Finite Group Databasebeta

← C2×C83×#1324 #35239269

Subgroups — C2×C83×#1324 #35239269

Order 21248.

510 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C2×#382×C83C211yesmaximal, characteristic
2C2×#324×C83C212yesmaximal
3C83×#1324C214yesmaximal, direct product factor
4C22×C4⋊C4×C83C411yescharacteristic
5C22×C4⋊C4×C83C2211yescharacteristic
6C22×C42×C83C411yescharacteristic
7C2×C22⋊C8×C83—22no—
8#382×C83—22no—
9#382×C83C412yes—
10#382×C83C2212yes—
11C2×#95×C83—22no—
12#324×C83—22no—
13#324×C83C2214yes—
14C23×C4×C83—21no—
15C23×C4×C83—21no—
16C23×C4×C83C2×C411yescharacteristic
17C23×C4×C83D412yes—
18C22×C8×C83—42no—
19C2×C4⋊C4×C83—21no—
20C2×C4⋊C4×C83—41no—
21C2×C4⋊C4×C83—41no—
22C2×C4⋊C4×C83—41no—
23C2×C4⋊C4×C83—41no—
24C2×C4⋊C4×C83C2×C412yes—
25C2×C4⋊C4×C83C2×C411yescharacteristic
26C2×C4⋊C4×C83D412yes—
27C2×C4⋊C4×C83C2311yescharacteristic
28C2×C42×C83—21no—
29C2×C42×C83—22no—
30C2×C42×C83C814yescomplemented
31C2×C42×C83C2×C412yes—
32C22⋊C8×C83—24no—
33C22⋊C8×C83—42no—
34#95×C83—24no—
35#95×C83—24no—
36C24×C83C22⋊C411yescharacteristic
37C22×C4×C83—21no—
38C22×C4×C83—21no—
39C22×C4×C83—22no—
40C22×C4×C83—24no—
41C22×C4×C83—22no—
42C22×C4×C83—22no—
43C22×C4×C83—22no—
44C22×C4×C83—22no—
45C22×C4×C83—42no—
46C22×C4×C83—42no—
47C22×C4×C83—44no—
48C22×C4×C83—44no—
49C22×C4×C83—41no—
50C22×C4×C83—41no—
51C22×C4×C83C22⋊C411yescharacteristic
52C22×C4×C83C22⋊C412yes—
53C22×C4×C83C2×C812yes—
54C22×C4×C83M1612yes—
55C22×C4×C83C22×C411yescharacteristic
56C22×C4×C83C2×D412yes—
57C2×C8×C83—44no—
58C2×C8×C83—84no—
59C4⋊C4×C83—41no—
60C4⋊C4×C83—42no—
61C4⋊C4×C83—41no—
62C4⋊C4×C83—42no—
63C4⋊C4×C83—42no—
64C42×C83—24no—
65C42×C83—22no—
66C42×C83C2×C814yescomplemented
67C23×C83—22no—
68C23×C83—22no—
69C23×C83C22⋊C812yes—
70C23×C83#9911yescharacteristic
71C23×C83#9911yescharacteristic
72C23×C83#10112yes—
73C23×C83C2×C22⋊C411yescharacteristic
74C2×C4×C83—22no—
75C2×C4×C83—22no—
76C2×C4×C83—22no—
77C2×C4×C83—22no—
78C2×C4×C83—21no—
79C2×C4×C83—21no—
80C2×C4×C83—21no—
81C2×C4×C83—21no—
82C2×C4×C83—24no—
83C2×C4×C83—22no—
84C2×C4×C83—22no—
85C2×C4×C83—48no—
86C2×C4×C83—42no—
87C2×C4×C83—42no—
88C2×C4×C83—44no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83—44no—
92C2×C4×C83—42no—
93C2×C4×C83—82no—
94C2×C4×C83—82no—
95C2×C4×C83—82no—
96C2×C4×C83C22⋊C812yes—
97C2×C4×C83C22×C811yescharacteristic
98C2×C4×C83C2×M1611yescharacteristic
99C8×C83—84no—
100C22×C83—24no—
101C22×C83—24no—
102C22×C83—21no—
103C22×C83—21no—
104C22×C83—21no—
105C22×C83—21no—
106C22×C83#32412yes—
107C22×C83#32412yes—
108C22×C83#35412yes—
109C22×C83#35512yes—
110C22×C83C2×C22⋊C811yescharacteristic
111C22×C83C2×#9911yescharacteristic
112C22×C83C2×#10111yescharacteristic
113C4×C83—22no—
114C4×C83—21no—
115C4×C83—21no—
116C4×C83—44no—
117C4×C83—42no—
118C4×C83—42no—
119C4×C83—82no—
120C2×#1324C8311yesmaximal, characteristic, direct product factor, Sylow
121C2×C83—21no—
122C2×C83—22no—
123C2×C83—21no—
