Finite Group Databasebeta

← C83×#11450 #35239274

Subgroups — C83×#11450 #35239274

Order 21248.

434 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2317C211yesmaximal, characteristic
2C83×#1458C212yesmaximal
3C83×#1325C214yesmaximal, complemented
4C2×#117×C83C411yescharacteristic
5C2×#117×C83C2211yescharacteristic
6C22×C4⋊C4×C83C411yescharacteristic
7#431×C83—22no—
8#389×C83—22no—
9#385×C83—22no—
10#384×C83C2212yes—
11#382×C83C412yes—
12#324×C83C2214yes—
13#323×C83—22no—
14C23×C4×C83—21no—
15C23×C4×C83C2×C411yescharacteristic
16#117×C83—22no—
17#117×C83—42no—
18#117×C83C814yescomplemented
19C2×C4⋊C4×C83—21no—
20C2×C4⋊C4×C83—21no—
21C2×C4⋊C4×C83—24no—
22C2×C4⋊C4×C83—42no—
23C2×C4⋊C4×C83C2×C412yes—
24C2×C4⋊C4×C83C2×C411yescharacteristic
25C2×C4⋊C4×C83C2311yescharacteristic
26C2×C22⋊C4×C83—21no—
27C2×C22⋊C4×C83D412yes—
28C2×C42×C83C2×C412yes—
29C2×C42×C83D412yes—
30C4⋊C8×C83—42no—
31C22⋊C8×C83—24no—
32C4×C8×C83—42no—
33#95×C83—24no—
34C24×C83C22⋊C411yescharacteristic
35C22×C4×C83—22no—
36C22×C4×C83—22no—
37C22×C4×C83—22no—
38C22×C4×C83—22no—
39C22×C4×C83—42no—
40C22×C4×C83—82no—
41C22×C4×C83C22⋊C412yes—
42C22×C4×C83C22⋊C411yescharacteristic
43C22×C4×C83C2×C812yes—
44C22×C4×C83M1612yes—
45C22×C4×C83C22×C411yescharacteristic
46C22×C4×C83C2×D412yes—
47C2×C8×C83—44no—
48C4⋊C4×C83—24no—
49C4⋊C4×C83—41no—
50C4⋊C4×C83—41no—
51C4⋊C4×C83—42no—
52C4⋊C4×C83—42no—
53C4⋊C4×C83—84no—
54C22⋊C4×C83—24no—
55C22⋊C4×C83—42no—
56C42×C83—22no—
57C42×C83—22no—
58C42×C83—22no—
59C42×C83C2×C814yes—
60C23×C83—21no—
61C23×C83—21no—
62C23×C83—41no—
63C23×C83—41no—
64C23×C83C22⋊C812yes—
65C23×C83C2×C22⋊C411yescharacteristic
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—24no—
69C2×C4×C83—24no—
70C2×C4×C83—24no—
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83—42no—
76C2×C4×C83—42no—
77C2×C4×C83—44no—
78C2×C4×C83—42no—
79C2×C4×C83—84no—
80C2×C4×C83C22⋊C812yes—
81C2×C4×C83#9912yes—
82C2×C4×C83#10112yes—
83C2×C4×C83C22×C811yescharacteristic
84C2×C4×C83C2×M1611yescharacteristic
85C8×C83—84no—
86C22×C83—21no—
87C22×C83—21no—
88C22×C83—22no—
89C22×C83—42no—
90C22×C83—42no—
91C22×C83—41no—
92C22×C83—41no—
93C22×C83C2×C22⋊C811yescharacteristic
94C22×C83C2×#9911yescharacteristic
95C22×C83C2×#10111yescharacteristic
96C4×C83—21no—
97C4×C83—21no—
98C4×C83—44no—
99C4×C83—42no—
100C4×C83—42no—
101C4×C83—82no—
102C4×C83#32414yes—
103#11450C8311yesmaximal, characteristic, direct product factor, Sylow
104C2×C83—21no—
105C2×C83—21no—
106C2×C83—42no—
107C2×C83C2×#32411yescharacteristic
108C2×C83#212811yescharacteristic
109C2×C83#213511yescharacteristic
110#2317C2×C8311yescharacteristic
111#1458C2×C8312yes—
112#1325C2×C8314yescomplemented
113C83#1145011yescharacteristic, direct product factor, Sylow
114C2×#117C4×C8311yescharacteristic
115C2×#117C22×C8311yescharacteristic
116C22×C4⋊C4C4×C8311yescharacteristic
117#431—22no—
118#389—22no—
119#385—22no—
120#384C22×C8312yes—
121#382C4×C8312yes—
122#324C22×C8314yes—
123#323—22no—
124C23×C4—21no—
125C23×C4C2×C4×C8311yescharacteristic
126#117—22no—
127#117—42no—
128#117C8×C8314yescomplemented
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4C2×C4×C8312yes—
134C2×C4⋊C4C2×C4×C8311yescharacteristic
135C2×C4⋊C4C23×C8311yescharacteristic
136C2×C22⋊C4—21no—
137C2×C22⋊C4D4×C8312yes—
138C2×C42C2×C4×C8312yes—
139C2×C42D4×C8312yes—
140C4⋊C8—42no—
141C22⋊C8—24no—
142C4×C8—42no—
143#95—24no—
144C24C22⋊C4×C8311yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—82no—
151C22×C4C22⋊C4×C8312yes—
152C22×C4C22⋊C4×C8311yescharacteristic
153C22×C4C2×C8×C8312yes—
154C22×C4M16×C8312yes—
155C22×C4C22×C4×C8311yescharacteristic
156C22×C4C2×D4×C8312yes—
157C2×C8—44no—
158C4⋊C4—24no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—84no—
164C22⋊C4—24no—
165C22⋊C4—42no—
166C42—22no—
167C42—22no—
168C42—22no—
169C42C2×C8×C8314yes—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23C22⋊C8×C8312yes—
175C23C2×C22⋊C4×C8311yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4C22⋊C8×C8312yes—
191C2×C4#99×C8312yes—
192C2×C4#101×C8312yes—
193C2×C4C22×C8×C8311yescharacteristic
194C2×C4C2×M16×C8311yescharacteristic
195C8—84no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×C22⋊C8×C8311yescharacteristic
204C22C2×#99×C8311yescharacteristic
205C22C2×#101×C8311yescharacteristic
206C4—21no—
207C4—21no—
208C4—44no—
209C4—42no—
210C4—42no—
211C4—82no—
212C4#324×C8314yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×#324×C8311yescharacteristic
217C2C83×#212811yescharacteristic
218C2C83×#213511yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC2×C4C22×C8×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC24×C83C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#1325C2semidirect
18. #117×C83C8semidirect
103. #11450C83direct (N × H)
112. #1325C2×C83semidirect
113. C83#11450direct (N × H)
128. #117C8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#23172
C83×#14582
C83×#13252
#1145083