Finite Group Databasebeta

← C7×#10389 #13187605

Subgroups — C7×#10389 #13187605

Order 1792.

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

normal subgroups only

This group has 406 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×#2608C211yesmaximal, characteristic
2C7×#1826C212yesmaximal
3C7×#1820C211yesmaximal, characteristic
4C7×#1306C211yesmaximal, characteristic
5C7×#1284C212yesmaximal
6C2×C7×#117C2211yescharacteristic
7C7×#407C2212yes—
8C7×#396—22no—
9C7×#389—22no—
10C7×#387—22no—
11C7×#381C2211yescharacteristic
12C7×#381C2211yescharacteristic
13C4×C7×C22⋊C4C2212yes—
14C7×#342—22no—
15C7×#339—22no—
16C7×#339—22no—
17#10389C711yesmaximal, characteristic, direct product factor, Sylow
18C23×C4×C7C2311yescharacteristic
19C2×C7×M16—22no—
20C7×#117—22no—
21C7×#117—22no—
22C2×C7×C4⋊C4—22no—
23C2×C7×C4⋊C4—22no—
24C2×C7×C4⋊C4—22no—
25C2×C7×C4⋊C4Q812yes—
26C2×C7×C22⋊C4—21no—
27C2×C7×C22⋊C4—22no—
28C2×C7×C22⋊C4—21no—
29C2×C7×C22⋊C4D412yes—
30C2×C42×C7—21no—
31C2×C42×C7D412yes—
32C2×C42×C7D412yes—
33C7×C22⋊C8—22no—
34C7×C22⋊C8—22no—
35C7×#95—22no—
36C7×#95—22no—
37C7×#95—22no—
38C7×#95—22no—
39#2608C2×C711yescharacteristic
40#1826C2×C712yes—
41#1820C2×C711yescharacteristic
42#1306C2×C711yescharacteristic
43#1284C2×C712yes—
44C24×C7C2×D411yescharacteristic
45C22×C4×C7—22no—
46C22×C4×C7—22no—
47C22×C4×C7—22no—
48C22×C4×C7—22no—
49C22×C4×C7—42no—
50C22×C4×C7—41no—
51C22×C4×C7C2×D412yes—
52C22×C4×C7C2×Q811yescharacteristic
53C22×C4×C7#4112yes—
54C22×C4×C7#4111yescharacteristic
55C7×M16—42no—
56C7×M16—42no—
57C2×C7×C8—42no—
58C7×C4⋊C4—24no—
59C7×C4⋊C4—44no—
60C7×C4⋊C4—44no—
61C7×C4⋊C4—82no—
62C7×C22⋊C4—44no—
63C7×C22⋊C4—41no—
64C7×C22⋊C4—41no—
65C7×C22⋊C4—42no—
66C7×C22⋊C4—42no—
67C42×C7—42no—
68C42×C7—42no—
69C42×C7—42no—
70C2×#117C22×C711yescharacteristic
71#407C22×C712yes—
72#396—22no—
73#389—22no—
74#387—22no—
75#381C22×C711yescharacteristic
76#381C22×C711yescharacteristic
77C4×C22⋊C4C22×C712yes—
78#342—22no—
79#339—22no—
80#339—22no—
81C23×C7—22no—
82C23×C7—42no—
83C23×C7#12011yescharacteristic
84C23×C7C22⋊Q811yescharacteristic
85C23×C7#12411yescharacteristic
86C2×C4×C7—22no—
87C2×C4×C7—22no—
88C2×C4×C7—24no—
89C2×C4×C7—41no—
90C2×C4×C7—41no—
91C2×C4×C7—42no—
92C2×C4×C7—42no—
93C2×C4×C7—42no—
94C2×C4×C7—42no—
95C2×C4×C7—42no—
96C2×C4×C7—42no—
97C2×C4×C7—42no—
98C2×C4×C7—42no—
99C2×C4×C7—42no—
100C2×C4×C7—42no—
101C2×C4×C7—82no—
102C2×C4×C7—81no—
103C2×C4×C7—82no—
104C2×C4×C7C22⋊Q812yes—
105C2×C4×C7#12412yes—
106C7×C8—82no—
107C23×C4C23×C711yescharacteristic
108C2×M16—22no—
109#117—22no—
110#117—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4C7×Q812yes—
115C2×C22⋊C4—21no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4C7×D412yes—
119C2×C42—21no—
120C2×C42C7×D412yes—
121C2×C42C7×D412yes—
122C22⋊C8—22no—
123C22⋊C8—22no—
124#95—22no—
125#95—22no—
126#95—22no—
127#95—22no—
128C22×C7—22no—
129C22×C7—21no—
130C22×C7—21no—
131C22×C7—22no—
132C22×C7—22no—
133C22×C7—82no—
134C22×C7#39311yescharacteristic
135C22×C7#45812yes—
136C4×C7—22no—
137C4×C7—22no—
138C4×C7—44no—
139C4×C7—82no—
140C4×C7—82no—
141C4×C7—82no—
142C4×C7—161no—
143C24C2×C7×D411yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—41no—
150C22×C4C2×C7×D412yes—
151C22×C4C2×C7×Q811yescharacteristic
152C22×C4C7×#4112yes—
153C22×C4C7×#4111yescharacteristic
154M16—42no—
155M16—42no—
156C2×C8—42no—
157C4⋊C4—24no—
158C4⋊C4—44no—
159C4⋊C4—44no—
160C4⋊C4—82no—
161C22⋊C4—44no—
162C22⋊C4—41no—
163C22⋊C4—41no—
164C22⋊C4—42no—
165C22⋊C4—42no—
166C42—42no—
167C42—42no—
168C42—42no—
169C2×C7—22no—
170C2×C7—41no—
171C2×C7—41no—
172C2×C7#203011yescharacteristic
173C2×C7#203112yes—
174C23—22no—
175C23—42no—
176C23C7×#12011yescharacteristic
177C23C7×C22⋊Q811yescharacteristic
178C23C7×#12411yescharacteristic
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—82no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4C7×C22⋊Q812yes—
198C2×C4C7×#12412yes—
199C8—82no—
200C7#1038911yescharacteristic, direct product factor, Sylow
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22C7×#39311yescharacteristic
208C22C7×#45812yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—82no—
215C4—161no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2C7×#203011yescharacteristic
220C2C7×#203112yes—
subgroupG/H
center, socleC22×C7#393
commutator, Frattini, cosocleC23×C4C23×C7
prime radicalC24×C7C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
17. #10389C7direct (N × H)
200. C7#10389direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#26082
C7×#18262
C7×#18202
C7×#13062
C7×#12842
#103897