Finite Group Databasebeta

← #35326939

Subgroups — #35326939

Order 21248.

1862 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581750C211yesmaximal, characteristic
2C2×#19127558C211yesmaximal, characteristic
3C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
4#24905711C214yesmaximal
5#24905693C211yesmaximal, characteristic, complemented
6#24905692C211yesmaximal, characteristic, complemented
7#24905692C211yesmaximal, characteristic, complemented
8#24905689C214yesmaximal, complemented
9C83×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D83C2211yescharacteristic
11C2×#14581750—24no—
12C2×#14581750—24no—
13C2×#14581750C418yescomplemented
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×(C2×D83)⋊C4C2212yes—
17C22×(C2×D83)⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2212yes—
19C22×C4×Dic83C2211yescharacteristic
20C22×C4×Dic83C2212yes—
21#19127558—24no—
22C4×(C2×D83)⋊C4—24no—
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2214yes—
26C2×C83⋊#95C2214yes—
27C2×C83⋊#95C2214yes—
28C22×C4⋊C4×C83C2211yescharacteristic
29C22×C4⋊C4×C83C2211yescharacteristic
30C22×C42×C83C2211yescharacteristic
31C2×#95×C83C2214yes—
32C24×D83C2311yescharacteristic
33C23×Dic83C2312yes—
34C23×Dic83C2312yes—
35C23×Dic83C2312yes—
36C23×Dic83C2311yescharacteristic
37C22×C4×D83—22no—
38C22×C4×D83—22no—
39C22×C4×D83—22no—
40C22×C4×D83—22no—
41C22×C4×D83C2×C414yes—
42C22×C4×D83D414yes—
43C22×C4×D83D414yes—
44#14581750—232no—
45C2×C4⋊Dic83—22no—
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83C2×C414yes—
51C2×(C2×D83)⋊C4—24no—
52C2×(C2×D83)⋊C4—24no—
53C2×(C2×D83)⋊C4—24no—
54C2×(C2×D83)⋊C4—24no—
55C2×(C2×D83)⋊C4—24no—
56C2×(C2×D83)⋊C4—24no—
57C2×(C2×D83)⋊C4—44no—
58C2×(C2×D83)⋊C4C2×C418yes—
59C2×C4×Dic83—24no—
60C2×C4×Dic83—24no—
61C2×C4×Dic83—22no—
62C2×C4×Dic83—22no—
63C2×C4×Dic83—22no—
64C2×C4×Dic83C2×C418yes—
65C83⋊#95—24no—
66C83⋊#95—24no—
67C83⋊#95—28no—
68C83⋊#95—28no—
69C83⋊#95—44no—
70C23×C4×C83C2312yes—
71C23×C4×C83C2312yes—
72C23×C4×C83C2312yes—
73C23×C4×C83C2311yescharacteristic
74C2×C4⋊C4×C83—22no—
75C2×C4⋊C4×C83—22no—
76C2×C4⋊C4×C83—22no—
77C2×C4⋊C4×C83—22no—
78C2×C4⋊C4×C83—22no—
79C2×C4⋊C4×C83C2×C414yes—
80C2×C42×C83—22no—
81C2×C42×C83—22no—
82C2×C42×C83—22no—
83#95×C83—44no—
84C23×D83—21no—
85C23×D83—21no—
86C23×D83—21no—
87C23×D83—21no—
88C23×D83—22no—
89C23×D83—22no—
90C23×D83—22no—
91C23×D83—22no—
92C23×D83C22×C412yes—
93C23×D83C2×D412yes—
94C23×D83C2×D412yes—
95C22×Dic83—21no—
96C22×Dic83—21no—
97C22×Dic83—21no—
98C22×Dic83—21no—
99C22×Dic83—22no—
100C22×Dic83—22no—
101C22×Dic83—22no—
102C22×Dic83—24no—
103C22×Dic83—24no—
104C22×Dic83—22no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—24no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—24no—
114C22×Dic83C22×C414yes—
115C22×Dic83C22×C412yes—
116C22×Dic83C2×D412yes—
117C22×Dic83C2×D412yes—
118C22×Dic83#4114yes—
119C2×C4×D83—28no—
120C2×C4×D83—28no—
121C2×C4×D83—28no—
122C2×C4×D83—28no—
123C2×C4×D83—28no—
124C2×C4×D83—28no—
125C2×C4×D83C22⋊C4116yes—
126C4⋊Dic83—28no—
127C4⋊Dic83—44no—
128(C2×D83)⋊C4—216no—
129(C2×D83)⋊C4—216no—
130(C2×D83)⋊C4—48no—
131C4×Dic83—216no—
132C4×Dic83—44no—
133C24×C83C2411yescharacteristic
134C22×C4×C83—22no—
135C22×C4×C83—22no—
