Finite Group Databasebeta

← C7×#9392 #13186608

Subgroups — C7×#9392 #13186608

Order 1792.

486 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982C211yesmaximal, characteristic
2C7×#2567C211yesmaximal, characteristic
3C7×#1801C211yesmaximal, characteristic
4C7×#1548C212yesmaximal
5C7×#1303C212yesmaximal
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×C8×Q8—24no—
9C7×#431—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#9392C711yesmaximal, 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—
43C4×C7×C8—24no—
44C4×C7×C8—22no—
45C7×#95—24no—
46C7×#95C2×C412yes—
47#2982C2×C711yescharacteristic
48#2567C2×C711yescharacteristic
49#1801C2×C711yescharacteristic
50#1548C2×C712yes—
51#1303C2×C712yes—
52C2×C7×Q8—22no—
53C2×C7×Q8—22no—
54C2×C7×Q8—24no—
55C2×C7×Q8—82no—
56C2×C7×Q8SD1612yes—
57C2×C7×Q8Q1612yes—
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—42no—
79C42×C7C2×D412yes—
80C42×C7#4112yes—
81C2×C4⋊Q8C22×C711yescharacteristic
82C2×C4×Q8C22×C711yescharacteristic
83C8×Q8—24no—
84#431—22no—
85#431C22×C712yes—
86#423C22×C712yes—
87C2×#101—21no—
88#395C4×C714yes—
89#391—21no—
90#389—22no—
91#384—21no—
92C4×C4⋊C4C22×C711yescharacteristic
93#343—21no—
94#333—24no—
95C23×C7C2×C22⋊C411yescharacteristic
96C7×Q8—24no—
97C7×Q8—24no—
98C7×Q8—84no—
99C2×C4×C7—22no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—24no—
103C2×C4×C7—22no—
104C2×C4×C7—41no—
105C2×C4×C7—42no—
106C2×C4×C7—42no—
107C2×C4×C7—42no—
108C2×C4×C7—44no—
109C2×C4×C7—42no—
110C2×C4×C7#10314yes—
111C2×C4×C7C4×D412yes—
112C2×C4×C7#12011yescharacteristic
113C2×C4×C7#12112yes—
114C2×C4×C7#12311yescharacteristic
115C2×C4×C7C2×SD1611yescharacteristic
116C2×C4×C7C2×Q1611yescharacteristic
117C2×C4×C7#13512yes—
118C7×C8—44no—
119C7×C8—82no—
120C22×Q8C2×C4×C712yes—
121C22×Q8C7×D411yescharacteristic
122C2×M16—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4C2×C4×C712yes—
132C2×C4⋊C4C7×D411yescharacteristic
133C2×C42—21no—
134C2×C42C7×D412yes—
135C2×C42C23×C711yescharacteristic
136C4⋊C8—24no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8C7×D414yes—
140#101—42no—
141C22⋊C8—22no—
142C4×C8—24no—
143C4×C8—22no—
144#95—24no—
145#95C2×C4×C712yes—
146C22×C7—21no—
147C22×C7—21no—
148C22×C7#38611yescharacteristic
149C22×C7C2×#10311yescharacteristic
150C22×C7#41611yescharacteristic
151C4×C7—21no—
152C4×C7—24no—
153C4×C7—22no—
154C4×C7—44no—
155C4×C7—42no—
156C4×C7—82no—
157C4×C7#45612yes—
158C4×C7#46512yes—
159C4×C7#46712yes—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—24no—
163C2×Q8—82no—
164C2×Q8C7×SD1612yes—
165C2×Q8C7×Q1612yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4C7×C22⋊C412yes—
169C22×C4C7×C22⋊C412yes—
170C22×C4C22×C4×C711yescharacteristic
171C22×C4C2×C7×D411yescharacteristic
172C22×C4C2×C7×D411yescharacteristic
173M16—42no—
174M16—42no—
175C2×C8—24no—
176C2×C8—42no—
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—41no—
183C4⋊C4—84no—
184C42—22no—
185C42—22no—
186C42—42no—
187C42C2×C7×D412yes—
188C42C7×#4112yes—
189C2×C7—21no—
190C2×C7—21no—
191C2×C7#188611yescharacteristic
192C2×C7#189211yescharacteristic
193C2×C7#191411yescharacteristic
194C23C2×C7×C22⋊C411yescharacteristic
195Q8—24no—
196Q8—24no—
197Q8—84no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4C7×#10314yes—
210C2×C4C4×C7×D412yes—
211C2×C4C7×#12011yescharacteristic
212C2×C4C7×#12112yes—
213C2×C4C7×#12311yescharacteristic
214C2×C4C2×C7×SD1611yescharacteristic
215C2×C4C2×C7×Q1611yescharacteristic
216C2×C4C7×#13512yes—
217C8—44no—
218C8—82no—
219C7#939211yescharacteristic, direct product factor, Sylow
220C22—21no—
221C22—21no—
222C22C7×#38611yescharacteristic
223C22C2×C7×#10311yescharacteristic
224C22C7×#41611yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—44no—
229C4—42no—
230C4—82no—
231C4C7×#45612yes—
232C4C7×#46512yes—
233C4C7×#46712yes—
234C2—21no—
235C2—21no—
236C2C7×#188611yescharacteristic
237C2C7×#189211yescharacteristic
238C2C7×#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. #9392C7direct (N × H)
219. C7#9392direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29822
C7×#25672
C7×#18012
C7×#15482
C7×#13032
#93927