Finite Group Databasebeta

← #35422560

Subgroups — #35422560

Order 21248.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127773C211yesmaximal, characteristic
2C2×#19127744C211yesmaximal, characteristic, complemented
3C22×#14581723C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic83C211yesmaximal, characteristic
5#24908229C211yesmaximal, characteristic, complemented
6#24908226C211yesmaximal, characteristic, complemented
7#24907662C211yesmaximal, characteristic, complemented
8#24907656C211yesmaximal, characteristic, complemented
9#24907655C211yesmaximal, characteristic, complemented
10#24907650C211yesmaximal, characteristic, complemented
11#24907632C211yesmaximal, characteristic, complemented
12#24907494C211yesmaximal, characteristic, complemented
13#24907490C211yesmaximal, characteristic, complemented
14#24907361C211yesmaximal, characteristic, complemented
15C83×#2352C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18C2×D4×Dic83—21no—
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21#19127773C418yescomplemented
22#19127744—24no—
23C2×#14581725C2211yescharacteristic
24C2×#14581725C2211yescharacteristic
25C2×#14581725C2211yescharacteristic
26C2×#14581725C2211yescharacteristic
27C2×#14581723—24no—
28C2×#14581723C2211yescharacteristic
29C2×#14581723C2211yescharacteristic
30C2×#14581723C2211yescharacteristic
31C2×#14581723C2211yescharacteristic
32C2×#14581723C2211yescharacteristic
33C2×#14581723C2211yescharacteristic
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×C22⋊(C83⋊C8)C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
37C2×#14581703C2211yescharacteristic
38#19127600—21no—
39#19127576—21no—
40#19127576—21no—
41#19127571C2211yescharacteristic
42#19127561C2211yescharacteristic
43#19127561C2211yescharacteristic
44C4×C4⋊Dic83C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51C2×C4×D4×C83C2211yescharacteristic
52C2×#117×C83C2211yescharacteristic
53C22×C4⋊C4×C83C2211yescharacteristic
54#388×C83—21no—
55#387×C83—21no—
56#386×C83—21no—
57#382×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60C4×C4⋊C4×C83C2211yescharacteristic
61C4×C22⋊C4×C83—21no—
62C23×Dic83—21no—
63C23×Dic83—21no—
64C2×#13050574—22no—
65C2×#13050574—22no—
66C2×#13050574C2×C414yescomplemented
67C22×C83⋊C8—22no—
68C22×C83⋊C8—22no—
69C22×C83⋊C8C2×C414yescomplemented
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74D4×Dic83—44no—
75C2×C4⋊Dic83—22no—
76C2×C4⋊Dic83—22no—
77C2×C4⋊Dic83—21no—
78C2×C4⋊Dic83—21no—
79C2×C4⋊Dic83—21no—
80C2×C4⋊Dic83—21no—
81C2×C4⋊Dic83—41no—
82C2×C4⋊Dic83—41no—
83C2×C4⋊Dic83C2311yescharacteristic
84C2×C4⋊Dic83C2311yescharacteristic
85C2×C4⋊Dic83C2311yescharacteristic
86C2×C4⋊Dic83C2311yescharacteristic
87C2×C22⋊Dic83—21no—
88C2×C22⋊Dic83—21no—
89C2×C4×Dic83—21no—
90#14581725—22no—
91#14581725—22no—
92#14581725—22no—
93#14581725—41no—
94#14581723—22no—
95#14581723—22no—
96#14581723—22no—
97#14581723—22no—
98#14581723—41no—
