Finite Group Databasebeta

← C83×#7507 #35235331

Subgroups — C83×#7507 #35235331

Order 21248.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C83×#2132C212yesmaximal
2C83×#1963C211yesmaximal, characteristic
3#532×C83C2211yescharacteristic
4#423×C83C411yescharacteristic
5C2×#104×C83—22no—
6#413×C83—22no—
7#376×C83C411yescharacteristic
8#356×C83—22no—
9#355×C83C414yescomplemented
10C2×#41×C83D412yes—
11C2×M16×C83—21no—
12C2×M16×C83—42no—
13C4⋊Q8×C83D411yescharacteristic
14#127×C83Q811yescharacteristic
15#124×C83C2×C412yes—
16#121×C83—41no—
17C4×D4×C83—41no—
18C2×C42×C83—21no—
19C2×C42×C83C2×C411yescharacteristic
20C4⋊C8×C83—41no—
21#104×C83—44no—
22#101×C83—24no—
23#100×C83—42no—
24#95×C83—41no—
25#41×C83—42no—
26#41×C83—42no—
27C2×Q8×C83C22⋊C412yes—
28C2×D4×C83—22no—
29C2×D4×C83—41no—
30C2×D4×C83C4⋊C412yes—
31C22×C4×C83—21no—
32C22×C4×C83—22no—
33C22×C4×C83—41no—
34C22×C4×C83C22⋊C411yescharacteristic
35M16×C83—44no—
36M16×C83—42no—
37M16×C83—82no—
38C2×C8×C83—41no—
39C2×C8×C83—82no—
40C4⋊C4×C83—41no—
41C22⋊C4×C83—42no—
42C42×C83—21no—
43C42×C83—22no—
44C42×C83—41no—
45C42×C83C4211yescharacteristic
46C42×C83C4⋊C411yescharacteristic
47C23×C83—22no—
48C23×C83#9911yescharacteristic
49Q8×C83—42no—
50D4×C83—42no—
51D4×C83—82no—
52D4×C83—82no—
53C2×C4×C83—21no—
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—22no—
58C2×C4×C83—42no—
59C2×C4×C83—42no—
60C2×C4×C83—42no—
61C2×C4×C83—81no—
62C2×C4×C83—82no—
63C2×C4×C83#9511yescharacteristic
64C2×C4×C83#9911yescharacteristic
65C8×C83—84no—
66C8×C83—81no—
67C22×C83—21no—
68C22×C83—41no—
69C22×C83—42no—
70C22×C83—82no—
71C22×C83#34211yescharacteristic
72C4×C83—21no—
73C4×C83—41no—
74C4×C83—41no—
75C4×C83—42no—
76C4×C83—82no—
77C4×C83#35311yescharacteristic
78C4×C83#35411yescharacteristic
79#7507C8311yesmaximal, characteristic, direct product factor, Sylow
80C2×C83—21no—
81C2×C83—41no—
82C2×C83—82no—
83C2×C83#139311yescharacteristic
84#2132C2×C8312yes—
85#1963C2×C8311yescharacteristic
86C83#750711yescharacteristic, direct product factor, Sylow
87#532C22×C8311yescharacteristic
88#423C4×C8311yescharacteristic
89C2×#104—22no—
90#413—22no—
91#376C4×C8311yescharacteristic
92#356—22no—
93#355C4×C8314yescomplemented
94C2×#41D4×C8312yes—
95C2×M16—21no—
96C2×M16—42no—
97C4⋊Q8D4×C8311yescharacteristic
98#127Q8×C8311yescharacteristic
99#124C2×C4×C8312yes—
100#121—41no—
101C4×D4—41no—
102C2×C42—21no—
103C2×C42C2×C4×C8311yescharacteristic
104C4⋊C8—41no—
105#104—44no—
106#101—24no—
107#100—42no—
108#95—41no—
109#41—42no—
110#41—42no—
111C2×Q8C22⋊C4×C8312yes—
112C2×D4—22no—
113C2×D4—41no—
114C2×D4C4⋊C4×C8312yes—
115C22×C4—21no—
116C22×C4—22no—
117C22×C4—41no—
118C22×C4C22⋊C4×C8311yescharacteristic
119M16—44no—
120M16—42no—
121M16—82no—
122C2×C8—41no—
123C2×C8—82no—
124C4⋊C4—41no—
125C22⋊C4—42no—
126C42—21no—
127C42—22no—
128C42—41no—
129C42C42×C8311yescharacteristic
130C42C4⋊C4×C8311yescharacteristic
131C23—22no—
132C23#99×C8311yescharacteristic
133Q8—42no—
134D4—42no—
135D4—82no—
136D4—82no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—81no—
146C2×C4—82no—
147C2×C4#95×C8311yescharacteristic
148C2×C4#99×C8311yescharacteristic
149C8—84no—
150C8—81no—
151C22—21no—
152C22—41no—
153C22—42no—
154C22—82no—
155C22#342×C8311yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—42no—
160C4—82no—
161C4#353×C8311yescharacteristic
162C4#354×C8311yescharacteristic
163C2—21no—
164C2—41no—
165C2—82no—
166C2C83×#139311yescharacteristic
subgroupG/H
centerC4×C83#353
commutatorC42C42×C83
Frattini, cosocle#532C22×C83
socleC2×C83#1393
prime radical#532×C83C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C83 ◁ C2×C4×C83 ◁ C22×C4×C83 ◁ #532×C83 ◁ G

Complements

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

NH ≅ G/Ntype
9. #355×C83C4semidirect
79. #7507C83direct (N × H)
86. C83#7507direct (N × H)
93. #355C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#21322
C83×#19632
#750783