Finite Group Databasebeta

← C7×#13431 #13190647

Subgroups — C7×#13431 #13190647

Order 1792.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C7×#3202C211yesmaximal, characteristic
2C7×#2135C212yesmaximal
3C7×#1915C212yesmaximal
4C7×#1858C211yesmaximal, characteristic
5C7×#1392C211yesmaximal, characteristic
6C7×#568C2211yescharacteristic
7C7×#536C2212yes—
8C7×#485—22no—
9C7×#470—21no—
10C7×#467—21no—
11C7×#451—22no—
12C7×#430—21no—
13C7×#413C2212yes—
14C7×#413C2211yescharacteristic
15C2×C7×#101—22no—
16C7×#408C2211yescharacteristic
17C7×#356—24no—
18C7×#344—22no—
19C7×#341—21no—
20#13431C711yesmaximal, characteristic, direct product factor, Sylow
21C2×C7×#41C2311yescharacteristic
22C22×C7×Q8D412yes—
23C2×C7×Q16—21no—
24C2×C7×Q16—21no—
25C7×#131—42no—
26C2×C7×M16—21no—
27C2×C7×M16—21no—
28C2×C7×M16—22no—
29C2×C7×M16—22no—
30C2×C7×M16D411yescharacteristic
31C22×C7×C8D411yescharacteristic
32C7×C4⋊Q8—22no—
33C7×#124—22no—
34C7×#123—22no—
35C7×#123—22no—
36C7×C22⋊Q8—22no—
37C7×C22⋊Q8—22no—
38C7×#117D412yes—
39C7×#108—42no—
40C7×#107—21no—
41C7×#106—21no—
42C7×#103—22no—
43C7×#103—22no—
44C7×#101—22no—
45C7×#101—44no—
46C7×#101D412yes—
47C7×#100—21no—
48C7×#100—22no—
49C7×C22⋊C8—22no—
50#3202C2×C711yescharacteristic
51#2135C2×C712yes—
52#1915C2×C712yes—
53#1858C2×C711yescharacteristic
54#1392C2×C711yescharacteristic
55C7×#41—41no—
56C7×#41—41no—
57C2×C7×Q8—22no—
58C2×C7×Q8—22no—
59C2×C7×Q8—42no—
60C2×C7×Q8—42no—
61C2×C7×Q8C2×D411yescharacteristic
62C2×C7×D4#4111yescharacteristic
63C2×C7×D4#4112yes—
64C22×C4×C7—22no—
65C22×C4×C7C2×D412yes—
66C22×C4×C7C2×D411yescharacteristic
67C7×Q16—81no—
68C7×Q16—81no—
69C7×M16—24no—
70C7×M16—22no—
71C7×M16—22no—
72C7×M16—41no—
73C7×M16—41no—
74C7×M16—41no—
75C7×M16—42no—
76C7×M16—42no—
77C2×C7×C8—21no—
78C2×C7×C8—21no—
79C2×C7×C8—41no—
80C2×C7×C8—41no—
81C2×C7×C8—42no—
82C2×C7×C8—41no—
83C2×C7×C8—42no—
84C7×C4⋊C4—22no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—42no—
87C7×C22⋊C4—22no—
88C7×C22⋊C4—42no—
89C7×C22⋊C4—42no—
90C42×C7—22no—
91#568C22×C711yescharacteristic
92#536C22×C712yes—
93#485—22no—
94#470—21no—
95#467—21no—
96#451—22no—
97#430—21no—
98#413C22×C712yes—
99#413C22×C711yescharacteristic
100C2×#101—22no—
101#408C22×C711yescharacteristic
102#356—24no—
103#344—22no—
104#341—21no—
105C23×C7#12312yes—
106C23×C7#12411yescharacteristic
107C7×Q8—41no—
108C7×Q8—42no—
109C7×Q8—42no—
110C7×Q8—82no—
111C7×D4—41no—
112C7×D4—42no—
113C2×C4×C7—21no—
114C2×C4×C7—22no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—44no—
118C2×C4×C7—42no—
119C2×C4×C7—42no—
120C2×C4×C7#12011yescharacteristic
121C2×C4×C7#12112yes—
122C2×C4×C7#12111yescharacteristic
123C7×C8—42no—
124C7×C8—41no—
125C7×C8—42no—
126C7×C8—41no—
127C7×C8—82no—
128C2×#41C23×C711yescharacteristic
129C22×Q8C7×D412yes—
130C2×Q16—21no—
131C2×Q16—21no—
132#131—42no—
133C2×M16—21no—
134C2×M16—22no—
135C2×M16—21no—
136C2×M16—22no—
137C2×M16C7×D411yescharacteristic
138C22×C8C7×D411yescharacteristic
139C4⋊Q8—22no—
140#124—22no—
141#123—22no—
142#123—22no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145#117C7×D412yes—
146#108—42no—
147#107—21no—
148#106—21no—
149#103—22no—
150#103—22no—
151#101—22no—
152#101—44no—
153#101C7×D412yes—
154#100—21no—
155#100—22no—
156C22⋊C8—22no—
157C22×C7—22no—
158C22×C7—21no—
159C22×C7—42no—
160C22×C7—41no—
161C22×C7#39411yescharacteristic
162C4×C7—21no—
163C4×C7—22no—
164C4×C7—82no—
165C4×C7—82no—
166C4×C7B(4,𝔽2)11yescharacteristic
167C4×C7#45811yescharacteristic
168#41—41no—
169#41—41no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—42no—
173C2×Q8—42no—
174C2×Q8C2×C7×D411yescharacteristic
175C2×D4C7×#4111yescharacteristic
176C2×D4C7×#4112yes—
177C22×C4—22no—
178C22×C4C2×C7×D412yes—
179C22×C4C2×C7×D411yescharacteristic
180Q16—81no—
181Q16—81no—
182M16—24no—
183M16—22no—
184M16—22no—
185M16—41no—
186M16—41no—
187M16—41no—
188M16—42no—
189M16—42no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—42no—
197C4⋊C4—22no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C22⋊C4—22no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C42—22no—
204C2×C7—21no—
205C2×C7—42no—
206C2×C7—41no—
207C2×C7#204411yescharacteristic
208C23C7×#12312yes—
209C23C7×#12411yescharacteristic
210Q8—41no—
211Q8—42no—
212Q8—42no—
213Q8—82no—
214D4—41no—
215D4—42no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4C7×#12011yescharacteristic
224C2×C4C7×#12112yes—
225C2×C4C7×#12111yescharacteristic
226C8—42no—
227C8—41no—
228C8—42no—
229C8—41no—
230C8—82no—
231C7#1343111yescharacteristic, direct product factor, Sylow
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22C7×#39411yescharacteristic
237C4—21no—
238C4—22no—
239C4—82no—
240C4—82no—
241C4C7×B(4,𝔽2)11yescharacteristic
242C4C7×#45811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2C7×#204411yescharacteristic
subgroupG/H
center, socleC2×C7#2044
commutator, Frattini, cosocleC2×#41C23×C7
prime radicalC2×C7×#41C23
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×#41 ◁ G

Complements

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

NH ≅ G/Ntype
20. #13431C7direct (N × H)
231. C7#13431direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#32022
C7×#21352
C7×#19152
C7×#18582
C7×#13922
#134317