Finite Group Databasebeta

← #24908293

Subgroups — #24908293

Order 10624.

320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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#19128247C211yesmaximal, characteristic
2#19127724C211yesmaximal, characteristic, complemented
3C2×#14581720C211yesmaximal, characteristic, complemented
4C2×#14581719C211yesmaximal, characteristic, complemented
5C2×#14581718C211yesmaximal, characteristic, complemented
6#19127547C211yesmaximal, characteristic, complemented
7C2×#104×C83C211yesmaximal, characteristic, complemented
8C2×#13050590C2211yescharacteristic
9C2×#13050574C2211yescharacteristic
10#14581790C411yescharacteristic, complemented
11#14581788C411yescharacteristic, complemented
12#14581781C411yescharacteristic, complemented
13#14581779C411yescharacteristic, complemented
14#14581764—22no—
15C4×C22⋊D83—22no—
16C2×C4×Dic83C2211yescharacteristic
17C2×C4×Dic83C2211yescharacteristic
18Dic83⋊C8—22no—
19#14581720—22no—
20#14581719—22no—
21#14581718—22no—
22C83⋊#95—22no—
23C2×#41×C83C2211yescharacteristic
24C2×M16×C83C2211yescharacteristic
25C2×C42×C83C2211yescharacteristic
26#104×C83—22no—
27#13050590—21no—
28#13050590—21no—
29#13050590—21no—
30#13050590—21no—
31C2×Dic166C2×C411yescharacteristic
32C2×D332C2×C411yescharacteristic
33C2×C22⋊D83—21no—
34C2×C22⋊D83—22no—
35C22×Dic83—21no—
36C22×Dic83D412yes—
37C2×C4×D83—21no—
38#13050574—21no—
39#13050574—21no—
40C2×C83⋊C8—21no—
41Dic83⋊C4—22no—
42C22⋊Dic83—22no—
43(C2×D83)⋊C4—22no—
44C4×Dic83—21no—
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83C2×C411yescharacteristic
47C4×Dic83D412yes—
48C4×Dic83D412yescomplemented
49#41×C83—21no—
50#41×C83—21no—
51#41×C83—21no—
52#41×C83—21no—
53C2×Q8×C83C2×C411yescharacteristic
54C2×D4×C83—21no—
55C2×D4×C83C2×C411yescharacteristic
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83C2311yescharacteristic
59M16×C83—21no—
60M16×C83—21no—
61C2×C8×C83—21no—
62C42×C83—21no—
63C42×C83D412yescomplemented
64C23×C83—21no—
65C23×C83C2×D411yescharacteristic
66C22×D83—21no—
67Q8×C83—21no—
68Q8×C83—21no—
69D4×C83—21no—
70D4×C83—21no—
71D4×C83—41no—
72D4×C83—41no—
73C2×C4×C83—21no—
74C2×C4×C83—22no—
75C2×C4×C83—42no—
76C2×C4×C83—41no—
77C2×C4×C83—41no—
78C2×C4×C83C22×C411yescharacteristic
79C2×C4×C83C2×D411yescharacteristic
80C2×C4×C83C2×D411yescharacteristic
81C2×C4×C83C2×D411yescharacteristic
82C2×C4×C83#4111yescharacteristic
83C2×C4×C83#4111yescharacteristic
84C22⋊D83—44no—
85C22⋊D83—41no—
86C22⋊D83—41no—
87C2×Dic83—21no—
88C2×Dic83—22no—
89C2×Dic83—42no—
90C2×Dic83—42no—
91C2×Dic83C22⋊C412yes—
92C2×Dic83C22⋊C412yes—
93D332—21no—
94D332—21no—
95C4×D83—41no—
96C4×D83—41no—
97Dic166—21no—
98Dic166—21no—
99C8×C83—41no—
100C83⋊C8—41no—
101C22×C83—22no—
102C22×C83—41no—
103C22×C83—42no—
104C22×C83C2×C22⋊C411yescharacteristic
105C22×C83#12111yescharacteristic
106C22×C83#12111yescharacteristic
107C2×D83—41no—
108C2×D83—42no—
109C4×C83—42no—
110C4×C83—41no—
111C4×C83C4×D411yescharacteristic
112C4×C83C4×D411yescharacteristic
113C4×C83#12411yescharacteristic
114C4×C83#12711yescharacteristic
115Dic83—22no—
116Dic83—22no—
117Dic83—42no—
118Dic83—41no—
119C2×C83—21no—
120C2×C83—21no—
121C2×C83—81no—
122C2×C83#39011yescharacteristic
