Finite Group Databasebeta

← #13053945

Subgroups — #13053945

Order 1344.

436 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C22×C3×C4×D7C211yesmaximal, characteristic
2C2×(C2×D7)⋊Dic3C212yesmaximal
3#10620670C211yesmaximal, characteristic, complemented
4C7×C3⋊#95C211yesmaximal, characteristic, complemented
5#10620529C212yesmaximal, complemented
6#89436—31nomaximal, Hall
7C23×C3×D7C2211yescharacteristic
8C22×C3×C4×C7C2211yescharacteristic
9C22×Dic21C2212yes—
10C22×C7×Dic3C2212yes—
11C22×C3×Dic7C2211yescharacteristic
12C2×C3×C4×D7—24no—
13C2×C3×C4×D7C414yescomplemented
14(C2×D7)⋊Dic3—24no—
15C22×C4×D7D311yescharacteristic
16C2×(C2×D7)⋊C4—32no—
17C7×#95—31no—
18C7⋊#95—31no—
19C7⋊#95—32no—
20#5211—71nomaximal, Hall
21C23×C3×C7C2311yescharacteristic
22C22×C3×D7—22no—
23C22×C3×D7—21no—
24C22×C3×D7—21no—
25C22×C3×D7C2×C412yes—
26C22×C3×D7D414yes—
27C2×C3×C4×C7—22no—
28C2×C3×C4×C7C2×C412yes—
29C2×Dic21—22no—
30C2×Dic21—22no—
31C2×Dic21—22no—
32C2×C7×Dic3—22no—
33C2×C7×Dic3—22no—
34C2×C7×Dic3—22no—
35C2×C3×Dic7—22no—
36C2×C3×Dic7C2×C412yes—
37C3×C4×D7—28no—
38C23×D7C2×D311yescharacteristic
39C22×C4×C7—32no—
40C22×C4×C7C2×D311yescharacteristic
41C22×Dic7—32no—
42C22×Dic7C2×D311yescharacteristic
43C2×C4×D7—24no—
44C2×C4×D7Dic314yescomplemented
45(C2×D7)⋊C4—64no—
46C23×C3×C4—71no—
47C2×#217—72no—
48C3⋊#95—71no—
49C3⋊#95—72no—
50C3⋊#95D711yescharacteristic, complemented
51C22×C3×C7C22×C411yescharacteristic
52C22×C3×C7C2×D412yes—
53C22×C3×C7#4112yes—
54C22×C3×C7#4111yescharacteristic
55C22×C3×C7#4111yescharacteristic
56C2×C3×D7—22no—
57C2×C3×D7—22no—
58C2×C3×D7—24no—
59C2×C3×D7—24no—
60C2×C3×D7C22⋊C414yes—
61C3×C4×C7—22no—
62Dic21—42no—
63C3×Dic7—22no—
64C7×Dic3—42no—
65#381—211noSylow
66C23×C7C22×D311yescharacteristic
67C22×D7—22no—
68C22×D7—21no—
69C22×D7—21no—
70C22×D7C2×Dic312yes—
71C22×D7#6714yes—
72C2×C4×C7—22no—
73C2×C4×C7—62no—
74C2×C4×C7—62no—
75C2×C4×C7—62no—
76C2×C4×C7C2×Dic312yes—
77C2×Dic7—22no—
78C2×Dic7—62no—
79C2×Dic7—62no—
80C2×Dic7—62no—
81C2×Dic7C2×Dic312yes—
82C4×D7—28no—
83C24×C3—71no—
84C22×C3×C4—71no—
85C22×C3×C4—74no—
86C22×C3×C4—144no—
87C22×C3×C4C2×D711yescharacteristic
88C22×Dic3—72no—
89C22×Dic3C2×D712yes—
90#217—144no—
91C2×C3×C7C2×C22⋊C411yescharacteristic
92C2×C3×C7#11711yescharacteristic
93C2×C3×C7#11711yescharacteristic
94C2×C3×C7#12312yes—
95C2×C3×C7#12312yes—
96C3×D7—24no—
97C23×C4—71no—
98C2×C22⋊C4—212no—
99#95—31no—
100#95—212no—
101#95—211no—
102C22×C7#23512yes—
103C22×C7#23511yescharacteristic
104C22×C7#23511yescharacteristic
105C22×C7C22×Dic311yescharacteristic
106C22×C7C2×#6712yes—
107C2×D7—22no—
108C2×D7—22no—
