Finite Group Databasebeta

← C2×D3×#1142 #13060221

Subgroups — C2×D3×#1142 #13060221

Order 1344.

596 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 160 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×D3×C7×D4C211yesmaximal, characteristic
2C2×D3×Dic14C211yesmaximal, characteristic, complemented
3C2×#66633C211yesmaximal, characteristic, complemented
4C2×C3×#1142C211yesmaximal, characteristic, complemented
5D3×#1142C218yesmaximal, direct product factor
6C2×#66567C211yesmaximal, characteristic, complemented
7C2×#66564C211yesmaximal, characteristic, complemented
8C2×D3×C7⋊C8C211yesmaximal, characteristic, complemented
9C22×#1142—31nomaximal, Hall
10C23×D3×C7—21no—
11C2×C3×C7×D4C2211yescharacteristic
12C2×Dic42C2211yescharacteristic, complemented
13C2×C7×#67—21no—
14D3×C7×D4—22no—
15D3×C7×D4C2214yes—
16C2×C7×D12C2211yescharacteristic
17C2×C4×D3×C7C2211yescharacteristic
18C2×C3×Dic14C2211yescharacteristic, complemented
19C2×#4248—21no—
20C2×D3×Dic7—21no—
21D3×Dic14—22no—
22D3×Dic14C2214yescomplemented
23#66633C2214yescomplemented
24C2×C3⋊(C7⋊C8)C2211yescharacteristic, complemented
25C3×#1142C2214yescomplemented
26C2×C3×C7⋊C8C2211yescharacteristic, complemented
27#66567C2214yescomplemented
28#66564C2214yescomplemented
29D3×C7⋊C8C2214yescomplemented
30C22×C7×D4—31no—
31C22×Dic14—31no—
32C2×#1142—31no—
33C2×#1142—31no—
34C2×#1142—38no—
35C2×#1142—31no—
36C2×#1142D311yescharacteristic, direct product factor
37C22×C7⋊C8—31no—
38C2×D3×SD16—71nomaximal, Hall
39C23×C3×C7—21no—
40C22×D3×C7—21no—
41C22×D3×C7—24no—
42C22×D3×C7—44no—
43C22×D3×C7D411yescharacteristic
44C3×C7×D4—21no—
45C3×C7×D4C2312yes—
46C2×C3×C4×C7C2311yescharacteristic
47C2×Dic21—21no—
48Dic42—21no—
49Dic42C2312yescomplemented
50C7×#67—24no—
51C2×C7×Dic3D411yescharacteristic
52C7×D12—21no—
53C7×D12C2312yes—
54C4×D3×C7D412yes—
55C4×D3×C7C2312yes—
56C2×C3×Dic7—21no—
57C3×Dic14—21no—
58C3×Dic14C2312yescomplemented
59#4248—24no—
60D3×Dic7—24no—
61C3⋊(C7⋊C8)C2312yescomplemented
62C3×C7⋊C8C2312yescomplemented
63C24×C7—61no—
64C2×C7×D4—34no—
65C2×C7×D4—31no—
66C2×C7×D4—62no—
67C2×C7×D4—61no—
68C2×C7×D4C2×D311yescharacteristic
69C22×C4×C7—31no—
70C22×Dic7—61no—
71C2×Dic14—31no—
72C2×Dic14—34no—
73C2×Dic14—62no—
74C2×Dic14—61no—
75C2×Dic14C2×D311yescharacteristic, complemented
76#1142—34no—
77#1142—34no—
78#1142—34no—
79#1142C2×D314yesdirect product factor
80C2×C7⋊C8—31no—
81C2×C7⋊C8—34no—
82C2×C7⋊C8C2×D311yescharacteristic, complemented
83C2×D3×Q8—71no—
84C2×D3×D4D711yescharacteristic
85C2×C3×SD16—71no—
86C2×#215—71no—
87C2×#214—71no—
88D3×SD16—78no—
89C2×#204—71no—
90C2×D3×C8—71no—
91C22×C3×C7—22no—
92C22×C3×C7—42no—
