Finite Group Databasebeta

← C83×#11428 #35239252

Subgroups — C83×#11428 #35239252

Order 21248.

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

normal subgroups only

This group has 526 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×#2310C211yesmaximal, characteristic
2C83×#1458C212yesmaximal
3C83×#1317C214yesmaximal
4C23×Q8×C83C411yescharacteristic
5C2×#117×C83C411yescharacteristic
6C2×#117×C83C2211yescharacteristic
7#431×C83—22no—
8#391×C83—22no—
9#391×C83—22no—
10#381×C83C412yes—
11#381×C83C2212yes—
12#324×C83—22no—
13#323×C83C2214yes—
14C22×Q8×C83—21no—
15C22×Q8×C83—21no—
16C22×Q8×C83—22no—
17C22×Q8×C83—42no—
18C22×Q8×C83—42no—
19C22×Q8×C83C814yescomplemented
20C23×C4×C83C2×C411yescharacteristic
21C23×C4×C83C2×C412yes—
22#117×C83—42no—
23#117×C83—42no—
24C2×C4⋊C4×C83—21no—
25C2×C4⋊C4×C83D412yes—
26C2×C22⋊C4×C83C2×C412yes—
27C2×C22⋊C4×C83C2×C411yescharacteristic
28C2×C22⋊C4×C83C2311yescharacteristic
29C2×C42×C83—21no—
30C2×C42×C83D412yes—
31C4⋊C8×C83—42no—
32C22⋊C8×C83—24no—
33C4×C8×C83—42no—
34#95×C83—24no—
35#95×C83—24no—
36C24×C83C22×C411yescharacteristic
37C2×Q8×C83—24no—
38C2×Q8×C83—24no—
39C2×Q8×C83—48no—
40C2×Q8×C83—42no—
41C2×Q8×C83—42no—
42C2×Q8×C83—48no—
43C2×Q8×C83—42no—
44C2×Q8×C83—42no—
45C22×C4×C83—22no—
46C22×C4×C83—22no—
47C22×C4×C83—22no—
48C22×C4×C83—22no—
49C22×C4×C83—22no—
50C22×C4×C83—42no—
51C22×C4×C83—42no—
52C22×C4×C83C22⋊C411yescharacteristic
53C22×C4×C83C22⋊C412yes—
54C22×C4×C83C22⋊C411yescharacteristic
55C22×C4×C83C2×C812yes—
56C22×C4×C83C2×C814yes—
57C22×C4×C83M1612yes—
58C22×C4×C83C2×D412yes—
59C2×C8×C83—44no—
60C4⋊C4×C83—42no—
61C4⋊C4×C83—42no—
62C22⋊C4×C83—41no—
63C22⋊C4×C83—41no—
64C22⋊C4×C83—42no—
65C42×C83—22no—
66C42×C83—22no—
67C42×C83—42no—
68C23×C83—21no—
69C23×C83—21no—
70C23×C83—42no—
71C23×C83C2×C22⋊C411yescharacteristic
72C23×C83C22×C811yescharacteristic
73C23×C83C2×M1611yescharacteristic
74Q8×C83—48no—
75Q8×C83—48no—
76C2×C4×C83—21no—
77C2×C4×C83—21no—
78C2×C4×C83—24no—
79C2×C4×C83—24no—
80C2×C4×C83—24no—
81C2×C4×C83—22no—
82C2×C4×C83—22no—
83C2×C4×C83—44no—
84C2×C4×C83—42no—
85C2×C4×C83—42no—
86C2×C4×C83—44no—
87C2×C4×C83—42no—
88C2×C4×C83—42no—
89C2×C4×C83—44no—
90C2×C4×C83—42no—
91C2×C4×C83C22⋊C812yes—
92C2×C4×C83C22⋊C812yes—
93C2×C4×C83#9912yes—
94C2×C4×C83#10012yes—
95C8×C83—84no—
96C22×C83—22no—
97C22×C83—21no—
98C22×C83—21no—
99C22×C83—41no—
100C22×C83—41no—
101C22×C83—42no—
102C22×C83—42no—
103C22×C83C2×C22⋊C811yescharacteristic
104C22×C83C2×#9911yescharacteristic
105C22×C83C2×#10011yescharacteristic
106C4×C83—22no—
107C4×C83—42no—
108C4×C83—42no—
109C4×C83—44no—
