Finite Group Databasebeta

← #35425347

Subgroups — #35425347

Order 21248.

912 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×#19127770C211yesmaximal, characteristic
2C2×#19127754C211yesmaximal, characteristic, complemented
3C4×#14581775C211yesmaximal, characteristic
4#24908180C211yesmaximal, characteristic, complemented
5#24908077C211yesmaximal, characteristic, complemented
6#24908067C211yesmaximal, characteristic, complemented
7#24908030C211yesmaximal, characteristic, complemented
8#24908018C211yesmaximal, characteristic, complemented
9#24907760C211yesmaximal, characteristic
10#24907646C211yesmaximal, characteristic, complemented
11#24907642C211yesmaximal, characteristic, complemented
12#24907334C211yesmaximal, characteristic, complemented
13#24907244C211yesmaximal, characteristic, complemented
14#24907233C211yesmaximal, characteristic, complemented
15C83×#1728C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C2×#14581775C411yescharacteristic
18C2×C4×C22⋊D83C2211yescharacteristic
19#19127770—24no—
20#19127754—24no—
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×Dic83⋊C8C2211yescharacteristic
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×(C2×D83)⋊C8C2211yescharacteristic
31C2×#14581702C2211yescharacteristic
32C2×#14581702C2211yescharacteristic
33C2×C4×C83⋊C8C2211yescharacteristic
34C2×C4×C83⋊C8C2211yescharacteristic
35C2×C8×Dic83C2211yescharacteristic
36#19127592C411yescharacteristic
37#19127592C411yescharacteristic
38#19127585C411yescharacteristic
39#19127585C411yescharacteristic
40#19127580C411yescharacteristic
41#19127574C411yescharacteristic
42#19127564C411yescharacteristic
43C4×Dic83⋊C4C2211yescharacteristic
44C4×Dic83⋊C4C2211yescharacteristic
45C4×(C2×D83)⋊C4C2211yescharacteristic
46C4×(C2×D83)⋊C4C2211yescharacteristic
47C4×C22⋊Dic83C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C22×M16×C83C2211yescharacteristic
55C22×M16×C83C2211yescharacteristic
56C22×C42×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×C22⋊D83C2×C411yescharacteristic
62C22×C4×D83C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C2×C8×D83—22no—
68C2×C8×D83—22no—
69C2×C8×D83—41no—
70#14581775—24no—
71C4×C22⋊D83—22no—
72C4×C22⋊D83—22no—
73C2×Dic83⋊C4C2×C411yescharacteristic
74C2×Dic83⋊C4C2×C411yescharacteristic
75C2×Dic83⋊C4C2×C411yescharacteristic
76C2×Dic83⋊C4C2×C411yescharacteristic
77C2×Dic83⋊C4C2×C411yescharacteristic
78C2×C22⋊Dic83C2×C411yescharacteristic
79C2×C22⋊Dic83C2×C411yescharacteristic
80C2×C22⋊Dic83C2×C411yescharacteristic
81C2×(C2×D83)⋊C4C2×C411yescharacteristic
82C2×(C2×D83)⋊C4C2×C411yescharacteristic
83C2×(C2×D83)⋊C4C2×C411yescharacteristic
84C2×(C2×D83)⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×C4×Dic83C2311yescharacteristic
87C2×C4×Dic83C2311yescharacteristic
88C2×C4×Dic83C2311yescharacteristic
89C4⋊(C83⋊C8)—22no—
90C4⋊(C83⋊C8)—22no—
91Dic83⋊C8—22no—
92Dic83⋊C8—22no—
93Dic83⋊C8—41no—
94C22⋊(C83⋊C8)—22no—
95C22⋊(C83⋊C8)D414yes—
96(C2×D83)⋊C8—22no—
97(C2×D83)⋊C8—22no—
98(C2×D83)⋊C8—41no—
99#14581702—22no—
100#14581702—22no—
101C4×C83⋊C8—22no—
102C4×C83⋊C8—22no—
103C8×Dic83—41no—
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
113C83⋊#95C2×C411yescharacteristic
114C23×C4×C83C2×C411yescharacteristic
