Finite Group Databasebeta

← C7×#13592 #13190808

Subgroups — C7×#13592 #13190808

Order 1792.

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

normal subgroups only

This group has 398 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×#3152C211yesmaximal, characteristic
2C7×#2132C212yesmaximal
3C7×#1411C214yesmaximal, complemented
4C2×C7×#137—22no—
5C7×#532C2211yescharacteristic
6C2×C7×C4⋊Q8C411yescharacteristic
7C7×#497—22no—
8C7×#494C2212yes—
9C7×#492C412yes—
10C7×#413—22no—
11C4×C7×M16C411yescharacteristic
12C7×#356C2214yes—
13C7×#355—22no—
14#13592C711yesmaximal, characteristic, direct product factor, Sylow
15C2×C7×#41D412yes—
16C22×C7×Q8—21no—
17C7×#137—44no—
18C7×#137—44no—
19C2×C7×Q16—24no—
20C2×C7×SD16—24no—
21C2×C7×M16—21no—
22C2×C7×M16—42no—
23C7×C4⋊Q8—21no—
24C7×C4⋊Q8—41no—
25C7×C4⋊Q8C2×C412yes—
26C7×C4⋊Q8C2311yescharacteristic
27C7×#127C2×C411yescharacteristic
28C7×#124D412yes—
29C7×#121—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4—41no—
32C2×C42×C7C2×C411yescharacteristic
33C7×#101—24no—
34C7×#100—42no—
35C7×#97—21no—
36C4×C7×C8C2×C412yes—
37#3152C2×C711yescharacteristic
38#2132C2×C712yes—
39#1411C2×C714yescomplemented
40C7×#41—42no—
41C7×#41—42no—
42C2×C7×Q8—22no—
43C2×C7×Q8—42no—
44C2×C7×Q8—42no—
45C2×C7×Q8—41no—
46C2×C7×Q8C2×D412yes—
47C2×C7×D4—22no—
48C2×C7×D4—41no—
49C2×C7×D4C22⋊C412yes—
50C22×C4×C7—21no—
51C22×C4×C7—22no—
52C22×C4×C7—41no—
53C22×C4×C7C22⋊C411yescharacteristic
54C7×Q16—48no—
55C7×SD16—48no—
56C7×M16—24no—
57C7×M16—44no—
58C7×M16—82no—
59C2×C7×C8—22no—
60C2×C7×C8—82no—
61C7×C4⋊C4—41no—
62C7×C4⋊C4—42no—
63C7×C4⋊C4—42no—
64C7×C22⋊C4—42no—
65C42×C7—21no—
66C42×C7C22⋊C411yescharacteristic
67C42×C7C22×C411yescharacteristic
68C2×#137—22no—
69#532C22×C711yescharacteristic
70C2×C4⋊Q8C4×C711yescharacteristic
71#497—22no—
72#494C22×C712yes—
73#492C4×C712yes—
74#413—22no—
75C4×M16C4×C711yescharacteristic
76#356C22×C714yes—
77#355—22no—
78C23×C7—22no—
79C23×C7#9911yescharacteristic
80C7×Q8—42no—
81C7×Q8—44no—
82C7×Q8—82no—
83C7×D4—42no—
84C7×D4—82no—
85C7×D4—82no—
86C2×C4×C7—21no—
87C2×C4×C7—22no—
88C2×C4×C7—21no—
89C2×C4×C7—22no—
90C2×C4×C7—42no—
91C2×C4×C7—42no—
92C2×C4×C7—42no—
93C2×C4×C7—42no—
94C2×C4×C7—81no—
95C2×C4×C7—81no—
96C2×C4×C7#9911yescharacteristic
97C2×C4×C7C2×C22⋊C411yescharacteristic
98C7×C8—24no—
99C7×C8—84no—
100C2×#41C7×D412yes—
101C22×Q8—21no—
102#137—44no—
103#137—44no—
104C2×Q16—24no—
105C2×SD16—24no—
106C2×M16—21no—
107C2×M16—42no—
108C4⋊Q8—21no—
109C4⋊Q8—41no—
110C4⋊Q8C2×C4×C712yes—
111C4⋊Q8C23×C711yescharacteristic
112#127C2×C4×C711yescharacteristic
113#124C7×D412yes—
114#121—41no—
115C4×D4—41no—
116C2×C4⋊C4—41no—
117C2×C42C2×C4×C711yescharacteristic
118#101—24no—
119#100—42no—
120#97—21no—
121C4×C8C2×C4×C712yes—
122C22×C7—21no—
123C22×C7—41no—
124C22×C7—42no—
125C22×C7—82no—
126C22×C7C2×#9911yescharacteristic
127C4×C7—22no—
128C4×C7—21no—
129C4×C7—41no—
130C4×C7—42no—
131C4×C7—82no—
132C4×C7#35312yes—
133#41—42no—
134#41—42no—
135C2×Q8—22no—
136C2×Q8—42no—
137C2×Q8—42no—
138C2×Q8—41no—
139C2×Q8C2×C7×D412yes—
140C2×D4—22no—
141C2×D4—41no—
142C2×D4C7×C22⋊C412yes—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—41no—
146C22×C4C7×C22⋊C411yescharacteristic
147Q16—48no—
148SD16—48no—
149M16—24no—
150M16—44no—
151M16—82no—
152C2×C8—22no—
153C2×C8—82no—
154C4⋊C4—41no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C22⋊C4—42no—
158C42—21no—
159C42C7×C22⋊C411yescharacteristic
160C42C22×C4×C711yescharacteristic
161C2×C7—21no—
162C2×C7—41no—
163C2×C7—82no—
164C2×C7C2×#35311yescharacteristic
165C23—22no—
166C23C7×#9911yescharacteristic
167Q8—42no—
168Q8—44no—
169Q8—82no—
170D4—42no—
171D4—82no—
172D4—82no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4C7×#9911yescharacteristic
184C2×C4C2×C7×C22⋊C411yescharacteristic
185C8—24no—
186C8—84no—
187C7#1359211yescharacteristic, direct product factor, Sylow
188C22—21no—
189C22—41no—
190C22—42no—
191C22—82no—
192C22C2×C7×#9911yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—42no—
197C4—82no—
198C4C7×#35312yes—
199C2—21no—
200C2—41no—
201C2—82no—
202C2C2×C7×#35311yescharacteristic
subgroupG/H
center, socleC2×C7C2×#353
commutatorC42C22×C4×C7
Frattini, cosocleC4⋊Q8C23×C7
prime radicalC7×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C22×C4×C7 ◁ C7×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1411C2semidirect
14. #13592C7direct (N × H)
39. #1411C2×C7semidirect
187. C7#13592direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31522
C7×#21322
C7×#14112
#135927