Finite Group Databasebeta

← #24909147

Subgroups — #24909147

Order 10624.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#19128252C211yesmaximal, characteristic
2#19127684C212yesmaximal, complemented
3#19127500C211yesmaximal, characteristic, complemented
4#19127497C212yesmaximal, complemented
5#356×C83C211yesmaximal, characteristic, complemented
6C2×#13050591C411yescharacteristic
7C2×#13050591C2211yescharacteristic
8M16×D83—22no—
9#14581789C411yescharacteristic
10#14581781C411yescharacteristic
11#14581781C2211yescharacteristic
12#14581767—22no—
13#14581754—22no—
14C42×D83C411yescharacteristic
15#14581711C2212yes—
16#14581708—22no—
17C4⋊Q8×C83C2211yescharacteristic
18#101×C83C2212yes—
19#13050591—41no—
20#13050591—41no—
21#13050591—41no—
22#13050591—41no—
23C2×D332—21no—
24C2×D332—22no—
25C2×D332C2×C411yescharacteristic
26C2×D332C2×C411yescharacteristic
27C2×D332D412yes—
28C2×C4×D83—21no—
29C2×C4×D83—21no—
30C2×C4×D83C2×C411yescharacteristic
31C2×C4×D83D412yes—
32#13050574—22no—
33#13050573—42no—
34C8×D83—42no—
35(C2×D83)⋊C4—22no—
36(C2×D83)⋊C4—22no—
37C4×Dic83—21no—
38C4×Dic83C2×C411yescharacteristic
39C2×Q8×C83C2×C411yescharacteristic
40C2×Q8×C83C2311yescharacteristic
41M16×C83—22no—
42C4⋊C4×C83—22no—
43C42×C83C2×C411yescharacteristic
44C22×D83—21no—
45C22×D83C22⋊C412yes—
46C22×D83C22⋊C411yescharacteristic
47Q8×C83—41no—
48Q8×C83—41no—
49C2×C4×C83—21no—
50C2×C4×C83—21no—
51C2×C4×C83C22×C411yescharacteristic
52C2×C4×C83C2×D412yes—
53C2×Dic83—21no—
54C2×Dic83C22⋊C411yescharacteristic
55D332—41no—
56D332—42no—
57D332—41no—
58D332—44no—
59D332—42no—
60C4×D83—22no—
61C4×D83—22no—
62C4×D83—21no—
63C4×D83—21no—
64C4×D83—42no—
65C4×D83—41no—
66C4×D83—41no—
67C8×C83—42no—
68C83⋊C8—42no—
69C22×C83C2×C22⋊C411yescharacteristic
70C2×D83—21no—
71C2×D83—22no—
72C2×D83—41no—
73C2×D83—42no—
74C2×D83—42no—
75C2×D83—41no—
76C4×C83—22no—
77C4×C83—22no—
78C4×C83—21no—
79C4×C83—41no—
80Dic83—41no—
81Dic83#9911yescharacteristic
82Dic83#9911yescharacteristic
83C2×C83—21no—
84C2×C83C2×#9911yescharacteristic
85D83—41no—
86D83—42no—
87D83—81no—
88#2132—831nomaximal, Sylow
89C83#213211yescharacteristic, complemented, Sylow
90#532—831no—
91#413—832no—
92#356—831no—
93#356D8311yescharacteristic, complemented
94#355—832no—
95C2×#41—831no—
96C2×#41—831no—
97C2×M16—1662no—
98C4⋊Q8C2×D8311yescharacteristic
99#127—831no—
100#124—831no—
101#124—831no—
102#121—1662no—
103C4×D4—1662no—
104C2×C42—831no—
105#101—832no—
106#101C2×D8312yes—
107#100—1662no—
108#41—3321no—
109#41—3321no—
110#41—3321no—
111#41—3321no—
112C2×Q8C4×D8311yescharacteristic
113C2×Q8C22×D8311yescharacteristic
114C2×D4—831no—
115C2×D4—831no—
116C2×D4—832no—
117C2×D4—1662no—
118C2×D4—1661no—
119C22×C4—831no—
120C22×C4—832no—
121C22×C4—1661no—
122C22×C4—1661no—
123M16—22no—
124M16—3322no—
125M16—1662no—
126C2×C8—3322no—
127C4⋊C4—22no—
128C22⋊C4—1662no—
129C22⋊C4—1662no—
130C42—831no—
131C42—1661no—
132C42C4×D8311yescharacteristic
133C23—832no—
134C23—831no—
135C23—1661no—
136Q8—41no—
137Q8—41no—
138D4—3321no—
139D4—3324no—
140D4—3322no—
141D4—3321no—
142D4—3322no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3322no—
146C2×C4—3321no—
147C2×C4—3321no—
148C2×C4—831no—
149C2×C4—1662no—
150C2×C4—1662no—
151C2×C4—1661no—
152C2×C4—1661no—
153C2×C4—1661no—
154C2×C4C2×C4×D8311yescharacteristic
155C2×C4D4×D8312yes—
156C8—42no—
157C8—3322no—
158C22—3321no—
159C22—3322no—
160C22—3322no—
161C22—3321no—
162C22—1661no—
163C22—1662no—
164C22C22⋊C4×D8311yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—3321no—
170C4—831no—
171C4—831no—
172C2—21no—
173C2—3321no—
174C2—3322no—
175C2—6641no—
176C2#99×D8311yescharacteristic
subgroupG/H
centerC2#99×D83
commutatorC2×C4×C83C22×C4
FrattiniC2×Q8C22×D83
Fitting#356×C83C2
socleC2×C83C2×#99
prime radical#19128252C2
cosocleC2×Q8×C83C23
hypercenter#356D83
hypocenterC83#2132
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #19127684C2semidirect
3. #19127500C2semidirect
4. #19127497C2semidirect
5. #356×C83C2semidirect
89. C83#2132semidirect
93. #356D83semidirect

Maximal subgroups

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

subgroupindex
#191282522
#191276842
#191275002
#191274972
#356×C832
#213283