Finite Group Databasebeta

← C7×#13595 #13190811

Subgroups — C7×#13595 #13190811

Order 1792.

388 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3138C211yesmaximal, characteristic
2C2×C7×#353C212yesmaximal
3C7×#1412C214yesmaximal, complemented
4C7×#533C411yescharacteristic, complemented
5C2×C7×#127C2211yescharacteristic
6C7×#490C412yescomplemented
7C7×#490C2212yes—
8C7×#486—22no—
9C7×#418—22no—
10C2×C7×#99—22no—
11C4×C7×M16C411yescharacteristic, complemented
12C7×#353—22no—
13C7×#353C2214yes—
14#13595C711yesmaximal, characteristic, direct product factor, Sylow
15C22×C7×D4—41no—
16C22×C7×D4D412yes—
17C2×C7×M16—21no—
18C7×C4⋊Q8—21no—
19C7×#127—41no—
20C7×#127C2×C411yescharacteristic
21C7×#127D412yes—
22C7×#127C2311yescharacteristic
23C7×#125C2×C412yescomplemented
24C7×C22⋊Q8—41no—
25C4×C7×Q8—41no—
26C7×#117—21no—
27C2×C7×C22⋊C4—42no—
28C2×C42×C7C2×C411yescharacteristic
29C7×#102—24no—
30C7×#102—24no—
31C7×#99—24no—
32C7×#99—42no—
33C7×#97C2×C412yescomplemented
34C4×C7×C8—21no—
35#3138C2×C711yescharacteristic
36C2×#353C2×C712yes—
37#1412C2×C714yescomplemented
38C24×C7—22no—
39C2×C7×Q8—41no—
40C2×C7×D4—22no—
41C2×C7×D4—42no—
42C2×C7×D4—42no—
43C2×C7×D4—41no—
44C2×C7×D4—42no—
45C2×C7×D4—41no—
46C2×C7×D4—84no—
47C2×C7×D4C22⋊C412yes—
48C2×C7×D4C2×D412yes—
49C22×C4×C7—21no—
50C22×C4×C7—82no—
51C22×C4×C7C22⋊C411yescharacteristic
52C7×M16—42no—
53C2×C7×C8—22no—
54C7×C4⋊C4—22no—
55C7×C4⋊C4—42no—
56C7×C4⋊C4—41no—
57C7×C22⋊C4—41no—
58C7×C22⋊C4—44no—
59C7×C22⋊C4—82no—
60C42×C7—21no—
61C42×C7—41no—
62C42×C7C22⋊C411yescharacteristic
63C42×C7C22×C411yescharacteristic
64#533C4×C711yescharacteristic, complemented
65C2×#127C22×C711yescharacteristic
66#490C4×C712yescomplemented
67#490C22×C712yes—
68#486—22no—
69#418—22no—
70C2×#99—22no—
71C4×M16C4×C711yescharacteristic, complemented
72#353—22no—
73#353C22×C714yes—
74C23×C7—22no—
75C23×C7—22no—
76C23×C7—42no—
77C23×C7—42no—
78C23×C7—84no—
79C23×C7#9911yescharacteristic
80C7×Q8—82no—
81C7×D4—42no—
82C7×D4—42no—
83C7×D4—82no—
84C7×D4—84no—
85C7×D4—82no—
86C7×D4—82no—
87C2×C4×C7—22no—
88C2×C4×C7—21no—
89C2×C4×C7—21no—
90C2×C4×C7—42no—
91C2×C4×C7—42no—
92C2×C4×C7—84no—
93C2×C4×C7—164no—
94C2×C4×C7#9911yescharacteristic
95C2×C4×C7C2×C22⋊C411yescharacteristic
96C7×C8—42no—
97C22×D4—41no—
98C22×D4C7×D412yes—
99C2×M16—21no—
100C4⋊Q8—21no—
101#127—41no—
102#127C2×C4×C711yescharacteristic
103#127C7×D412yes—
104#127C23×C711yescharacteristic
105#125C2×C4×C712yescomplemented
106C22⋊Q8—41no—
107C4×Q8—41no—
108#117—21no—
109C2×C22⋊C4—42no—
110C2×C42C2×C4×C711yescharacteristic
111#102—24no—
112#102—24no—
113#99—24no—
114#99—42no—
115#97C2×C4×C712yescomplemented
116C4×C8—21no—
117C22×C7—41no—
118C22×C7—42no—
119C22×C7—42no—
120C22×C7—82no—
121C22×C7—82no—
122C22×C7—84no—
123C22×C7—162no—
124C22×C7#35412yes—
125C22×C7C2×#9911yescharacteristic
126C4×C7—22no—
127C4×C7—21no—
128C4×C7—21no—
129C4×C7—41no—
130C4×C7—82no—
131C4×C7—164no—
132C24—22no—
133C2×Q8—41no—
134C2×D4—22no—
135C2×D4—42no—
136C2×D4—42no—
137C2×D4—41no—
138C2×D4—42no—
139C2×D4—41no—
140C2×D4—84no—
141C2×D4C7×C22⋊C412yes—
142C2×D4C2×C7×D412yes—
143C22×C4—21no—
144C22×C4—82no—
145C22×C4C7×C22⋊C411yescharacteristic
146M16—42no—
147C2×C8—22no—
148C4⋊C4—22no—
149C4⋊C4—42no—
150C4⋊C4—41no—
151C22⋊C4—41no—
152C22⋊C4—44no—
153C22⋊C4—82no—
154C42—21no—
155C42—41no—
156C42C7×C22⋊C411yescharacteristic
157C42C22×C4×C711yescharacteristic
158C2×C7—21no—
159C2×C7—22no—
160C2×C7—82no—
161C2×C7—82no—
162C2×C7C2×#35411yescharacteristic
163C23—22no—
164C23—22no—
165C23—42no—
166C23—42no—
167C23—84no—
168C23C7×#9911yescharacteristic
169Q8—82no—
170D4—42no—
171D4—42no—
172D4—82no—
173D4—84no—
174D4—82no—
175D4—82no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—84no—
182C2×C4—164no—
183C2×C4C7×#9911yescharacteristic
184C2×C4C2×C7×C22⋊C411yescharacteristic
185C8—42no—
186C7#1359511yescharacteristic, direct product factor, Sylow
187C22—41no—
188C22—42no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—84no—
193C22—162no—
194C22C7×#35412yes—
195C22C2×C7×#9911yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—82no—
201C4—164no—
202C2—21no—
203C2—22no—
204C2—82no—
205C2—82no—
206C2C2×C7×#35411yescharacteristic
subgroupG/H
center, socleC2×C7C2×#354
commutatorC42C22×C4×C7
Frattini, cosocle#127C23×C7
prime radicalC2×C7×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C23×C7 ◁ C22×C4×C7 ◁ C2×C7×#127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1412C2semidirect
4. C7×#533C4semidirect
6. C7×#490C4semidirect
11. C4×C7×M16C4semidirect
14. #13595C7direct (N × H)
23. C7×#125C2×C4semidirect
33. C7×#97C2×C4semidirect
37. #1412C2×C7semidirect
64. #533C4×C7semidirect
66. #490C4×C7semidirect
71. C4×M16C4×C7semidirect
105. #125C2×C4×C7semidirect
115. #97C2×C4×C7semidirect
186. C7#13595direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31382
C2×C7×#3532
C7×#14122
#135957