Finite Group Databasebeta

← #35303752

Subgroups — #35303752

Order 21248.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917788C211yesmaximal, characteristic
2C4⋊C4×C83⋊C8C211yesmaximal, characteristic, complemented
3#24906209C211yesmaximal, characteristic, complemented
4#24905957C211yesmaximal, characteristic
5#24905866C211yesmaximal, characteristic, complemented
6#24905863C211yesmaximal, characteristic
7C83×#1503C211yesmaximal, characteristic, complemented
8#19128251C2211yescharacteristic
9#19128058—21no—
10#19128058—21no—
11#19128053C411yescharacteristic, complemented
12#19128053C411yescharacteristic, complemented
13#19128049C411yescharacteristic, complemented
14#19128049C411yescharacteristic, complemented
15#19127754C2211yescharacteristic
16C2×C4⋊(C83⋊C8)C2211yescharacteristic
17#19127695—21no—
18#19127695—21no—
19C2×C4×C83⋊C8—21no—
20C2×C4×C83⋊C8C2211yescharacteristic
21#19127456—21no—
22#19127453—21no—
23#19127451—21no—
24#19127434—22no—
25Q8⋊(C83⋊C8)—22no—
26#19127430—22no—
27#533×C83C2211yescharacteristic
28#431×C83C2211yescharacteristic
29C4×C4⋊C4×C83C2211yescharacteristic
30#328×C83—22no—
31C2×#13050590—21no—
32C22×C83⋊C8—21no—
33C22×C83⋊C8D411yescharacteristic
34C22×C83⋊C8D411yescharacteristic
35#14581792C2×C411yescharacteristic
36#14581789C2×C411yescharacteristic
37#14581780—21no—
38#14581766—21no—
39#14581766—21no—
40C4×D332—21no—
41C4×D332—21no—
42C4⋊(C83⋊C8)—21no—
43C4⋊(C83⋊C8)—21no—
44C4⋊(C83⋊C8)D412yes—
45#14581715—21no—
46#14581715—21no—
47#14581715—21no—
48#14581715—21no—
49#14581712—21no—
50#14581712—21no—
51#14581712—21no—
52#14581712—21no—
53C22⋊(C83⋊C8)—21no—
54C4×C83⋊C8—21no—
55C4×C83⋊C8—42no—
56C4×C83⋊C8C2×C411yescharacteristic
57C4×C83⋊C8C2×C411yescharacteristic
58C4×C83⋊C8D411yescharacteristic
59C4×C83⋊C8D411yescharacteristic
60C4⋊Q8×C83C2×C411yescharacteristic
61C4⋊Q8×C83C2×C411yescharacteristic
62#125×C83—21no—
63C22⋊Q8×C83—21no—
64C22⋊Q8×C83—21no—
65C4×Q8×C83—21no—
66C4×Q8×C83—21no—
67#117×C83—21no—
68C2×C4⋊C4×C83—21no—
69C2×C42×C83—21no—
70C2×C42×C83C2311yescharacteristic
71C4⋊C8×C83—21no—
72C22⋊C8×C83—21no—
73C4×C8×C83—21no—
74#95×C83D412yes—
75#13050590—41no—
76#13050590—41no—
77#13050590—41no—
78#13050590—41no—
79C2×Dic166—21no—
80C2×D332—21no—
81C2×D332—21no—
82C2×D332—21no—
83C2×C22⋊D83—41no—
84C2×C4×D83—41no—
85C2×C83⋊C8—21no—
86C2×C83⋊C8—21no—
87C2×C83⋊C8—21no—
88C2×C83⋊C8—21no—
89C2×C83⋊C8—22no—
90C2×C83⋊C8—41no—
91C2×C83⋊C8—41no—
92C2×C83⋊C8—41no—
93C2×C83⋊C8C22⋊C411yescharacteristic
94C2×C83⋊C8C22⋊C411yescharacteristic
95C2×C83⋊C8C22⋊C411yescharacteristic
96C2×C83⋊C8C22⋊C411yescharacteristic
97C4⋊Dic83—21no—
98C4⋊Dic83—21no—
99(C2×D83)⋊C4—41no—
100(C2×D83)⋊C4—41no—
101C2×Q8×C83—21no—
102C2×Q8×C83—21no—
103C22×C4×C83—22no—
104C22×C4×C83C2×D411yescharacteristic
105C22×C4×C83C2×D411yescharacteristic
106C22×C4×C83#4111yescharacteristic
107C2×C8×C83—41no—
108C4⋊C4×C83—24no—
109C4⋊C4×C83—21no—
110C4⋊C4×C83—21no—
111C4⋊C4×C83—21no—
112C4⋊C4×C83—21no—
113C4⋊C4×C83—41no—
114C4⋊C4×C83—41no—
115C22⋊C4×C83—41no—