115C23×C4×C83C2×C411yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C2×M16×C83—22no—
118C2×M16×C83—22no—
119C2×M16×C83—22no—
120C2×M16×C83—22no—
121C2×M16×C83—41no—
122C2×M16×C83—41no—
123C22×C8×C83C2311yescharacteristic
124C22×C8×C83C2311yescharacteristic
125C22×C8×C83C2311yescharacteristic
126C22×C8×C83C2311yescharacteristic
127C2×C42×C83—22no—
128C2×C42×C83—22no—
129C2×C42×C83C2×C411yescharacteristic
130C2×C42×C83C2×C411yescharacteristic
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2311yescharacteristic
133C23×D83C22×C411yescharacteristic
134C2×C22⋊D83—22no—
135C2×C22⋊D83—22no—
136C2×C22⋊D83—41no—
137C22×Dic83C22×C411yescharacteristic
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C22×Dic83C22×C411yescharacteristic
143C22×Dic83C22×C411yescharacteristic
144C2×C4×D83—21no—
145C2×C4×D83—21no—
146C2×C4×D83—21no—
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8C2×D412yes—
161C2×C83⋊C8C2×D412yes—
162C8×D83—44no—
163Dic83⋊C4—22no—
164Dic83⋊C4—22no—
165Dic83⋊C4—22no—
166Dic83⋊C4—22no—
167Dic83⋊C4—22no—
168C22⋊Dic83—22no—
169C22⋊Dic83—22no—
170C22⋊Dic83—41no—
171(C2×D83)⋊C4—22no—
172(C2×D83)⋊C4—22no—
173(C2×D83)⋊C4—22no—
174(C2×D83)⋊C4—22no—
175(C2×D83)⋊C4M1614yescomplemented
176C4×Dic83—21no—
177C4×Dic83—21no—
178C4×Dic83—21no—
179C4×Dic83—21no—
180C4×Dic83—21no—
181C4×Dic83—21no—
182C24×C83C22×C411yescharacteristic
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—41no—
193C22×C4×C83C22×C411yescharacteristic
194C22×C4×C83C22×C411yescharacteristic
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C2×D412yes—
199C22×C4×C83#4112yes—
200C22×C4×C83C2411yescharacteristic
201M16×C83—44no—
202M16×C83—44no—
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—21no—
212C2×C8×C83—21no—
213C2×C8×C83#4112yes—
214C2×C8×C83#4112yes—
215C42×C83—22no—
216C42×C83—22no—
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×C83—21no—
226C23×C83—21no—
227C23×C83C4×D412yes—
228C23×C83C23×C411yescharacteristic
229C22×D83—21no—
230C22×D83—21no—
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83—21no—
235C22×D83C2×M1612yes—
236C2×C4×C83—28no—
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—22no—
246C2×C4×C83—22no—
247C2×C4×C83—22no—
248C2×C4×C83—22no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—44no—
253C2×C4×C83C4×D412yes—
254C2×C4×C83C2×M1612yes—
255C2×C4×C83#13112yes—
256C2×C4×C83#13112yes—
257C2×C4×C83C22×D411yescharacteristic
258C2×C4×C83C2×#4111yescharacteristic
259C2×C4×C83C2×#4111yescharacteristic
260C2×C4×C83C2×#4111yescharacteristic
261C2×C4×C83H(5,𝔽2)11yescharacteristic
262C2×C4×C832−1+411yescharacteristic
263C22⋊D83—44no—
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—21no—
281C2×Dic83—21no—
282C2×Dic83—21no—
283C2×Dic83—21no—
284C2×Dic83C2×M1612yes—
285C4×D83—41no—
286C4×D83—41no—
287C4×D83—41no—
288C4×D83—41no—
289C8×C83—22no—
290C8×C83—22no—
291C8×C83—41no—
292C8×C83—41no—
293C83⋊C8—22no—
294C83⋊C8—22no—
295C83⋊C8—41no—
296C83⋊C8—41no—
297C22×C83—22no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—41no—
301C22×C83—41no—
302C22×C83—41no—
303C22×C83—41no—
304C22×C83C2×C4×D411yescharacteristic
305C22×C83C4×#4111yescharacteristic
306C22×C83#52011yescharacteristic
307C22×C83C22×M1611yescharacteristic
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—22no—