99#14581723D414yescomplemented
100C4⋊(C83⋊C8)C2×C414yescomplemented
101C22⋊(C83⋊C8)C2×C414yescomplemented
102C22⋊(C83⋊C8)C2×C414yescomplemented
103#14581703C2×C414yescomplemented
104C83⋊#95—21no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C22×D4×C83D411yescharacteristic
108C23×C4×C83—21no—
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C4×D4×C83C2×C414yes—
112C4×D4×C83Q814yes—
113#117×C83—22no—
114#117×C83—41no—
115C2×C4⋊C4×C83—22no—
116C2×C4⋊C4×C83—21no—
117C2×C4⋊C4×C83—41no—
118C2×C4⋊C4×C83D411yescharacteristic
119C2×C4⋊C4×C83C2311yescharacteristic
120C2×C4⋊C4×C83C2311yescharacteristic
121C2×C4⋊C4×C83C2311yescharacteristic
122C2×C4⋊C4×C83C2311yescharacteristic
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83D411yescharacteristic
127C2×C22⋊C4×C83D411yescharacteristic
128C2×C42×C83—21no—
129C2×C42×C83—21no—
130C2×C42×C83C2311yescharacteristic
131#95×C83—21no—
132#95×C83—21no—
133#95×C83—21no—
134#95×C83—21no—
135#95×C83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—42no—
141C22×Dic83—42no—
142C22×Dic83—42no—
143C22×Dic83—42no—
144C22×Dic83—81no—
145C22×Dic83—81no—
146#13050574—28no—
147C2×C83⋊C8—21no—
148C2×C83⋊C8—21no—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—28no—
154C2×C83⋊C8C22×C412yes—
155C2×C83⋊C8C22×C412yes—
156C2×C83⋊C8C22×C412yes—
157C2×C83⋊C8C22×C412yes—
158C2×C83⋊C8C2×D412yes—
159C2×C83⋊C8#4112yes—
160C4⋊Dic83—21no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83—42no—
168C4⋊Dic83—42no—
169C4⋊Dic83—42no—
170C4⋊Dic83—81no—
171C4⋊Dic83C2×D412yes—
172C22⋊Dic83—42no—
173C22⋊Dic83—42no—
174C4×Dic83—42no—
175C24×C83C2×D411yescharacteristic
176C24×C83C2×D411yescharacteristic
177C2×D4×C83—22no—
178C2×D4×C83—22no—
179C2×D4×C83C4⋊C414yes—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—42no—
193C22×C4×C83—42no—
194C22×C4×C83—81no—
195C22×C4×C83C22×C412yes—
196C22×C4×C83C22×C412yes—
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2×D411yescharacteristic
199C22×C4×C83C2×D411yescharacteristic
200C22×C4×C83C2×D411yescharacteristic
201C22×C4×C83C2×Q812yes—
202C22×C4×C83C2×Q812yes—
203C22×C4×C83C2411yescharacteristic
204C4⋊C4×C83—21no—
205C4⋊C4×C83—21no—
206C4⋊C4×C83—21no—
207C4⋊C4×C83—21no—
208C4⋊C4×C83—21no—
209C4⋊C4×C83—21no—
210C4⋊C4×C83—21no—
211C4⋊C4×C83—42no—
212C4⋊C4×C83C4⋊C414yes—
213C4⋊C4×C83C2×D412yes—
214C22⋊C4×C83—42no—
215C22⋊C4×C83—42no—
216C22⋊C4×C83—81no—
217C22⋊C4×C83C4⋊C414yes—
218C22⋊C4×C83C4⋊C414yes—
219C42×C83—42no—
220C42×C83—81no—
221C42×C83C22×C412yes—
222C42×C83C2×Q812yes—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83—21no—
228C23×C83—21no—
229C23×C83—21no—
230C23×C83—21no—
231C23×C83—21no—
232C23×C83—21no—
233C23×C83C2×C4⋊C412yes—
234C23×C83C2×C4⋊C412yes—
235C23×C83AGL(1,ℤ/8)12yes—
236C23×C83#13712yes—
237C23×C83C22×D411yescharacteristic
238D4×C83—28no—
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—22no—
