Finite Group Databasebeta

← C83×#11434 #35239258

Subgroups — C83×#11434 #35239258

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×#1319C214yesmaximal, complemented
4C23×Q8×C83C411yescharacteristic
5C2×#117×C83C411yescharacteristic
6C2×#117×C83C2211yescharacteristic
7#431×C83—22no—
8#391×C83—22no—
9#391×C83C412yes—
10#391×C83C2212yes—
11#381×C83—22no—
12#324×C83C2214yes—
13#323×C83—22no—
14C22×Q8×C83—21no—
15C22×Q8×C83—22no—
16C22×Q8×C83—42no—
17C22×Q8×C83—42no—
18C22×Q8×C83C814yescomplemented
19C22×Q8×C83C2×C412yes—
20C23×C4×C83—21no—
21C23×C4×C83C2×C411yescharacteristic
22#117×C83—42no—
23#117×C83—42no—
24C2×C4⋊C4×C83—21no—
25C2×C4⋊C4×C83C2×C411yescharacteristic
26C2×C4⋊C4×C83C2311yescharacteristic
27C2×C22⋊C4×C83—21no—
28C2×C22⋊C4×C83D412yes—
29C2×C42×C83C2×C412yes—
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—22no—
39C2×Q8×C83—48no—
40C2×Q8×C83—48no—
41C2×Q8×C83—42no—
42C2×Q8×C83—42no—
43C2×Q8×C83—42no—
44C2×Q8×C83—42no—
45C2×Q8×C83C2×C814yes—
46C22×C4×C83—22no—
47C22×C4×C83—22no—
48C22×C4×C83—24no—
49C22×C4×C83—22no—
50C22×C4×C83—22no—
51C22×C4×C83—42no—
52C22×C4×C83—42no—
53C22×C4×C83C22⋊C412yes—
54C22×C4×C83C22⋊C411yescharacteristic
55C22×C4×C83C2×C812yes—
56C22×C4×C83M1612yes—
57C22×C4×C83C22×C411yescharacteristic
58C22×C4×C83C2×D412yes—
59C2×C8×C83—44no—
60C4⋊C4×C83—41no—
61C4⋊C4×C83—41no—
62C4⋊C4×C83—42no—
63C22⋊C4×C83—42no—
64C22⋊C4×C83—42no—
65C42×C83—22no—
66C42×C83—22no—
67C42×C83—42no—
68C23×C83—21no—
69C23×C83—21no—
70C23×C83—41no—
71C23×C83—41no—
72C23×C83C22⋊C812yes—
73C23×C83C2×C22⋊C411yescharacteristic
74Q8×C83—44no—
75Q8×C83—44no—
76Q8×C83—48no—
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83—24no—
80C2×C4×C83—24no—
81C2×C4×C83—24no—
82C2×C4×C83—22no—
83C2×C4×C83—22no—
84C2×C4×C83—48no—
85C2×C4×C83—42no—
86C2×C4×C83—42no—
87C2×C4×C83—42no—
88C2×C4×C83—42no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83—42no—
92C2×C4×C83C22⋊C812yes—
93C2×C4×C83#9912yes—
94C2×C4×C83#10012yes—
95C2×C4×C83C22×C811yescharacteristic
96C2×C4×C83C2×M1611yescharacteristic
97C8×C83—84no—
98C22×C83—21no—
99C22×C83—21no—
100C22×C83—22no—
101C22×C83—42no—
102C22×C83—42no—
103C22×C83—41no—
104C22×C83—41no—
105C22×C83C2×C22⋊C811yescharacteristic
106C22×C83C2×#9911yescharacteristic
107C22×C83C2×#10011yescharacteristic
108C4×C83—21no—
109C4×C83—21no—
110C4×C83—42no—
111C4×C83—42no—
112C4×C83—44no—
113C4×C83—82no—
114C4×C83#32314yes—
115#11434C8311yesmaximal, characteristic, direct product factor, Sylow
116C2×C83—21no—
117C2×C83—21no—
118C2×C83—42no—
119C2×C83C2×#32311yescharacteristic
120C2×C83#212911yescharacteristic
121C2×C83#213511yescharacteristic
122#2310C2×C8311yescharacteristic
123#1458C2×C8312yes—
124#1319C2×C8314yescomplemented
125C83#1143411yescharacteristic, direct product factor, Sylow
126C23×Q8C4×C8311yescharacteristic
127C2×#117C4×C8311yescharacteristic
128C2×#117C22×C8311yescharacteristic
129#431—22no—
130#391—22no—
131#391C4×C8312yes—
132#391C22×C8312yes—
133#381—22no—
134#324C22×C8314yes—
135#323—22no—
136C22×Q8—21no—
137C22×Q8—22no—
138C22×Q8—42no—
139C22×Q8—42no—
140C22×Q8C8×C8314yescomplemented
141C22×Q8C2×C4×C8312yes—
142C23×C4—21no—
143C23×C4C2×C4×C8311yescharacteristic
144#117—42no—
145#117—42no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×C4×C8311yescharacteristic
148C2×C4⋊C4C23×C8311yescharacteristic
149C2×C22⋊C4—21no—
150C2×C22⋊C4D4×C8312yes—
151C2×C42C2×C4×C8312yes—
152C2×C42D4×C8312yes—
153C4⋊C8—42no—
154C22⋊C8—24no—
155C4×C8—42no—
156#95—24no—
157#95—24no—
158C24C22⋊C4×C8311yescharacteristic
159C2×Q8—24no—
160C2×Q8—22no—
161C2×Q8—48no—
162C2×Q8—48no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8C2×C8×C8314yes—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4C22⋊C4×C8312yes—
176C22×C4C22⋊C4×C8311yescharacteristic
177C22×C4C2×C8×C8312yes—
178C22×C4M16×C8312yes—
179C22×C4C22×C4×C8311yescharacteristic
180C22×C4C2×D4×C8312yes—
181C2×C8—44no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42—22no—
188C42—22no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23C22⋊C8×C8312yes—
195C23C2×C22⋊C4×C8311yescharacteristic
196Q8—44no—
197Q8—44no—
198Q8—48no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—48no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4C22⋊C8×C8312yes—
215C2×C4#99×C8312yes—
216C2×C4#100×C8312yes—
217C2×C4C22×C8×C8311yescharacteristic
218C2×C4C2×M16×C8311yescharacteristic
219C8—84no—
220C22—21no—
221C22—21no—
222C22—22no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22C2×C22⋊C8×C8311yescharacteristic
228C22C2×#99×C8311yescharacteristic
229C22C2×#100×C8311yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—44no—
235C4—82no—
236C4#323×C8314yes—
237C2—21no—
238C2—21no—
239C2—42no—
240C2C2×#323×C8311yescharacteristic
241C2C83×#212911yescharacteristic
242C2C83×#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×#1319C2semidirect
18. C22×Q8×C83C8semidirect
115. #11434C83direct (N × H)
124. #1319C2×C83semidirect
125. C83#11434direct (N × H)
140. 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×#13192
#1143483