93C22×C3×C7C2×D411yescharacteristic
94C2×D3×C7—22no—
95C2×D3×C7—42no—
96C2×D3×C7—48no—
97C2×D3×C7SD1614yescomplemented
98C2×D3×C7C2×D412yes—
99C3×C4×C7C2×D411yescharacteristic
100C3×C4×C7C2411yescharacteristic
101Dic21—22no—
102C3×Dic7—22no—
103C7×Dic3C2×D412yes—
104C22×SD16—211noSylow
105C23×C7—21no—
106C23×C7—31no—
107C23×C7—64no—
108C23×C7—61no—
109C23×C7—124no—
110C7×D4—21no—
111C7×D4—32no—
112C7×D4—64no—
113C7×D4—61no—
114C7×D4C22×D312yes—
115C2×C4×C7—31no—
116C2×C4×C7—32no—
117C2×C4×C7—32no—
118C2×C4×C7C22×D311yescharacteristic
119C2×Dic7—21no—
120C2×Dic7—64no—
121C2×Dic7—61no—
122Dic14—21no—
123Dic14—32no—
124Dic14—64no—
125Dic14—61no—
126Dic14C22×D312yescomplemented
127C7⋊C8—32no—
128C7⋊C8C22×D312yescomplemented
129C23×D3—21no—
130C2×C3×Q8—71no—
131C2×C3×D4C2×D711yescharacteristic
132C2×#67—21no—
133D3×Q8—74no—
134D3×Q8—142no—
135D3×D4—22no—
136D3×D4C2×D714yes—
137C2×D12C2×D711yescharacteristic
138C2×C4×D3—141no—
139C2×C4×D3C2×D711yescharacteristic
140C2×Dic6—71no—
141C2×Dic6—141no—
142C3×SD16—74no—
143C2×C3×C8—71no—
144#215—74no—
145#214—74no—
146C2×C3⋊C8—71no—
147#204—74no—
148D3×C8—74no—
149C2×C3×C7—42no—
150C2×C3×C7C2×SD1612yescomplemented
151C2×C3×C7C22×D411yescharacteristic
152D3×C7—42no—
153D3×C7C2×SD1614yescomplemented
154C22×Q8—211no—
155C22×D4—31no—
156C2×SD16—71no—
157C2×SD16—211no—
158C2×SD16—218no—
159C2×SD16—211no—
160C2×SD16—211no—
161C22×C8—211no—
162C22×C7—22no—
163C22×C7—34no—
164C22×C7—32no—
165C22×C7—42no—
166C22×C7—62no—
167C22×C7—128no—
168C22×C7—122no—
169C22×C7D3×D411yescharacteristic
170C4×C7—32no—
171C4×C7D3×D411yescharacteristic
172C4×C7C23×D311yescharacteristic
173Dic7—22no—
174Dic7—62no—
175C23×C3—21no—
176C22×D3—21no—
177C22×D3—24no—
178C22×D3—44no—
179C22×D3C22⋊D711yescharacteristic
180C3×Q8—72no—
181C3×Q8—141no—
182C3×D4—21no—
183C3×D4C22×D712yes—
184C2×C3×C4—141no—
185C2×C3×C4C22×D711yescharacteristic
186#67—24no—
187C2×Dic3—141no—
188C2×Dic3C22⋊D711yescharacteristic
189D12—21no—
190D12C22×D712yes—
191C4×D3—144no—
192C4×D3C22⋊D712yes—
193C4×D3C22×D712yes—
194Dic6—72no—
195Dic6—141no—
196Dic6—144no—
197C3×C8—72no—
198C3⋊C8—72no—
199C3×C7C22×SD1611yescharacteristic, complemented, Hall
200C24—61no—
201C2×Q8—71no—
202C2×Q8—214no—
203C2×Q8—211no—
204C2×Q8—421no—
205C2×Q8—422no—
206C2×D4—34no—
207C2×D4—31no—
208C2×D4—62no—
209C2×D4—61no—
210C2×D4D3×D711yescharacteristic
211C22×C4—31no—
212C22×C4—421no—
213SD16—74no—
214SD16—214no—
215SD16—214no—
216SD16—214no—
217C2×C8—71no—
218C2×C8—214no—
219C2×C8—211no—
220C2×C7—34no—
221C2×C7—42no—
222C2×C7—122no—
223C2×C7D3×SD1612yescomplemented
224C2×C7C2×D3×D411yescharacteristic
225C22×C3—22no—
226C22×C3—42no—
