Finite Group Databasebeta

← #35423500

Subgroups — #35423500

Order 21248.

894 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D83C211yesmaximal, characteristic, complemented
2#24909900C211yesmaximal, characteristic
3#24908079C211yesmaximal, characteristic, complemented
4#24908072C211yesmaximal, characteristic, complemented
5#24908027C211yesmaximal, characteristic, complemented
6#24908020C211yesmaximal, characteristic, complemented
7#24907752C211yesmaximal, characteristic
8#24907752C211yesmaximal, characteristic
9#24907582C211yesmaximal, characteristic, complemented
10#24907447C211yesmaximal, characteristic, complemented
11#24907440C211yesmaximal, characteristic, complemented
12#24907322C211yesmaximal, characteristic, complemented
13#24907240C211yesmaximal, characteristic, complemented
14C8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
15C2×#433×C83C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×C4×C22⋊D83C2211yescharacteristic
19C2×C42×D83C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×Dic83⋊C8C2211yescharacteristic
23C2×Dic83⋊C8C2211yescharacteristic
24C4⋊C8×D83—24no—
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×(C2×D83)⋊C8C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×#14581702C2211yescharacteristic
30C2×C8×Dic83C2211yescharacteristic
31#19127589C411yescharacteristic
32#19127589C411yescharacteristic
33#19127582C411yescharacteristic
34#19127582C411yescharacteristic
35#19127577C411yescharacteristic
36#19127577C411yescharacteristic
37#19127572C411yescharacteristic
38#19127572C411yescharacteristic
39C4×Dic83⋊C4C2211yescharacteristic
40C4×(C2×D83)⋊C4C2211yescharacteristic
41C4×C22⋊Dic83C2211yescharacteristic
42#19127547C2211yescharacteristic
43#19127456C2211yescharacteristic
44#19127456C2211yescharacteristic
45#19127455C2211yescharacteristic
46#19127455C2211yescharacteristic
47#19127455C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53C2×#117×C83C2211yescharacteristic
54#433×C83—24no—
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×#97×C83C2211yescharacteristic
60C2×C4×C8×C83C2211yescharacteristic
61C22×C22⋊D83C2×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—22no—
72C2×C8×D83—22no—
73C2×C8×D83—41no—
74C2×C8×D83—41no—
75C4×C22⋊D83—22no—
76C4×C22⋊D83—22no—
77C2×Dic83⋊C4C2×C411yescharacteristic
78C2×Dic83⋊C4C2×C411yescharacteristic
79C2×Dic83⋊C4C2×C411yescharacteristic
80C2×C22⋊Dic83C2×C411yescharacteristic
81C2×C22⋊Dic83C2×C411yescharacteristic
82C2×C22⋊Dic83C2×C411yescharacteristic
83C2×(C2×D83)⋊C4C2×C411yescharacteristic
84C2×(C2×D83)⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×C4×Dic83C2×C411yescharacteristic
87C2×C4×Dic83C2×C411yescharacteristic
88C2×C4×Dic83C2311yescharacteristic
89C2×C4×Dic83C2311yescharacteristic
90C2×C4×Dic83C2311yescharacteristic
91C42×D83—22no—
92C42×D83—22no—
93C4⋊(C83⋊C8)—22no—
94C4⋊(C83⋊C8)—22no—
95Dic83⋊C8—22no—
96Dic83⋊C8—22no—
97C22⋊(C83⋊C8)—41no—
98C22⋊(C83⋊C8)—41no—
99(C2×D83)⋊C8—22no—
100(C2×D83)⋊C8—22no—
101#14581702—41no—
102C8×Dic83—41no—
103C83⋊#95C2×C411yescharacteristic
104C83⋊#95C2×C411yescharacteristic
105C83⋊#95C2×C411yescharacteristic
106C83⋊#95C2×C411yescharacteristic
107C83⋊#95C2×C411yescharacteristic
108C83⋊#95C2×C411yescharacteristic
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
118#117×C83—22no—
119#117×C83—22no—
120C2×C4⋊C4×C83C2×C411yescharacteristic
121C2×C4⋊C4×C83C2×C411yescharacteristic
122C2×C22⋊C4×C83C2×C411yescharacteristic
123C2×C22⋊C4×C83C2×C411yescharacteristic
124C2×C42×C83C2311yescharacteristic
