Finite Group Databasebeta

← C83×#10373 #35238197

Subgroups — C83×#10373 #35238197

Order 21248.

364 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2402C211yesmaximal, characteristic
2C83×#1995C211yesmaximal, characteristic
3C83×#1503C212yesmaximal
4C83×#1303C212yesmaximal
5C83×#1274C211yesmaximal, characteristic
6#533×C83C2211yescharacteristic
7#431×C83C2212yes—
8#423×C83C2211yescharacteristic
9#400×C83—22no—
10#398×C83—22no—
11C4×C4⋊C4×C83—22no—
12C4×C4⋊C4×C83C2212yes—
13#376×C83C2211yescharacteristic
14#339×C83—22no—
15#328×C83—22no—
16#328×C83—22no—
17C2×M16×C83—21no—
18C4⋊Q8×C83Q812yes—
19#125×C83—21no—
20C22⋊Q8×C83—22no—
21C4×Q8×C83—22no—
22#117×C83—21no—
23C2×C4⋊C4×C83—22no—
24C2×C4⋊C4×C83—22no—
25C2×C4⋊C4×C83—22no—
26C2×C42×C83—22no—
27C2×C42×C83D412yes—
28C2×C42×C83C2311yescharacteristic
29C4⋊C8×C83—22no—
30C4⋊C8×C83—22no—
31C22⋊C8×C83—22no—
32C4×C8×C83—22no—
33#95×C83—22no—
34#95×C83—22no—
35#95×C83—22no—
36#95×C83D412yes—
37#95×C83D412yes—
38C2×Q8×C83—22no—
39C22×C4×C83—22no—
40C22×C4×C83—22no—
41C22×C4×C83—22no—
42C22×C4×C83C2×D412yes—
43C22×C4×C83C2×D411yescharacteristic
44M16×C83—42no—
45C2×C8×C83—42no—
46C2×C8×C83—41no—
47C4⋊C4×C83—22no—
48C4⋊C4×C83—22no—
49C4⋊C4×C83—44no—
50C4⋊C4×C83—44no—
51C4⋊C4×C83—44no—
52C4⋊C4×C83—42no—
53C22⋊C4×C83—41no—
54C42×C83—22no—
55C42×C83—22no—
56C42×C83—41no—
57C42×C83—42no—
58C42×C83—42no—
59C42×C83C2×Q811yescharacteristic
60C42×C83#4111yescharacteristic
61C42×C83#4112yes—
62C23×C83#12011yescharacteristic
63Q8×C83—82no—
64C2×C4×C83—24no—
65C2×C4×C83—42no—
66C2×C4×C83—42no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83—42no—
70C2×C4×C83—42no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83C22⋊Q812yes—
76C2×C4×C83C22⋊Q811yescharacteristic
77C2×C4×C83#12412yes—
78C2×C4×C83#12411yescharacteristic
79C2×C4×C83#13512yes—
80C2×C4×C83#13712yes—
81C8×C83—82no—
82C8×C83—81no—
83C22×C83—22no—
84C22×C83#39311yescharacteristic
85C22×C83#45212yes—
86C4×C83—22no—
87C4×C83—22no—
88C4×C83—44no—
89C4×C83—82no—
90C4×C83—82no—
91C4×C83—82no—
92C4×C83#47912yes—
93C4×C83#48811yescharacteristic
94C4×C83#49111yescharacteristic
95#10373C8311yesmaximal, characteristic, direct product factor, Sylow
96C2×C83—22no—
97C2×C83#202611yescharacteristic
98C2×C83#203112yes—
99#2402C2×C8311yescharacteristic
100#1995C2×C8311yescharacteristic
101#1503C2×C8312yes—
102#1303C2×C8312yes—
103#1274C2×C8311yescharacteristic
104C83#1037311yescharacteristic, direct product factor, Sylow
105#533C22×C8311yescharacteristic
106#431C22×C8312yes—
107#423C22×C8311yescharacteristic
108#400—22no—
109#398—22no—
110C4×C4⋊C4—22no—
111C4×C4⋊C4C22×C8312yes—
112#376C22×C8311yescharacteristic
113#339—22no—
114#328—22no—
115#328—22no—
116C2×M16—21no—
117C4⋊Q8Q8×C8312yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42D4×C8312yes—
127C2×C42C23×C8311yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—22no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95D4×C8312yes—
136#95D4×C8312yes—
137C2×Q8—22no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C2×D4×C8312yes—
142C22×C4C2×D4×C8311yescharacteristic
143M16—42no—
144C2×C8—42no—
145C2×C8—41no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—44no—
149C4⋊C4—44no—
150C4⋊C4—44no—
151C4⋊C4—42no—
152C22⋊C4—41no—
153C42—22no—
154C42—22no—
155C42—41no—
156C42—42no—
157C42—42no—
158C42C2×Q8×C8311yescharacteristic
159C42#41×C8312yes—
160C42#41×C8311yescharacteristic
161C23#120×C8311yescharacteristic
162Q8—82no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4C22⋊Q8×C8312yes—
175C2×C4C22⋊Q8×C8311yescharacteristic
176C2×C4#124×C8312yes—
177C2×C4#124×C8311yescharacteristic
178C2×C4#135×C8312yes—
179C2×C4#137×C8312yes—
180C8—82no—
181C8—81no—
182C22—22no—
183C22#393×C8311yescharacteristic
184C22#452×C8312yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—82no—
191C4#479×C8312yes—
192C4#488×C8311yescharacteristic
193C4#491×C8311yescharacteristic
194C2—22no—
195C2C83×#202611yescharacteristic
196C2C83×#203112yes—
subgroupG/H
centerC2×C4×C83#124
commutator, Frattini, cosocleC2×C42C23×C83
socleC22×C83#393
prime radicalC23×C83#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
95. #10373C83direct (N × H)
104. C83#10373direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#24022
C83×#19952
C83×#15032
C83×#13032
C83×#12742
#1037383