Finite Group Databasebeta

← D3×C7×#99 #13055778

Subgroups — D3×C7×#99 #13055778

Order 1344.

420 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 106 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
2D3×C7×C22⋊C4C212yesmaximal, complemented
3C3×C7×#99C211yesmaximal, characteristic, complemented
4C7×#834C211yesmaximal, characteristic, complemented
5C7×#806C212yesmaximal, complemented
6C2×C7×#99—31nomaximal, Hall
7C23×D3×C7C411yescharacteristic, complemented
8C23×D3×C7C2211yescharacteristic
9C2×C3×C7×D4C2211yescharacteristic
10C2×C7×#67C411yescharacteristic, complemented
11C2×C7×#67C2211yescharacteristic
12D3×C7×D4—22no—
13D3×C7×D4—22no—
14C2×C7×D12C411yescharacteristic, complemented
15C2×C4×D3×C7—22no—
16C2×C4×D3×C7C411yescharacteristic, complemented
17C3×C7×C22⋊C4C2212yescomplemented
18C7×#217C2212yescomplemented
19C7×(C2×D3)⋊C4—22no—
20C22×C7×D4—31no—
21C2×C7×C22⋊C4—32no—
22C7×#99—31no—
23C7×#99—32no—
24C7×#99D311yescharacteristic, direct product factor
25D3×#99C711yesmaximal, characteristic, direct product factor, Hall
26C23×C3×C7C2×C411yescharacteristic, complemented
27C23×C3×C7C2311yescharacteristic
28C22×D3×C7—21no—
29C22×D3×C7—21no—
30C22×D3×C7—42no—
31C22×D3×C7—42no—
32C22×D3×C7C2×C411yescharacteristic
33C22×D3×C7C2×C411yescharacteristic
34C22×D3×C7C2×C411yescharacteristic, complemented
35C22×D3×C7D412yes—
36C22×D3×C7D412yes—
37C3×C7×D4—22no—
38C2×C3×C4×C7—22no—
39C2×C3×C4×C7C2×C411yescharacteristic, complemented
40C7×#67—22no—
41C7×#67—22no—
42C2×C7×Dic3—22no—
43C2×C7×Dic3C2×C411yescharacteristic, complemented
44C7×D12—22no—
45C4×D3×C7—21no—
46C4×D3×C7—21no—
47C4×D3×C7—44no—
48C24×C7—31no—
49C24×C7—31no—
50C2×C7×D4—31no—
51C2×C7×D4—31no—
52C2×C7×D4—31no—
53C2×C7×D4—62no—
54C2×C7×D4—62no—
55C2×C7×D4C2×D311yescharacteristic
56C22×C4×C7—31no—
57C22×C4×C7—62no—
58C7×C22⋊C4—32no—
59C7×C22⋊C4—62no—
60C7×C22⋊C4C2×D312yescomplemented
61C2×D3×D4C2×C711yescharacteristic
62D3×C22⋊C4C2×C712yescomplemented
63C3×#99C2×C711yescharacteristic, complemented
64#834C2×C711yescharacteristic, complemented
65#806C2×C712yescomplemented
66C22×C3×C7—21no—
67C22×C3×C7—41no—
68C22×C3×C7—41no—
69C22×C3×C7C22×C411yescharacteristic
70C22×C3×C7C2×D412yes—
71C2×D3×C7—24no—
72C2×D3×C7—22no—
73C2×D3×C7—21no—
74C2×D3×C7—41no—
75C2×D3×C7—42no—
76C2×D3×C7—42no—
77C2×D3×C7—42no—
78C2×D3×C7—41no—
79C2×D3×C7C22⋊C411yescharacteristic
80C2×D3×C7C22⋊C412yes—
81C2×D3×C7C22⋊C411yescharacteristic
82C3×C4×C7—21no—
83C3×C4×C7—42no—
84C7×Dic3—21no—
85C7×Dic3—42no—
86C2×#99—31noSylow
87C23×C7—31no—
88C23×C7—32no—
89C23×C7—31no—
90C23×C7—32no—
91C23×C7—31no—
92C23×C7—61no—
93C23×C7—61no—
94C23×C7—122no—
95C23×C7—122no—
96C23×C7C4×D311yescharacteristic, complemented
97C23×C7C22×D311yescharacteristic
98C7×D4—22no—
99C7×D4—62no—
100C7×D4—62no—
101C7×D4—62no—
102C2×C4×C7—22no—
103C2×C4×C7—31no—
104C2×C4×C7—61no—
105C2×C4×C7—61no—
106C2×C4×C7—62no—
107C2×C4×C7—124no—
108C2×C4×C7C4×D311yescharacteristic, complemented
109C23×D3C4×C711yescharacteristic, complemented
110C23×D3C22×C711yescharacteristic
111C2×C3×D4C22×C711yescharacteristic
112C2×#67C4×C711yescharacteristic, complemented
113C2×#67C22×C711yescharacteristic
114D3×D4—22no—
115D3×D4—22no—
116C2×D12C4×C711yescharacteristic, complemented
117C2×C4×D3—22no—
118C2×C4×D3C4×C711yescharacteristic, complemented
119C3×C22⋊C4C22×C712yescomplemented
120#217C22×C712yescomplemented
121(C2×D3)⋊C4—22no—
