Finite Group Databasebeta

← #35422554

Subgroups — #35422554

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×#19127772C211yesmaximal, characteristic
2C2×#19127740C211yesmaximal, characteristic, complemented
3#24910388C211yesmaximal, characteristic
4C4⋊C4×C22⋊D83C211yesmaximal, characteristic
5#24908232C211yesmaximal, characteristic, complemented
6#24908223C211yesmaximal, characteristic, complemented
7#24907661C211yesmaximal, characteristic, complemented
8#24907656C211yesmaximal, characteristic, complemented
9#24907654C211yesmaximal, characteristic, complemented
10#24907651C211yesmaximal, characteristic, complemented
11#24907628C211yesmaximal, characteristic, complemented
12#24907493C211yesmaximal, characteristic, complemented
13#24907492C211yesmaximal, characteristic, complemented
14#24907363C211yesmaximal, characteristic, complemented
15C22×#106×C83C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C2×C4×C22⋊D83—21no—
18C2×C4×C22⋊D83C2211yescharacteristic
19C2×#14581750C2211yescharacteristic
20C2×C4⋊C4×D83C2211yescharacteristic
21#19127772C418yescomplemented
22#19127740—24no—
23C2×#14581726C2211yescharacteristic
24C2×#14581726C2211yescharacteristic
25C2×#14581725C2211yescharacteristic
26C2×#14581725C2211yescharacteristic
27C2×#14581723C2211yescharacteristic
28C2×#14581723C2211yescharacteristic
29C2×Dic83⋊C8C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×#14581702C2211yescharacteristic
33#19127596—21no—
34#19127591—21no—
35#19127582—21no—
36#19127580—21no—
37#19127574—21no—
38#19127572—21no—
39#19127570C2211yescharacteristic
40#19127566C2211yescharacteristic
41#19127561C2211yescharacteristic
42#19127561C2211yescharacteristic
43#19127558C2211yescharacteristic
44#19127558C2211yescharacteristic
45C4⋊C4×Dic83C2211yescharacteristic
46C4⋊C4×Dic83C2211yescharacteristic
47C4×C22⋊Dic83—21no—
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53#19127463C2211yescharacteristic
54C23×C8×C83C2211yescharacteristic
55C22×C4⋊C4×C83C2211yescharacteristic
56C22×C4⋊C4×C83C2211yescharacteristic
57C2×#106×C83—24no—
58C2×#106×C83C2211yescharacteristic
59C2×#106×C83C2211yescharacteristic
60C2×#106×C83C2211yescharacteristic
61C2×#106×C83C2211yescharacteristic
62C22×C22⋊D83D411yescharacteristic
63C22×C4×D83—21no—
64C22×C4×D83C2311yescharacteristic
65C2×#13050573—22no—
66C2×#13050573—22no—
67C2×#13050573C2×C414yescomplemented
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C4×C22⋊D83—44no—
71C4×C22⋊D83C2×C414yes—
72C4×C22⋊D83Q814yes—
73#14581750—22no—
74#14581750—41no—
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C4⋊Dic83C2311yescharacteristic
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×Dic83⋊C4D411yescharacteristic
83C4⋊C4×D83—22no—
84C4⋊C4×D83—41no—
85C2×C22⋊Dic83—21no—
86C2×C22⋊Dic83—21no—
87C2×C22⋊Dic83D411yescharacteristic
88C2×(C2×D83)⋊C4—21no—
89C2×(C2×D83)⋊C4—21no—
90C2×(C2×D83)⋊C4—21no—
91C2×(C2×D83)⋊C4D411yescharacteristic
92C2×C4×Dic83—21no—
93C2×C4×Dic83—21no—
94C2×C4×Dic83—21no—
95C2×C4×Dic83C2311yescharacteristic
96#14581726—22no—
97#14581726—22no—
