Finite Group Databasebeta

← C3×D7×#102 #13055201

Subgroups — C3×D7×#102 #13055201

Order 1344.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×D4×D7C211yesmaximal, characteristic
2C2×C3×C8×D7C211yesmaximal, characteristic, complemented
3C3×D7×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C7×#102C211yesmaximal, characteristic, complemented
5C3×#6406C211yesmaximal, characteristic, complemented
6C3×#6395C211yesmaximal, characteristic, complemented
7C3×#6383C211yesmaximal, characteristic, complemented
8D7×#102C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×D7—21no—
10C2×C3×C7×D4C2211yescharacteristic
11C2×C3×C22⋊D7—21no—
12C3×D4×D7—22no—
13C3×D4×D7C414yescomplemented
14C2×C3×D28C2211yescharacteristic
15C2×C3×C4×D7—21no—
16C2×C3×C4×D7C2211yescharacteristic
17C2×C3×C7×C8C2211yescharacteristic, complemented
18C3×C7×C4⋊C4C2211yescharacteristic, complemented
19C3×C4⋊Dic7C2211yescharacteristic, complemented
20C3×Dic7⋊C4—21no—
21C2×C3×C7⋊C8C2211yescharacteristic, complemented
22C3×C8×D7—22no—
23C2×D4×D7C2×C311yescharacteristic
24C2×C8×D7C2×C311yescharacteristic, complemented
25D7×C4⋊C4C2×C311yescharacteristic, complemented
26C7×#102C2×C311yescharacteristic, complemented
27#6406C2×C311yescharacteristic, complemented
28#6395C2×C311yescharacteristic, complemented
29#6383C2×C311yescharacteristic, complemented
30C2×C3×#102—71nomaximal, Hall
31C23×C3×C7—21no—
32C22×C3×D7—21no—
33C22×C3×D7—24no—
34C22×C3×D7—42no—
35C22×C3×D7—42no—
36C22×C3×D7D411yescharacteristic
37C3×C7×D4—21no—
38C3×C7×D4C2×C412yescomplemented
39C2×C3×C4×C7—21no—
40C2×C3×C4×C7C2311yescharacteristic
41C3×C22⋊D7—24no—
42C2×C3×Dic7—21no—
43C2×C3×Dic7D411yescharacteristic
44C3×D28—21no—
45C3×D28C2×C412yescomplemented
46C3×C4×D7—42no—
47C3×C4×D7C2×C412yes—
48C3×C4×D7D412yes—
49C3×C7×C8—21no—
50C3×C7⋊C8—21no—
51C23×D7—21no—
52C2×C7×D4C22×C311yescharacteristic
53C2×C22⋊D7—21no—
54D4×D7—22no—
55D4×D7C3×C414yescomplemented
56C2×D28C22×C311yescharacteristic
57C2×C4×D7—21no—
58C2×C4×D7C22×C311yescharacteristic
59C2×C7×C8C22×C311yescharacteristic, complemented
60C7×C4⋊C4C22×C311yescharacteristic, complemented
61C4⋊Dic7C22×C311yescharacteristic, complemented
62Dic7⋊C4—21no—
63C2×C7⋊C8C22×C311yescharacteristic, complemented
64C8×D7—22no—
65C22×C3×D4—71no—
66C22×C3×C8—71no—
67C2×C3×C4⋊C4—71no—
68C3×#102—71no—
69C3×#102—71no—
70C3×#102—71no—
71C3×#102D711yescharacteristic, direct product factor
72C22×C3×C7—22no—
73C22×C3×C7—41no—
74C22×C3×C7—41no—
75C22×C3×C7C2×D411yescharacteristic
76C2×C3×D7—22no—
77C2×C3×D7—41no—
78C2×C3×D7—41no—
79C2×C3×D7—48no—
80C2×C3×D7C22⋊C412yes—
81C2×C3×D7D812yes—
82C2×C3×D7SD1612yes—
83C3×C4×C7—41no—