322C4×C83—41no—
323C4×C83#54611yescharacteristic
324C4×C83#54711yescharacteristic
325C4×C83#55111yescharacteristic
326C4×C83#55211yescharacteristic
327Dic83—22no—
328Dic83—41no—
329Dic83—41no—
330Dic83—41no—
331Dic83—41no—
332Dic83—41no—
333Dic83—41no—
334#22904—831nomaximal, Sylow
335C2×C83—42no—
336C2×C83#235911yescharacteristic
337C2×C83#292911yescharacteristic
338C2×C83D4×M1611yescharacteristic
339C2×C83#296511yescharacteristic
340C2×C83#296911yescharacteristic
341C2×C83#299011yescharacteristic
342C2×C83#299311yescharacteristic
343D83—42no—
344C2×#435—831no—
345C2×#431—831no—
346C4×#123—831no—
347#1939—831no—
348#1924—831no—
349#1923—831no—
350#1917—831no—
351#1916—831no—
352#1870—831no—
353#1851—831no—
354#1850—831no—
355#1771—831no—
356#1753—831no—
357C8×C22⋊C4—831no—
358#1728D8311yescharacteristic, complemented
359C83#2290411yescharacteristic, complemented, Sylow
360C22×M16C2×D8311yescharacteristic
361C22×M16C2×D8311yescharacteristic
362C23×C8—831no—
363C2×#123—831no—
364C2×C4×D4—831no—
365C22×C42C2×D8311yescharacteristic
366#435—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⋊C8—831no—
378C2×#97—831no—
379C2×#97—831no—
380C2×C4×C8—831no—
381C2×C4×C8—831no—
382C2×C4×C8—831no—
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⋊C4—831no—
395#336—831no—
396#336—831no—
397#336—831no—
398#336—831no—
399#336—831no—
400#336—831no—
401#336C2×D8311yescharacteristic
402#336C2×D8311yescharacteristic
403#336C2×D8311yescharacteristic
404#336C2×D8311yescharacteristic
405C22×D4—831no—
406C23×C4—831no—
407C23×C4C4×D8311yescharacteristic
408C23×C4C4×D8311yescharacteristic
409C23×C4C22×D8311yescharacteristic
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—41no—
415C2×M16—41no—
416C22×C8—3321no—
417C22×C8—831no—
418C22×C8—831no—
419C22×C8—831no—
420C22×C8—831no—
421C22×C8—1662no—
422C22×C8—1662no—
423C22×C8C22×D8311yescharacteristic
424C22×C8C22×D8311yescharacteristic
425C22×C8C22×D8311yescharacteristic
426C22×C8C22×D8311yescharacteristic
427#123—1664no—
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⋊C4—831no—
442C2×C22⋊C4—831no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—831no—
446C2×C42—831no—
447C2×C42—831no—
448C2×C42C4×D8311yescharacteristic
449C2×C42C4×D8311yescharacteristic
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—834no—
459C22⋊C8—1662no—
460C22⋊C8—1662no—
461C22⋊C8—1662no—
462#97—1662no—
463#97—1662no—
464C4×C8—3321no—
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#95—831no—
476#95—831no—
477C24—831no—
478C24C2×C4×D8311yescharacteristic
479C2×D4—3321no—
480C2×D4—1662no—
481C2×D4—1662no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—831no—
493C22×C4—831no—
494C22×C4—831no—
495C22×C4—831no—
496C22×C4—831no—
497C22×C4—831no—
498C22×C4—831no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1661no—
505C22×C4C2×C4×D8311yescharacteristic
506C22×C4C2×C4×D8311yescharacteristic
507C22×C4C2×C4×D8311yescharacteristic
508C22×C4C2×C4×D8311yescharacteristic
509C22×C4C2×C4×D8311yescharacteristic
510C22×C4D4×D8312yes—
511C22×C4#1305058912yes—
512C22×C4C23×D8311yescharacteristic
513M16—44no—
514M16—44no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—3324no—
526C2×C8—832no—
527C2×C8—832no—
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×C8—1661no—
