Finite Group Databasebeta

← C83×#11538 #35239362

Subgroups — C83×#11538 #35239362

Order 21248.

334 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2930C211yesmaximal, characteristic
2C83×#2166C212yesmaximal, complemented
3C83×#1321C212yesmaximal, complemented
4C83×#1320C212yesmaximal, complemented
5C2×#131×C83C411yescharacteristic
6C22×M16×C83C411yescharacteristic
7#525×C83C411yescharacteristic
8#436×C83—22no—
9#435×C83—22no—
10#424×C83C411yescharacteristic
11#408×C83C2211yescharacteristic
12#407×C83C2211yescharacteristic
13#405×C83C2211yescharacteristic
14#364×C83—22no—
15#349×C83C2214yes—
16#347×C83—22no—
17C2×#41×C83C2×C411yescharacteristic
18C23×C4×C83C2×C411yescharacteristic
19#131×C83—42no—
20C2×M16×C83—21no—
21C2×M16×C83—21no—
22C2×M16×C83—21no—
23C2×M16×C83—42no—
24C2×M16×C83C2×C411yescharacteristic
25C2×M16×C83C2311yescharacteristic
26C22×C8×C83—21no—
27C22×C8×C83C2×C411yescharacteristic
28C22×C8×C83C2×C411yescharacteristic
29#123×C83—21no—
30C22⋊Q8×C83—21no—
31#121×C83—21no—
32#120×C83—21no—
33C4×D4×C83—22no—
34#117×C83C2×C411yescharacteristic
35M32×C83—24no—
36C4⋊C8×C83—22no—
37C22⋊C8×C83—22no—
38C22⋊C8×C83—22no—
39#97×C83D412yes—
40C4×C8×C83D412yes—
41C24×C83M1611yescharacteristic
42#41×C83—41no—
43#41×C83—41no—
44C2×Q8×C83M1611yescharacteristic
45C2×D4×C83—21no—
46C2×D4×C83—22no—
47C2×D4×C83M1611yescharacteristic
48C22×C4×C83—21no—
49C22×C4×C83—21no—
50C22×C4×C83—21no—
51C22×C4×C83—41no—
52C22×C4×C83—41no—
53C22×C4×C83M1611yescharacteristic
54C22×C4×C83C22×C411yescharacteristic
55M16×C83—41no—
56M16×C83—42no—
57M16×C83—42no—
58M16×C83—42no—
59M16×C83—41no—
60C2×C8×C83—22no—
61C2×C8×C83—21no—
62C2×C8×C83—21no—
63C2×C8×C83—42no—
64C2×C8×C83—41no—
65C2×C8×C83C22⋊C411yescharacteristic
66C2×C8×C83C22⋊C411yescharacteristic
67C2×C8×C83C2×D412yes—
68C4⋊C4×C83—22no—
69C4⋊C4×C83—21no—
70C22⋊C4×C83—22no—
71C22⋊C4×C83—22no—
72C22⋊C4×C83—21no—
73C42×C83C22⋊C412yes—
74C16×C83—44no—
75C23×C83—21no—
76C23×C83—21no—
77C23×C83—41no—
78C23×C83—81no—
79C23×C83C2×M1611yescharacteristic
80Q8×C83—41no—
81D4×C83—41no—
82D4×C83—42no—
83D4×C83—82no—
84C2×C4×C83—21no—
85C2×C4×C83—21no—
86C2×C4×C83—22no—
87C2×C4×C83—21no—
88C2×C4×C83—21no—
89C2×C4×C83—42no—
90C2×C4×C83—41no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—41no—
95C2×C4×C83C2×C22⋊C411yescharacteristic
96C2×C4×C83C2×M1611yescharacteristic
97C8×C83—22no—
98C8×C83—21no—
99C8×C83—41no—
100C8×C83—41no—
101C8×C83#10012yes—
102C22×C83—21no—
103C22×C83—41no—
104C22×C83—41no—
105C22×C83—42no—
106C22×C83—41no—
107C22×C83—41no—
108C22×C83—41no—
109C22×C83—82no—
110C22×C83#40711yescharacteristic
111C4×C83—21no—
112C4×C83—42no—
113C4×C83—41no—
114C4×C83—41no—
115C4×C83#41011yescharacteristic
116C4×C83C2×#10011yescharacteristic
117#11538C8311yesmaximal, characteristic, direct product factor, Sylow
118C2×C83—21no—
119C2×C83—41no—