84C3×C4×C7C22×C411yescharacteristic
85C3×C4×C7C2×D411yescharacteristic
86C3×Dic7—41no—
87C3×Dic7C22⋊C412yes—
88C2×#102—71noSylow
89C23×C7—21no—
90C22×D7—21no—
91C22×D7—24no—
92C22×D7—42no—
93C22×D7—42no—
94C22×D7C3×D411yescharacteristic
95C7×D4—21no—
96C7×D4C2×C3×C412yescomplemented
97C2×C4×C7—21no—
98C2×C4×C7C23×C311yescharacteristic
99C22⋊D7—24no—
100C2×Dic7—21no—
101C2×Dic7C3×D411yescharacteristic
102D28—21no—
103D28C2×C3×C412yescomplemented
104C4×D7—42no—
105C4×D7C2×C3×C412yes—
106C4×D7C3×D412yes—
107C7×C8—21no—
108C7⋊C8—21no—
109C24×C3—141no—
110C2×C3×D4—74no—
111C2×C3×D4—71no—
112C2×C3×D4—142no—
113C2×C3×D4—141no—
114C2×C3×D4C2×D711yescharacteristic
115C22×C3×C4—71no—
116C22×C3×C4—141no—
117C2×C3×C8—71no—
118C2×C3×C8—142no—
119C2×C3×C8C2×D711yescharacteristic, complemented
120C3×C4⋊C4—71no—
121C3×C4⋊C4—141no—
122C3×C4⋊C4C2×D711yescharacteristic, complemented
123C2×C3×C7—42no—
124C2×C3×C7C2×C22⋊C411yescharacteristic
125C2×C3×C7C2×D811yescharacteristic
126C2×C3×C7C2×SD1611yescharacteristic
127C3×D7—42no—
128C3×D7#10214yesdirect product factor
129C22×D4—71no—
130C22×C8—71no—
131C2×C4⋊C4—71no—
132#102—71no—
133#102—71no—
134#102—71no—
135#102C3×D711yescharacteristic, direct product factor
136C22×C7—22no—
137C22×C7—41no—
138C22×C7—41no—
139C22×C7C2×C3×D411yescharacteristic
140C2×D7—22no—
141C2×D7—41no—
142C2×D7—41no—
143C2×D7—48no—
144C2×D7C3×C22⋊C412yes—
145C2×D7C3×D812yes—
146C2×D7C3×SD1612yes—
147C4×C7—41no—
148C4×C7C22×C3×C411yescharacteristic
149C4×C7C2×C3×D411yescharacteristic
150Dic7—41no—
151Dic7C3×C22⋊C412yes—
152C23×C3—21no—
153C23×C3—71no—
154C23×C3—144no—
155C23×C3—141no—
156C23×C3—282no—
157C23×C3—282no—
158C3×D4—21no—
159C3×D4—72no—
160C3×D4—144no—
161C3×D4—141no—
162C3×D4C4×D712yescomplemented
163C2×C3×C4—21no—
164C2×C3×C4—71no—
165C2×C3×C4—72no—
166C2×C3×C4—72no—
167C2×C3×C4—141no—
168C2×C3×C4—282no—
169C2×C3×C4C22×D711yescharacteristic
170C3×C8—21no—
171C3×C8—141no—
172C3×C7C2×#10211yescharacteristic, complemented, Hall
173C24—141no—
174C2×D4—74no—
175C2×D4—71no—
176C2×D4—142no—
177C2×D4—141no—
178C2×D4C2×C3×D711yescharacteristic
179C22×C4—71no—
180C22×C4—141no—
181C2×C8—71no—
182C2×C8—142no—
183C2×C8C2×C3×D711yescharacteristic, complemented
184C4⋊C4—71no—
185C4⋊C4—141no—
186C4⋊C4C2×C3×D711yescharacteristic, complemented
187C2×C7—42no—
188C2×C7C2×C3×C22⋊C411yescharacteristic
189C2×C7C2×C3×D811yescharacteristic
190C2×C7C2×C3×SD1611yescharacteristic
191D7—42no—
192D7C3×#10214yesdirect product factor
193C22×C3—22no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3—72no—
197C22×C3—72no—
198C22×C3—72no—
199C22×C3—142no—
200C22×C3—288no—
201C22×C3—281no—
202C22×C3—281no—
