Finite Group Databasebeta

← #1297×D83 #35294522

Subgroups — #1297×D83 #35294522

Order 21248.

1226 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1226 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D83C211yesmaximal, characteristic
2C4×C22⋊C4×D83C212yesmaximal
3#24905349C212yesmaximal, complemented
4#24905348C211yesmaximal, characteristic, complemented
5C83×#1297C211yesmaximal, characteristic, complemented
6C23×C4×D83C2211yescharacteristic
7C2×M16×D83C412yescomplemented
8C2×C22⋊C4×D83—22no—
9C2×C42×D83—22no—
10#19127665C2211yescharacteristic
11#19127664C412yescomplemented
12#19127663—22no—
13C22⋊C8×D83—22no—
14C22⋊C4×Dic83—22no—
15C4×(C2×D83)⋊C4—22no—
16C4×C22⋊Dic83C2212yes—
17#19127548C414yescomplemented
18#95×D83C414yescomplemented
19#407×C83C2211yescharacteristic
20C4×C22⋊C4×C83C2212yes—
21C24×D83D411yescharacteristic
22C23×Dic83D411yescharacteristic
23C22×C4×D83—24no—
24C22×C4×D83—44no—
25C22×C4×D83C2×C411yescharacteristic
26C22×C4×D83C2×C411yescharacteristic
27C22×C4×D83C2×C412yes—
28C22×C4×D83C2×C412yes—
29C22×C4×D83D412yes—
30C22×C4×D83D412yes—
31C22×C4×D83Q811yescharacteristic
32C22×C4×D83Q811yescharacteristic
33C2×#13050574C2×C412yescomplemented
34C2×#13050573—22no—
35M16×D83—44no—
36C2×C8×D83—22no—
37C2×C22⋊Dic83—22no—
38C2×(C2×D83)⋊C4—24no—
39C22⋊C4×D83—216no—
40C2×C4×Dic83—24no—
41C2×C4×Dic83—22no—
42C42×D83—48no—
43C22⋊(C83⋊C8)—22no—
44(C2×D83)⋊C8—24no—
45C83⋊#95—24no—
46C83⋊#95C2×C414yescomplemented
47C23×C4×C83C2311yescharacteristic
48C2×M16×C83C2×C412yescomplemented
49C2×C22⋊C4×C83—22no—
50C2×C42×C83—22no—
51C22⋊C8×C83—22no—
52#95×C83C2×C414yescomplemented
53C23×D83—28no—
54C23×D83—42no—
55C23×D83C22⋊C412yes—
56C23×D83C22⋊C412yes—
57C23×D83C4⋊C411yescharacteristic
58C23×D83C4⋊C411yescharacteristic
59C22×Dic83—24no—
60C22×Dic83—42no—
61C22×Dic83C22⋊C412yes—
62C22×Dic83C22⋊C412yes—
63C22×Dic83C4⋊C411yescharacteristic
64C22×Dic83C4⋊C411yescharacteristic
65C2×C4×D83—24no—
66C2×C4×D83—28no—
67C2×C4×D83—216no—
68C2×C4×D83—44no—
69C2×C4×D83—42no—
70C2×C4×D83—42no—
71C2×C4×D83—44no—
72C2×C4×D83—44no—
73C2×C4×D83—42no—
74C2×C4×D83—48no—
75C2×C4×D83—48no—
76C2×C4×D83C4211yescharacteristic
77C2×C4×D83C4211yescharacteristic
78C2×C4×D83C4212yes—
79C2×C4×D83C22⋊C411yescharacteristic
80C2×C4×D83C22⋊C412yes—
81C2×C4×D83C22⋊C411yescharacteristic
82C2×C4×D83C4⋊C412yes—
83C2×C4×D83C4⋊C412yes—
84C2×C4×D83C4⋊C412yes—
85C2×C4×D83C4⋊C412yes—
86#13050574—42no—
87#13050573—44no—
88C2×C83⋊C8—22no—
89C8×D83—44no—
90C22⋊Dic83—28no—
91(C2×D83)⋊C4—216no—
92C4×Dic83—48no—
93C4×Dic83—44no—
94C24×C83C2×D411yescharacteristic
95C22×C4×C83—24no—
96C22×C4×C83—42no—
97C22×C4×C83C22×C411yescharacteristic
98C22×C4×C83C22×C412yes—
99C22×C4×C83C2×D412yes—
100C22×C4×C83C2×Q811yescharacteristic
101M16×C83—42no—
102C2×C8×C83—22no—
103C22⋊C4×C83—28no—
104C42×C83—44no—
105C23×C83—24no—
106C23×C83—41no—
107C23×C83C2×C22⋊C412yes—
108C23×C83C2×C4⋊C411yescharacteristic
