Finite Group Databasebeta

← #13247277

Subgroups — #13247277

Order 1792.

418 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11739674C211yesmaximal, characteristic
2C7×#1820C211yesmaximal, characteristic
3#11729343C211yesmaximal, characteristic
4#11725434C214yesmaximal
5C2×C7×#117C2211yescharacteristic
6C7×#381C2212yes—
7C4×C22⋊Dic7C2212yes—
8#89979C2212yes—
9#89753—22no—
10#89723—22no—
11C4×C4⋊Dic7C412yescomplemented
12#89704C411yescharacteristic, complemented
13C42×Dic7C411yescharacteristic, complemented
14C7×#342—22no—
15#89325—22no—
16#8741—71nomaximal, Sylow
17C23×C4×C7C2311yescharacteristic
18C7×#117—24no—
19C2×C7×C4⋊C4D412yes—
20C2×C7×C22⋊C4—22no—
21C2×C7×C22⋊C4D412yes—
22C2×C42×C7C2×C411yescharacteristic
23C2×C42×C7C2×C411yescharacteristic
24C2×C22⋊Dic7—22no—
25C2×C4⋊Dic7—22no—
26C2×C4×Dic7—22no—
27C2×C4×Dic7C2×C412yes—
28C2×C4×Dic7C2×C412yes—
29C2×#1136—22no—
30C7×#95—24no—
31C7⋊#95—22no—
32C7⋊#95—22no—
33C7⋊#95—22no—
34C22⋊(C7⋊C8)—24no—
35#2298—71no—
36#1822—71no—
37#1820D711yescharacteristic
38#1284—74no—
39C24×C7C2×D411yescharacteristic
40C22×C4×C7—42no—
41C22×C4×C7—42no—
42C22×C4×C7C22⋊C412yes—
43C22×C4×C7C22⋊C412yes—
44C22×C4×C7C22×C411yescharacteristic
45C22×C4×C7C2×D411yescharacteristic
46C22×C4×C7#4114yes—
47C22×Dic7—22no—
48C22×Dic7—22no—
49C7×C4⋊C4—24no—
50C7×C22⋊C4—24no—
51C7×C22⋊C4—44no—
52C42×C7—22no—
53C42×C7—22no—
54C22⋊Dic7—44no—
55C4⋊Dic7—44no—
56C4×Dic7—44no—
57C4×Dic7—42no—
58C4×Dic7—42no—
59#1136—44no—
60C2×C7⋊C8—42no—
61C2×#117C2×D711yescharacteristic
62#407—72no—
63#388—142no—
64#387—142no—
65#381C2×D712yes—
66C4×C4⋊C4—72no—
67C4×C22⋊C4—72no—
68#376—71no—
69C43—71no—
70#343—142no—
71#342—22no—
72C23×C7—22no—
73C23×C7—42no—
74C23×C7C2×C22⋊C411yescharacteristic
75C23×C7#12312yes—
76C2×C4×C7—22no—
77C2×C4×C7—22no—
78C2×C4×C7—22no—
79C2×C4×C7—22no—
80C2×C4×C7—44no—
81C2×C4×C7—42no—
82C2×C4×C7—42no—
83C2×C4×C7—82no—
84C2×C4×C7—84no—
85C2×C4×C7#11712yes—
86C2×C4×C7#12312yes—
87C2×Dic7—24no—
88C2×Dic7—42no—
89C2×Dic7—42no—
90C2×Dic7—42no—
91C2×Dic7—42no—
92C2×Dic7—42no—
93C7⋊C8—82no—
94C23×C4C22×D711yescharacteristic
95C2×M16—142no—
96#117—24no—
97C2×C4⋊C4—142no—
98C2×C4⋊C4D2812yes—
99C2×C22⋊C4—22no—
100C2×C22⋊C4—142no—
101C2×C22⋊C4C22⋊D712yes—
102C2×C42—72no—
103C2×C42—72no—
104C2×C42—142no—
105C2×C42C4×D711yescharacteristic
106C2×C42C4×D711yescharacteristic
107C22⋊C8—144no—
108#95—24no—
109#95—142no—
110#95—142no—
111#95—142no—
112C22×C7—22no—
113C22×C7—22no—
114C22×C7—24no—
115C22×C7—82no—
116C22×C7#38111yescharacteristic
117C22×C7#41012yes—
118C4×C7—22no—
119C4×C7—22no—
120C4×C7—42no—
121C4×C7—42no—
122C4×C7—162no—
123Dic7—44no—
124Dic7—82no—
125C24C2×C22⋊D711yescharacteristic
126C22×C4—42no—
127C22×C4—42no—
128C22×C4—142no—
129C22×C4—142no—
130C22×C4(C2×D7)⋊C412yes—
131C22×C4(C2×D7)⋊C412yes—
132C22×C4C2×C4×D711yescharacteristic
133C22×C4C2×D2811yescharacteristic
134C22×C4#115914yes—
135M16—284no—
136C2×C8—282no—
137C4⋊C4—24no—
138C4⋊C4—284no—
139C22⋊C4—24no—
140C22⋊C4—44no—
141C22⋊C4—284no—
142C42—22no—
143C42—22no—
144C42—282no—
145C42—282no—
146C42—284no—
147C2×C7—22no—
148C2×C7—42no—
149C2×C7#182011yescharacteristic
150C2×C7#182712yes—
151C23—22no—
152C23—42no—
153C23C2×(C2×D7)⋊C411yescharacteristic
154C23#649812yes—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—44no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—82no—
163C2×C4—84no—
164C2×C4—144no—
165C2×C4—282no—
166C2×C4—282no—
167C2×C4—282no—
168C2×C4—282no—
169C2×C4—282no—
170C2×C4#644012yes—
171C2×C4#644912yes—
172C8—562no—
173C7#874111yescharacteristic, complemented, Sylow
174C22—22no—
175C22—24no—
176C22—22no—
177C22—82no—
178C22#8971511yescharacteristic
179C22#8977812yes—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—162no—
185C4—284no—
186C4—562no—
187C2—22no—
188C2—42no—
189C2#1172728811yescharacteristic
190C2#1172779312yes—
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1820C2
socleC22×C7#381
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1820D7
hypocenterC7#8741
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
11. C4×C4⋊Dic7C4semidirect
12. #89704C4semidirect
13. C42×Dic7C4semidirect
173. C7#8741semidirect

Maximal subgroups

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

subgroupindex
#117396742
C7×#18202
#117293432
#117254342
#87417