136C22×C4×C83—22no—
137C22×C4×C83—22no—
138C22×C4×C83—22no—
139C22×C4×C83—22no—
140C22×C4×C83—22no—
141C22×C4×C83—24no—
142C22×C4×C83—24no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—22no—
147C22×C4×C83—24no—
148C22×C4×C83—24no—
149C22×C4×C83C22×C414yes—
150C22×C4×C83C22×C412yes—
151C22×C4×C83C2×D412yes—
152C22×C4×C83C2×D412yes—
153C22×C4×C83#4112yes—
154C22×C4×C83#4112yes—
155C22×C4×C83#4112yes—
156C22×C4×C83#4114yes—
157C22×C4×C83#4112yes—
158C4⋊C4×C83—28no—
159C4⋊C4×C83—44no—
160C42×C83—44no—
161C23×C83C23×C411yescharacteristic
162C23×C83C22×D411yescharacteristic
163C23×C83C22×D411yescharacteristic
164C23×C83C2×#4112yes—
165C23×C83C2×#4111yescharacteristic
166C23×C83C2×#4111yescharacteristic
167C23×C83C2×#4111yescharacteristic
168C23×C83C2×#4111yescharacteristic
169C23×C83C2×#4112yes—
170C23×C83H(5,𝔽2)12yes—
171C23×C832−1+412yes—
172C22×D83—22no—
173C22×D83—22no—
174C22×D83—24no—
175C22×D83—24no—
176C22×D83—22no—
177C22×D83—22no—
178C22×D83—22no—
179C22×D83—22no—
180C22×D83—24no—
181C22×D83—22no—
182C22×D83—22no—
183C22×D83—22no—
184C22×D83—22no—
185C22×D83—24no—
186C22×D83—42no—
187C22×D83—42no—
188C22×D83—42no—
189C22×D83—42no—
190C22×D83—42no—
191C22×D83—42no—
192C22×D83—42no—
193C22×D83—42no—
194C22×D83C2×C22⋊C414yes—
195C2×C4×C83—24no—
196C2×C4×C83—28no—
197C2×C4×C83—24no—
198C2×C4×C83—24no—
199C2×C4×C83—24no—
200C2×C4×C83—42no—
201C2×C4×C83—42no—
202C2×C4×C83—42no—
203C2×C4×C83—44no—
204C2×C4×C83—42no—
205C2×C4×C83—42no—
206C2×C4×C83—42no—
207C2×C4×C83—42no—
208C2×C4×C83—42no—
209C2×C4×C83—42no—
210C2×C4×C83—44no—
211C2×C4×C83—44no—
212C2×C4×C83C2×C22⋊C414yes—
213C2×C4×C83#11714yes—
214C2×C4×C83#11714yes—
215C2×C4×C83#12314yes—
216C2×C4×C83#12314yes—
217C2×C4×C83#12314yes—
218C2×C4×C83#12314yes—
219C2×Dic83—22no—
220C2×Dic83—22no—
221C2×Dic83—22no—
222C2×Dic83—22no—
223C2×Dic83—22no—
224C2×Dic83—22no—
225C2×Dic83—24no—
226C2×Dic83—28no—
227C2×Dic83—24no—
228C2×Dic83—24no—
229C2×Dic83—24no—
230C2×Dic83—42no—
231C2×Dic83—44no—
232C2×Dic83—42no—
233C2×Dic83—42no—
234C2×Dic83—42no—
235C2×Dic83—42no—
236C2×Dic83—42no—
237C2×Dic83—42no—
238C2×Dic83—42no—
239C2×Dic83—42no—
240C2×Dic83—44no—
241C2×Dic83—44no—
242C2×Dic83C2×C22⋊C414yes—
243C4×D83—232no—
244C22×C83C22×C22⋊C411yescharacteristic
245C22×C83C2×#11711yescharacteristic
246C22×C83C2×#11711yescharacteristic
247C22×C83C4×#4112yes—
248C22×C83#52012yes—
249C22×C83C2×#12311yescharacteristic
250C22×C83C2×#12311yescharacteristic
251C22×C83C2×#12311yescharacteristic
252C22×C83C2×#12311yescharacteristic
253C22×C83#52512yes—
254C22×C83#53211yescharacteristic
255C22×C83#53211yescharacteristic
256C22×C83#53511yescharacteristic
257C22×C83#53611yescharacteristic
258C22×C83#53712yes—
259C22×C83#55212yes—
260C22×C83#55212yes—
261C22×C83#55312yes—
262C22×C83#55312yes—
263C22×C83#55512yes—
264C22×C83#55512yes—
265C22×C83#55612yes—
266C22×C83#55612yes—
267C2×D83—24no—
268C2×D83—24no—
269C2×D83—24no—
270C2×D83—44no—
271C2×D83—44no—
272C2×D83—44no—
273C2×D83—44no—
274C2×D83—42no—
275C2×D83—42no—
276C2×D83—42no—
277C2×D83—42no—
278C4×C83—44no—
279C4×C83—44no—
280C4×C83—82no—
281C4×C83#38118yes—
282Dic83—24no—
283Dic83—44no—
284Dic83—44no—
285Dic83—82no—
286#13939—831nomaximal, Sylow
