Finite Group Databasebeta

← #35301047

Subgroups — #35301047

Order 21248.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918588C211yesmaximal, characteristic
2#24908436C211yesmaximal, characteristic, complemented
3#24906145C211yesmaximal, characteristic, complemented
4#24906023C211yesmaximal, characteristic
5#24905323C211yesmaximal, characteristic, complemented
6#24905294C211yesmaximal, characteristic, complemented
7C83×#2932C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9#19128097C412yescomplemented
10#19128047C412yescomplemented
11#19128017—22no—
12#19127991—22no—
13#19127754C2211yescharacteristic
14#19127754C2211yescharacteristic
15#19127567C2211yescharacteristic
16#19127464—21no—
17#19127464—21no—
18#19127449—22no—
19#19127435—22no—
20C2×#131×C83—21no—
21#532×C83C2211yescharacteristic
22#435×C83—22no—
23#435×C83—22no—
24#423×C83C2211yescharacteristic
25#408×C83—21no—
26C2×#97×C83C2211yescharacteristic
27C22×Dic166—21no—
28#14581792—21no—
29#14581792—21no—
30#14581792—21no—
31#14581792C2×C412yes—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35#14581723—24no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38#14581713—24no—
39C22⋊(C83⋊C8)—21no—
40C22⋊(C83⋊C8)—21no—
41C4×C83⋊C8—21no—
42C4×C83⋊C8C2×C412yes—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C2×#41×C83—21no—
46#131×C83—42no—
47#131×C83—42no—
48C2×M16×C83—22no—
49C2×M16×C83—21no—
50C22×C8×C83—22no—
51C22×C8×C83D411yescharacteristic
52C22×C8×C83D411yescharacteristic
53C4⋊Q8×C83C2×C411yescharacteristic
54#127×C83C2×C411yescharacteristic
55#124×C83—21no—
56#121×C83—21no—
57#121×C83D412yes—
58C4×D4×C83—21no—
59C4×D4×C83D412yes—
60C2×C42×C83C2311yescharacteristic
61C4⋊C8×C83—21no—
62C4⋊C8×C83D412yes—
63C22⋊C8×C83—24no—
64#97×C83—21no—
65#97×C83—21no—
66C2×Dic166—22no—
67C2×Dic166—41no—
68C2×Dic166—82no—
69C22×Dic83—41no—
70C22×Dic83—41no—
71C2×C83⋊C8—22no—
72C2×C83⋊C8—41no—
73C4⋊Dic83—22no—
74C4⋊Dic83—22no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C4⋊Dic83—41no—
78C4⋊Dic83—41no—
79#41×C83—41no—
80#41×C83—41no—
81#41×C83—41no—
82#41×C83—41no—
83C2×Q8×C83—21no—
84C2×D4×C83—22no—
85C2×D4×C83—21no—
86C2×D4×C83—21no—
87C2×D4×C83C22⋊C412yes—
88C22×C4×C83—22no—
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83#4111yescharacteristic
92M16×C83—44no—
93M16×C83—41no—
94M16×C83—41no—
95C2×C8×C83—21no—
96C2×C8×C83—21no—
97C2×C8×C83—21no—
98C2×C8×C83—22no—
99C2×C8×C83—21no—
100C2×C8×C83—21no—
101C2×C8×C83—44no—
102C2×C8×C83SD1612yes—
103C4⋊C4×C83—21no—
104C4⋊C4×C83C22⋊C412yes—
105C22⋊C4×C83—22no—
106C22⋊C4×C83—22no—
107C42×C83C22×C411yescharacteristic
108C42×C83C2×D411yescharacteristic
109C42×C83C2×D411yescharacteristic
110C42×C83#4111yescharacteristic
111C23×C83—22no—
112C23×C83#12111yescharacteristic
113Q8×C83—41no—
114Q8×C83—41no—
115D4×C83—42no—
116D4×C83—42no—
117D4×C83—42no—
118D4×C83—41no—
119D4×C83—41no—
120D4×C83—81no—
121C2×C4×C83—22no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83C2×C22⋊C411yescharacteristic
127C2×C4×C83C4×D411yescharacteristic
128C2×C4×C83C4×D411yescharacteristic
129C2×C4×C83#12011yescharacteristic
130C2×C4×C83#12111yescharacteristic
131C2×C4×C83#12311yescharacteristic
132C2×C4×C83C2×SD1611yescharacteristic
133C2×C4×C83#13511yescharacteristic
134C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C83#13711yescharacteristic
136C2×Dic83—42no—
137C2×Dic83—82no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140C2×Dic83—81no—
141Dic166—82no—
142Dic166—82no—
143C8×C83—22no—
144C8×C83—42no—
145C8×C83—41no—
146C83⋊C8—42no—
147C83⋊C8—81no—
148C22×C83—21no—
149C22×C83—21no—
150C22×C83—42no—
151C22×C83—42no—
152C22×C83—42no—
153C22×C83#38611yescharacteristic
154C22×C83#46111yescharacteristic
155C22×C83#46311yescharacteristic
156C4×C83—21no—
157C4×C83—21no—
158C4×C83—21no—
159C4×C83—21no—
160C4×C83—42no—
161C4×C83C4×SD1611yescharacteristic
162C4×C83#44011yescharacteristic
163C4×C83#45011yescharacteristic
164C4×C83#45211yescharacteristic
165Dic83—82no—
166Dic83—161no—
167#9287—831nomaximal, Sylow