122C2×C3×C7—22no—
123C2×C3×C7—21no—
124C2×C3×C7—41no—
125C2×C3×C7C2×C22⋊C411yescharacteristic
126D3×C7—21no—
127D3×C7—22no—
128D3×C7—41no—
129D3×C7#9912yesdirect product factor
130C22×D4—31no—
131C2×C22⋊C4—32no—
132#99—31no—
133#99—32no—
134#99D3×C711yescharacteristic, direct product factor
135C22×C7—21no—
136C22×C7—31no—
137C22×C7—31no—
138C22×C7—32no—
139C22×C7—41no—
140C22×C7—41no—
141C22×C7—64no—
142C22×C7—62no—
143C22×C7—61no—
144C22×C7—122no—
145C22×C7—121no—
146C22×C7—121no—
147C22×C7—122no—
148C22×C7—122no—
149C22×C7C2×C4×D311yescharacteristic
150C22×C7D3×D412yes—
151C4×C7—21no—
152C4×C7—42no—
153C4×C7—61no—
154C4×C7—122no—
155C23×C3C2×C4×C711yescharacteristic, complemented
156C23×C3C23×C711yescharacteristic
157C22×D3—21no—
158C22×D3—21no—
159C22×D3—42no—
160C22×D3—42no—
161C22×D3C2×C4×C711yescharacteristic
162C22×D3C2×C4×C711yescharacteristic
163C22×D3C2×C4×C711yescharacteristic, complemented
164C22×D3C7×D412yes—
165C22×D3C7×D412yes—
166C3×D4—22no—
167C2×C3×C4—22no—
168C2×C3×C4C2×C4×C711yescharacteristic, complemented
169#67—22no—
170#67—22no—
171C2×Dic3—22no—
172C2×Dic3C2×C4×C711yescharacteristic, complemented
173D12—22no—
174C4×D3—21no—
175C4×D3—21no—
176C4×D3—44no—
177C3×C7C2×#9911yescharacteristic, complemented, Hall
178C24—31no—
179C24—31no—
180C2×D4—31no—
181C2×D4—31no—
182C2×D4—31no—
183C2×D4—62no—
184C2×D4—62no—
185C2×D4C2×D3×C711yescharacteristic
186C22×C4—31no—
187C22×C4—62no—
188C22⋊C4—32no—
189C22⋊C4—62no—
190C22⋊C4C2×D3×C712yescomplemented
191C2×C7—22no—
192C2×C7—21no—
193C2×C7—32no—
194C2×C7—41no—
195C2×C7—61no—
196C2×C7—62no—
197C2×C7—121no—
198C2×C7D3×C22⋊C411yescharacteristic
199C22×C3—21no—
200C22×C3—41no—
201C22×C3—41no—
202C22×C3C22×C4×C711yescharacteristic
203C22×C3C2×C7×D412yes—
204C2×D3—24no—
205C2×D3—22no—
206C2×D3—21no—
207C2×D3—41no—
208C2×D3—42no—
209C2×D3—42no—
210C2×D3—42no—
211C2×D3—41no—
212C2×D3C7×C22⋊C411yescharacteristic
213C2×D3C7×C22⋊C412yes—
214C2×D3C7×C22⋊C411yescharacteristic
215C3×C4—21no—
216C3×C4—42no—
217Dic3—21no—
218Dic3—42no—
219C23—31no—
220C23—32no—
221C23—31no—
222C23—32no—
223C23—31no—
224C23—61no—
225C23—61no—
226C23—122no—
227C23—122no—
228C23C4×D3×C711yescharacteristic, complemented
229C23C22×D3×C711yescharacteristic
230D4—22no—
231D4—62no—
232D4—62no—
233D4—62no—
234C2×C4—22no—
235C2×C4—31no—
236C2×C4—61no—
237C2×C4—61no—
238C2×C4—62no—
239C2×C4—124no—
240C2×C4C4×D3×C711yescharacteristic, complemented
241C7D3×#9911yescharacteristic, direct product factor, Sylow
242C2×C3—22no—
243C2×C3—21no—
244C2×C3—41no—
245C2×C3C2×C7×C22⋊C411yescharacteristic
246D3—21no—
247D3—22no—
248D3—41no—
249D3C7×#9912yesdirect product factor
250C22—21no—
251C22—31no—
252C22—31no—
253C22—32no—
254C22—41no—
255C22—41no—
256C22—64no—
257C22—62no—
258C22—61no—
259C22—122no—
260C22—121no—
261C22—121no—
262C22—122no—
263C22—122no—
264C22C2×C4×D3×C711yescharacteristic
265C22D3×C7×D412yes—
266C4—21no—
267C4—42no—
268C4—61no—
269C4—122no—
270C3C2×C7×#9911yescharacteristic, complemented, Sylow
271C2—22no—
272C2—21no—
273C2—32no—
274C2—41no—
275C2—61no—
276C2—62no—
277C2—121no—
278C2D3×C7×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C7D3×C22⋊C4
commutatorC22×C3C22×C4×C7
FrattiniC23C22×D3×C7
FittingC3×C7×#99C2
socleC2×C3×C7C2×C22⋊C4
prime radicalC2×D3×C7×D4C2
cosocleC23×C3C23×C7
hypercenterC7×#99D3
hypocenterC3C2×C7×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C7 ◁ C23×C7 ◁ C7×#99