109C2×D7—24no—
110C2×D7—24no—
111C2×D7#21714yes—
112C4×C7—22no—
113C4×C7—122no—
114Dic7—22no—
115Dic7—122no—
116C23×C3—72no—
117C23×C3—74no—
118C23×C3—142no—
119C23×C3—141no—
120C23×C3—141no—
121C23×C3C22×D711yescharacteristic
122C2×C3×C4—22no—
123C2×C3×C4—72no—
124C2×C3×C4—148no—
125C2×C3×C4—142no—
126C2×C3×C4C4×D712yes—
127C2×Dic3—22no—
128C2×Dic3—22no—
129C2×Dic3—22no—
130C2×Dic3—142no—
131C2×Dic3—142no—
132C2×Dic3—142no—
133C3×C7#38111yescharacteristic, complemented, Hall
134C24—71no—
135C22×C4—32no—
136C22×C4—71no—
137C22×C4—74no—
138C22×C4—144no—
139C22×C4—212no—
140C22×C4D3×D711yescharacteristic
141C22⋊C4—424no—
142C2×C7#92611yescharacteristic
143C2×C7#92611yescharacteristic
144C2×C7#92912yes—
145C2×C7#92912yes—
146C2×C7C2×#21711yescharacteristic
147D7—24no—
148C22×C3—74no—
149C22×C3—142no—
150C22×C3—144no—
151C22×C3—142no—
152C22×C3—144no—
153C22×C3C2×C4×D711yescharacteristic
154C22×C3#115712yes—
155C22×C3D4×D712yes—
156C22×C3#115911yescharacteristic
157C22×C3#116111yescharacteristic
158C3×C4—22no—
159C3×C4—142no—
160Dic3—42no—
161Dic3—282no—
162C23—72no—
163C23—74no—
164C23—142no—
165C23—141no—
166C23—141no—
167C23C2×D3×D711yescharacteristic
168C2×C4—22no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—72no—
173C2×C4—148no—
174C2×C4—142no—
175C2×C4—422no—
176C2×C4—422no—
177C2×C4—422no—
178C2×C4Dic3×D712yes—
179C7#521111yescharacteristic, complemented, Sylow
180C2×C3—144no—
181C2×C3#643511yescharacteristic
182C2×C3D7×C22⋊C411yescharacteristic
183C2×C3#644612yes—
184C2×C3#645511yescharacteristic
185C2×C3#645712yes—
186C22—74no—
187C22—144no—
188C22—144no—
189C22—142no—
190C22—142no—
191C22#6667512yes—
192C22#6667611yescharacteristic
193C22#6667711yescharacteristic
194C22C2×Dic3×D711yescharacteristic
195C22D7×#6712yes—
196C4—22no—
197C4—122no—
198C4—142no—
199C4—842no—
200C3#8943611yescharacteristic, complemented, Sylow
201C2—144no—
202C2#1062091012yes—
203C2#1062091911yescharacteristic
204C2#1062092011yescharacteristic
205C2#1062100912yes—
206C2D7×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×D7
commutatorC22×C3×C7C22×C4
FittingC22×C3×C4×C7C22
socle, cosocleC23×C3×C7C23
prime radicalC23×C3×D7C22
hypercenterC22×C4D3×D7
hypocenterC3×C7#381
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10620670C2semidirect
4. C7×C3⋊#95C2semidirect
5. #10620529C2semidirect
13. C2×C3×C4×D7C4semidirect
44. C2×C4×D7Dic3semidirect
50. C3⋊#95D7semidirect
133. C3×C7#381semidirect
179. C7#5211semidirect
200. C3#89436semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D72
C2×(C2×D7)⋊Dic32
#106206702
C7×C3⋊#952
#106205292
#894363
#52117