98#14581725—22no—
99#14581725—41no—
100#14581723—22no—
101#14581723—41no—
102Dic83⋊C8C2×C414yescomplemented
103C22⋊(C83⋊C8)C2×C414yescomplemented
104(C2×D83)⋊C8C2×C414yescomplemented
105#14581702C2×C414yescomplemented
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C83⋊#95—21no—
110C83⋊#95—21no—
111C83⋊#95—21no—
112C83⋊#95—21no—
113C83⋊#95—21no—
114C23×C4×C83—21no—
115C23×C4×C83—21no—
116C23×C4×C83C2311yescharacteristic
117C22×C8×C83—22no—
118C22×C8×C83—22no—
119C22×C8×C83C2×C414yescomplemented
120C22×C8×C83C2311yescharacteristic
121C22×C8×C83C2311yescharacteristic
122C2×C4⋊C4×C83—22no—
123C2×C4⋊C4×C83—22no—
124C2×C4⋊C4×C83—21no—
125C2×C4⋊C4×C83—21no—
126C2×C4⋊C4×C83—41no—
127C2×C4⋊C4×C83—41no—
128C2×C4⋊C4×C83C2311yescharacteristic
129C2×C4⋊C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83C2311yescharacteristic
131C2×C4⋊C4×C83C2311yescharacteristic
132#106×C83—22no—
133#106×C83—22no—
134#106×C83—22no—
135#106×C83D414yescomplemented
136C23×D83C2×D411yescharacteristic
137C2×C22⋊D83—22no—
138C2×C22⋊D83—22no—
139C2×C22⋊D83C4⋊C414yes—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83C2×D411yescharacteristic
145C22×Dic83C2×D411yescharacteristic
146C22×Dic83C2×D411yescharacteristic
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—42no—
152C2×C4×D83—42no—
153C2×C4×D83—81no—
154C2×C4×D83C22×C412yes—
155C2×C4×D83C2×Q812yes—
156#13050573—28no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8C22×C412yes—
162C2×C83⋊C8C22×C412yes—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171Dic83⋊C4—42no—
172Dic83⋊C4—42no—
173Dic83⋊C4—81no—
174Dic83⋊C4C4⋊C414yes—
175C22⋊Dic83—42no—
176C22⋊Dic83—42no—
177C22⋊Dic83C4⋊C414yes—
178(C2×D83)⋊C4—42no—
179(C2×D83)⋊C4—42no—
180(C2×D83)⋊C4—81no—
181(C2×D83)⋊C4C4⋊C414yes—
182C4×Dic83—42no—
183C4×Dic83—42no—
184C4×Dic83—81no—
185C4×Dic83C22×C412yes—
186C4×Dic83C2×Q812yes—
187C24×C83C2×D411yescharacteristic
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—42no—
197C22×C4×C83—42no—
198C22×C4×C83—42no—
199C22×C4×C83—42no—
200C22×C4×C83—81no—
201C22×C4×C83—81no—
202C22×C4×C83C22×C412yes—
203C22×C4×C83C2×D411yescharacteristic
204C22×C4×C83C2×Q812yes—
205C22×C4×C83C2411yescharacteristic
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—28no—
209C2×C8×C83C22×C412yes—
210C2×C8×C83C22×C412yes—
211C2×C8×C83C2×D412yes—
212C2×C8×C83#4112yes—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—21no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—42no—
220C4⋊C4×C83—42no—
221C4⋊C4×C83C2×D412yes—
222C4⋊C4×C83C2×D412yes—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83C2×C4⋊C412yes—
228C23×C83AGL(1,ℤ/8)12yes—
229C23×C83#13712yes—
230C23×C83C22×D411yescharacteristic
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83—21no—
235C22×D83—21no—
236C22×D83—21no—
237C22×D83C2×C4⋊C412yes—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—22no—
241C2×C4×C83—22no—
242C2×C4×C83—22no—
243C2×C4×C83—22no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—41no—
250C2×C4×C83—41no—
251C2×C4×C83—41no—
252C2×C4×C83—41no—
253C2×C4×C83—41no—
254C2×C4×C83—41no—
