Finite Group Databasebeta

← C7×#7430 #13184646

Subgroups — C7×#7430 #13184646

Order 1792.

236 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2027C211yesmaximal, characteristic
2C7×#1393C211yesmaximal, characteristic
3C7×#1270C211yesmaximal, characteristic
4C7×#544C411yescharacteristic, complemented
5C7×#418—21no—
6C2×C7×#99—21no—
7C7×#390C2211yescharacteristic
8C7×#343C411yescharacteristic, complemented
9C7×#339—21no—
10C7×#336—21no—
11#7430C711yesmaximal, characteristic, direct product factor, Sylow
12C22×C7×D4D411yescharacteristic
13C2×C7×M16—21no—
14C22×C7×C8—41no—
15C7×C4⋊Q8—41no—
16C7×#125—41no—
17C7×C22⋊Q8—41no—
18C7×#117—21no—
19C2×C7×C4⋊C4C2×C411yescharacteristic
20C2×C7×C22⋊C4—41no—
21C2×C7×C22⋊C4—41no—
22C2×C42×C7D411yescharacteristic
23C7×#102—41no—
24C7×#102—41no—
25C7×#99—22no—
26C7×#99—41no—
27#2027C2×C711yescharacteristic
28#1393C2×C711yescharacteristic
29#1270C2×C711yescharacteristic
30C24×C7—21no—
31C2×C7×Q8—41no—
32C2×C7×D4—21no—
33C2×C7×D4—41no—
34C2×C7×D4—41no—
35C2×C7×D4SD1611yescharacteristic
36C2×C7×D4Q1611yescharacteristic
37C22×C4×C7—21no—
38C22×C4×C7—21no—
39C22×C4×C7—81no—
40C22×C4×C7C22⋊C411yescharacteristic
41C7×M16—41no—
42C7×M16—41no—
43C2×C7×C8—41no—
44C2×C7×C8—42no—
45C2×C7×C8—81no—
46C2×C7×C8—81no—
47C7×C4⋊C4—21no—
48C7×C4⋊C4—21no—
49C7×C4⋊C4—41no—
50C7×C4⋊C4—41no—
51C7×C4⋊C4—42no—
52C7×C22⋊C4—41no—
53C7×C22⋊C4—42no—
54C7×C22⋊C4—81no—
55C7×C22⋊C4—81no—
56C7×C22⋊C4—81no—
57C42×C7—41no—
58C42×C7—41no—
59#544C4×C711yescharacteristic, complemented
60#418—21no—
61C2×#99—21no—
62#390C22×C711yescharacteristic
63#343C4×C711yescharacteristic, complemented
64#339—21no—
65#336—21no—
66C23×C7—21no—
67C23×C7—21no—
68C23×C7—41no—
69C23×C7—41no—
70C23×C7—81no—
71C23×C7—81no—
72C23×C7#9911yescharacteristic
73C7×Q8—161no—
74C7×D4—41no—
75C7×D4—41no—
76C7×D4—81no—
77C2×C4×C7—21no—
78C2×C4×C7—21no—
79C2×C4×C7—21no—
80C2×C4×C7—21no—
81C2×C4×C7—41no—
82C2×C4×C7—41no—
83C2×C4×C7—41no—
84C2×C4×C7—41no—
85C2×C4×C7—41no—
86C2×C4×C7—81no—
87C2×C4×C7—82no—
88C2×C4×C7—161no—
89C2×C4×C7—161no—
90C2×C4×C7#10311yescharacteristic
91C2×C4×C7#10411yescharacteristic
92C7×C8—81no—
93C7×C8—82no—
94C22×D4C7×D411yescharacteristic
95C2×M16—21no—
96C22×C8—41no—
97C4⋊Q8—41no—
98#125—41no—
99C22⋊Q8—41no—
100#117—21no—
101C2×C4⋊C4C2×C4×C711yescharacteristic
102C2×C22⋊C4—41no—
103C2×C22⋊C4—41no—
104C2×C42C7×D411yescharacteristic
105#102—41no—
106#102—41no—
107#99—22no—
108#99—41no—
109C22×C7—21no—
110C22×C7—21no—
111C22×C7—41no—
112C22×C7—41no—
113C22×C7—81no—
114C22×C7—81no—
115C22×C7—81no—
116C22×C7—81no—
117C22×C7—161no—
118C22×C7#32811yescharacteristic
119C22×C7AΣL(1,𝔽16)11yescharacteristic
120C22×C7#35411yescharacteristic
121C4×C7—21no—
122C4×C7—21no—
123C4×C7—41no—
124C4×C7—41no—
125C4×C7—81no—
126C4×C7—81no—
127C4×C7—81no—
128C4×C7—162no—
129C24—21no—
130C2×Q8—41no—
131C2×D4—21no—
132C2×D4—41no—
133C2×D4—41no—
134C2×D4C7×SD1611yescharacteristic
135C2×D4C7×Q1611yescharacteristic
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—81no—
139C22×C4C7×C22⋊C411yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—41no—
143C2×C8—42no—
144C2×C8—81no—
145C2×C8—81no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—42no—
151C22⋊C4—41no—
152C22⋊C4—42no—
153C22⋊C4—81no—
154C22⋊C4—81no—
155C22⋊C4—81no—
156C42—41no—
157C42—41no—
158C2×C7—21no—
159C2×C7—21no—
160C2×C7—81no—
161C2×C7—81no—
162C2×C7#135111yescharacteristic
163C2×C7#140211yescharacteristic
164C2×C7#140411yescharacteristic
165C23—21no—
166C23—21no—
167C23—41no—
168C23—41no—
169C23—81no—
170C23—81no—
171C23C7×#9911yescharacteristic
172Q8—161no—
173D4—41no—
174D4—41no—
175D4—81no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—82no—
187C2×C4—161no—
188C2×C4—161no—
189C2×C4C7×#10311yescharacteristic
190C2×C4C7×#10411yescharacteristic
191C8—81no—
192C8—82no—
193C7#743011yescharacteristic, direct product factor, Sylow
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22C7×#32811yescharacteristic
204C22C7×AΣL(1,𝔽16)11yescharacteristic
205C22C7×#35411yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—81no—
212C4—81no—
213C4—162no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2C7×#135111yescharacteristic
219C2C7×#140211yescharacteristic
220C2C7×#140411yescharacteristic
subgroupG/H
center, socleC22×C7AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C7
Frattini, cosocle#390C22×C7
prime radicalC22×C7×D4D4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C4×C7 ◁ C7×#390 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#544C4semidirect
8. C7×#343C4semidirect
11. #7430C7direct (N × H)
59. #544C4×C7semidirect
63. #343C4×C7semidirect
193. C7#7430direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#20272
C7×#13932
C7×#12702
#74307