Finite Group Databasebeta

← C2×C7×#1414 #13190817

Subgroups — C2×C7×#1414 #13190817

Order 1792.

340 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 94 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×C7×#488C211yesmaximal, characteristic
2C2×C7×#355C211yesmaximal, characteristic
3C2×C7×#354C211yesmaximal, characteristic
4C7×#1414C214yesmaximal, direct product factor
5C2×C7×#125C411yescharacteristic, complemented
6C2×C7×#124C2211yescharacteristic
7C7×#488—21no—
8C7×#488—21no—
9C7×#488C412yescomplemented
10C7×#488C2212yes—
11C2×C7×#103—21no—
12C2×C7×#102—21no—
13C2×C7×#101—21no—
14C2×C7×#99—21no—
15C2×C4×C7×C8C411yescharacteristic, complemented
16C7×#355—21no—
17C7×#355C2212yes—
18C7×#354—21no—
19C7×#354C2212yes—
20C2×#1414C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×C7×D4D411yescharacteristic
23C2×C7×M16—41no—
24C22×C7×C8—21no—
25C7×#125—21no—
26C7×#125—41no—
27C7×#125C2×C412yescomplemented
28C7×#124—41no—
29C7×#124C2×C411yescharacteristic
30C7×#124D411yescharacteristic
31C7×#124D411yescharacteristic
32C7×#124C2311yescharacteristic
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C22⋊C4—41no—
36C2×C7×C22⋊C4—41no—
37C2×C42×C7C2×C411yescharacteristic
38C7×#103—22no—
39C7×#103—22no—
40C7×#102—22no—
41C7×#102—22no—
42C7×#101—22no—
43C7×#101—41no—
44C7×#99—22no—
45C7×#99—41no—
46C4×C7×C8—21no—
47C4×C7×C8C2×C412yescomplemented
48C2×#488C2×C711yescharacteristic
49C2×#355C2×C711yescharacteristic
50C2×#354C2×C711yescharacteristic
51#1414C2×C714yesdirect product factor
52C24×C7—21no—
53C2×C7×Q8—21no—
54C2×C7×Q8—41no—
55C2×C7×Q8—41no—
56C2×C7×Q8C22⋊C411yescharacteristic
57C2×C7×Q8C2×D411yescharacteristic
58C2×C7×D4—21no—
59C2×C7×D4—41no—
60C2×C7×D4—41no—
61C2×C7×D4C22⋊C411yescharacteristic
62C2×C7×D4C2×D411yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—41no—
66C22×C4×C7—81no—
67C22×C4×C7C22⋊C411yescharacteristic
68C7×M16—42no—
69C7×M16—81no—
70C2×C7×C8—22no—
71C2×C7×C8—41no—
72C2×C7×C8—41no—
73C2×C7×C8—81no—
74C7×C4⋊C4—22no—
75C7×C4⋊C4—42no—
76C7×C4⋊C4—42no—
77C7×C4⋊C4—41no—
78C7×C22⋊C4—41no—
79C7×C22⋊C4—41no—
80C7×C22⋊C4—41no—
81C7×C22⋊C4—41no—
82C7×C22⋊C4—42no—
83C7×C22⋊C4—81no—
84C42×C7—21no—
85C42×C7C22⋊C411yescharacteristic
86C42×C7C22×C411yescharacteristic
87C2×#125C4×C711yescharacteristic, complemented
88C2×#124C22×C711yescharacteristic
89#488—21no—
90#488—21no—
91#488C4×C712yescomplemented
92#488C22×C712yes—
93C2×#103—21no—
94C2×#102—21no—
95C2×#101—21no—
96C2×#99—21no—
97C2×C4×C8C4×C711yescharacteristic, complemented
98#355—21no—
99#355C22×C712yes—
100#354—21no—
101#354C22×C712yes—
102C23×C7—21no—
103C23×C7—21no—
104C23×C7—41no—
105C23×C7—41no—
106C23×C7—82no—
107C23×C7#9911yescharacteristic
108C7×Q8—41no—
109C7×Q8—41no—
110C7×Q8—81no—
111C7×D4—41no—
112C7×D4—41no—
113C7×D4—81no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—42no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7—42no—
124C2×C4×C7—82no—
125C2×C4×C7—82no—
126C2×C4×C7—162no—
127C2×C4×C7#9911yescharacteristic
128C2×C4×C7C2×C22⋊C411yescharacteristic
129C7×C8—42no—
130C7×C8—82no—
131C22×Q8C7×D411yescharacteristic
132C22×D4C7×D411yescharacteristic
133C2×M16—41no—
134C22×C8—21no—
