Finite Group Databasebeta

← #2100×D83 #35434310

Subgroups — #2100×D83 #35434310

Order 21248.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D83C211yesmaximal, characteristic
2#384×D83C211yesmaximal, characteristic
3#24909029C212yesmaximal, complemented
4#24909028C212yesmaximal, complemented
5#24909027C211yesmaximal, characteristic, complemented
6#24909026C211yesmaximal, characteristic, complemented
7#24909025C211yesmaximal, characteristic, complemented
8#340×D83C212yesmaximal
9#340×D83C212yesmaximal
10#336×D83C211yesmaximal, characteristic
11C83×#2100C211yesmaximal, characteristic, complemented
12C22×C8×D83C2212yes—
13C2×C4⋊C4×D83—21no—
14C2×C4⋊C4×D83—21no—
15C2×C4⋊C4×D83—21no—
16C2×C4⋊C4×D83C2212yes—
17C2×C4⋊C4×D83C2211yescharacteristic
18C2×C4⋊C4×D83C2211yescharacteristic
19C2×C42×D83C2211yescharacteristic
20#19127600C2211yescharacteristic
21#19127599C2211yescharacteristic
22#19127598—21no—
23#19127597C2211yescharacteristic
24#19127596—21no—
25#19127571C2211yescharacteristic
26#19127570—21no—
27#19127570—21no—
28#19127570C2212yes—
29#95×D83—21no—
30#19127464C2212yes—
31#19127464C2212yes—
32#19127463C2212yes—
33#19127463C2212yes—
34#19127463C2212yes—
35#19127463C2212yes—
36#19127456C2211yescharacteristic
37#19127455C2212yes—
38#389×C83C2211yescharacteristic
39#384×C83C2211yescharacteristic
40#340×C83C2212yes—
41#340×C83C2212yes—
42#336×C83C2211yescharacteristic
43C22×C4×D83—21no—
44C22×C4×D83—22no—
45C22×C4×D83—21no—
46C22×C4×D83D411yescharacteristic
47C22×C4×D83D411yescharacteristic
48C22×C4×D83C2311yescharacteristic
49C22×C83⋊C8C2312yes—
50C2×C8×D83—24no—
51C2×C8×D83—24no—
52C2×C8×D83—24no—
53C2×C4⋊Dic83—21no—
54C2×C4⋊Dic83—21no—
55C2×C4⋊Dic83—21no—
56C2×C4⋊Dic83C2312yes—
57C2×C4⋊Dic83C2311yescharacteristic
58C2×C4⋊Dic83C2311yescharacteristic
59C2×Dic83⋊C4—21no—
60C2×Dic83⋊C4—22no—
61C2×Dic83⋊C4—22no—
62C2×Dic83⋊C4—22no—
63C2×Dic83⋊C4—21no—
64C2×Dic83⋊C4—21no—
65C2×Dic83⋊C4—21no—
66C4⋊C4×D83—22no—
67C4⋊C4×D83—24no—
68C4⋊C4×D83—28no—
69C4⋊C4×D83—44no—
70C4⋊C4×D83—44no—
71C4⋊C4×D83—44no—
72C4⋊C4×D83Q814yes—
73C2×C4×Dic83D411yescharacteristic
74C2×C4×Dic83D411yescharacteristic
75C2×C4×Dic83C2311yescharacteristic
76C42×D83—24no—
77C83⋊#95—21no—
78C83⋊#95—21no—
79C83⋊#95—21no—
80C22×C8×C83C2312yes—
81C2×C4⋊C4×C83—21no—
82C2×C4⋊C4×C83—21no—
83C2×C4⋊C4×C83—21no—
84C2×C4⋊C4×C83C2312yes—
85C2×C4⋊C4×C83C2311yescharacteristic
86C2×C4⋊C4×C83C2311yescharacteristic
87C2×C42×C83C2311yescharacteristic
88#95×C83—21no—
89C23×D83C2×D411yescharacteristic
90C22×Dic83—21no—
91C22×Dic83—21no—
92C22×Dic83—22no—
93C22×Dic83C2×D411yescharacteristic
94C22×Dic83C2×D411yescharacteristic
95C22×Dic83C2×D411yescharacteristic
96C2×C4×D83—22no—
97C2×C4×D83—22no—
98C2×C4×D83—22no—
99C2×C4×D83—22no—