125C2×C42×C83C2311yescharacteristic
126C4⋊C8×C83—22no—
127C4⋊C8×C83D414yescomplemented
128C22⋊C8×C83—22no—
129C22⋊C8×C83—22no—
130#97×C83—22no—
131C4×C8×C83—22no—
132C23×D83C22×C411yescharacteristic
133C2×C22⋊D83—22no—
134C2×C22⋊D83—22no—
135C2×C22⋊D83—22no—
136C22×Dic83C22×C411yescharacteristic
137C22×Dic83C22×C411yescharacteristic
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C22×Dic83C22×C411yescharacteristic
143C2×C4×D83—22no—
144C2×C4×D83—22no—
145C2×C4×D83—21no—
146C2×C4×D83—21no—
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—22no—
150C2×C4×D83—22no—
151C2×C4×D83—22no—
152C2×C4×D83—41no—
153C2×C4×D83#4112yes—
154C2×C4×D83#4112yes—
155C2×C83⋊C8—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—
167C8×D83—44no—
168C8×D83—44no—
169Dic83⋊C4—22no—
170Dic83⋊C4—22no—
171Dic83⋊C4—41no—
172C22⋊Dic83—22no—
173C22⋊Dic83—22no—
174C22⋊Dic83—41no—
175(C2×D83)⋊C4—22no—
176(C2×D83)⋊C4—22no—
177(C2×D83)⋊C4—22no—
178C4×Dic83—22no—
179C4×Dic83—22no—
180C4×Dic83—21no—
181C4×Dic83—21no—
182C4×Dic83—21no—
183C4×Dic83—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C24×C83C22×C411yescharacteristic
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83C22×C411yescharacteristic
194C22×C4×C83C22×C411yescharacteristic
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C2411yescharacteristic
199C2×C8×C83—21no—
200C2×C8×C83—21no—
201C2×C8×C83—21no—
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×C83C2×D412yes—
210C2×C8×C83C2×D412yes—
211C4⋊C4×C83—22no—
212C4⋊C4×C83—22no—
213C22⋊C4×C83—22no—
214C22⋊C4×C83—22no—
215C42×C83—21no—
216C42×C83—21no—
217C42×C83C2×D412yes—
218C42×C83#4112yes—
219C23×C83—21no—
220C23×C83—21no—
221C23×C83—21no—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83C23×C411yescharacteristic
227C22×D83—21no—
228C22×D83—21no—
229C22×D83—21no—
230C22×D83—21no—
231C22×D83#11712yes—
232C22×D83#13112yes—
233C22×D83#13112yes—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
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—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—41no—
250C2×C4×C83—41no—
251C2×C4×C83C4×D412yes—
252C2×C4×C83C4×D412yes—
253C2×C4×C83C22×D411yescharacteristic
254C2×C4×C83C2×#4111yescharacteristic
255C2×C4×C83C2×#4111yescharacteristic
256C2×C4×C83C2×#4111yescharacteristic
257C2×C4×C83H(5,𝔽2)11yescharacteristic
258C2×C4×C832−1+411yescharacteristic
259C22⋊D83—44no—
260C2×Dic83—21no—
261C2×Dic83—21no—
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—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#11712yes—
280C2×Dic83#13112yes—
281C4×D83—28no—
282C4×D83—22no—
283C4×D83—22no—
284C4×D83—22no—
285C4×D83—22no—
286C4×D83—44no—
287C8×C83—22no—
288C8×C83—22no—
289C8×C83—41no—
290C8×C83—41no—
291C83⋊C8—41no—
292C83⋊C8—41no—
293C83⋊C8—41no—
294C83⋊C8—41no—
295C22×C83—41no—
296C22×C83—41no—
297C22×C83—41no—
298C22×C83—41no—
299C22×C83—41no—
300C22×C83—41no—
301C22×C83—41no—
302C22×C83C2×#11711yescharacteristic
303C22×C83C2×C4×D411yescharacteristic
304C22×C83#52011yescharacteristic
305C22×C83C2×#13111yescharacteristic
306C22×C83C2×#13111yescharacteristic
307C22×C83C2×#13111yescharacteristic
308C22×C83#56811yescharacteristic
309C2×D83—22no—
310C2×D83—22no—
311C2×D83—22no—
312C2×D83—22no—
313C2×D83—22no—
314C2×D83—22no—
315C2×D83#43314yescomplemented
316C4×C83—22no—
317C4×C83—22no—
318C4×C83—41no—
319C4×C83—41no—
320C4×C83—41no—
321C4×C83#54611yescharacteristic
322C4×C83#54811yescharacteristic
323C4×C83#55211yescharacteristic
324C4×C83#55311yescharacteristic
325Dic83—22no—
326Dic83—22no—