124C2×C83#132414yesdirect product factor
125C2×C83C2×#32411yescharacteristic
126C2×C83C2×#35411yescharacteristic
127C2×C83C2×#35511yescharacteristic
128C2×#382C2×C8311yescharacteristic
129C2×#324C2×C8312yes—
130#1324C2×C8314yesdirect product factor
131C83C2×#132411yescharacteristic, direct product factor, Sylow
132C22×C4⋊C4C4×C8311yescharacteristic
133C22×C4⋊C4C22×C8311yescharacteristic
134C22×C42C4×C8311yescharacteristic
135C2×C22⋊C8—22no—
136#382—22no—
137#382C4×C8312yes—
138#382C22×C8312yes—
139C2×#95—22no—
140#324—22no—
141#324C22×C8314yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×C4×C8311yescharacteristic
145C23×C4D4×C8312yes—
146C22×C8—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C2×C4×C8312yes—
153C2×C4⋊C4C2×C4×C8311yescharacteristic
154C2×C4⋊C4D4×C8312yes—
155C2×C4⋊C4C23×C8311yescharacteristic
156C2×C42—21no—
157C2×C42—22no—
158C2×C42C8×C8314yescomplemented
159C2×C42C2×C4×C8312yes—
160C22⋊C8—24no—
161C22⋊C8—42no—
162#95—24no—
163#95—24no—
164C24C22⋊C4×C8311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—44no—
176C22×C4—44no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C22⋊C4×C8311yescharacteristic
180C22×C4C22⋊C4×C8312yes—
181C22×C4C2×C8×C8312yes—
182C22×C4M16×C8312yes—
183C22×C4C22×C4×C8311yescharacteristic
184C22×C4C2×D4×C8312yes—
185C2×C8—44no—
186C2×C8—84no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C42—24no—
193C42—22no—
194C42C2×C8×C8314yescomplemented
195C23—22no—
196C23—22no—
197C23C22⋊C8×C8312yes—
198C23#99×C8311yescharacteristic
199C23#99×C8311yescharacteristic
200C23#101×C8312yes—
201C23C2×C22⋊C4×C8311yescharacteristic
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4C22⋊C8×C8312yes—
225C2×C4C22×C8×C8311yescharacteristic
226C2×C4C2×M16×C8311yescharacteristic
227C8—84no—
228C22—24no—
229C22—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22#324×C8312yes—
235C22#324×C8312yes—
236C22#354×C8312yes—
237C22#355×C8312yes—
238C22C2×C22⋊C8×C8311yescharacteristic
239C22C2×#99×C8311yescharacteristic
240C22C2×#101×C8311yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—44no—
245C4—42no—
246C4—42no—
247C4—82no—
248C2—21no—
249C2—22no—
250C2—21no—
251C2C83×#132414yesdirect product factor
252C2C2×#324×C8311yescharacteristic
253C2C2×#354×C8311yescharacteristic
254C2C2×#355×C8311yescharacteristic
subgroupG/H
center, socleC23×C83#99
commutatorC2×C4C22×C8×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC24×C83C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C24×C83 ◁ C22×C4⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#1324C2direct (N × H)
30. C2×C42×C83C8semidirect
66. C42×C83C2×C8semidirect
120. C2×#1324C83direct (N × H)
124. C2×C83#1324direct (N × H)
130. #1324C2×C83direct (N × H)
131. C83C2×#1324direct (N × H)
158. C2×C42C8×C83semidirect
194. C42C2×C8×C83semidirect
251. C2C83×#1324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#382×C832
C2×#324×C832
C83×#13242
C2×#132483