168C2×C83—21no—
169C2×C83—21no—
170C2×C83—82no—
171C2×C83#187711yescharacteristic
172C2×C83#190311yescharacteristic
173C2×C83#190911yescharacteristic
174#3227—831no—
175#2932D8311yescharacteristic
176#1993—831no—
177#1548—831no—
178#1517—831no—
179#1286—831no—
180#1275—831no—
181C83#928711yescharacteristic, complemented, Sylow
182C2×#131—21no—
183#532C2×D8311yescharacteristic
184C2×C4⋊Q8—831no—
185#498—832no—
186#486—832no—
187#481—1662no—
188#476—1662no—
189#435—22no—
190#435—22no—
191#431—831no—
192#431—831no—
193#423C2×D8311yescharacteristic
194#408—21no—
195C2×#97C2×D8311yescharacteristic
196#382—831no—
197#340—1661no—
198#340—1661no—
199#333—1662no—
200#327—1662no—
201C2×#41—21no—
202C22×Q8—1661no—
203#131—42no—
204#131—42no—
205C2×M16—22no—
206C2×M16—21no—
207C22×C8—22no—
208C22×C8C22⋊D8311yescharacteristic
209C22×C8C22⋊D8311yescharacteristic
210C4⋊Q8—832no—
211C4⋊Q8—1661no—
212C4⋊Q8—1661no—
213C4⋊Q8—1661no—
214C4⋊Q8C4×D8311yescharacteristic
215#127C4×D8311yescharacteristic
216#124—21no—
217#121—21no—
218#121D33212yes—
219C4×D4—21no—
220C4×D4C22⋊D8312yes—
221C2×C4⋊C4—1661no—
222C2×C4⋊C4—1661no—
223C2×C4⋊C4—1661no—
224C2×C42C22×D8311yescharacteristic
225#106—1664no—
226C4⋊C8—21no—
227C4⋊C8—1661no—
228C4⋊C8—1661no—
229C4⋊C8C22⋊D8312yes—
230#102—1664no—
231C22⋊C8—24no—
232C22⋊C8—1661no—
233C22⋊C8—1661no—
234#97—21no—
235#97—21no—
236C4×C8—832no—
237C4×C8—1661no—
238#95—1661no—
239#95—1661no—
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—3321no—
246C2×Q8—6642no—
247C2×Q8—1662no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4(C2×D83)⋊C412yes—
252C22×C4—22no—
253C22×C4—3321no—
254C22×C4—3321no—
255C22×C4C2×C22⋊D8311yescharacteristic
256C22×C4C2×D33211yescharacteristic
257C22×C4#1305059011yescharacteristic
258M16—44no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—44no—
268C2×C8—3321no—
269C2×C8—1662no—
270C2×C8#1305057812yes—
271C4⋊C4—21no—
272C4⋊C4—3321no—
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C4⋊C4—3321no—
276C4⋊C4—1662no—
277C4⋊C4—1662no—
278C4⋊C4(C2×D83)⋊C412yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×C4×D8311yescharacteristic
282C42C2×C22⋊D8311yescharacteristic
283C42C2×C22⋊D8311yescharacteristic
284C42#1305059011yescharacteristic
285C23—22no—
286C23#1458176611yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—6642no—
290Q8—6642no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—3322no—
303C2×C4—6641no—
304C2×C4—6641no—
305C2×C4—6641no—
306C2×C4—6642no—
307C2×C4C2×(C2×D83)⋊C411yescharacteristic
308C2×C4C4×C22⋊D8311yescharacteristic
309C2×C4C4×C22⋊D8311yescharacteristic
310C2×C4#1458176111yescharacteristic
311C2×C4#1458176611yescharacteristic
312C2×C4#1458177511yescharacteristic
313C2×C4C2×#1305057811yescharacteristic
314C2×C4#1458181211yescharacteristic
315C2×C4#1458181811yescharacteristic
316C2×C4#1458182211yescharacteristic
317C8—22no—
318C8—42no—
319C8—41no—
320C8—3322no—
321C8—6641no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#1912758011yescharacteristic
328C22#1912790611yescharacteristic
329C22#1912791611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—13281no—
336C4—6642no—
337C4C4×#1305057811yescharacteristic
338C4#1912780111yescharacteristic
339C4#1912785211yescharacteristic
340C4#1912786311yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#2490779711yescharacteristic
345C2#2490794311yescharacteristic
346C2#2490798511yescharacteristic
subgroupG/H
centerC22#19127580
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2932C2
socleC22×C83#386
prime radical#532×C83C22
cosocleC2×C42×C83C23
hypercenter#2932D83
hypocenterC83#9287
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #24908436C2semidirect
3. #24906145C2semidirect
5. #24905323C2semidirect
6. #24905294C2semidirect
9. #19128097C4semidirect
10. #19128047C4semidirect
181. C83#9287semidirect

Maximal subgroups

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

subgroupindex
#249185882
#249084362
#249061452
#249060232
#249053232
#249052942
C83×#29322
#928783