327Dic83—41no—
328Dic83—41no—
329Dic83—41no—
330Dic83—41no—
331Dic83—41no—
332#22754—831nomaximal, Sylow
333C2×C83—81no—
334C2×C83#235211yescharacteristic
335C2×C83C2×#43311yescharacteristic
336C2×C83#292511yescharacteristic
337C2×C83#292911yescharacteristic
338C2×C83#293311yescharacteristic
339C2×C83#299211yescharacteristic
340C2×C83#299411yescharacteristic
341D83—24no—
342C2×#433D8311yescharacteristic, complemented
343C22×C4⋊C8—831no—
344#2290—831no—
345#1924—831no—
346#1923—831no—
347#1917—831no—
348#1916—831no—
349#1869—831no—
350#1869—831no—
351#1832—831no—
352#1798—831no—
353#1797—831no—
354#1768—831no—
355#1752—831no—
356C8×C22⋊C4—831no—
357C83#2275411yescharacteristic, complemented, Sylow
358C23×C8—831no—
359C23×C8—831no—
360C2×C4×D4—831no—
361C2×#117C2×D8311yescharacteristic
362C22×C42—831no—
363#433—24no—
364C2×C4⋊C8—831no—
365C2×C4⋊C8—831no—
366C2×C4⋊C8—831no—
367C2×C4⋊C8—831no—
368C2×C4⋊C8—1664no—
369C2×C4⋊C8C2×D8311yescharacteristic
370C2×C4⋊C8C2×D8311yescharacteristic
371C2×C22⋊C8—831no—
372C2×C22⋊C8—831no—
373C2×C22⋊C8—831no—
374C2×C22⋊C8—831no—
375C2×C22⋊C8C2×D8311yescharacteristic
376C2×C22⋊C8C2×D8311yescharacteristic
377C2×#97—831no—
378C2×#97C2×D8311yescharacteristic
379C2×C4×C8—831no—
380C2×C4×C8C2×D8311yescharacteristic
381#388—831no—
382#388—831no—
383#387—831no—
384#387—831no—
385#386—831no—
386#386—831no—
387#385—831no—
388#385—831no—
389C4×C4⋊C4—831no—
390C4×C22⋊C4—831no—
391C4×C22⋊C4—831no—
392#376—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—
403C22×D4—831no—
404C23×C4—831no—
405C23×C4—831no—
406C23×C4—831no—
407C23×C4C22×D8311yescharacteristic
408C22×C8—3321no—
409C22×C8—3321no—
410C22×C8—831no—
411C22×C8—831no—
412C22×C8—831no—
413C22×C8—831no—
414C22×C8—1662no—
415C22×C8—1662no—
416C22×C8—1662no—
417C22×C8—1662no—
418C22×C8C22×D8311yescharacteristic
419C22×C8C22×D8311yescharacteristic
420C22×C8C22×D8311yescharacteristic
421C22×C8C22×D8311yescharacteristic
422C4×D4—1662no—
423C4×D4—1662no—
424#117—22no—
425#117—22no—
426C2×C4⋊C4—831no—
427C2×C4⋊C4—831no—
428C2×C4⋊C4—831no—
429C2×C4⋊C4C4×D8311yescharacteristic
430C2×C4⋊C4C4×D8311yescharacteristic
431C2×C22⋊C4—831no—
432C2×C22⋊C4—831no—
433C2×C22⋊C4—831no—
434C2×C22⋊C4—831no—
435C2×C22⋊C4—831no—
436C2×C22⋊C4—831no—
437C2×C22⋊C4C4×D8311yescharacteristic
438C2×C22⋊C4C4×D8311yescharacteristic
439C2×C42—831no—
440C2×C42—831no—
441C2×C42—831no—
442C2×C42—831no—
443C2×C42—831no—
444C2×C42—1662no—
445C2×C42—1662no—
446C2×C42C22×D8311yescharacteristic
447C2×C42C22×D8311yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—1662no—
450C4⋊C8—1662no—
451C4⋊C8—1662no—
452C4⋊C8—1662no—
453C4⋊C8C22⋊D8314yescomplemented
454C22⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8—3321no—
457C22⋊C8—3321no—
458C22⋊C8—1662no—
459C22⋊C8—1662no—
460#97—22no—
461#97—3321no—
462C4×C8—22no—
463C4×C8—3321no—
464#95—831no—
465#95—831no—
466#95—831no—
467#95—831no—
468#95—831no—
469#95—831no—
470#95—831no—
471#95—831no—
472#95—831no—
473#95—831no—
474C24—831no—
475C24C2×C4×D8311yescharacteristic
476C2×D4—1662no—
477C2×D4—1662no—
478C2×D4—1662no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—3321no—
486C22×C4—831no—
487C22×C4—831no—
488C22×C4—832no—
489C22×C4—832no—
490C22×C4—831no—
491C22×C4—831no—
492C22×C4—831no—
493C22×C4—831no—
494C22×C4—831no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1662no—
504C22×C4C2×C4×D8311yescharacteristic
505C22×C4C2×C4×D8311yescharacteristic
506C22×C4C2×C4×D8311yescharacteristic
507C22×C4C2×C4×D8311yescharacteristic
508C22×C4C2×C4×D8311yescharacteristic