110C4×C83—82no—
111C4×C83#32314yes—
112#11428C8311yesmaximal, characteristic, direct product factor, Sylow
113C2×C83—21no—
114C2×C83—21no—
115C2×C83—41no—
116C2×C83—41no—
117C2×C83C2×#32311yescharacteristic
118C2×C83#212312yes—
119#2310C2×C8311yescharacteristic
120#1458C2×C8312yes—
121#1317C2×C8314yes—
122C83#1142811yescharacteristic, direct product factor, Sylow
123C23×Q8C4×C8311yescharacteristic
124C2×#117C4×C8311yescharacteristic
125C2×#117C22×C8311yescharacteristic
126#431—22no—
127#391—22no—
128#391—22no—
129#381C4×C8312yes—
130#381C22×C8312yes—
131#324—22no—
132#323C22×C8314yes—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—22no—
136C22×Q8—42no—
137C22×Q8—42no—
138C22×Q8C8×C8314yescomplemented
139C23×C4C2×C4×C8311yescharacteristic
140C23×C4C2×C4×C8312yes—
141#117—42no—
142#117—42no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4D4×C8312yes—
145C2×C22⋊C4C2×C4×C8312yes—
146C2×C22⋊C4C2×C4×C8311yescharacteristic
147C2×C22⋊C4C23×C8311yescharacteristic
148C2×C42—21no—
149C2×C42D4×C8312yes—
150C4⋊C8—42no—
151C22⋊C8—24no—
152C4×C8—42no—
153#95—24no—
154#95—24no—
155C24C22×C4×C8311yescharacteristic
156C2×Q8—24no—
157C2×Q8—24no—
158C2×Q8—48no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4C22⋊C4×C8311yescharacteristic
172C22×C4C22⋊C4×C8312yes—
173C22×C4C22⋊C4×C8311yescharacteristic
174C22×C4C2×C8×C8312yes—
175C22×C4C2×C8×C8314yes—
176C22×C4M16×C8312yes—
177C22×C4C2×D4×C8312yes—
178C2×C8—44no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—42no—
184C42—22no—
185C42—22no—
186C42—42no—
187C23—21no—
188C23—21no—
189C23—42no—
190C23C2×C22⋊C4×C8311yescharacteristic
191C23C22×C8×C8311yescharacteristic
192C23C2×M16×C8311yescharacteristic
193Q8—48no—
194Q8—48no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4C22⋊C8×C8312yes—
211C2×C4C22⋊C8×C8312yes—
212C2×C4#99×C8312yes—
213C2×C4#100×C8312yes—
214C8—84no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22—42no—
222C22C2×C22⋊C8×C8311yescharacteristic
223C22C2×#99×C8311yescharacteristic
224C22C2×#100×C8311yescharacteristic
225C4—22no—
226C4—42no—
227C4—42no—
228C4—44no—
229C4—82no—
230C4#323×C8314yes—
231C2—21no—
232C2—21no—
233C2—41no—
234C2—41no—
235C2C2×#323×C8311yescharacteristic
236C2C83×#212312yes—
subgroupG/H
center, socleC22×C83C2×#99
commutatorC23C22×C8×C83
Frattini, cosocleC2×C22⋊C4C23×C83
prime radicalC24×C83C22×C4
LCSG ▷ C23 ▷ 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
19. C22×Q8×C83C8semidirect
112. #11428C83direct (N × H)
122. C83#11428direct (N × H)
138. C22×Q8C8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#23102
C83×#14582
C83×#13172
#1142883