Finite Group Databasebeta

← #35322250

Subgroups — #35322250

Order 21248.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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#24909257C211yesmaximal, characteristic, complemented
2#24909210C211yesmaximal, characteristic
3#24909190C211yesmaximal, characteristic
4#24908351C211yesmaximal, characteristic
5#24905576C211yesmaximal, characteristic, complemented
6#24905545C211yesmaximal, characteristic, complemented
7C4×#108×C83C211yesmaximal, characteristic, complemented
8C2×#14581814C2211yescharacteristic
9C2×#14581732C2211yescharacteristic
10C2×#14581732C2211yescharacteristic
11C2×#14581728C2211yescharacteristic
12C2×#14581720—21no—
13#19127667—21no—
14#19127530—22no—
15#19127516C412yescomplemented
16#19127513C412yescomplemented
17#19127507—22no—
18C2×#108×C83C2211yescharacteristic
19C2×#108×C83C2211yescharacteristic
20C4×M16×C83—21no—
21C2×C4×C8×C83C2211yescharacteristic
22#341×C83—21no—
23C2×#13050590—21no—
24#14581814—21no—
25#14581814—21no—
26#14581814—21no—
27#14581814—21no—
28C2×Dic332C2×C411yescharacteristic
29C2×#13050579—21no—
30C2×D664C2×C411yescharacteristic
31C2×#13050574—21no—
32#14581732—21no—
33#14581732—21no—
34#14581732—21no—
35#14581732C2×C412yes—
36C2×C83⋊C16—21no—
37C2×C83⋊C16—21no—
38#14581728—21no—
39#14581728—21no—
40#14581720—41no—
41#14581720—41no—
42(C2×D83)⋊C8—42no—
43C2×M16×C83—21no—
44C2×M16×C83—21no—
45C22×C8×C83D411yescharacteristic
46C22×C8×C83C2311yescharacteristic
47C2×C42×C83D411yescharacteristic
48#108×C83—21no—
49#108×C83—21no—
50#108×C83C2×C412yes—
51#108×C83D412yes—
52#97×C83—41no—
53C4×C8×C83—21no—
54C4×C8×C83—21no—
55C4×C8×C83—41no—
56#13050590—41no—
57#13050590—41no—
58#13050590—41no—
59#13050590—41no—
60C2×Dic166—21no—
61C2×D332—21no—
62C2×C22⋊D83—41no—
63C2×C4×D83—41no—
64Dic332—21no—
65Dic332—21no—
66#13050579—41no—
67#13050579—41no—
68D664—21no—
69D664—21no—
70#13050574—41no—
71#13050574—41no—
72C2×C83⋊C8—41no—
73C83⋊C16—22no—
74C83⋊C16—41no—
75C22×C4×C83—21no—
76C22×C4×C83C2×D411yescharacteristic
77M16×C83—22no—
78M16×C83—22no—
79M16×C83—41no—
80M16×C83—41no—
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C2×C8×C83C22×C411yescharacteristic
87C2×C8×C83C2×D411yescharacteristic
88C2×C8×C83#4111yescharacteristic
89C2×C8×C83#4111yescharacteristic
90C2×C8×C83#4111yescharacteristic
91C2×C8×C83#4111yescharacteristic
92C42×C83—21no—
93C42×C83D811yescharacteristic
94C42×C83D811yescharacteristic
95C23×C83#13711yescharacteristic
96C22×D83—41no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—42no—
100C2×C4×C83C4×D411yescharacteristic
101C2×C4×C83#12111yescharacteristic
102C2×C4×C83#12311yescharacteristic
103C2×C4×C83C2×D811yescharacteristic
104C2×C4×C83#13511yescharacteristic
105C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
106C22⋊D83—81no—
107C22⋊D83—81no—
108C2×Dic83—41no—
109D332—41no—
110D332—41no—
111C4×D83—81no—
112C4×D83—81no—
113Dic166—41no—
114Dic166—41no—
115C8×C83—42no—
116C8×C83—42no—
117C8×C83—41no—
118C8×C83#11711yescharacteristic
119C8×C83C4×D411yescharacteristic
120C8×C83#12411yescharacteristic
121C8×C83#12611yescharacteristic
122C83⋊C8—81no—
123C22×C83—41no—
124C22×C83#44011yescharacteristic
125C22×C83#46411yescharacteristic
126C22×C83#48011yescharacteristic
127C2×D83—82no—
128C2×D83—81no—
129C4×C83—22no—
130C4×C83—41no—
131C4×C83#38811yescharacteristic
132C4×C83C4×D811yescharacteristic
133C4×C83#45911yescharacteristic
134C4×C83#48211yescharacteristic
135Dic83—81no—
136#13137—831nomaximal, Sylow
137C2×C83—21no—
138C2×C83—21no—
139C2×C83—21no—
140C2×C83#192511yescharacteristic