248C2×C4×C83—22no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—41no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—41no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—84no—
268C2×C4×C83C2×C4⋊C412yes—
269C2×C4×C83C2×C4⋊C412yes—
270C2×C4×C83C2×C4⋊C412yes—
271C2×C4×C83C2×C4⋊C412yes—
272C2×C4×C83C23×C411yescharacteristic
273C2×C4×C83C22×D411yescharacteristic
274C2×C4×C83C22×Q811yescharacteristic
275C2×C4×C83C2×#4111yescharacteristic
276C2×C4×C83H(5,𝔽2)11yescharacteristic
277C2×C4×C832−1+411yescharacteristic
278C2×Dic83—22no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—41no—
285C2×Dic83—41no—
286C2×Dic83—41no—
287C2×Dic83—41no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—84no—
291C2×Dic83—84no—
292C83⋊C8—22no—
293C83⋊C8—22no—
294C83⋊C8—22no—
295C83⋊C8C4×D414yescomplemented
296C22×C83—22no—
297C22×C83—22no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—22no—
301C22×C83—22no—
302C22×C83—22no—
303C22×C83—22no—
304C22×C83—22no—
305C22×C83—41no—
306C22×C83—41no—
307C22×C83—41no—
308C22×C83—41no—
309C22×C83#42814yescomplemented
310C22×C83C22×C4⋊C411yescharacteristic
311C22×C83D4211yescharacteristic
312C22×C83#54711yescharacteristic
313C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C83C2×#13711yescharacteristic
315C22×C83#57711yescharacteristic
316C22×C83#57711yescharacteristic
317C4×C83—22no—
318C4×C83—22no—
319C4×C83—22no—
320C4×C83—22no—
321C4×C83—42no—
322C4×C83—81no—
323C4×C83—81no—
324C4×C83—81no—
325C4×C83C2×C4×D411yescharacteristic
326C4×C83#52011yescharacteristic
327C4×C83D4×Q811yescharacteristic
328C4×C83#55411yescharacteristic
329Dic83—42no—
330Dic83—81no—
331Dic83—81no—
332Dic83—81no—
333#22659—831nomaximal, Sylow
334C2×C83—24no—
335C2×C83—42no—
336C2×C83D4×C4⋊C411yescharacteristic
337C2×C83C2×#42811yescharacteristic
338C2×C83#291211yescharacteristic
339C2×C83#326511yescharacteristic
340C2×C83#326611yescharacteristic
341C2×C83#334411yescharacteristic
342C2×C83#334511yescharacteristic
343C2×#435—831no—
344C2×#428—831no—
345C22×#106—831no—
346#2352D8311yescharacteristic
347D4×C4⋊C4—831no—
348#1949—831no—
349#1948—831no—
350#1854—831no—
351#1853—831no—
352#1853—831no—
353#1852—831no—
354#1847—831no—
355#1809—831no—
356#1808—831no—
357#1776—831no—
358C83#2265911yescharacteristic, complemented, Sylow
359C22×M16—831no—
360C23×C8—831no—
361C2×C4×D4—1661no—
362C2×C4×D4C2×D8311yescharacteristic
363C2×#117C2×D8311yescharacteristic
364C22×C4⋊C4—831no—
365C22×C4⋊C4—831no—
366C22×C4⋊C4C2×D8311yescharacteristic
367#435—838no—
368#428—1664no—
369C2×#107—831no—
370C2×#107—831no—
371C2×#107—831no—
372C2×#107—831no—
373C2×#106—831no—
374C2×#106—831no—
375C2×#106—831no—
376C2×#106—831no—
377C2×#106—831no—
378C2×#106—831no—
379C2×#106—1664no—
380C2×C4⋊C8—831no—
381C2×C22⋊C8—831no—
382C2×C22⋊C8—831no—
383C2×#97—831no—
384#389—1661no—
385#388—21no—
386#387—21no—
387#386—21no—
388#385—1661no—
389#385—1661no—
390#384—831no—
391#382C2×D8311yescharacteristic
392#380—831no—
