Finite Group Databasebeta

← #34001453

Subgroups — #34001453

Order 18688.

408 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 118 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#22625846C212yesmaximal
2#22624749C214yesmaximal
3#125×Dic73C211yesmaximal, characteristic
4C2×C4⋊#10596833—22no—
5#17989453—22no—
6#17989453C2214yes—
7#17988486C2212yes—
8#17988473—22no—
9#17988453C411yescharacteristic
10C4⋊C4×Dic73—22no—
11C4⋊C4×Dic73C412yes—
12C42×Dic73C2211yescharacteristic
13C2×#125×C73C411yescharacteristic
14C22×#10596833—24no—
15C4⋊#10596833—44no—
16C2×C4⋊Dic73—22no—
17C2×C4⋊Dic73C2×C412yes—
18C2×C4×Dic73—22no—
19C2×C4×Dic73C2×C411yescharacteristic
20C2×C4×Dic73D412yes—
21C2×C4×Dic73D412yes—
22C2×C4×Dic73C2311yescharacteristic
23#14556498—22no—
24#14556498—22no—
25#14556498—22no—
26#125×C73—22no—
27#125×C73C814yescomplemented
28C2×C4⋊C4×C73—22no—
29C2×C4⋊C4×C73C2×C412yes—
30C2×C42×C73C2×C411yescharacteristic
31C2×#10596833—44no—
32C2×#10596833—44no—
33C2×#10596833—44no—
34C22×Dic73—22no—
35C22×Dic73C22⋊C411yescharacteristic
36C22×Dic73C22⋊C411yescharacteristic
37C22×Dic73C2×D412yes—
38C4⋊Dic73—42no—
39C4⋊Dic73—42no—
40C4⋊Dic73—42no—
41C4×Dic73—22no—
42C4×Dic73—22no—
43C4×Dic73—22no—
44C4×Dic73—42no—
45C4×Dic73—41no—
46C4×Dic73—44no—
47C22×C4×C73—22no—
48C22×C4×C73C22⋊C412yes—
49C22×C4×C73C22×C411yescharacteristic
50C4⋊C4×C73—28no—
51C4⋊C4×C73—22no—
52C4⋊C4×C73C2×C814yes—
53C42×C73C2×C812yes—
54C42×C73M1612yes—
55C23×C73C2×C22⋊C411yescharacteristic
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—24no—
61C2×C4×C73—42no—
62C2×C4×C73—42no—
63C2×C4×C73C22⋊C814yes—
64C2×C4×C73C22×C811yescharacteristic
65C2×C4×C73C2×M1611yescharacteristic
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—22no—
69C2×Dic73—21no—
70C2×Dic73—22no—
71C2×Dic73—42no—
72C2×Dic73—42no—
73C2×Dic73—42no—
74C2×Dic73#10112yes—
75C2×Dic73AGL(1,ℤ/8)12yes—
76C2×Dic73#13712yes—
77#10596833—84no—
78C22×C73C2×C22⋊C811yescharacteristic
79C22×C73#41011yescharacteristic
80C22×C73C2×#10111yescharacteristic
81C22×C73#41712yes—
82C22×C73#42112yes—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—24no—
86C4×C73—44no—
87Dic73—22no—
88Dic73—22no—
89Dic73—22no—
90Dic73—41no—
91Dic73—82no—
92#7602—731nomaximal, Sylow
93C2×C73#146111yescharacteristic
94C2×C73#147712yes—
95C2×C73#151212yes—
96C2×C73#153411yescharacteristic
97C2×C73#156111yescharacteristic
98C4×#125—731no—
99#1831—732no—
100#1271—734no—
101C73#760211yescharacteristic, complemented, Sylow
102C2×#125#6440811yescharacteristic
103C2×C4⋊C8—1462no—
104#389—732no—
105#387—1462no—
106#382—731no—
107C4×C4⋊C4—732no—
108C4×C4⋊C4—1462no—
109C43—731no—
110#336—734no—
111#336—1462no—
112C22×C8—1464no—
113#125—22no—
114#125#1059683314yescomplemented
115C2×C4⋊C4—22no—
116C2×C4⋊C4—732no—
117C2×C4⋊C4—1462no—
118C2×C4⋊C4C2×#6440812yes—
119C2×C42—732no—
120C2×C42—731no—
121C2×C42—732no—
122C2×C42—731no—
123C2×C42—1462no—
124C2×C42C2×#6440811yescharacteristic
125C4⋊C8—2924no—
126#95—1462no—
127#95—1462no—
128#95—1462no—
129C22×C4—22no—
130C22×C4—731no—
131C22×C4—732no—
132C22×C4—731no—
133C22×C4—1462no—
134C22×C4C22⋊#6440812yes—
135C22×C4C22×#6440811yescharacteristic
136C2×C8—2924no—
137C2×C8—2924no—
138C2×C8—2924no—
139C4⋊C4—22no—
140C4⋊C4—28no—
141C4⋊C4—2922no—
142C4⋊C4—2922no—
143C4⋊C4—2922no—
144C4⋊C4C2×#1059683314yes—
145C42—2921no—
146C42—2922no—
147C42—2924no—
148C42—1462no—
149C42—1462no—
150C42—1462no—
151C42C2×#1059683312yes—
152C42#1192403712yes—
153C23C2×C22⋊#6440811yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—2922no—
162C2×C4—2922no—
163C2×C4—2922no—
164C2×C4—732no—
165C2×C4—732no—
166C2×C4—732no—
167C2×C4—1461no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4—1462no—
172C2×C4C22⋊#1059683314yes—
173C2×C4C22×#1059683311yescharacteristic
174C2×C4C2×#1192403711yescharacteristic
175C8—5844no—
176C22C2×C22⋊#1059683311yescharacteristic
177C22#1798956811yescharacteristic
178C22D73⋊#10111yescharacteristic
179C22#1798957812yes—
180C22#1798958412yes—
181C4—21no—
182C4—21no—
183C4—24no—
184C4—44no—
185C4—2921no—
186C4—5842no—
187C4—1462no—
188C4—1462no—
189C4—1462no—
190C2#2262517411yescharacteristic
191C2#2262522612yes—
192C2#2262534512yes—
193C2#2262541411yescharacteristic
194C2#2262547111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×#125×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×#125#64408
hypocenterC73#7602
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
27. #125×C73C8semidirect
101. C73#7602semidirect
114. #125#10596833semidirect

Maximal subgroups

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

subgroupindex
#226258462
#226247492
#125×Dic732
#760273