Finite Group Databasebeta

← C7×#9402 #13186618

Subgroups — C7×#9402 #13186618

Order 1792.

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

normal subgroups only

This group has 486 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×#2546C211yesmaximal, characteristic
3C7×#1801C211yesmaximal, characteristic
4C7×#1546C212yesmaximal
5C7×#1303C212yesmaximal
6C2×C7×C4⋊Q8—21no—
7C2×C7×C4⋊Q8C2211yescharacteristic
8C2×C4×C7×Q8C2211yescharacteristic
9C7×#446—24no—
10C7×#432—22no—
11C7×#431C2212yes—
12C7×#423C2212yes—
13C2×C7×#101—21no—
14C7×#398C414yes—
15C7×#391—21no—
16C7×#389—22no—
17C4×C7×C4⋊C4C2211yescharacteristic
18C7×#343—21no—
19C7×#332—24no—
20#9402C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8D411yescharacteristic
23C2×C7×M16—22no—
24C7×C4⋊Q8—22no—
25C7×C4⋊Q8—22no—
26C7×C4⋊Q8—44no—
27C4×C7×Q8—22no—
28C4×C7×Q8—22no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—24no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C42×C7—21no—
36C2×C42×C7D412yes—
37C2×C42×C7C2311yescharacteristic
38C7×C4⋊C8—24no—
39C7×C4⋊C8—22no—
40C7×C4⋊C8—22no—
41C7×C4⋊C8D414yes—
42C7×#101—42no—
43C7×C22⋊C8—22no—
44C7×#97—24no—
45C4×C7×C8—22no—
46C7×#95—24no—
47C7×#95C2×C412yes—
48#2983C2×C711yescharacteristic
49#2546C2×C711yescharacteristic
50#1801C2×C711yescharacteristic
51#1546C2×C712yes—
52#1303C2×C712yes—
53C2×C7×Q8—22no—
54C2×C7×Q8—21no—
55C2×C7×Q8—22no—
56C2×C7×Q8—21no—
57C2×C7×Q8—42no—
58C2×C7×Q8—42no—
59C2×C7×Q8—41no—
60C2×C7×Q8—41no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7C22⋊C412yes—
64C22×C4×C7C22⋊C412yes—
65C22×C4×C7C22×C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C7×M16—42no—
69C7×M16—42no—
70C2×C7×C8—24no—
71C2×C7×C8—42no—
72C7×C4⋊C4—24no—
73C7×C4⋊C4—24no—
74C7×C4⋊C4—22no—
75C7×C4⋊C4—24no—
76C7×C4⋊C4—48no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C42×C7—22no—
80C42×C7—22no—
81C42×C7—42no—
82C42×C7C2×D412yes—
83C42×C7#4112yes—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8C22×C711yescharacteristic
86C2×C4×Q8C22×C711yescharacteristic
87#446—24no—
88#432—22no—
89#431C22×C712yes—
90#423C22×C712yes—
91C2×#101—21no—
92#398C4×C714yes—
93#391—21no—
94#389—22no—
95C4×C4⋊C4C22×C711yescharacteristic
96#343—21no—
97#332—24no—
98C23×C7C2×C22⋊C411yescharacteristic
99C7×Q8—42no—
100C7×Q8—42no—
101C7×Q8—82no—
102C7×Q8—82no—
103C2×C4×C7—22no—
104C2×C4×C7—24no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—22no—
108C2×C4×C7—22no—
109C2×C4×C7—41no—
110C2×C4×C7—42no—
111C2×C4×C7—42no—
112C2×C4×C7—42no—
113C2×C4×C7—42no—
114C2×C4×C7—42no—
115C2×C4×C7—42no—
116C2×C4×C7C4×D412yes—
117C2×C4×C7#12011yescharacteristic
118C2×C4×C7#12112yes—
119C2×C4×C7#12311yescharacteristic
120C2×C4×C7AGL(1,ℤ/8)12yes—
121C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C7#13711yescharacteristic
123C7×C8—44no—
124C7×C8—82no—
125C22×Q8—21no—
126C22×Q8C7×D411yescharacteristic
127C2×M16—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—44no—
131C4×Q8—22no—
132C4×Q8—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C2×C4×C712yes—
137C2×C4⋊C4C2×C4×C712yes—
138C2×C4⋊C4C7×D411yescharacteristic
139C2×C42—21no—
140C2×C42C7×D412yes—
141C2×C42C23×C711yescharacteristic
142C4⋊C8—24no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8C7×D414yes—
146#101—42no—
147C22⋊C8—22no—
148#97—24no—
149C4×C8—22no—
150#95—24no—
151#95C2×C4×C712yes—
152C22×C7—21no—
153C22×C7—21no—
154C22×C7#38611yescharacteristic
155C22×C7#41711yescharacteristic
156C22×C7#41811yescharacteristic
157C4×C7—21no—
158C4×C7—22no—
159C4×C7—44no—
160C4×C7—42no—
161C4×C7—42no—
162C4×C7—82no—
163C4×C7#45612yes—
164C4×C7#46812yes—
165C4×C7#46912yes—
166C2×Q8—22no—
167C2×Q8—21no—
168C2×Q8—22no—
169C2×Q8—21no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—41no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4C7×C22⋊C412yes—
177C22×C4C7×C22⋊C412yes—
178C22×C4C22×C4×C711yescharacteristic
179C22×C4C2×C7×D411yescharacteristic
180C22×C4C2×C7×D411yescharacteristic
181M16—42no—
182M16—42no—
183C2×C8—24no—
184C2×C8—42no—
185C4⋊C4—24no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—24no—
189C4⋊C4—48no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C42—22no—
193C42—22no—
194C42—42no—
195C42C2×C7×D412yes—
196C42C7×#4112yes—
197C2×C7—21no—
198C2×C7—21no—
199C2×C7#188611yescharacteristic
200C2×C7#189511yescharacteristic
201C2×C7#191511yescharacteristic
202C23C2×C7×C22⋊C411yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—82no—
206Q8—82no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4C4×C7×D412yes—
221C2×C4C7×#12011yescharacteristic
222C2×C4C7×#12112yes—
223C2×C4C7×#12311yescharacteristic
224C2×C4C7×AGL(1,ℤ/8)12yes—
225C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
226C2×C4C7×#13711yescharacteristic
227C8—44no—
228C8—82no—
229C7#940211yescharacteristic, direct product factor, Sylow
230C22—21no—
231C22—21no—
232C22C7×#38611yescharacteristic
233C22C7×#41711yescharacteristic
234C22C7×#41811yescharacteristic
235C4—21no—
236C4—22no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4C7×#45612yes—
242C4C7×#46812yes—
243C4C7×#46912yes—
244C2—21no—
245C2—21no—
246C2C7×#188611yescharacteristic
247C2C7×#189511yescharacteristic
248C2C7×#191511yescharacteristic
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. #9402C7direct (N × H)
229. C7#9402direct (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×#25462
C7×#18012
C7×#15462
C7×#13032
#94027