Complements

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

NH ≅ G/Ntype
2. D3×C7×C22⋊C4C2semidirect
3. C3×C7×#99C2semidirect
4. C7×#834C2semidirect
5. C7×#806C2semidirect
7. C23×D3×C7C4semidirect
10. C2×C7×#67C4semidirect
14. C2×C7×D12C4semidirect
16. C2×C4×D3×C7C4semidirect
17. C3×C7×C22⋊C4C22semidirect
18. C7×#217C22semidirect
24. C7×#99D3direct (N × H)
25. D3×#99C7direct (N × H)
26. C23×C3×C7C2×C4semidirect
34. C22×D3×C7C2×C4semidirect
39. C2×C3×C4×C7C2×C4semidirect
43. C2×C7×Dic3C2×C4semidirect
60. C7×C22⋊C4C2×D3semidirect
62. D3×C22⋊C4C2×C7semidirect
63. C3×#99C2×C7semidirect
64. #834C2×C7semidirect
65. #806C2×C7semidirect
96. C23×C7C4×D3semidirect
108. C2×C4×C7C4×D3semidirect
109. C23×D3C4×C7semidirect
112. C2×#67C4×C7semidirect
116. C2×D12C4×C7semidirect
118. C2×C4×D3C4×C7semidirect
119. C3×C22⋊C4C22×C7semidirect
120. #217C22×C7semidirect
129. D3×C7#99direct (N × H)
134. #99D3×C7direct (N × H)
155. C23×C3C2×C4×C7semidirect
163. C22×D3C2×C4×C7semidirect
168. C2×C3×C4C2×C4×C7semidirect
172. C2×Dic3C2×C4×C7semidirect
177. C3×C7C2×#99semidirect
190. C22⋊C4C2×D3×C7semidirect
228. C23C4×D3×C7semidirect
240. C2×C4C4×D3×C7semidirect
241. C7D3×#99direct (N × H)
249. D3C7×#99direct (N × H)
270. C3C2×C7×#99semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C7×D42
D3×C7×C22⋊C42
C3×C7×#992
C7×#8342
C7×#8062
C2×C7×#993
D3×#997