393#380—831no—
394#380C2×D8311yescharacteristic
395#380C2×D8311yescharacteristic
396C4×C4⋊C4—831no—
397C4×C4⋊C4C2×D8311yescharacteristic
398C4×C22⋊C4—21no—
399#340—831no—
400#340—831no—
401#340—831no—
402#340—831no—
403#340—831no—
404#340—831no—
405C22×D4C22⋊D8311yescharacteristic
406C23×C4—21no—
407C23×C4—1661no—
408C23×C4—1661no—
409C23×C4C22×D8311yescharacteristic
410C23×C4C22×D8311yescharacteristic
411C2×M16—834no—
412C2×M16—1662no—
413C2×M16—1662no—
414C22×C8—831no—
415C22×C8—834no—
416C22×C8—831no—
417C22×C8—831no—
418C22×C8—831no—
419C22×C8—1662no—
420C22×C8—1662no—
421C4×D4—3324no—
422C4×D4Dic16614yes—
423C4×D4C4×D8314yes—
424#117—22no—
425#117—41no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—3321no—
430C2×C4⋊C4—3321no—
431C2×C4⋊C4—831no—
432C2×C4⋊C4—831no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—831no—
435C2×C4⋊C4—1661no—
436C2×C4⋊C4—1661no—
437C2×C4⋊C4—1661no—
438C2×C4⋊C4—1662no—
439C2×C4⋊C4—1662no—
440C2×C4⋊C4—1661no—
441C2×C4⋊C4C22⋊D8311yescharacteristic
442C2×C4⋊C4C22×D8311yescharacteristic
443C2×C4⋊C4C22×D8311yescharacteristic
444C2×C4⋊C4C22×D8311yescharacteristic
445C2×C4⋊C4C22×D8311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—1661no—
450C2×C22⋊C4—1661no—
451C2×C22⋊C4C22⋊D8311yescharacteristic
452C2×C22⋊C4C22⋊D8311yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—1661no—
456C2×C42C22×D8311yescharacteristic
457#107—3321no—
458#107—1662no—
459#107—1662no—
460#107—1662no—
461#106—3321no—
462#106—834no—
463#106—1662no—
464#106—1662no—
465#106—1662no—
466#106—1662no—
467C4⋊C8—834no—
468C22⋊C8—834no—
469C22⋊C8—834no—
470#97—834no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—1661no—
477#95—1661no—
478#95—1661no—
479C24C2×C22⋊D8311yescharacteristic
480C24C2×C22⋊D8311yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic83⋊C414yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—3322no—
500C22×C4—3322no—
501C22×C4—3322no—
502C22×C4—3322no—
503C22×C4—6641no—
504C22×C4—6641no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4C2×C4×D8312yes—
510C22×C4C2×C4×D8312yes—
511C22×C4C2×C22⋊D8311yescharacteristic
512C22×C4C2×C22⋊D8311yescharacteristic
513C22×C4C2×C22⋊D8311yescharacteristic
514C22×C4C2×C22⋊D8311yescharacteristic
515C22×C4C2×Dic16612yes—
516C22×C4C2×Dic16612yes—
517C22×C4C23×D8311yescharacteristic
518M16—1668no—
519C2×C8—832no—
520C2×C8—832no—
521C2×C8—832no—
522C2×C8—832no—
523C2×C8—832no—
524C2×C8—832no—
525C2×C8—1668no—
526C2×C8—1661no—
527C2×C8—1661no—
528C2×C8—1661no—
529C2×C8—1661no—
530C2×C8—1661no—
531C2×C8—1661no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—3322no—
541C4⋊C4—3322no—
542C4⋊C4—3322no—
543C4⋊C4—832no—
544C4⋊C4—6641no—
545C4⋊C4—1661no—
546C4⋊C4—1661no—
547C4⋊C4—1661no—
548C4⋊C4—1661no—
549C4⋊C4—1661no—
550C4⋊C4—1661no—
551C4⋊C4—1661no—
552C4⋊C4Dic83⋊C414yes—
553C4⋊C4D4×D8312yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—3322no—
558C22⋊C4—3322no—