123C2×C83#42112yes—
124D83—81no—
125#1963—831nomaximal, Sylow
126C83#196311yescharacteristic, complemented, Sylow
127#532—831no—
128#423—831no—
129C2×#104—831no—
130C2×#104—831no—
131C2×#104—831no—
132C2×#104D8311yescharacteristic, complemented
133#376—831no—
134C2×#41—831no—
135C2×#41C2×D8311yescharacteristic
136C2×M16—831no—
137C2×M16C2×D8311yescharacteristic
138C4⋊Q8—831no—
139#127—831no—
140#124—831no—
141#124—831no—
142#121—1662no—
143C4×D4—1662no—
144C2×C42—831no—
145C2×C42—831no—
146C2×C42C2×D8311yescharacteristic
147C4⋊C8—1662no—
148#104—22no—
149#104—1662no—
150#104—1662no—
151#104—1662no—
152#95—1662no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—1661no—
158#41—1661no—
159#41—1661no—
160#41—1661no—
161C2×Q8—831no—
162C2×Q8C4×D8311yescharacteristic
163C2×D4—21no—
164C2×D4—831no—
165C2×D4—1662no—
166C2×D4—1661no—
167C2×D4C4×D8311yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—832no—
171C22×C4—1661no—
172C22×C4—1661no—
173C22×C4C22×D8311yescharacteristic
174M16—21no—
175M16—21no—
176M16—1661no—
177M16—1661no—
178C2×C8—21no—
179C2×C8—1661no—
180C4⋊C4—1662no—
181C22⋊C4—1662no—
182C22⋊C4—1662no—
183C42—21no—
184C42—831no—
185C42—831no—
186C42—832no—
187C42—832no—
188C42—1661no—
189C42C22⋊D8312yescomplemented
190C23—21no—
191C23—1661no—
192C23D4×D8311yescharacteristic
193Q8—21no—
194Q8—21no—
195Q8—1661no—
196Q8—1661no—
197D4—21no—
198D4—21no—
199D4—41no—
200D4—41no—
201D4—3321no—
202D4—3321no—
203D4—3324no—
204D4—1661no—
205D4—1661no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3322no—
212C2×C4—3321no—
213C2×C4—3321no—
214C2×C4—3322no—
215C2×C4—832no—
216C2×C4—832no—
217C2×C4—1662no—
218C2×C4—1661no—
219C2×C4C2×C4×D8311yescharacteristic
220C2×C4D4×D8311yescharacteristic
221C2×C4D4×D8311yescharacteristic
222C2×C4C2×C22⋊D8311yescharacteristic
223C2×C4#1305058911yescharacteristic
224C2×C4#1305059011yescharacteristic
225C8—41no—
226C8—3321no—
227C22—22no—
228C22—41no—
229C22—42no—
230C22—3321no—
231C22—3322no—
232C22C22⋊C4×D8311yescharacteristic
233C22#1458176411yescharacteristic
234C22#1458176511yescharacteristic
235C4—42no—
236C4—41no—
237C4—3322no—
238C4—3321no—
239C4—1662no—
240C4—1662no—
241C4(C22⋊D83)⋊C411yescharacteristic
242C4C4×C22⋊D8311yescharacteristic
243C4#1458177811yescharacteristic
244C4#1458178811yescharacteristic
245C2—21no—
246C2—21no—
247C2—81no—
248C2—6641no—
249C2#1912760111yescharacteristic
250C2#1912771612yes—
subgroupG/H
centerC2×C4D4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
FittingC2×#104×C83C2
socleC22×C83C2×C22⋊C4
prime radical#19128247C2
cosocleC22×C4×C83C23
hypercenterC2×#104D83
hypocenterC83#1963
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #19127724C2semidirect
3. C2×#14581720C2semidirect
4. C2×#14581719C2semidirect
5. C2×#14581718C2semidirect
6. #19127547C2semidirect
7. C2×#104×C83C2semidirect
10. #14581790C4semidirect
11. #14581788C4semidirect
12. #14581781C4semidirect
13. #14581779C4semidirect
48. C4×Dic83D4semidirect
63. C42×C83D4semidirect
126. C83#1963semidirect
132. C2×#104D83semidirect
189. C42C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
#191282472
#191277242
C2×#145817202
C2×#145817192
C2×#145817182
#191275472
C2×#104×C832
#196383