287C2×C83C2×#38111yescharacteristic
288C2×C83#229711yescharacteristic
289C2×C83#231111yescharacteristic
290C2×C83#234612yes—
291C2×C83#234712yes—
292C2×C83#248512yes—
293C2×C83#248512yes—
294C2×C83#249911yescharacteristic
295C2×C83#249911yescharacteristic
296C2×C83#250011yescharacteristic
297C2×C83#250011yescharacteristic
298D83—44no—
299C22×#117—831no—
300C2×#380—831no—
301C2×C4×C22⋊C4—831no—
302#1440—834no—
303C4⋊#95—831no—
304C4⋊#95—831no—
305C4⋊#95—831no—
306C4⋊#95D8311yescharacteristic, complemented
307#1434—834no—
308C83#1393911yescharacteristic, complemented, Sylow
309C24×C4—831no—
310C2×#117—838no—
311C2×#117—1664no—
312C2×#117—1664no—
313C22×C4⋊C4—831no—
314C22×C4⋊C4—831no—
315C22×C4⋊C4C2×D8311yescharacteristic
316C22×C4⋊C4C2×D8311yescharacteristic
317C22×C22⋊C4—832no—
318C22×C22⋊C4—832no—
319C22×C22⋊C4—832no—
320C22×C42—832no—
321C22×C42—831no—
322C22×C42C2×D8311yescharacteristic
323#380—1664no—
324C4×C22⋊C4—1664no—
325C2×#95—834no—
326C2×#95—832no—
327C2×#95—832no—
328C2×#95—834no—
329C2×#95—834no—
330C2×#95C2×D8314yes—
331C25—831no—
332C23×C4—831no—
333C23×C4—834no—
334C23×C4—834no—
335C23×C4—834no—
336C23×C4—832no—
337C23×C4—832no—
338C23×C4—832no—
339C23×C4—1662no—
340C23×C4—1662no—
341C23×C4—1662no—
342C23×C4—1662no—
343C23×C4C22×D8312yes—
344C23×C4C22×D8312yes—
345C23×C4C22×D8312yes—
346C23×C4C22×D8311yescharacteristic
347#117—16632no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—834no—
354C2×C4⋊C4—1662no—
355C2×C4⋊C4—1662no—
356C2×C4⋊C4—1662no—
357C2×C4⋊C4—1662no—
358C2×C4⋊C4—1662no—
359C2×C4⋊C4C4×D8314yes—
360C2×C22⋊C4—3324no—
361C2×C22⋊C4—838no—
362C2×C22⋊C4—1664no—
363C2×C22⋊C4—1664no—
364C2×C22⋊C4—1664no—
365C2×C22⋊C4—1664no—
366C2×C22⋊C4—1664no—
367C2×C22⋊C4—1664no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—838no—
372C2×C42—1662no—
373C2×C42—1662no—
374C2×C42—1662no—
375C2×C42—1664no—
376C2×C42—1664no—
377#95—44no—
378#95—3324no—
379#95—1664no—
380#95—1664no—
381#95—1668no—
382#95—1668no—
383C24—832no—
384C24—832no—
385C24—832no—
386C24—1662no—
387C24—1661no—
388C24—1661no—
389C24—1661no—
390C24—1662no—
391C24—1661no—
392C24—1662no—
393C24—1662no—
394C24C23×D8311yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—832no—
411C22×C4—832no—
412C22×C4—832no—
413C22×C4—8316no—
414C22×C4—834no—
415C22×C4—834no—
416C22×C4—1662no—
417C22×C4—1662no—
418C22×C4—1664no—
419C22×C4—1662no—
420C22×C4—1664no—
421C22×C4—1662no—
422C22×C4—1662no—
423C22×C4—1662no—
424C22×C4—1664no—
425C22×C4—1662no—
426C22×C4—1664no—
427C22×C4—1662no—
428C22×C4—1662no—
429C22×C4—1662no—
430C22×C4—1662no—
431C22×C4—1661no—
432C22×C4—1661no—
433C22×C4—1661no—
434C22×C4—1661no—
435C22×C4—1668no—
436C22×C4—1668no—
437C22×C4—1668no—
438C22×C4—1668no—
439C22×C4—1668no—
440C22×C4—1668no—
441C22×C4C2×C4×D8314yes—
442C22×C4C2×C4×D8312yes—
443C22×C4D4×D8312yes—
444C22×C4D4×D8312yes—
445C22×C4#1305058912yes—
446C22×C4#1305059012yes—
447C22×C4#1305059012yes—
448C22×C4#1305059114yes—
449C22×C4#1305059112yes—
450C4⋊C4—28no—
451C4⋊C4—44no—
452C4⋊C4—3324no—
453C4⋊C4—1668no—
454C22⋊C4—3328no—
455C22⋊C4—16616no—
456C22⋊C4—16616no—
457C42—44no—
458C42—3324no—
459C42—16616no—
460C23—3322no—
461C23—3322no—
462C23—3322no—
463C23—3322no—
464C23—3322no—
