Finite Group Databasebeta

← #13056303

Subgroups — #13056303

Order 1344.

268 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×C4⋊Dic21C211yesmaximal, characteristic
2C2×#66629C211yesmaximal, characteristic
3C3×C7×#95C211yesmaximal, characteristic
4#10620670C212yesmaximal
5#10620670C212yesmaximal
6#89431—31nomaximal, Hall
7C22×C3×C4×C7C2212yes—
8C22×C3×C4×C7C2211yescharacteristic
9C22×Dic21C2211yescharacteristic
10C22×Dic21C2212yes—
11C22×Dic21C2211yescharacteristic
12C4⋊Dic21—22no—
13#66629—22no—
14C2×C4⋊Dic7—31no—
15C2×Dic7⋊C4—31no—
16C7×#95D311yescharacteristic
17C7⋊#95—32no—
18C7⋊#95—32no—
19#4659—71nomaximal, Hall
20C23×C3×C7C2311yescharacteristic
21C2×C3×C4×C7—22no—
22C2×C3×C4×C7—22no—
23C2×C3×C4×C7—22no—
24C2×C3×C4×C7—22no—
25C2×C3×C4×C7D412yes—
26C2×Dic21—21no—
27C2×Dic21—21no—
28C2×Dic21—21no—
29C2×Dic21—22no—
30C2×Dic21—24no—
31C2×Dic21—22no—
32C2×Dic21Q812yes—
33C22×C4×C7C2×D312yes—
34C22×C4×C7C2×D311yescharacteristic
35C22×Dic7—31no—
36C22×Dic7—31no—
37C22×Dic7—32no—
38C4⋊Dic7—62no—
39Dic7⋊C4—62no—
40C2×C4⋊Dic3—71no—
41C2×Dic3⋊C4—71no—
42C3×#95D711yescharacteristic
43C3⋊#95—72no—
44C3⋊#95—72no—
45C22×C3×C7C2×D411yescharacteristic
46C22×C3×C7C2×Q811yescharacteristic
47C22×C3×C7#4112yes—
48C22×C3×C7#4111yescharacteristic
49C22×C3×C7#4112yes—
50C3×C4×C7—22no—
51C3×C4×C7—42no—
52Dic21—22no—
53Dic21—41no—
54Dic21—42no—
55#400—211noSylow
56C23×C7C22×D311yescharacteristic
57C2×C4×C7—22no—
58C2×C4×C7—22no—
59C2×C4×C7—22no—
60C2×C4×C7—22no—
61C2×C4×C7D1212yes—
62C2×Dic7—32no—
63C2×Dic7—61no—
64C2×Dic7—61no—
65C2×Dic7—61no—
66C2×Dic7—62no—
67C2×Dic7—64no—
68C2×Dic7—62no—
69C22×C3×C4C2×D712yes—
70C22×C3×C4C2×D711yescharacteristic
71C22×Dic3—71no—
72C22×Dic3—71no—
73C22×Dic3—72no—
74C4⋊Dic3—142no—
75Dic3⋊C4—142no—
76C2×C3×C7C22⋊Q811yescharacteristic
77C2×C3×C7#12311yescharacteristic
78C2×C3×C7#12411yescharacteristic
79C2×C3×C7#12512yes—
80C2×C3×C7#12612yes—
81C2×C4⋊C4—211no—
82C2×C4⋊C4—211no—
83#95—212no—
84#95—212no—
85#95D2111yescharacteristic
86C22×C7C2×D1211yescharacteristic
87C22×C7#23512yes—
88C22×C7#23711yescharacteristic
89C22×C7#23712yes—
90C22×C7D3×Q811yescharacteristic
91C4×C7—22no—
92C4×C7—42no—
93Dic7—62no—
94Dic7—122no—
95Dic7—121no—
96C23×C3C22×D711yescharacteristic
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—22no—
101C2×C3×C4D2812yes—
102C2×Dic3—72no—
103C2×Dic3—141no—
104C2×Dic3—141no—
105C2×Dic3—141no—
106C2×Dic3—142no—
107C2×Dic3—144no—
108C2×Dic3—142no—
109C3×C7#40011yescharacteristic, complemented, Hall
110C22×C4—211no—
111C22×C4—212no—
112C22×C4—211no—
113C22×C4C2×D2112yes—
114C22×C4C2×D2111yescharacteristic
115C4⋊C4—422no—
116C4⋊C4—422no—
117C2×C7#87511yescharacteristic
118C2×C7#87912yes—
119C2×C7#88611yescharacteristic
120C2×C7#88912yes—
121C2×C7#89711yescharacteristic
122C22×C3C2×D2811yescharacteristic
123C22×C3#115712yes—
124C22×C3#115911yescharacteristic
125C22×C3#115912yes—
126C22×C3Q8×D711yescharacteristic
127C3×C4—22no—
128C3×C4—42no—
129Dic3—142no—
130Dic3—282no—
131Dic3—281no—
132C23C22×D2111yescharacteristic
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—212no—
138C2×C4—421no—
139C2×C4—421no—
140C2×C4—422no—
141C2×C4—421no—
142C2×C4—424no—
143C2×C4—422no—
144C2×C4D8412yes—
145C7#465911yescharacteristic, complemented, Sylow
146C2×C3#643811yescharacteristic
147C2×C3#644212yes—
148C2×C3#644911yescharacteristic
149C2×C3#645212yes—
150C2×C3#646011yescharacteristic
151C22C2×D8411yescharacteristic
152C22#6672812yes—
153C22#6673011yescharacteristic
154C22#6673012yes—
155C22Q8×D2111yescharacteristic
156C4—22no—
157C4—42no—
158C4—422no—
159C4—842no—
160C4—841no—
161C3#8943111yescharacteristic, complemented, Sylow
162C2#1062135811yescharacteristic
163C2#1062136212yes—
164C2#1062136911yescharacteristic
165C2#1062137212yes—
166C2#1062138011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D21
commutator, socle, prime radical, cosocleC23×C3×C7C23
FittingC3×C7×#95C2
hypercenter#95D21
hypocenterC3×C7#400
LCSG ▷ C23×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
109. C3×C7#400semidirect
145. C7#4659semidirect
161. C3#89431semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Dic212
C2×#666292
C3×C7×#952
#106206702
#894313
#46597