509C22×C4C23×D8311yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—3324no—
521C2×C8—3324no—
522C2×C8—1661no—
523C2×C8—1661no—
524C2×C8—1661no—
525C2×C8—1661no—
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×C8C2×C22⋊D8312yes—
535C2×C8C2×C22⋊D8312yes—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—3321no—
539C4⋊C4—1662no—
540C4⋊C4—1662no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—3321no—
544C22⋊C4—1662no—
545C22⋊C4—1662no—
546C22⋊C4—1662no—
547C22⋊C4—1662no—
548C22⋊C4—1662no—
549C42—21no—
550C42—21no—
551C42—1661no—
552C42—1661no—
553C42—1661no—
554C42—1661no—
555C42—1661no—
556C42—1661no—
557C42—1662no—
558C42—1662no—
559C42C2×C22⋊D8312yes—
560C42#1305059012yes—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—832no—
569C23—832no—
570C23—832no—
571C23—1661no—
572C23—1661no—
573C23—1661no—
574C23—1661no—
575C23C22×C4×D8311yescharacteristic
576D4—3324no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
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—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—3324no—
595C2×C4—832no—
596C2×C4—832no—
597C2×C4—1668no—
598C2×C4—1661no—
599C2×C4—1661no—
600C2×C4—1661no—
601C2×C4—1661no—
602C2×C4—1661no—
603C2×C4—1661no—
604C2×C4—1661no—
605C2×C4—1661no—
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—1662no—
618C2×C4—1662no—
619C2×C4—1662no—
620C2×C4—1662no—
621C2×C4C4×C22⋊D8312yes—
622C2×C4C4×C22⋊D8312yes—
623C2×C4C22×C22⋊D8311yescharacteristic
624C2×C4#41×D8311yescharacteristic
625C2×C4#41×D8311yescharacteristic
626C2×C4C2×#1305059011yescharacteristic
627C2×C4#1458183811yescharacteristic
628C2×C4#1458183911yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C8—3321no—
634C8—3321no—
635C8—3321no—
636C8—3321no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—834no—
645C22—1662no—
646C22—1662no—
647C22—1662no—
648C22—1662no—
649C22—1662no—
650C22—1662no—
651C22#117×D8311yescharacteristic
652C22C2×C4×C22⋊D8311yescharacteristic
653C22#1912818111yescharacteristic
654C22#131×D8311yescharacteristic
655C22#131×D8311yescharacteristic
656C22#131×D8311yescharacteristic
657C22#1912846611yescharacteristic
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—3321no—
664C4—3321no—
665C4—3321no—
666C4—3321no—
667C4—3321no—
668C4—1662no—
669C4—1662no—
670C4#1912833911yescharacteristic
671C4#1912835811yescharacteristic
672C4#1912839011yescharacteristic
673C4#1912839511yescharacteristic
674C2—81no—
675C2—1664no—
676C2#2491039311yescharacteristic
677C2#433×D8311yescharacteristic
678C2#2491612611yescharacteristic
679C2#2491615511yescharacteristic
680C2#2491618511yescharacteristic
681C2#2491659711yescharacteristic
682C2#2491661711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#433×C83C2
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenterC2×#433D83
hypocenterC83#22754
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C8×D83C2semidirect
3. #24908079C2semidirect
4. #24908072C2semidirect
5. #24908027C2semidirect
6. #24908020C2semidirect
9. #24907582C2semidirect
10. #24907447C2semidirect
11. #24907440C2semidirect
12. #24907322C2semidirect
13. #24907240C2semidirect
14. C8×(C2×D83)⋊C4C2semidirect
15. C2×#433×C83C2semidirect
127. C4⋊C8×C83D4semidirect
315. C2×D83#433semidirect
342. C2×#433D83semidirect
357. C83#22754semidirect
453. C4⋊C8C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D832
#249099002
#249080792
#249080722
#249080272
#249080202
#249077522
#249075822
#249074472
#249074402
#249073222
#249072402
C8×(C2×D83)⋊C42
C2×#433×C832
#2275483