100C2×C4×D83—24no—
101C2×C4×D83—42no—
102C2×C4×D83—42no—
103C2×C4×D83—42no—
104C2×C4×D83—44no—
105C2×C4×D83—42no—
106C2×C4×D83—42no—
107C2×C4×D83—44no—
108C2×C4×D83—44no—
109C2×C4×D83SD1614yes—
110C2×C4×D83Q1614yes—
111C2×C4×D83C2×Q812yes—
112C2×C4×D83#4114yes—
113C2×C4×D83#4114yes—
114C2×C4×D83#4112yes—
115C2×C83⋊C8—22no—
116C2×C83⋊C8—22no—
117C2×C83⋊C8—22no—
118C8×D83—48no—
119C4⋊Dic83—21no—
120C4⋊Dic83—22no—
121C4⋊Dic83—24no—
122C4⋊Dic83—42no—
123C4⋊Dic83—42no—
124C4⋊Dic83—42no—
125C4⋊Dic83C2×Q812yes—
126Dic83⋊C4—24no—
127Dic83⋊C4—44no—
128Dic83⋊C4—44no—
129Dic83⋊C4—42no—
130Dic83⋊C4—42no—
131Dic83⋊C4—44no—
132Dic83⋊C4—42no—
133C4×Dic83—22no—
134C4×Dic83—22no—
135C4×Dic83—22no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—22no—
139C22×C4×C83C2×D411yescharacteristic
140C22×C4×C83C2×D411yescharacteristic
141C22×C4×C83C2411yescharacteristic
142C2×C8×C83—22no—
143C2×C8×C83—22no—
144C2×C8×C83—22no—
145C4⋊C4×C83—21no—
146C4⋊C4×C83—22no—
147C4⋊C4×C83—24no—
148C4⋊C4×C83—42no—
149C4⋊C4×C83—42no—
150C4⋊C4×C83—42no—
151C4⋊C4×C83C2×Q812yes—
152C42×C83—22no—
153C23×C83C22×D411yescharacteristic
154C22×D83C22⋊Q812yes—
155C22×D83#12312yes—
156C22×D83#12412yes—
157C22×D83C2×SD1612yes—
158C22×D83C2×Q1612yes—
159C22×D83AGL(1,ℤ/8)12yes—
160C22×D83AGL(1,ℤ/8)12yes—
161C2×C4×C83—21no—
162C2×C4×C83—21no—
163C2×C4×C83—21no—
164C2×C4×C83—21no—
165C2×C4×C83—22no—
166C2×C4×C83—41no—
167C2×C4×C83—41no—
168C2×C4×C83—41no—
169C2×C4×C83—42no—
170C2×C4×C83—41no—
171C2×C4×C83—42no—
172C2×C4×C83—42no—
173C2×C4×C83—41no—
174C2×C4×C83C2×SD1612yes—
175C2×C4×C83C2×Q1612yes—
176C2×C4×C83C22×Q811yescharacteristic
177C2×C4×C83C2×#4112yes—
178C2×C4×C83C2×#4112yes—
179C2×C4×C83C2×#4111yescharacteristic
180C2×Dic83—21no—
181C2×Dic83—21no—
182C2×Dic83—21no—
183C2×Dic83—21no—
184C2×Dic83—22no—
185C2×Dic83—41no—
186C2×Dic83—41no—
187C2×Dic83—41no—
188C2×Dic83—42no—
189C2×Dic83—41no—
190C2×Dic83—42no—
191C2×Dic83—42no—
192C2×Dic83—41no—
193C2×Dic83C22⋊Q812yes—
194C2×Dic83#12312yes—
195C2×Dic83#12412yes—
196C2×Dic83C2×SD1612yes—
197C2×Dic83C2×Q1612yes—
198C4×D83—28no—
199C4×D83—28no—
200C4×D83—48no—
201C4×D83—84no—
202C4×D83—88no—
203C4×D83#12518yes—
204C4×D83#12618yes—
205C8×C83—42no—
206C83⋊C8—42no—
207C22×C83C2×C22⋊Q811yescharacteristic
208C22×C83C2×#12311yescharacteristic
209C22×C83C2×#12411yescharacteristic
210C22×C83C22×SD1611yescharacteristic
211C22×C83C22×Q1611yescharacteristic
212C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
213C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
214C2×D83#40014yes—
215C2×D83#47614yes—
216C2×D83#47714yes—
217C2×D83#48114yes—
218C2×D83#48414yes—
219C2×D83#48714yes—
220C2×D83#49014yes—
221C4×C83—22no—
222C4×C83—22no—
223C4×C83—42no—
224C4×C83—81no—