116C42×C83—41no—
117C42×C83—41no—
118C42×C83—41no—
119C42×C83C22×C411yescharacteristic
120C42×C83C2×D411yescharacteristic
121C42×C83C2×D411yescharacteristic
122C42×C83#4111yescharacteristic
123C23×C83#12111yescharacteristic
124C22×D83—41no—
125Q8×C83—42no—
126Q8×C83—81no—
127C2×C4×C83—22no—
128C2×C4×C83—24no—
129C2×C4×C83—41no—
130C2×C4×C83—42no—
131C2×C4×C83—42no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83C2×C22⋊C411yescharacteristic
135C2×C4×C83C4×D411yescharacteristic
136C2×C4×C83C4×D411yescharacteristic
137C2×C4×C83#12111yescharacteristic
138C2×C4×C83#12411yescharacteristic
139C2×C4×C83#12711yescharacteristic
140C2×C4×C83#13511yescharacteristic
141C2×C4×C83#13511yescharacteristic
142C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C83#13711yescharacteristic
144C22⋊D83—81no—
145C22⋊D83—81no—
146C2×Dic83—41no—
147D332—41no—
148D332—41no—
149D332—42no—
150D332—81no—
151C4×D83—81no—
152C4×D83—81no—
153Dic166—41no—
154Dic166—41no—
155C8×C83—81no—
156C83⋊C8—21no—
157C83⋊C8—21no—
158C83⋊C8—21no—
159C83⋊C8—21no—
160C83⋊C8—42no—
161C83⋊C8—81no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83#39011yescharacteristic
165C22×C83#46311yescharacteristic
166C22×C83#46411yescharacteristic
167C2×D83—81no—
168C2×D83—81no—
169C2×D83—81no—
170C4×C83—21no—
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—44no—
174C4×C83—81no—
175C4×C83—81no—
176C4×C83#41611yescharacteristic
177C4×C83#41711yescharacteristic
178C4×C83#44312yes—
179C4×C83#46311yescharacteristic
180C4×C83#46411yescharacteristic
181Dic83—81no—
182#9751—831nomaximal, Sylow
183C2×C83—21no—
184C2×C83—21no—
185C2×C83#197411yescharacteristic
186C2×C83#197611yescharacteristic
187C2×C83#198311yescharacteristic
188D83—161no—
189#3131—831no—
190C8×C4⋊C4—831no—
191#1564—831no—
192#1503D8311yescharacteristic, complemented
193#1502—831no—
194#1481—831no—
195#1480—831no—
196C83#975111yescharacteristic, complemented, Sylow
197#533C2×D8311yescharacteristic
198#532—831no—
199#488—1661no—
200#488—1661no—
201#487—831no—
202#487—831no—
203#486—831no—
204#486—831no—
205#431—831no—
206#431C2×D8311yescharacteristic
207C2×C4⋊C8—831no—
208#416—1661no—
209#416—1661no—
210C2×C4×C8—831no—
211C2×C4×C8—1661no—
212C4×C4⋊C4C2×D8311yescharacteristic
213#336—1661no—
214#335—1661no—
215#334—1661no—
216#328—22no—
217#327—1662no—
218Q8⋊C8—1662no—
219D4⋊C8—1662no—
220C2×#41—1661no—
221C22×C8—831no—
222C22×C8—831no—
223C22×C8—1661no—
224C4⋊Q8—831no—
225C4⋊Q8C4×D8311yescharacteristic
226C4⋊Q8C4×D8311yescharacteristic
227#127—831no—
228#125—21no—
229#124—1661no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—1661no—
233#121—1661no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—1661no—
237C4×D4—1661no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D8311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—832no—
244C4⋊C8—1661no—
245C4⋊C8—1661no—
246#103—1661no—
247#103—1661no—
248#103—1661no—
249#103—1661no—
250#102—1661no—
251#102—1661no—
252#102—1661no—
253#102—1661no—
254C22⋊C8—21no—