227C22×C3C2×C22⋊D711yescharacteristic
228C2×D3—22no—
229C2×D3—42no—
230C2×D3—48no—
231C2×D3#114214yesdirect product factor
232C2×D3C2×C22⋊D712yes—
233C3×C4—142no—
234C3×C4C2×C22⋊D711yescharacteristic
235C3×C4C23×D711yescharacteristic
236Dic3—142no—
237Dic3C2×C22⋊D712yes—
238C23—21no—
239C23—31no—
240C23—64no—
241C23—61no—
242C23—124no—
243Q8—72no—
244Q8—141no—
245Q8—212no—
246Q8—424no—
247Q8—421no—
248D4—21no—
249D4—32no—
250D4—64no—
251D4—61no—
252D4C2×D3×D712yes—
253C2×C4—31no—
254C2×C4—32no—
255C2×C4—32no—
256C2×C4—141no—
257C2×C4—424no—
258C2×C4—421no—
259C2×C4C2×D3×D711yescharacteristic
260C8—72no—
261C8—212no—
262C7C2×D3×SD1611yescharacteristic, complemented, Sylow
263C2×C3—42no—
264C2×C3C2×#114212yescomplemented
265C2×C3C22×C22⋊D711yescharacteristic
266D3—42no—
267D3C2×#114214yesdirect product factor
268C22—22no—
269C22—34no—
270C22—32no—
271C22—42no—
272C22—62no—
273C22—128no—
274C22—122no—
275C22D3×C22⋊D711yescharacteristic
276C4—32no—
277C4—142no—
278C4—422no—
279C4D3×C22⋊D711yescharacteristic
280C4C22×D3×D711yescharacteristic
281C3C22×#114211yescharacteristic, complemented, Sylow
282C2—34no—
283C2—42no—
284C2—122no—
285C2D3×#114212yesdirect product factor
286C2C2×D3×C22⋊D711yescharacteristic
subgroupG/H
centerC22D3×C22⋊D7
commutator, cosocleC3×C4×C7C24
FrattiniC4C22×D3×D7
FittingC2×C3×C7×D4C22
socleC22×C3×C7C2×D4
prime radicalC2×D3×C7×D4C2
hypercenterC2×D4D3×D7
hypocenterC3×C7C22×SD16
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic14C2semidirect
3. C2×#66633C2semidirect
4. C2×C3×#1142C2semidirect
5. D3×#1142C2direct (N × H)
6. C2×#66567C2semidirect
7. C2×#66564C2semidirect
8. C2×D3×C7⋊C8C2semidirect
12. C2×Dic42C22semidirect
18. C2×C3×Dic14C22semidirect
22. D3×Dic14C22semidirect
23. #66633C22semidirect
24. C2×C3⋊(C7⋊C8)C22semidirect
25. C3×#1142C22semidirect
26. C2×C3×C7⋊C8C22semidirect
27. #66567C22semidirect
28. #66564C22semidirect
29. D3×C7⋊C8C22semidirect
36. C2×#1142D3direct (N × H)
49. Dic42C23semidirect
58. C3×Dic14C23semidirect
61. C3⋊(C7⋊C8)C23semidirect
62. C3×C7⋊C8C23semidirect
75. C2×Dic14C2×D3semidirect
79. #1142C2×D3direct (N × H)
82. C2×C7⋊C8C2×D3semidirect
97. C2×D3×C7SD16semidirect
126. Dic14C22×D3semidirect
128. C7⋊C8C22×D3semidirect
150. C2×C3×C7C2×SD16semidirect
153. D3×C7C2×SD16semidirect
199. C3×C7C22×SD16semidirect
223. C2×C7D3×SD16semidirect
231. C2×D3#1142direct (N × H)
262. C7C2×D3×SD16semidirect
264. C2×C3C2×#1142semidirect
267. D3C2×#1142direct (N × H)
281. C3C22×#1142semidirect
285. C2D3×#1142direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C7×D42
C2×D3×Dic142
C2×#666332
C2×C3×#11422
D3×#11422
C2×#665672
C2×#665642
C2×D3×C7⋊C82
C22×#11423
C2×D3×SD167