141D83—161no—
142#2161—831no—
143#2148—831no—
144#2143—831no—
145#1974—831no—
146C4×#108D8311yescharacteristic, complemented
147#1388—831no—
148#1376—831no—
149C83#1313711yescharacteristic, complemented, Sylow
150C2×#135—831no—
151C2×M32—831no—
152C2×M32—831no—
153C2×#108—831no—
154C2×#108C2×D8311yescharacteristic
155C2×#108C2×D8311yescharacteristic
156C2×#104—1661no—
157#408—1661no—
158C4×M16—21no—
159C2×C4×C8C2×D8311yescharacteristic
160#368—1662no—
161#362—832no—
162#361—832no—
163#359—1662no—
164#341—21no—
165C2×#41—1661no—
166#135—1661no—
167#135—1661no—
168#135—1661no—
169#135—1661no—
170C2×Q16—831no—
171C2×SD16—1661no—
172C2×D8—831no—
173C2×M16—21no—
174C2×M16—21no—
175C2×M16—1661no—
176C22×C8C22⋊D8311yescharacteristic
177C22×C8C22×D8311yescharacteristic
178C2×C42C22⋊D8311yescharacteristic
179M32—832no—
180M32—1661no—
181M32—1661no—
182M32—1661no—
183C2×C16—1661no—
184C2×C16—1661no—
185#108—21no—
186#108—21no—
187#108—1661no—
188#108—1661no—
189#108C4×D8312yes—
190#108D33212yes—
191#104—3321no—
192#104—3321no—
193C22⋊C8—3322no—
194#97—41no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—41no—
198#41—3321no—
199#41—3321no—
200#41—3321no—
201#41—3321no—
202C2×Q8—1661no—
203C2×D4—3321no—
204C2×D4—1661no—
205C22×C4—21no—
206C22×C4—3321no—
207C22×C4C2×C22⋊D8311yescharacteristic
208Q16—1661no—
209Q16—1661no—
210SD16—3321no—
211SD16—3321no—
212D8—1661no—
213D8—1661no—
214M16—22no—
215M16—22no—
216M16—41no—
217M16—41no—
218M16—3321no—
219M16—3321no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—3321no—
226C2×C8C2×C4×D8311yescharacteristic
227C2×C8C2×D33211yescharacteristic
228C2×C8#1305059011yescharacteristic
229C2×C8#1305059011yescharacteristic
230C2×C8#1305059011yescharacteristic
231C2×C8#1305059011yescharacteristic
232C42—21no—
233C42#1305057511yescharacteristic
234C42#1305057511yescharacteristic
235C16—3321no—
236C16—1662no—
237C23—3321no—
238C23#1458182311yescharacteristic
239Q8—3321no—
240Q8—3321no—
241D4—3321no—
242D4—3321no—
243D4—6641no—
244D4—6641no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—3321no—
249C2×C4—6641no—
250C2×C4—6641no—
251C2×C4C4×C22⋊D8311yescharacteristic
252C2×C4#1458176611yescharacteristic
253C2×C4#1458177511yescharacteristic
254C2×C4C2×#1305057511yescharacteristic
255C2×C4#1458181211yescharacteristic
256C2×C4#1458181711yescharacteristic
257C8—42no—
258C8—41no—
259C8—42no—
260C8—6641no—
261C8#1458174911yescharacteristic
262C8C4×D33211yescharacteristic
263C8#1458178011yescharacteristic
264C8#1458178611yescharacteristic
265C22—41no—
266C22—6642no—
267C22—6641no—
268C22#1912779911yescharacteristic
269C22#1912792311yescharacteristic
270C22#1912801411yescharacteristic
271C4—22no—
272C4—41no—
273C4—6641no—
274C4#1912759211yescharacteristic
275C4C4×#1305057511yescharacteristic
276C4#1912789611yescharacteristic
277C4#1912802511yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—13281no—
282C2#2490808311yescharacteristic
subgroupG/H
centerC4#19127896
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC4×#108×C83C2
socleC2×C83#1925
prime radicalC2×#14581814C22
cosocleC22×C8×C83C23
hypercenterC4×#108D83
hypocenterC83#13137
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
1. #24909257C2semidirect
5. #24905576C2semidirect
6. #24905545C2semidirect
7. C4×#108×C83C2semidirect
15. #19127516C4semidirect
16. #19127513C4semidirect
146. C4×#108D83semidirect
149. C83#13137semidirect

Maximal subgroups

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

subgroupindex
#249092572
#249092102
#249091902
#249083512
#249055762
#249055452
C4×#108×C832
#1313783