120C2×C83—81no—
121C2×C83—81no—
122C2×C83#146611yescharacteristic
123#2930C2×C8311yescharacteristic
124#2166C2×C8312yescomplemented
125#1321C2×C8312yescomplemented
126#1320C2×C8312yescomplemented
127C83#1153811yescharacteristic, direct product factor, Sylow
128C2×#131C4×C8311yescharacteristic
129C22×M16C4×C8311yescharacteristic
130#525C4×C8311yescharacteristic
131#436—22no—
132#435—22no—
133#424C4×C8311yescharacteristic
134#408C22×C8311yescharacteristic
135#407C22×C8311yescharacteristic
136#405C22×C8311yescharacteristic
137#364—22no—
138#349C22×C8314yes—
139#347—22no—
140C2×#41C2×C4×C8311yescharacteristic
141C23×C4C2×C4×C8311yescharacteristic
142#131—42no—
143C2×M16—21no—
144C2×M16—21no—
145C2×M16—21no—
146C2×M16—42no—
147C2×M16C2×C4×C8311yescharacteristic
148C2×M16C23×C8311yescharacteristic
149C22×C8—21no—
150C22×C8C2×C4×C8311yescharacteristic
151C22×C8C2×C4×C8311yescharacteristic
152#123—21no—
153C22⋊Q8—21no—
154#121—21no—
155#120—21no—
156C4×D4—22no—
157#117C2×C4×C8311yescharacteristic
158M32—24no—
159C4⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162#97D4×C8312yes—
163C4×C8D4×C8312yes—
164C24M16×C8311yescharacteristic
165#41—41no—
166#41—41no—
167C2×Q8M16×C8311yescharacteristic
168C2×D4—21no—
169C2×D4—22no—
170C2×D4M16×C8311yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4M16×C8311yescharacteristic
177C22×C4C22×C4×C8311yescharacteristic
178M16—41no—
179M16—42no—
180M16—42no—
181M16—42no—
182M16—41no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8C22⋊C4×C8311yescharacteristic
189C2×C8C22⋊C4×C8311yescharacteristic
190C2×C8C2×D4×C8312yes—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—21no—
196C42C22⋊C4×C8312yes—
197C16—44no—
198C23—21no—
199C23—21no—
200C23—41no—
201C23—81no—
202C23C2×M16×C8311yescharacteristic
203Q8—41no—
204D4—41no—
205D4—42no—
206D4—82no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C2×C22⋊C4×C8311yescharacteristic
219C2×C4C2×M16×C8311yescharacteristic
220C8—22no—
221C8—21no—
222C8—41no—
223C8—41no—
224C8#100×C8312yes—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—82no—
233C22#407×C8311yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4#410×C8311yescharacteristic
239C4C2×#100×C8311yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—81no—
244C2C83×#146611yescharacteristic
subgroupG/H
centerC4×C83#410
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×M16C23×C83
socleC2×C83#1466
prime radical#525×C83C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C83 ◁ C2×C8×C83 ◁ #405×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2166C2semidirect
3. C83×#1321C2semidirect
4. C83×#1320C2semidirect
117. #11538C83direct (N × H)
124. #2166C2×C83semidirect
125. #1321C2×C83semidirect
126. #1320C2×C83semidirect
127. C83#11538direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29302
C83×#21662
C83×#13212
C83×#13202
#1153883