255C2×C4×C83—41no—
256C2×C4×C83—84no—
257C2×C4×C83—84no—
258C2×C4×C83C2×C4⋊C412yes—
259C2×C4×C83C23×C411yescharacteristic
260C2×C4×C83C22×D411yescharacteristic
261C2×C4×C83C22×Q811yescharacteristic
262C2×C4×C83C2×#4111yescharacteristic
263C2×C4×C83H(5,𝔽2)11yescharacteristic
264C2×C4×C832−1+411yescharacteristic
265C22⋊D83—28no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—21no—
269C2×Dic83—21no—
270C2×Dic83—21no—
271C2×Dic83—21no—
272C2×Dic83—41no—
273C2×Dic83—41no—
274C2×Dic83—41no—
275C2×Dic83—41no—
276C2×Dic83—41no—
277C2×Dic83—41no—
278C2×Dic83—41no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83C2×C4⋊C412yes—
285C2×Dic83C2×C4⋊C412yes—
286C2×Dic83C2×C4⋊C412yes—
287C4×D83—22no—
288C4×D83—22no—
289C4×D83—22no—
290C4×D83—22no—
291C4×D83—84no—
292C8×C83—22no—
293C8×C83C4×D414yescomplemented
294C83⋊C8—22no—
295C83⋊C8—22no—
296C22×C83—22no—
297C22×C83—22no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—22no—
301C22×C83—22no—
302C22×C83#42814yescomplemented
303C22×C83C22×C4⋊C411yescharacteristic
304C22×C83D4211yescharacteristic
305C22×C83#54711yescharacteristic
306C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C83C2×#13711yescharacteristic
308C22×C83#57711yescharacteristic
309C22×C83#57711yescharacteristic
310C2×D83—22no—
311C2×D83—22no—
312C2×D83—22no—
313C2×D83—41no—
314C2×D83—41no—
315C2×D83—41no—
316C2×D83—41no—
317C4×C83—22no—
318C4×C83—42no—
319C4×C83—42no—
320C4×C83—81no—
321C4×C83—81no—
322C4×C83C2×C4×D411yescharacteristic
323C4×C83#52011yescharacteristic
324C4×C83D4×Q811yescharacteristic
325C4×C83#55411yescharacteristic
326Dic83—22no—
327Dic83—22no—
328Dic83—22no—
329Dic83—81no—
330Dic83—81no—
331Dic83—81no—
332Dic83—81no—
333#22659—831nomaximal, Sylow
334C2×C83—24no—
335C2×C83D4×C4⋊C411yescharacteristic
336C2×C83C2×#42811yescharacteristic
337C2×C83#291211yescharacteristic
338C2×C83#326511yescharacteristic
339C2×C83#326611yescharacteristic
340C2×C83#334411yescharacteristic
341C2×C83#334511yescharacteristic
342D83—42no—
343C2×#435—831no—
344C2×#428—831no—
345C22×#106D8311yescharacteristic, complemented
346#2352—831no—
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×C8C2×D8311yescharacteristic
361C2×C4×D4—831no—
362C2×C4×D4—1661no—
363C2×#117—831no—
364C22×C4⋊C4—831no—
365C22×C4⋊C4C2×D8311yescharacteristic
366C22×C4⋊C4C2×D8311yescharacteristic
367#435—838no—
368#428—1664no—
369C2×#107—831no—
370C2×#107—831no—
371C2×#107—831no—
372C2×#107—831no—
373C2×#106—24no—
374C2×#106—831no—
375C2×#106—831no—
376C2×#106C2×D8311yescharacteristic
377C2×#106C2×D8311yescharacteristic
378C2×#106C2×D8311yescharacteristic
379C2×#106C2×D8311yescharacteristic
380C2×C4⋊C8—831no—
381C2×C22⋊C8—831no—
382C2×C22⋊C8—831no—
383C2×#97—831no—
384#389—1661no—
385#388—1661no—
386#387—1661no—
387#386—1661no—
388#385—1661no—
389#385—1661no—
390#384—831no—
391#382—831no—
392#380—831no—
393#380—831no—
394#380—831no—
395#380—831no—
396C4×C4⋊C4—831no—
397C4×C4⋊C4—831no—
398C4×C22⋊C4—1661no—
399#340—831no—
400#340—831no—
401#340—831no—
402#340—831no—
403#340—831no—
404#340—831no—