109C22×D83—24no—
110C22×D83—24no—
111C22×D83—24no—
112C22×D83—24no—
113C22×D83—24no—
114C22×D83—24no—
115C22×D83—22no—
116C22×D83—42no—
117C22×D83—41no—
118C22×D83—416no—
119C22×D83#9511yescharacteristic
120C22×D83#9512yes—
121C22×D83#9511yescharacteristic
122C22×D83#10418yes—
123C2×C4×C83—24no—
124C2×C4×C83—22no—
125C2×C4×C83—28no—
126C2×C4×C83—42no—
127C2×C4×C83—41no—
128C2×C4×C83—44no—
129C2×C4×C83—44no—
130C2×C4×C83C2×C4211yescharacteristic
131C2×C4×C83C2×C22⋊C411yescharacteristic
132C2×C4×C83C2×C4⋊C412yes—
133C2×Dic83—24no—
134C2×Dic83—22no—
135C2×Dic83—28no—
136C2×Dic83—42no—
137C2×Dic83—41no—
138C2×Dic83—44no—
139C2×Dic83—44no—
140C2×Dic83#9511yescharacteristic
141C2×Dic83#9512yes—
142C2×Dic83#9511yescharacteristic
143C4×D83—22no—
144C4×D83—24no—
145C4×D83—22no—
146C4×D83—24no—
147C4×D83—22no—
148C4×D83—24no—
149C4×D83—42no—
150C4×D83—42no—
151C4×D83—42no—
152C4×D83—432no—
153C4×D83#9914yes—
154C8×C83—42no—
155C83⋊C8—42no—
156C22×C83—22no—
157C22×C83—22no—
158C22×C83—22no—
159C22×C83—21no—
160C22×C83—44no—
161C22×C83C2×#9511yescharacteristic
162C22×C83C2×#10414yes—
163C2×D83—22no—
164C2×D83—22no—
165C2×D83—216no—
166C2×D83—22no—
167C2×D83—21no—
168C2×D83—44no—
169C2×D83—48no—
170C2×D83—44no—
171C2×D83#33914yes—
172C2×D83#33914yes—
173C2×D83#34212yes—
174C4×C83—21no—
175C4×C83—22no—
176C4×C83—48no—
177C4×C83C2×#9912yes—
178Dic83—21no—
179Dic83—22no—
180Dic83—48no—
181Dic83#34212yes—
182C2×#1297—831nomaximal, Sylow
183C2×C83—24no—
184C2×C83—41no—
185C2×C83C2×#33912yes—
186C2×C83C2×#34211yescharacteristic
187D83—24no—
188D83—41no—
189D83#129714yesdirect product factor
190C2×#407—831no—
191C2×C4×C22⋊C4—832no—
192#1297—831no—
193#1297—832no—
194#1297D8311yescharacteristic, direct product factor
195C83C2×#129711yescharacteristic, complemented, Sylow
196C24×C4—831no—
197C22×M16—832no—
198C22×C22⋊C4—1662no—
199C22×C42—1662no—
200#407—831no—
201#407—832no—
202#407—1662no—
203#407C2×D8311yescharacteristic
204C2×C22⋊C8—1662no—
205C4×C22⋊C4—832no—
206C4×C22⋊C4—834no—
207C4×C22⋊C4—1662no—
208C4×C22⋊C4—1662no—
209C4×C22⋊C4C2×D8312yes—
210C2×#95—834no—
211C25—831no—
212C23×C4—3324no—
213C23×C4—831no—
214C23×C4—832no—
215C23×C4—832no—
216C23×C4—831no—
217C23×C4—832no—
218C23×C4—831no—
219C23×C4—831no—
220C23×C4—831no—
221C23×C4—832no—
222C23×C4—1664no—
223C23×C4C22×D8311yescharacteristic
224C2×M16—3324no—
225C2×M16—832no—
226C2×M16—1662no—
227C2×M16C4×D8312yescomplemented
228C22×C8—1662no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—16616no—
231C2×C22⋊C4—1664no—
232C2×C22⋊C4—1662no—
233C2×C42—22no—
234C2×C42—3328no—
235C2×C42—1664no—
236C2×C42—1662no—
237C22⋊C8—22no—
238C22⋊C8—1664no—
239C22⋊C8—1662no—
240#95—834no—
241#95—1664no—
242#95C4×D8314yescomplemented
243C24—3322no—
244C24—832no—
245C24—831no—
246C24—832no—
247C24—831no—
248C24—1668no—
249C24D4×D8311yescharacteristic
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—3324no—
253C22×C4—3322no—
254C22×C4—3328no—