225C4×C83—82no—
226C4×C83C2×#12512yes—
227C4×C83C2×#12612yes—
228Dic83—22no—
229Dic83—22no—
230Dic83—42no—
231Dic83—81no—
232Dic83—82no—
233Dic83#40014yes—
234C2×#2100—831nomaximal, Sylow
235C2×C83C2×#40011yescharacteristic
236C2×C83C2×#47611yescharacteristic
237C2×C83C2×#47711yescharacteristic
238C2×C83C2×#48111yescharacteristic
239C2×C83C2×#48411yescharacteristic
240C2×C83C2×#48711yescharacteristic
241C2×C83C2×#49011yescharacteristic
242D83#210018yesdirect product factor
243C2×#389—831no—
244C2×#384—831no—
245#2100—831no—
246#2100—831no—
247#2100—832no—
248#2100—832no—
249#2100—831no—
250#2100D8311yescharacteristic, direct product factor
251C2×#340—832no—
252C2×#340—832no—
253C2×#336—831no—
254C83C2×#210011yescharacteristic, complemented, Sylow
255C23×C8—832no—
256C22×C4⋊C4—831no—
257C22×C4⋊C4—832no—
258C22×C4⋊C4—831no—
259C22×C4⋊C4—1661no—
260C22×C4⋊C4—1661no—
261C22×C4⋊C4—1661no—
262C22×C42—831no—
263#389—831no—
264#389—831no—
265#389—831no—
266#389—1661no—
267#389—1661no—
268#389C2×D8311yescharacteristic
269#384—832no—
270#384—831no—
271#384—1661no—
272#384—1661no—
273#384C2×D8311yescharacteristic
274C2×#95—1661no—
275#340—832no—
276#340—832no—
277#340—832no—
278#340—832no—
279#340—832no—
280#340—832no—
281#340C2×D8312yes—
282#340C2×D8312yes—
283#336—832no—
284#336—831no—
285#336C2×D8311yescharacteristic
286C23×C4—831no—
287C23×C4—831no—
288C23×C4—831no—
289C23×C4—1662no—
290C23×C4—1661no—
291C23×C4—1661no—
292C22×C8—832no—
293C22×C8—1664no—
294C22×C8—1664no—
295C22×C8—1664no—
296C22×C8C22×D8312yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—3324no—
301C2×C4⋊C4—3324no—
302C2×C4⋊C4—3324no—
303C2×C4⋊C4—831no—
304C2×C4⋊C4—834no—
305C2×C4⋊C4—832no—
306C2×C4⋊C4—831no—
307C2×C4⋊C4—1664no—
308C2×C4⋊C4—1668no—
309C2×C4⋊C4—1662no—
310C2×C4⋊C4—1662no—
311C2×C4⋊C4—1661no—
312C2×C4⋊C4—1662no—
313C2×C4⋊C4—1662no—
314C2×C4⋊C4—1661no—
315C2×C4⋊C4—1661no—
316C2×C4⋊C4—1661no—
317C2×C4⋊C4—1661no—
318C2×C4⋊C4—1661no—
319C2×C4⋊C4—1661no—
320C2×C4⋊C4C22×D8312yes—
321C2×C4⋊C4C22×D8311yescharacteristic
322C2×C4⋊C4C22×D8311yescharacteristic
323C2×C42—831no—
324C2×C42—831no—
325C2×C42—831no—
326C2×C42—1664no—
327C2×C42C22×D8311yescharacteristic
328#95—21no—
329#95—1661no—
330#95—1661no—
331#95—1661no—
332C24—831no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—3322no—
337C22×C4—3322no—
338C22×C4—3322no—
339C22×C4—3324no—
340C22×C4—3324no—
341C22×C4—3322no—
342C22×C4—3324no—
343C22×C4—3322no—
344C22×C4—831no—
345C22×C4—832no—
346C22×C4—834no—
347C22×C4—834no—
348C22×C4—832no—
349C22×C4—831no—
350C22×C4—831no—
351C22×C4—834no—
352C22×C4—834no—
353C22×C4—1664no—
354C22×C4—1662no—
355C22×C4—1662no—
356C22×C4—1662no—
357C22×C4—1662no—
358C22×C4—1661no—
359C22×C4—1662no—
360C22×C4—1661no—
