Finite Group Databasebeta

← #34005287

Subgroups — #34005287

Order 18688.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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×#17989432C212yesmaximal
2#22624774C214yesmaximal
3#22612532C211yesmaximal, characteristic
4C2×C22⋊#10596833C2214yes—
5#17989432—22no—
6#17989432—22no—
7C22×C4⋊Dic73C2211yescharacteristic
8#17988472—22no—
9#17988470—22no—
10#17988450C411yescharacteristic
11#17988445C412yes—
12C22⋊C4×Dic73C2212yes—
13#381×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—24no—
16C22⋊#10596833—24no—
17C23×Dic73C2×C411yescharacteristic
18C23×Dic73C2311yescharacteristic
19C2×C4⋊Dic73—24no—
20C2×C4⋊Dic73D412yes—
21C2×C4⋊Dic73D412yes—
22C2×#11924007—22no—
23C2×C22⋊Dic73C2×C412yes—
24C2×C4×Dic73—22no—
25#14556498—22no—
26#14556498—22no—
27#14556498—21no—
28#14556498—21no—
29C23×C4×C73C2×C411yescharacteristic
30C2×C22⋊C4×C73C2×C412yes—
31#95×C73—21no—
32#95×C73—21no—
33C2×#10596833—44no—
34C2×#10596833—84no—
35C22×Dic73—22no—
36C22×Dic73—22no—
37C22×Dic73—81no—
38C22×Dic73—81no—
39C22×Dic73C22⋊C412yes—
40C22×Dic73C2×D412yes—
41C22×Dic73#4114yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—24no—
44#11924007—82no—
45C22⋊Dic73—24no—
46C4×Dic73—82no—
47C24×C73C22×C411yescharacteristic
48C22×C4×C73—22no—
49C22×C4×C73—24no—
50C22×C4×C73—22no—
51C22×C4×C73C22⋊C411yescharacteristic
52C22×C4×C73C22⋊C411yescharacteristic
53C22⋊C4×C73—24no—
54C23×C73—41no—
55C23×C73—41no—
56C23×C73C2×C22⋊C411yescharacteristic
57C23×C73#11712yes—
58C23×C73#13114yes—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—44no—
64C2×C4×C73—42no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×Dic73—22no—
68C2×Dic73—42no—
69C2×Dic73—44no—
70C2×Dic73—42no—
71C2×Dic73—42no—
72C2×Dic73—42no—
73C2×Dic73—42no—
74C2×Dic73—82no—
75C2×Dic73#12314yes—
76#10596833—84no—
77C22×C73—21no—
78C22×C73—22no—
79C22×C73—21no—
80C22×C73—22no—
81C22×C73—44no—
82C22×C73#38111yescharacteristic
83C22×C73#40812yes—
84C22×C73#43314yes—
85C4×C73—41no—
86C4×C73—41no—
87C4×C73—82no—
88Dic73—24no—
89Dic73—42no—
90Dic73—82no—
91#8737—731nomaximal, Sylow
92C2×C73—22no—
93C2×C73—24no—
94C2×C73#181811yescharacteristic
95C2×C73#182811yescharacteristic
96C2×C73#183011yescharacteristic
97#2313—731no—
98C2×#324—732no—
99#1282—734no—
100C73#873711yescharacteristic, complemented, Sylow
101C22×C4⋊C4—731no—
102C2×C22⋊C8—734no—
103#387—1462no—
104#387—1462no—
105#381—731no—
106#381#6440811yescharacteristic
107#380—732no—
108C4×C22⋊C4—732no—
109#324—1462no—
110#324—1462no—
111C23×C4—731no—
112C23×C4—731no—
113C23×C4C2×#6440811yescharacteristic
114C22×C8—1464no—
115C2×C4⋊C4—732no—
116C2×C4⋊C4—732no—
117C2×C4⋊C4—1462no—
118C2×C4⋊C4—1464no—
119C2×C22⋊C4—732no—
120C2×C22⋊C4C2×#6440812yes—
121C2×C42—1462no—
122C22⋊C8—1464no—
123C22⋊C8—1464no—
124#95—21no—
125#95—21no—
126#95—1462no—
127#95—1462no—
128#95—1461no—
129#95—1461no—
130C24C22×#6440811yescharacteristic
131C22×C4—24no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—5841no—
135C22×C4—5841no—
136C22×C4—732no—
137C22×C4—734no—
138C22×C4—732no—
139C22×C4—1462no—
140C22×C4—1462no—
141C22×C4C22⋊#6440811yescharacteristic
142C22×C4C22⋊#6440811yescharacteristic
143C2×C8—2924no—
144C2×C8—5844no—
145C4⋊C4—5842no—
146C4⋊C4—1464no—
147C4⋊C4—1464no—
148C22⋊C4—24no—
149C22⋊C4—1464no—
150C42—5842no—
151C23—41no—
152C23—41no—
153C23C2×C22⋊#6440811yescharacteristic
154C23#1455667012yes—
155C23#1455667814yes—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2922no—
165C2×C4—2922no—
166C2×C4—2922no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—2924no—
170C2×C4—5842no—
171C2×C4—734no—
172C2×C4—1462no—
173C8—5844no—
174C22—21no—
175C22—22no—
176C22—21no—
177C22—22no—
178C22—44no—
179C22#1798953011yescharacteristic
180C22#1798956012yes—
181C22#1798961114yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—2922no—
186C4—5842no—
187C4—1464no—
188C2—22no—
189C2—24no—
190C2#2262582411yescharacteristic
191C2#2262584311yescharacteristic
192C2#2262584511yescharacteristic
subgroupG/H
centerC22#17989530
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
Fitting#381×C73C4
socleC22×C73#381
cosocleC23×Dic73C23
hypercenter#381#64408
hypocenterC73#8737
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
100. C73#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#179894322
#226247742
#226125322
#873773