Finite Group Databasebeta

← #2845×D71 #32204039

Subgroups — #2845×D71 #32204039

Order 18176.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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#22596615C213yesmaximal, complemented
2#22596614C2112yesmaximal, complemented
3#398×D71C2112yesmaximal
4#382×D71C213yesmaximal
5C71×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D71C2216yes—
7C2×C4⋊C4×D71C22112yes—
8C2×C42×D71C2211yescharacteristic
9#17985933C22112yes—
10#17985933C22112yes—
11#17985932C22112yes—
12#17985932C22112yes—
13#17985931C22112yes—
14#17985930C22112yes—
15#17985929C22112yes—
16#17985865C2213yes—
17#17985864C2216yes—
18#17985863C22112yes—
19#95×D71C22112yes—
20#95×D71C2214yes—
21#398×C71C22112yes—
22#382×C71C2213yes—
23C22×C4×D71C23112yes—
24C22×C4×D71C2313yes—
25C2×C4⋊Dic71C2316yes—
26C2×C4⋊Dic71C23112yes—
27C2×Dic71⋊C4C23112yes—
28C2×Dic71⋊C4C23112yes—
29C2×Dic71⋊C4C23112yes—
30C4⋊C4×D71—412no—
31C4⋊C4×D71—424no—
32C2×C4×Dic71C2313yes—
33C42×D71Q818yes—
34C71⋊#95C23112yes—
35C71⋊#95C23112yes—
36C71⋊#95C23112yes—
37C71⋊#95C23112yes—
38C2×C4⋊C4×C71C2316yes—
39C2×C4⋊C4×C71C23112yes—
40C2×C42×C71C2311yescharacteristic
41#95×C71C23112yes—
42#95×C71C2314yes—
43C23×D71C2411yescharacteristic
44C22×Dic71C24112yes—
45C22×Dic71C2413yes—
46C2×C4×D71—26no—
47C2×C4×D71—26no—
48C2×C4×D71—224no—
49C2×C4×D71—224no—
50C2×C4×D71—224no—
51C2×C4×D71C2×Q8112yes—
52C4⋊Dic71—412no—
53C4⋊Dic71—46no—
54Dic71⋊C4—412no—
55Dic71⋊C4—412no—
56Dic71⋊C4—412no—
57C4×Dic71C2×Q8112yes—
58C22×C4×C71C24112yes—
59C22×C4×C71C2413yes—
60C4⋊C4×C71—46no—
61C4⋊C4×C71—412no—
62C42×C71C2×Q814yes—
63C23×C71C2511yescharacteristic
64C22×D71C22×Q812yes—
65C22×D71H(5,𝔽2)16yes—
66C22×D712−1+416yes—
67C2×C4×C71—23no—
68C2×C4×C71—23no—
69C2×C4×C71—212no—
70C2×C4×C71—212no—
71C2×C4×C71—212no—
72C2×C4×C71C22×Q816yes—
73C2×Dic71—23no—
74C2×Dic71—23no—
75C2×Dic71—212no—
76C2×Dic71—212no—
77C2×Dic71—212no—
78C2×Dic71C22×Q816yes—
79C4×D71—224no—
80C4×D71—448no—
81C22×C71C23×Q811yescharacteristic
82C22×C71C2×H(5,𝔽2)13yes—
83C22×C71C2×2−1+413yes—
84C2×D71#544112yes—
85C2×D71#562112yes—
86C2×D71#56414yes—
87C4×C71—26no—
88C4×C71—412no—
89Dic71—26no—
90Dic71—412no—
91C2×#2845—711nomaximal, Sylow
92C2×C71C2×#54413yes—
93C2×C71C2×#56213yes—
94C2×C71C2×#56411yescharacteristic
95D71#284518yesdirect product factor
96#2845—7112no—
97#2845—713no—
98#2845D7111yescharacteristic, direct product factor
99C2×#398—7112no—
100C2×#382—713no—
101C71C2×#284511yescharacteristic, complemented, Sylow
102C22×C4⋊C4—7112no—
103C22×C4⋊C4—716no—
104C22×C42—711no—
105#398—7112no—
106#398—7112no—
107#398—7112no—
108#398—7112no—
109#398—7112no—
110#398—7112no—
111#398—7112no—
112#398C2×D71112yes—
113#382—716no—
114#382—713no—
115#382—7112no—
116#382C2×D7113yes—
117C2×#95—714no—
118C2×#95—7112no—
119C23×C4—713no—
120C23×C4—7112no—
121C2×C4⋊C4—28424no—
122C2×C4⋊C4—28412no—
123C2×C4⋊C4—7112no—
124C2×C4⋊C4—716no—
125C2×C4⋊C4—7112no—
126C2×C4⋊C4—7112no—
127C2×C4⋊C4—7112no—
128C2×C4⋊C4C22×D7116yes—
129C2×C4⋊C4C22×D71112yes—
130C2×C42—713no—
131C2×C42—718no—
132C2×C42C22×D7111yescharacteristic
133#95—7112no—
134#95—7112no—
135#95—7112no—
136#95—7112no—
137#95C22×D71112yes—
138#95C22×D7114yes—
139C24—711no—
140C22×C4—713no—
141C22×C4—7112no—
142C22×C4—7112no—
143C22×C4—14224no—
144C22×C4—14224no—
145C22×C4—14224no—
146C22×C4—1426no—
147C22×C4—1426no—
148C22×C4C23×D71112yes—
149C22×C4C23×D7113yes—
150C4⋊C4—46no—
151C4⋊C4—412no—
152C4⋊C4—28412no—
153C4⋊C4—28412no—
154C4⋊C4—28412no—
155C4⋊C4—2846no—
156C4⋊C4—28412no—
157C42—7112no—
158C42Q8×D7114yes—
159C23—712no—
160C23—716no—
161C23—716no—
162C23C24×D7111yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—28448no—
169C2×C4—716no—
170C2×C4—14224no—
171C2×C4—14212no—
172C2×C4—14212no—
173C2×C4—14212no—
174C2×C4—1423no—
175C2×C4—1423no—
176C2×C4C2×Q8×D7116yes—
177C22—7112no—
178C22—7112no—
179C22—714no—
180C22C22×Q8×D7111yescharacteristic
181C22H(5,𝔽2)×D7113yes—
182C222−1+4×D7113yes—
183C4—26no—
184C4—412no—
185C4—28412no—
186C4—1426no—
187C2—718no—
188C2#544×D7113yes—
189C2#562×D7113yes—
190C2#564×D7111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2845C2
prime radicalC23×D71C24
hypercenter#2845D71
hypocenterC71C2×#2845
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #22596615C2semidirect
2. #22596614C2semidirect
5. C71×#2845C2semidirect
95. D71#2845direct (N × H)
98. #2845D71direct (N × H)
101. C71C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#225966152
#225966142
#398×D712
#382×D712
C71×#28452
C2×#284571