135#125—21no—
136#125—41no—
137#125C2×C4×C712yescomplemented
138#124—41no—
139#124C2×C4×C711yescharacteristic
140#124C7×D411yescharacteristic
141#124C7×D411yescharacteristic
142#124C23×C711yescharacteristic
143C2×C4⋊C4—21no—
144C2×C4⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C22⋊C4—41no—
147C2×C42C2×C4×C711yescharacteristic
148#103—22no—
149#103—22no—
150#102—22no—
151#102—22no—
152#101—22no—
153#101—41no—
154#99—22no—
155#99—41no—
156C4×C8—21no—
157C4×C8C2×C4×C712yescomplemented
158C22×C7—22no—
159C22×C7—41no—
160C22×C7—41no—
161C22×C7—81no—
162C22×C7—81no—
163C22×C7—82no—
164C22×C7—161no—
165C22×C7#35411yescharacteristic
166C22×C7#35411yescharacteristic
167C22×C7C2×#9911yescharacteristic
168C4×C7—21no—
169C4×C7—21no—
170C4×C7—41no—
171C4×C7—41no—
172C4×C7—41no—
173C4×C7—41no—
174C4×C7—82no—
175C4×C7—162no—
176C24—21no—
177C2×Q8—21no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C7×C22⋊C411yescharacteristic
181C2×Q8C2×C7×D411yescharacteristic
182C2×D4—21no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4C7×C22⋊C411yescharacteristic
186C2×D4C2×C7×D411yescharacteristic
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—41no—
190C22×C4—81no—
191C22×C4C7×C22⋊C411yescharacteristic
192M16—42no—
193M16—81no—
194C2×C8—22no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—81no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—42no—
207C22⋊C4—81no—
208C42—21no—
209C42C7×C22⋊C411yescharacteristic
210C42C22×C4×C711yescharacteristic
211C2×C7—21no—
212C2×C7—21no—
213C2×C7—81no—
214C2×C7—81no—
215C2×C7#141412yesdirect product factor
216C2×C7C2×#35411yescharacteristic
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23—82no—
222C23C7×#9911yescharacteristic
223Q8—41no—
224Q8—41no—
225Q8—81no—
226D4—41no—
227D4—41no—
228D4—81no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—162no—
242C2×C4C7×#9911yescharacteristic
243C2×C4C2×C7×C22⋊C411yescharacteristic
244C8—42no—
245C8—82no—
246C7C2×#141411yescharacteristic, direct product factor, Sylow
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—82no—
253C22—161no—
254C22C7×#35411yescharacteristic
255C22C7×#35411yescharacteristic
256C22C2×C7×#9911yescharacteristic
257C4—21no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—82no—
264C4—162no—
265C2—21no—
266C2—21no—
267C2—81no—
268C2—81no—
269C2C7×#141412yesdirect product factor
270C2C2×C7×#35411yescharacteristic
subgroupG/H
center, socleC22×C7#354
commutatorC42C22×C4×C7
Frattini, cosocle#124C23×C7
prime radicalC22×C7×D4D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C4×C7 ◁ C2×C7×#124 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1414C2direct (N × H)
5. C2×C7×#125C4semidirect
9. C7×#488C4semidirect
15. C2×C4×C7×C8C4semidirect
20. C2×#1414C7direct (N × H)
27. C7×#125C2×C4semidirect
47. C4×C7×C8C2×C4semidirect
51. #1414C2×C7direct (N × H)
87. C2×#125C4×C7semidirect
91. #488C4×C7semidirect
97. C2×C4×C8C4×C7semidirect
137. #125C2×C4×C7semidirect
157. C4×C8C2×C4×C7semidirect
215. C2×C7#1414direct (N × H)
246. C7C2×#1414direct (N × H)
269. C2C7×#1414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4882
C2×C7×#3552
C2×C7×#3542
C7×#14142
C2×#14147