405C22×D4—831no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—831no—
409C23×C4—1661no—
410C23×C4C22×D8311yescharacteristic
411C2×M16—834no—
412C2×M16—1662no—
413C2×M16—1662no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—831no—
417C22×C8—831no—
418C22×C8C4×D8314yescomplemented
419C22×C8C22×D8311yescharacteristic
420C22×C8C22×D8311yescharacteristic
421C4×D4—3324no—
422C4×D4—834no—
423C4×D4—834no—
424#117—3321no—
425#117—1662no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—3321no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—831no—
435C2×C4⋊C4—831no—
436C2×C4⋊C4—831no—
437C2×C4⋊C4—831no—
438C2×C4⋊C4—1661no—
439C2×C4⋊C4—1661no—
440C2×C4⋊C4—1662no—
441C2×C4⋊C4—1661no—
442C2×C4⋊C4C22×D8311yescharacteristic
443C2×C4⋊C4C22×D8311yescharacteristic
444C2×C4⋊C4C22×D8311yescharacteristic
445C2×C4⋊C4C22×D8311yescharacteristic
446C2×C22⋊C4—831no—
447C2×C22⋊C4—831no—
448C2×C22⋊C4—1661no—
449C2×C22⋊C4—1661no—
450C2×C22⋊C4—1661no—
451C2×C22⋊C4—1661no—
452C2×C22⋊C4—1661no—
453C2×C42—831no—
454C2×C42—1661no—
455C2×C42—1661no—
456C2×C42—1661no—
457#107—3321no—
458#107—1662no—
459#107—1662no—
460#107—1662no—
461#106—22no—
462#106—22no—
463#106—22no—
464#106—3321no—
465#106—1662no—
466#106C22⋊D8314yescomplemented
467C4⋊C8—834no—
468C22⋊C8—834no—
469C22⋊C8—834no—
470#97—834no—
471#95—1661no—
472#95—1661no—
473#95—1661no—
474#95—1661no—
475#95—1661no—
476#95—1661no—
477#95—1661no—
478#95—1661no—
479C24—831no—
480C24D4×D8311yescharacteristic
481C2×D4—834no—
482C2×D4—1662no—
483C2×D4—1662no—
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—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—3322no—
499C22×C4—3322no—
500C22×C4—831no—
501C22×C4—831no—
502C22×C4—831no—
503C22×C4—832no—
504C22×C4—832no—
505C22×C4—6641no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4—1661no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4—1661no—
513C22×C4—1661no—
514C22×C4C2×C4×D8312yes—
515C22×C4D4×D8311yescharacteristic
516C22×C4Q8×D8312yes—
517C22×C4C23×D8311yescharacteristic
518M16—1668no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—28no—
522C2×C8—832no—
523C2×C8—832no—
524C2×C8—1661no—
525C2×C8—1661no—
526C2×C8—1661no—
527C2×C8—1661no—
528C2×C8C2×C4×D8312yes—
529C2×C8C2×C4×D8312yes—
530C2×C8C2×C22⋊D8312yes—
531C2×C8#1305059012yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—3322no—
541C4⋊C4—3322no—
542C4⋊C4—834no—
543C4⋊C4—6641no—
544C4⋊C4—1661no—
545C4⋊C4—1661no—
546C4⋊C4—1661no—
547C4⋊C4—1661no—
548C4⋊C4—1661no—
549C4⋊C4—1661no—
550C4⋊C4—1661no—
551C4⋊C4—1661no—
552C4⋊C4C2×C22⋊D8312yes—
553C4⋊C4C2×C22⋊D8312yes—
554C22⋊C4—3322no—
555C22⋊C4—3322no—
556C22⋊C4—3322no—
557C22⋊C4—3322no—
558C22⋊C4—834no—
559C22⋊C4—834no—
560C22⋊C4—6641no—
561C42—3322no—
562C42—3322no—
563C42—832no—
564C42—832no—
565C42—6641no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—832no—
571C23—1661no—
572C23—1661no—
573C23—1661no—
574C23—1661no—
575C23—1661no—
576C23—1661no—
577C23C4⋊C4×D8312yes—
578C23#1458181912yes—
579C23#1458182112yes—
580C23C2×D4×D8311yescharacteristic