203C22×C3D4×D711yescharacteristic
204C3×C4—41no—
205C3×C4—72no—
206C3×C4—281no—
207C3×C4C2×C4×D711yescharacteristic
208C3×C4D4×D711yescharacteristic
209C23—21no—
210C23—71no—
211C23—144no—
212C23—141no—
213C23—282no—
214C23—282no—
215D4—21no—
216D4—72no—
217D4—144no—
218D4—141no—
219D4C3×C4×D712yescomplemented
220C2×C4—21no—
221C2×C4—71no—
222C2×C4—72no—
223C2×C4—72no—
224C2×C4—141no—
225C2×C4—282no—
226C2×C4C22×C3×D711yescharacteristic
227C8—21no—
228C8—141no—
229C7C2×C3×#10211yescharacteristic, complemented, Sylow
230C2×C3—42no—
231C2×C3—74no—
232C2×C3—282no—
233C2×C3D7×C22⋊C411yescharacteristic
234C2×C3D7×D811yescharacteristic
235C2×C3D7×SD1611yescharacteristic
236C22—22no—
237C22—41no—
238C22—41no—
239C22—72no—
240C22—72no—
241C22—72no—
242C22—142no—
243C22—288no—
244C22—281no—
245C22—281no—
246C22C3×D4×D711yescharacteristic
247C4—41no—
248C4—72no—
249C4—281no—
250C4C2×C3×C4×D711yescharacteristic
251C4C3×D4×D711yescharacteristic
252C3D7×#10211yescharacteristic, direct product factor, Sylow
253C2—42no—
254C2—74no—
255C2—282no—
256C2C3×D7×C22⋊C411yescharacteristic
257C2C3×D7×D811yescharacteristic
258C2C3×D7×SD1611yescharacteristic
subgroupG/H
centerC22×C3D4×D7
commutatorC4×C7C22×C3×C4
FrattiniC2×C4C22×C3×D7
FittingC3×C7×#102C2
socleC22×C3×C7C2×D4
prime radicalC2×C3×D4×D7C2
cosocleC2×C4×C7C23×C3
hypercenterC3×#102D7
hypocenterC7C2×C3×#102
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×D7C2semidirect
3. C3×D7×C4⋊C4C2semidirect
4. C3×C7×#102C2semidirect
5. C3×#6406C2semidirect
6. C3×#6395C2semidirect
7. C3×#6383C2semidirect
8. D7×#102C3direct (N × H)
13. C3×D4×D7C4semidirect
17. C2×C3×C7×C8C22semidirect
18. C3×C7×C4⋊C4C22semidirect
19. C3×C4⋊Dic7C22semidirect
21. C2×C3×C7⋊C8C22semidirect
24. C2×C8×D7C2×C3semidirect
25. D7×C4⋊C4C2×C3semidirect
26. C7×#102C2×C3semidirect
27. #6406C2×C3semidirect
28. #6395C2×C3semidirect
29. #6383C2×C3semidirect
38. C3×C7×D4C2×C4semidirect
45. C3×D28C2×C4semidirect
55. D4×D7C3×C4semidirect
59. C2×C7×C8C22×C3semidirect
60. C7×C4⋊C4C22×C3semidirect
61. C4⋊Dic7C22×C3semidirect
63. C2×C7⋊C8C22×C3semidirect
71. C3×#102D7direct (N × H)
96. C7×D4C2×C3×C4semidirect
103. D28C2×C3×C4semidirect
119. C2×C3×C8C2×D7semidirect
122. C3×C4⋊C4C2×D7semidirect
128. C3×D7#102direct (N × H)
135. #102C3×D7direct (N × H)
162. C3×D4C4×D7semidirect
172. C3×C7C2×#102semidirect
183. C2×C8C2×C3×D7semidirect
186. C4⋊C4C2×C3×D7semidirect
192. D7C3×#102direct (N × H)
219. D4C3×C4×D7semidirect
229. C7C2×C3×#102semidirect
252. C3D7×#102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×D72
C2×C3×C8×D72
C3×D7×C4⋊C42
C3×C7×#1022
C3×#64062
C3×#63952
C3×#63832
D7×#1023
C2×C3×#1027