361C22×C4D4×D8311yescharacteristic
362C22×C4D4×D8311yescharacteristic
363C22×C4C23×D8311yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—3328no—
368C2×C8—1662no—
369C2×C8—1662no—
370C2×C8—1662no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—3322no—
378C4⋊C4—3322no—
379C4⋊C4—3322no—
380C4⋊C4—3322no—
381C4⋊C4—3322no—
382C4⋊C4—3324no—
383C4⋊C4—3324no—
384C4⋊C4—3324no—
385C4⋊C4—3322no—
386C4⋊C4—832no—
387C4⋊C4—1664no—
388C4⋊C4—1662no—
389C4⋊C4—1664no—
390C4⋊C4—1661no—
391C4⋊C4Q8×D8312yes—
392C42—22no—
393C42—1662no—
394C42—1662no—
395C42—1662no—
396C23—832no—
397C23—832no—
398C23—832no—
399C23—832no—
400C23—832no—
401C23—832no—
402C23—832no—
403C23C2×D4×D8311yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—3328no—
418C2×C4—3321no—
419C2×C4—3321no—
420C2×C4—3321no—
421C2×C4—3322no—
422C2×C4—3321no—
423C2×C4—3322no—
424C2×C4—3322no—
425C2×C4—3321no—
426C2×C4—832no—
427C2×C4—832no—
428C2×C4—832no—
429C2×C4—838no—
430C2×C4—838no—
431C2×C4—832no—
432C2×C4—832no—
433C2×C4—6648no—
434C2×C4—6644no—
435C2×C4—1668no—
436C2×C4—1668no—
437C2×C4—1662no—
438C2×C4—1661no—
439C2×C4—1661no—
440C2×C4—1661no—
441C2×C4—1661no—
442C2×C4SD16×D8312yes—
443C2×C4Q16×D8312yes—
444C2×C4C2×Q8×D8311yescharacteristic
445C2×C4#41×D8312yes—
446C2×C4#41×D8312yes—
447C2×C4#41×D8311yescharacteristic
448C8—42no—
449C8—3322no—
450C22—834no—
451C22—834no—
452C22—834no—
453C22—834no—
454C22—834no—
455C22—834no—
456C22—834no—
457C22C22⋊Q8×D8311yescharacteristic
458C22#123×D8311yescharacteristic
459C22#124×D8311yescharacteristic
460C22C2×SD16×D8311yescharacteristic
461C22C2×Q16×D8311yescharacteristic
462C22AGL(1,ℤ/8)×D8311yescharacteristic
463C22AGL(1,ℤ/8)×D8311yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—3322no—
470C4—834no—
471C4—6642no—
472C4—6641no—
473C4—1662no—
474C4—1662no—
475C4#125×D8312yes—
476C4#126×D8312yes—
477C2—838no—
478C2#400×D8311yescharacteristic
479C2#476×D8311yescharacteristic
480C2#477×D8311yescharacteristic
481C2#481×D8311yescharacteristic
482C2#484×D8311yescharacteristic
483C2#487×D8311yescharacteristic
484C2#490×D8311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2100C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
hypercenter#2100D83
hypocenterC83C2×#2100
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
3. #24909029C2semidirect
4. #24909028C2semidirect
5. #24909027C2semidirect
6. #24909026C2semidirect
7. #24909025C2semidirect
11. C83×#2100C2semidirect
242. D83#2100direct (N × H)
250. #2100D83direct (N × H)
254. C83C2×#2100semidirect

Maximal subgroups

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

subgroupindex
#389×D832
#384×D832
#249090292
#249090282
#249090272
#249090262
#249090252
#340×D832
#336×D832
C83×#21002
C2×#210083