255C22×C4—3328no—
256C22×C4—3324no—
257C22×C4—3322no—
258C22×C4—3324no—
259C22×C4—3322no—
260C22×C4—3322no—
261C22×C4—832no—
262C22×C4—831no—
263C22×C4—832no—
264C22×C4—832no—
265C22×C4—832no—
266C22×C4—831no—
267C22×C4—832no—
268C22×C4—831no—
269C22×C4—831no—
270C22×C4—831no—
271C22×C4—832no—
272C22×C4—831no—
273C22×C4—832no—
274C22×C4—832no—
275C22×C4—16616no—
276C22×C4—1668no—
277C22×C4—1664no—
278C22×C4—1664no—
279C22×C4C2×C4×D8311yescharacteristic
280C22×C4C2×C4×D8312yes—
281C22×C4D4×D8312yes—
282C22×C4Q8×D8311yescharacteristic
283M16—42no—
284M16—3324no—
285M16—3322no—
286C2×C8—22no—
287C2×C8—3324no—
288C2×C8—1662no—
289C22⋊C4—28no—
290C22⋊C4—16616no—
291C22⋊C4—1668no—
292C42—44no—
293C42—3324no—
294C42—3328no—
295C23—24no—
296C23—41no—
297C23—3322no—
298C23—3321no—
299C23—33216no—
300C23—831no—
301C23—838no—
302C23—832no—
303C23—831no—
304C23—1664no—
305C23—1662no—
306C23—1664no—
307C23—1664no—
308C23—1664no—
309C23—1664no—
310C23—1664no—
311C23C22⋊C4×D8312yes—
312C23C4⋊C4×D8311yescharacteristic
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—28no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—3322no—
321C2×C4—3322no—
322C2×C4—3322no—
323C2×C4—33232no—
324C2×C4—3324no—
325C2×C4—3324no—
326C2×C4—3322no—
327C2×C4—3321no—
328C2×C4—831no—
329C2×C4—834no—
330C2×C4—831no—
331C2×C4—832no—
332C2×C4—1662no—
333C2×C4—1664no—
334C2×C4—1662no—
335C2×C4—1664no—
336C2×C4—1668no—
337C2×C4—1664no—
338C2×C4—1662no—
339C2×C4—1662no—
340C2×C4—1664no—
341C2×C4C42×D8311yescharacteristic
342C2×C4C22⋊C4×D8311yescharacteristic
343C2×C4C4⋊C4×D8312yes—
344C8—42no—
345C8—3322no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—21no—
350C22—44no—
351C22—3328no—
352C22—3324no—
353C22—3324no—
354C22—834no—
355C22—832no—
356C22—834no—
357C22—16616no—
358C22—1662no—
359C22—1661no—
360C22—1662no—
361C22—1662no—
362C22#95×D8311yescharacteristic
363C22#104×D8314yes—
364C4—21no—
365C4—22no—
366C4—48no—
367C4—3328no—
368C4—832no—
369C4—1662no—
370C4—1661no—
371C4#99×D8312yes—
372C2—24no—
373C2—41no—
374C2—3321no—
375C2—834no—
376C2—1664no—
377C2#339×D8312yes—
378C2#342×D8311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC83×#1297C2
socleC22×C83C2×#95
prime radicalC24×D83D4
cosocleC23×C4×C83C23
hypercenter#1297D83
hypocenterC83C2×#1297
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #24905349C2semidirect
4. #24905348C2semidirect
5. C83×#1297C2semidirect
7. C2×M16×D83C4semidirect
11. #19127664C4semidirect
17. #19127548C4semidirect
18. #95×D83C4semidirect
33. C2×#13050574C2×C4semidirect
46. C83⋊#95C2×C4semidirect
48. C2×M16×C83C2×C4semidirect
52. #95×C83C2×C4semidirect
189. D83#1297direct (N × H)
194. #1297D83direct (N × H)
195. C83C2×#1297semidirect
227. C2×M16C4×D83semidirect
242. #95C4×D83semidirect

Maximal subgroups

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

subgroupindex
#407×D832
C4×C22⋊C4×D832
#249053492
#249053482
C83×#12972
C2×#129783