255C22⋊C8—1661no—
256C4×C8—21no—
257C4×C8—3322no—
258C4×C8—831no—
259C4×C8—831no—
260C4×C8—831no—
261C4×C8—831no—
262C4×C8—1661no—
263#95C22⋊D8312yes—
264#41—3321no—
265#41—3321no—
266#41—3321no—
267#41—3321no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—1661no—
271C2×D4—3321no—
272C2×D4—1661no—
273C2×D4—1661no—
274C2×D4—1661no—
275C22×C4—22no—
276C22×C4—3321no—
277C22×C4D4×D8311yescharacteristic
278C22×C4C2×C22⋊D8311yescharacteristic
279C22×C4#1305058911yescharacteristic
280C2×C8—41no—
281C2×C8—3321no—
282C2×C8—3321no—
283C2×C8—3321no—
284C2×C8—831no—
285C2×C8—831no—
286C2×C8—831no—
287C2×C8—831no—
288C2×C8—1662no—
289C2×C8—1661no—
290C2×C8—1661no—
291C2×C8—1661no—
292C2×C8—1661no—
293C4⋊C4—24no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1661no—
301C4⋊C4—1661no—
302C22⋊C4—41no—
303C22⋊C4—3321no—
304C22⋊C4—3321no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×C4×D8311yescharacteristic
309C42D4×D8311yescharacteristic
310C42D4×D8311yescharacteristic
311C42#1305059011yescharacteristic
312C23—3321no—
313C23#1458176411yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—3321no—
317Q8—3321no—
318D4—3322no—
319D4—3321no—
320D4—3321no—
321D4—6641no—
322D4—6641no—
323D4—6641no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—3321no—
332C2×C4—6641no—
333C2×C4—6641no—
334C2×C4C22⋊C4×D8311yescharacteristic
335C2×C4(C22⋊D83)⋊C411yescharacteristic
336C2×C4C4×C22⋊D8311yescharacteristic
337C2×C4#1458176511yescharacteristic
338C2×C4#1458177811yescharacteristic
339C2×C4#1458178811yescharacteristic
340C2×C4#1458181311yescharacteristic
341C2×C4#1458181511yescharacteristic
342C2×C4#1458181911yescharacteristic
343C2×C4#1458182411yescharacteristic
344C8—81no—
345C8—3322no—
346C8—6641no—
347C8—1661no—
348C8—1661no—
349C8—1661no—
350C8—1661no—
351C22—21no—
352C22—21no—
353C22—6641no—
354C22—6641no—
355C22—6641no—
356C22#1912760111yescharacteristic
357C22#1912791811yescharacteristic
358C22#1912792511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—81no—
364C4—81no—
365C4—6641no—
366C4#1912769611yescharacteristic
367C4#1912770111yescharacteristic
368C4#1912781512yes—
369C4#1912791911yescharacteristic
370C4#1912792611yescharacteristic
371C2—21no—
372C2—21no—
373C2—13281no—
374C2#2490834811yescharacteristic
375C2#2490835811yescharacteristic
376C2#2490839211yescharacteristic
subgroupG/H
centerC2×C4#14581765
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1503C2
socleC22×C83#390
prime radical#19128251C22
cosocleC2×C42×C83C23
hypercenter#1503D83
hypocenterC83#9751
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C83⋊C8C2semidirect
3. #24906209C2semidirect
5. #24905866C2semidirect
7. C83×#1503C2semidirect
11. #19128053C4semidirect
12. #19128053C4semidirect
13. #19128049C4semidirect
14. #19128049C4semidirect
192. #1503D83semidirect
196. C83#9751semidirect

Maximal subgroups

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

subgroupindex
#249177882
C4⋊C4×C83⋊C82
#249062092
#249059572
#249058662
#249058632
C83×#15032
#975183