×D8311yescharacteristic
475#95C4×D8311yescharacteristic
476C24—831no—
477C24C2×C4×D8311yescharacteristic
478C2×D4—834no—
479C2×D4—1662no—
480C2×D4—1662no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—3321no—
488C22×C4—3321no—
489C22×C4—3321no—
490C22×C4—3321no—
491C22×C4—3321no—
492C22×C4—3321no—
493C22×C4—3321no—
494C22×C4—3321no—
495C22×C4—834no—
496C22×C4—834no—
497C22×C4—834no—
498C22×C4—831no—
499C22×C4—831no—
500C22×C4—831no—
501C22×C4—831no—
502C22×C4—831no—
503C22×C4—832no—
504C22×C4—832no—
505C22×C4—831no—
506C22×C4—831no—
507C22×C4—1662no—
508C22×C4—1661no—
509C22×C4—1661no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4C2×C4×D8311yescharacteristic
513C22×C4C2×C4×D8311yescharacteristic
514C22×C4C2×C4×D8311yescharacteristic
515C22×C4C2×C4×D8311yescharacteristic
516C22×C4C2×C4×D8311yescharacteristic
517C22×C4C23×D8311yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—3324no—
531C2×C8—3324no—
532C2×C8—1661no—
533C2×C8—1661no—
534C2×C8—1661no—
535C2×C8—1661no—
536C2×C8—1661no—
537C2×C8—1661no—
538C2×C8—1661no—
539C2×C8—1661no—
540C2×C8—1661no—
541C2×C8—1661no—
542C2×C8—1661no—
543C2×C8—1661no—
544C4⋊C4—834no—
545C4⋊C4—1662no—
546C4⋊C4—1662no—
547C22⋊C4—22no—
548C22⋊C4—834no—
549C22⋊C4—1662no—
550C22⋊C4—1662no—
551C22⋊C4—1662no—
552C22⋊C4C8×D8314yescomplemented
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—3321no—
558C42—3321no—
559C42—3321no—
560C42—3321no—
561C42—3321no—
562C42—3321no—
563C42—834no—
564C42—1662no—
565C42—1661no—
566C42—1661no—
567C42—1661no—
568C42—1661no—
569C42—1661no—
570C42—1661no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—832no—
578C23—832no—
579C23—832no—
580C23—1661no—
581C23—1661no—
582C23—1661no—
583C23—1661no—
584C23C2×C8×D8312yes—
585C23C22×C4×D8311yescharacteristic
586D4—1668no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—3324no—
604C2×C4—3324no—
605C2×C4—3324no—
606C2×C4—3324no—
607C2×C4—832no—
608C2×C4—832no—
609C2×C4—832no—
610C2×C4—832no—
611C2×C4—832no—
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—1661no—
624C2×C4—1661no—
625C2×C4—1661no—
626C2×C4—1661no—
627C2×C4—1661no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4C2×C8×D8312yes—
633C2×C4C2×C8×D8312yes—
634C2×C4M16×D8312yes—
635C2×C4#41×D8311yescharacteristic
636C2×C4#41×D8311yescharacteristic
637C2×C4#1458183711yescharacteristic
638C2×C4#1458183711yescharacteristic
639C2×C4#1458183811yescharacteristic
640C2×C4#1458183911yescharacteristic
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—3321no—
646C8—3321no—
647C8—3321no—
648C8—3321no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—834no—
657C22—1662no—
658C22—1662no—
659C22—1662no—
660C22—1662no—
661C22—1662no—
662C22—1662no—
663C22#117×D8311yescharacteristic
664C22#1912817311yescharacteristic
665C22#1912818011yescharacteristic
666C22C22×C8×D8311yescharacteristic
667C22C2×M16×D8311yescharacteristic
668C22#1912846611yescharacteristic
669C22#1912846611yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—3321no—
676C4—3321no—
677C4—1662no—
678C4—1662no—
679C4—1662no—
680C4—1662no—
681C4—1662no—
682C4#1912828311yescharacteristic
683C4#1912828511yescharacteristic
684C4#1912829211yescharacteristic
685C4#1912829411yescharacteristic
686C2—42no—
687C2—1664no—
688C2#2491009311yescharacteristic
689C2#431×D8311yescharacteristic
690C2#2491611111yescharacteristic
691C2#2491648411yescharacteristic
692C2#2491648811yescharacteristic
693C2#2491657011yescharacteristic
694C2#2491657811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C23×C8
FittingC83×#1923C2
socleC23×C83C23×C4
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1923D83
hypocenterC83#21996
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #24908071C2semidirect
3. #24908020C2semidirect
4. #24908018C2semidirect
7. #24907642C2semidirect
8. #24907639C2semidirect
9. #24907605C2semidirect
10. #24907579C2semidirect
11. #24907529C2semidirect
12. #24907441C2semidirect
13. C4×(C2×D83)⋊C8C2semidirect
14. #336×D83C2semidirect
15. C83×#1923C2semidirect
78. (C22⋊D83)⋊C4C8semidirect
137. C22×Dic83C2×C8semidirect
173. Dic83⋊C4C2×C8semidirect
191. C4×Dic83C2×C8semidirect
218. C22⋊C4×C83C2×C8semidirect
350. #1923D83semidirect
363. C83#21996semidirect
552. C22⋊C4C8×D83semidirect

Maximal subgroups

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

subgroupindex
C4×(C22⋊D83)⋊C42
#249080712
#249080202
#249080182
#249077522
#249076422
#249076392
#249076052
#249075792
#249075292
#249074412
C4×(C2×D83)⋊C82
#336×D832
C83×#19232
#2199683