Finite Group Databasebeta

← C7×#9400 #13186616

Subgroups — C7×#9400 #13186616

Order 1792.

466 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2983C211yesmaximal, characteristic
2C7×#2567C211yesmaximal, characteristic
3C7×#1801C211yesmaximal, characteristic
4C7×#1548C212yesmaximal
5C7×#1303C212yesmaximal
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#446—24no—
9C7×#432—22no—
10C7×#431C2212yes—
11C7×#423C2212yes—
12C2×C7×#101—21no—
13C7×#395C414yes—
14C7×#391—21no—
15C7×#389—22no—
16C7×#384—21no—
17C4×C7×C4⋊C4C2211yescharacteristic
18C7×#343—21no—
19C7×#333—24no—
20#9400C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8C2×C412yes—
22C22×C7×Q8D411yescharacteristic
23C2×C7×M16—22no—
24C7×C4⋊Q8—22no—
25C7×C4⋊Q8—22no—
26C4×C7×Q8—22no—
27C4×C7×Q8—22no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—24no—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C42×C7—21no—
35C2×C42×C7D412yes—
36C2×C42×C7C2311yescharacteristic
37C7×C4⋊C8—24no—
38C7×C4⋊C8—22no—
39C7×C4⋊C8—22no—
40C7×C4⋊C8D414yes—
41C7×#101—42no—
42C7×C22⋊C8—22no—
43C7×#97—24no—
44C4×C7×C8—22no—
45C7×#95—24no—
46C7×#95C2×C412yes—
47#2983C2×C711yescharacteristic
48#2567C2×C711yescharacteristic
49#1801C2×C711yescharacteristic
50#1548C2×C712yes—
51#1303C2×C712yes—
52C2×C7×Q8—22no—
53C2×C7×Q8—21no—
54C2×C7×Q8—21no—
55C2×C7×Q8—22no—
56C2×C7×Q8—24no—
57C2×C7×Q8—82no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7C22⋊C412yes—
61C22×C4×C7C22⋊C412yes—
62C22×C4×C7C22×C411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C7×M16—42no—
66C7×M16—42no—
67C2×C7×C8—24no—
68C2×C7×C8—42no—
69C7×C4⋊C4—24no—
70C7×C4⋊C4—24no—
71C7×C4⋊C4—22no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—42no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—84no—
76C42×C7—22no—
77C42×C7—22no—
78C42×C7—41no—
79C42×C7—41no—
80C42×C7C2×D412yes—
81C42×C7#4112yes—
82C2×C4⋊Q8C22×C711yescharacteristic
83C2×C4×Q8C22×C711yescharacteristic
84#446—24no—
85#432—22no—
86#431C22×C712yes—
87#423C22×C712yes—
88C2×#101—21no—
89#395C4×C714yes—
90#391—21no—
91#389—22no—
92#384—21no—
93C4×C4⋊C4C22×C711yescharacteristic
94#343—21no—
95#333—24no—
96C23×C7C2×C22⋊C411yescharacteristic
97C7×Q8—42no—
98C7×Q8—42no—
99C7×Q8—84no—
100C2×C4×C7—22no—
101C2×C4×C7—24no—
102C2×C4×C7—22no—
103C2×C4×C7—22no—
104C2×C4×C7—22no—
105C2×C4×C7—22no—
106C2×C4×C7—41no—
107C2×C4×C7—42no—
108C2×C4×C7—42no—
109C2×C4×C7—42no—
110C2×C4×C7—44no—
111C2×C4×C7—42no—
112C2×C4×C7C4×D412yes—
113C2×C4×C7#12011yescharacteristic
114C2×C4×C7#12112yes—
115C2×C4×C7#12311yescharacteristic
116C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C7#13712yes—
118C2×C4×C7#13711yescharacteristic
119C7×C8—44no—
120C7×C8—82no—
121C22×Q8C2×C4×C712yes—
122C22×Q8C7×D411yescharacteristic
123C2×M16—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4C2×C4×C712yes—
133C2×C4⋊C4C7×D411yescharacteristic
134C2×C42—21no—
135C2×C42C7×D412yes—
136C2×C42C23×C711yescharacteristic
137C4⋊C8—24no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8C7×D414yes—
141#101—42no—
142C22⋊C8—22no—
143#97—24no—
144C4×C8—22no—
145#95—24no—
146#95C2×C4×C712yes—
147C22×C7—21no—
148C22×C7—21no—
149C22×C7#38611yescharacteristic
150C22×C7#41711yescharacteristic
151C22×C7#41911yescharacteristic
152C4×C7—21no—
153C4×C7—22no—
154C4×C7—44no—
155C4×C7—42no—
156C4×C7—42no—
157C4×C7—82no—
158C4×C7#45612yes—
159C4×C7#46812yes—
160C4×C7#47012yes—
161C2×Q8—22no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—22no—
165C2×Q8—24no—
166C2×Q8—82no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4C7×C22⋊C412yes—
170C22×C4C7×C22⋊C412yes—
171C22×C4C22×C4×C711yescharacteristic
172C22×C4C2×C7×D411yescharacteristic
173C22×C4C2×C7×D411yescharacteristic
174M16—42no—
175M16—42no—
176C2×C8—24no—
177C2×C8—42no—
178C4⋊C4—24no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—84no—
185C42—22no—
186C42—22no—
187C42—41no—
188C42—41no—
189C42C2×C7×D412yes—
190C42C7×#4112yes—
191C2×C7—21no—
192C2×C7—21no—
193C2×C7#188611yescharacteristic
194C2×C7#189411yescharacteristic
195C2×C7#191411yescharacteristic
196C23C2×C7×C22⋊C411yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—84no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4C4×C7×D412yes—
213C2×C4C7×#12011yescharacteristic
214C2×C4C7×#12112yes—
215C2×C4C7×#12311yescharacteristic
216C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
217C2×C4C7×#13712yes—
218C2×C4C7×#13711yescharacteristic
219C8—44no—
220C8—82no—
221C7#940011yescharacteristic, direct product factor, Sylow
222C22—21no—
223C22—21no—
224C22C7×#38611yescharacteristic
225C22C7×#41711yescharacteristic
226C22C7×#41911yescharacteristic
227C4—21no—
228C4—22no—
229C4—44no—
230C4—42no—
231C4—42no—
232C4—82no—
233C4C7×#45612yes—
234C4C7×#46812yes—
235C4C7×#47012yes—
236C2—21no—
237C2—21no—
238C2C7×#188611yescharacteristic
239C2C7×#189411yescharacteristic
240C2C7×#191411yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C42C23×C7
prime radicalC23×C7C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
20. #9400C7direct (N × H)
221. C7#9400direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29832
C7×#25672
C7×#18012
C7×#15482
C7×#13032
#94007