581D4—1668no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—3321no—
603C2×C4—3321no—
604C2×C4—3321no—
605C2×C4—3321no—
606C2×C4—3321no—
607C2×C4—3321no—
608C2×C4—3321no—
609C2×C4—3321no—
610C2×C4—3321no—
611C2×C4—3321no—
612C2×C4—3321no—
613C2×C4—3321no—
614C2×C4—832no—
615C2×C4—832no—
616C2×C4—832no—
617C2×C4—6644no—
618C2×C4—1661no—
619C2×C4—1661no—
620C2×C4—1661no—
621C2×C4—1661no—
622C2×C4—1661no—
623C2×C4—1661no—
624C2×C4—1662no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4C4⋊C4×D8312yes—
629C2×C4C22×C4×D8311yescharacteristic
630C2×C4C22×C22⋊D8311yescharacteristic
631C2×C4C2×Q8×D8311yescharacteristic
632C2×C4C2×#1305059011yescharacteristic
633C2×C4#1458183711yescharacteristic
634C2×C4#1458184011yescharacteristic
635C8—22no—
636C8—1662no—
637C8—1662no—
638C8C4×C22⋊D8314yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—3321no—
646C22—3321no—
647C22—3321no—
648C22—3321no—
649C22—1662no—
650C22—1662no—
651C22—1662no—
652C22#1912774014yescomplemented
653C22C2×C4⋊C4×D8311yescharacteristic
654C22D4×C22⋊D8311yescharacteristic
655C22#1912835211yescharacteristic
656C22C2×#1458181911yescharacteristic
657C22C2×#1458182111yescharacteristic
658C22#1912850711yescharacteristic
659C22#1912850711yescharacteristic
660C4—22no—
661C4—42no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—6641no—
666C4—6641no—
667C4—6641no—
668C4—6641no—
669C4—1662no—
670C4—1662no—
671C4—1662no—
672C4C2×C4×C22⋊D8311yescharacteristic
673C4#1912818211yescharacteristic
674C4Q8×C22⋊D8311yescharacteristic
675C4#1912840611yescharacteristic
676C2—24no—
677C2—3322no—
678C2C4⋊C4×C22⋊D8311yescharacteristic
679C2C2×#1912774011yescharacteristic
680C2#2491605411yescharacteristic
681C2#2491895811yescharacteristic
682C2#2491897311yescharacteristic
683C2#2491991411yescharacteristic
684C2#2491992911yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC22×#106×C83C2
socleC23×C83C22×D4
prime radicalC22×C22⋊D83D4
cosocleC22×C4×C83C24
hypercenterC22×#106D83
hypocenterC83#22659
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#19127740C2semidirect
5. #24908232C2semidirect
6. #24908223C2semidirect
7. #24907661C2semidirect
8. #24907656C2semidirect
9. #24907654C2semidirect
10. #24907651C2semidirect
11. #24907628C2semidirect
12. #24907493C2semidirect
13. #24907492C2semidirect
14. #24907363C2semidirect
15. C22×#106×C83C2semidirect
21. #19127772C4semidirect
67. C2×#13050573C2×C4semidirect
102. Dic83⋊C8C2×C4semidirect
103. C22⋊(C83⋊C8)C2×C4semidirect
104. (C2×D83)⋊C8C2×C4semidirect
105. #14581702C2×C4semidirect
119. C22×C8×C83C2×C4semidirect
135. #106×C83D4semidirect
293. C8×C83C4×D4semidirect
302. C22×C83#428semidirect
345. C22×#106D83semidirect
358. C83#22659semidirect
418. C22×C8C4×D83semidirect
466. #106C22⋊D83semidirect
638. C8C4×C22⋊D83semidirect
652. C22#19127740semidirect

Maximal subgroups

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

subgroupindex
C2×#191277722
C2×#191277402
#249103882
C4⋊C4×C22⋊D832
#249082322
#249082232
#249076612
#249076562
#249076542
#249076512
#249076282
#249074932
#249074922
#249073632
C22×#106×C832
#2265983