465C23—3322no—
466C23—3322no—
467C23—3322no—
468C23—834no—
469C23—1662no—
470C23—1662no—
471C23—1664no—
472C23—1664no—
473C23—1662no—
474C23—1662no—
475C23—1662no—
476C23—1662no—
477C23—1664no—
478C23—1662no—
479C23—1662no—
480C23—1662no—
481C23—1662no—
482C23—1664no—
483C23C22×C4×D8311yescharacteristic
484C23C2×D4×D8311yescharacteristic
485C23C2×D4×D8311yescharacteristic
486C23#41×D8312yes—
487C23C2×#1305058911yescharacteristic
488C23C2×#1305059011yescharacteristic
489C23C2×#1305059011yescharacteristic
490C23C2×#1305059111yescharacteristic
491C23C2×#1305059112yes—
492C23#1458183712yes—
493C23#1458183912yes—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—28no—
498C2×C4—24no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—3322no—
512C2×C4—3322no—
513C2×C4—3322no—
514C2×C4—3324no—
515C2×C4—3322no—
516C2×C4—3322no—
517C2×C4—3322no—
518C2×C4—3324no—
519C2×C4—3324no—
520C2×C4—3322no—
521C2×C4—3322no—
522C2×C4—3322no—
523C2×C4—834no—
524C2×C4—1664no—
525C2×C4—1664no—
526C2×C4—1664no—
527C2×C4—1668no—
528C2×C4—1664no—
529C2×C4—1662no—
530C2×C4—1662no—
531C2×C4—1662no—
532C2×C4—1662no—
533C2×C4—1662no—
534C2×C4—1662no—
535C2×C4—16632no—
536C2×C4C22⋊C4×D8314yes—
537C2×C4#1458174914yes—
538C2×C4#1458175014yes—
539C2×C4#1458177414yes—
540C2×C4#1458177414yes—
541C2×C4#1458177714yes—
542C2×C4#1458177714yes—
543C22—3324no—
544C22—3324no—
545C22—3322no—
546C22—3322no—
547C22—3322no—
548C22—3322no—
549C22—3324no—
550C22—3324no—
551C22—1664no—
552C22—1664no—
553C22—1664no—
554C22C2×C22⋊C4×D8311yescharacteristic
555C22C2×#1458174911yescharacteristic
556C22C2×#1458175011yescharacteristic
557C22C4×#1305059112yes—
558C22#1912818012yes—
559C22C2×#1458177411yescharacteristic
560C22C2×#1458177411yescharacteristic
561C22C2×#1458177711yescharacteristic
562C22C2×#1458177711yescharacteristic
563C22#1912821412yes—
564C22#1912825011yescharacteristic
565C22#1912825211yescharacteristic
566C22#1912826411yescharacteristic
567C22#1912827111yescharacteristic
568C22#1912828012yes—
569C22#1912838912yes—
570C22#1912839312yes—
571C22#1912839912yes—
572C22#1912840112yes—
573C22#1912841512yes—
574C22#1912841712yes—
575C22#1912841912yes—
576C22#1912842412yes—
577C4—44no—
578C4—44no—
579C4—82no—
580C4—3324no—
581C4—3324no—
582C4—6642no—
583C4—1664no—
584C4#1912756318yes—
585C2—3324no—
586C2C2×#1912756311yescharacteristic
587C2#2490995211yescharacteristic
588C2#2491005311yescharacteristic
589C2#2491034712yes—
590C2#2491035212yes—
591C2#2491176212yes—
592C2#2491176312yes—
593C2#2491191811yescharacteristic
594C2#2491191911yescharacteristic
595C2#2491192211yescharacteristic
596C2#2491192411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C4⋊#95C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC4⋊#95D83
hypocenterC83#13939
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. #24905693C2semidirect
6. #24905692C2semidirect
7. #24905692C2semidirect
8. #24905689C2semidirect
9. C83×C4⋊#95C2semidirect
13. C2×#14581750C4semidirect
306. C4⋊#95D83semidirect
308. C83#13939semidirect

Maximal subgroups

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

subgroupindex
C22×#145817502
C2×#191275582
C2×C4×(C2×D83)⋊C42
#249057112
#249056932
#249056922
#249056892
C83×C4⋊#952
#1393983