559C22⋊C4Dic83⋊C414yes—
560C22⋊C4Dic83⋊C414yes—
561C42—42no—
562C42—81no—
563C42—3322no—
564C42C2×C4×D8312yes—
565C42C2×Dic16612yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic83⋊C412yes—
577C23C2×Dic83⋊C412yes—
578C23#1458181712yes—
579C23#1458182212yes—
580C23C22×C22⋊D8311yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—3321no—
612C2×C4—3321no—
613C2×C4—3321no—
614C2×C4—3321no—
615C2×C4—3321no—
616C2×C4—3321no—
617C2×C4—3321no—
618C2×C4—3321no—
619C2×C4—3321no—
620C2×C4—3321no—
621C2×C4—3321no—
622C2×C4—6644no—
623C2×C4—6644no—
624C2×C4—1662no—
625C2×C4C2×Dic83⋊C412yes—
626C2×C4C2×Dic83⋊C412yes—
627C2×C4C2×Dic83⋊C412yes—
628C2×C4C2×Dic83⋊C412yes—
629C2×C4C22×C4×D8311yescharacteristic
630C2×C4C2×D4×D8311yescharacteristic
631C2×C4C22×Dic16611yescharacteristic
632C2×C4#41×D8311yescharacteristic
633C2×C4#1458183711yescharacteristic
634C2×C4#1458183911yescharacteristic
635C8—834no—
636C8—1662no—
637C8—1662no—
638C8—1662no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1912774414yescomplemented
653C22C22×Dic83⋊C411yescharacteristic
654C22D4×C22⋊D8311yescharacteristic
655C22#1912835011yescharacteristic
656C22C2×#1458181711yescharacteristic
657C22C2×#1458182211yescharacteristic
658C22#1912850911yescharacteristic
659C22#1912851211yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—3322no—
669C4—6641no—
670C4—6641no—
671C4—6641no—
672C4C4×D4×D8311yescharacteristic
673C4#1912818011yescharacteristic
674C4D4×Dic16611yescharacteristic
675C4#1912841011yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic83⋊C411yescharacteristic
679C2C2×#1912774411yescharacteristic
680C2#2491605611yescharacteristic
681C2#2491895911yescharacteristic
682C2#2491896911yescharacteristic
683C2#2491991811yescharacteristic
684C2#2491992711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2352C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
cosocleC22×C4×C83C24
hypercenter#2352D83
hypocenterC83#22659
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#19127744C2semidirect
3. C22×#14581723C2semidirect
5. #24908229C2semidirect
6. #24908226C2semidirect
7. #24907662C2semidirect
8. #24907656C2semidirect
9. #24907655C2semidirect
10. #24907650C2semidirect
11. #24907632C2semidirect
12. #24907494C2semidirect
13. #24907490C2semidirect
14. #24907361C2semidirect
21. #19127773C4semidirect
66. C2×#13050574C2×C4semidirect
69. C22×C83⋊C8C2×C4semidirect
99. #14581723D4semidirect
100. C4⋊(C83⋊C8)C2×C4semidirect
101. C22⋊(C83⋊C8)C2×C4semidirect
102. C22⋊(C83⋊C8)C2×C4semidirect
103. #14581703C2×C4semidirect
295. C83⋊C8C4×D4semidirect
309. C22×C83#428semidirect
358. C83#22659semidirect
652. C22#19127744semidirect

Maximal subgroups

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

subgroupindex
C2×#191277732
C2×#191277442
C22×#145817232
D4×C4⋊Dic832
#249082292
#249082262
#249076622
#249076562
#249076552
#249076502
#249076322
#249074942
#249074902
#249073612
C83×#23522
#2265983