538C2×C8#1305059012yes—
539C2×C8#1305059012yes—
540C4⋊C4—1662no—
541C4⋊C4—1662no—
542C4⋊C4—1662no—
543C4⋊C4—1662no—
544C4⋊C4—1662no—
545C22⋊C4—3321no—
546C22⋊C4—834no—
547C22⋊C4—1662no—
548C22⋊C4—1662no—
549C22⋊C4—1662no—
550C22⋊C4—1662no—
551C22⋊C4—1662no—
552C22⋊C4—1662no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—22no—
558C42—22no—
559C42—1661no—
560C42—1661no—
561C42—1661no—
562C42—1661no—
563C42—1661no—
564C42—1661no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—832no—
572C23—1661no—
573C23—1661no—
574C23—1661no—
575C23—1661no—
576C23—1661no—
577C23—1661no—
578C23(C22⋊D83)⋊C412yes—
579C23C22×C4×D8311yescharacteristic
580D4—3324no—
581C2×C4—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—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—44no—
598C2×C4—3321no—
599C2×C4—3321no—
600C2×C4—3321no—
601C2×C4—3321no—
602C2×C4—832no—
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—1661no—
618C2×C4—1661no—
619C2×C4—1661no—
620C2×C4—1661no—
621C2×C4—1661no—
622C2×C4—1661no—
623C2×C4(C22⋊D83)⋊C412yes—
624C2×C4M16×D8312yes—
625C2×C4#1458180012yes—
626C2×C4#1458180012yes—
627C2×C4C2×D4×D8311yescharacteristic
628C2×C4C2×#1305058911yescharacteristic
629C2×C4C2×#1305059011yescharacteristic
630C2×C4C2×#1305059011yescharacteristic
631C2×C4#1458183711yescharacteristic
632C2×C4#1458184011yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C8—3321no—
638C8—3321no—
639C8—1662no—
640C8—1662no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—3321no—
649C22—3321no—
650C22—3321no—
651C22—3321no—
652C22—1662no—
653C22—1662no—
654C22—1662no—
655C22C2×(C22⋊D83)⋊C411yescharacteristic
656C22C4×#1305059011yescharacteristic
657C22#1912818211yescharacteristic
658C22C2×M16×D8311yescharacteristic
659C22C2×#1458180011yescharacteristic
660C22C2×#1458180011yescharacteristic
661C22#1912846711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—3321no—
668C4—3321no—
669C4—3321no—
670C4—3321no—
671C4—3321no—
672C4—3321no—
673C4—1662no—
674C4#1912834111yescharacteristic
675C4#1912835211yescharacteristic
676C4#1912837711yescharacteristic
677C4#1912838611yescharacteristic
678C2—42no—
679C2—3322no—
680C2#2491045111yescharacteristic
681C2#2491615311yescharacteristic
682C2#2491619511yescharacteristic
683C2#2491642511yescharacteristic
684C2#2491646711yescharacteristic
685C2#2491658911yescharacteristic
686C2#2491660811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1728C2
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1728D83
hypocenterC83#22904
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. C2×#19127754C2semidirect
4. #24908180C2semidirect
5. #24908077C2semidirect
6. #24908067C2semidirect
7. #24908030C2semidirect
8. #24908018C2semidirect
10. #24907646C2semidirect
11. #24907642C2semidirect
12. #24907334C2semidirect
13. #24907244C2semidirect
14. #24907233C2semidirect
15. C83×#1728C2semidirect
175. (C2×D83)⋊C4M16semidirect
358. #1728D83semidirect
359. C83#22904semidirect

Maximal subgroups

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

subgroupindex
C2×#191277702
C2×#191277542
C4×#145817752
#249081802
#249080772
#249080672
#249080302
#249080182
#249077602
#249076462
#249076422
#249073342
#249072442
#249072332
C83×#17282
#2290483