Finite Group Databasebeta

← #34005289

Subgroups — #34005289

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×#17989433C212yesmaximal
2#22624774C214yesmaximal
3#22612533C211yesmaximal, characteristic
4C2×C22⋊#10596833C2214yes—
5#17989433—22no—
6#17989433—22no—
7C22×#11924007C2211yescharacteristic
8#17988474—22no—
9#17988468—22no—
10#17988448C412yes—
11#17988447C411yescharacteristic
12C22⋊C4×Dic73C2212yes—
13#380×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—24no—
16C22⋊#10596833—24no—
17C23×Dic73C2×C411yescharacteristic
18C23×Dic73C2311yescharacteristic
19C2×C4⋊Dic73—21no—
20C2×#11924007—24no—
21C2×#11924007D412yes—
22C2×#11924007D412yes—
23C2×C22⋊Dic73C2×C412yes—
24C2×C4×Dic73—22no—
25#14556498—24no—
26#14556498—22no—
27#14556498—21no—
28C23×C4×C73C2×C411yescharacteristic
29C2×C4⋊C4×C73—21no—
30C2×C22⋊C4×C73C2×C412yes—
31#95×C73—21no—
32C2×#10596833—44no—
33C2×#10596833—84no—
34C22×Dic73—22no—
35C22×Dic73—22no—
36C22×Dic73—22no—
37C22×Dic73—22no—
38C22×Dic73—81no—
39C22×Dic73C22⋊C412yes—
40C22×Dic73C2×D412yes—
41C22×Dic73#4114yes—
42C4⋊Dic73—81no—
43#11924007—24no—
44#11924007—24no—
45C22⋊Dic73—24no—
46C4×Dic73—82no—
47C24×C73C22×C411yescharacteristic
48C22×C4×C73—22no—
49C22×C4×C73—22no—
50C22×C4×C73—81no—
51C22×C4×C73C22⋊C411yescharacteristic
52C22×C4×C73C22⋊C411yescharacteristic
53C4⋊C4×C73—81no—
54C22⋊C4×C73—24no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73C2×C22⋊C411yescharacteristic
58C23×C73#11712yes—
59C23×C73#13112yes—
60C23×C73#13112yes—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×C4×C73—42no—
68C2×C4×C73—82no—
69C2×Dic73—22no—
70C2×Dic73—22no—
71C2×Dic73—22no—
72C2×Dic73—42no—
73C2×Dic73—44no—
74C2×Dic73—44no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73#12314yes—
79#10596833—84no—
80C22×C73—21no—
81C22×C73—22no—
82C22×C73—21no—
83C22×C73—22no—
84C22×C73—42no—
85C22×C73—42no—
86C22×C73#38111yescharacteristic
87C22×C73#40811yescharacteristic
88C22×C73#40811yescharacteristic
89C22×C73#43314yes—
90C4×C73—41no—
91C4×C73—41no—
92C4×C73—82no—
93Dic73—24no—
94Dic73—42no—
95Dic73—82no—
96#8737—731nomaximal, Sylow
97C2×C73—21no—
98C2×C73—21no—
99C2×C73—24no—
100C2×C73#181811yescharacteristic
101C2×C73#182811yescharacteristic
102C2×C73#183011yescharacteristic
103#2313—731no—
104C2×#324—732no—
105#1282—734no—
106C73#873711yescharacteristic, complemented, Sylow
107C22×C4⋊C4—731no—
108C2×C22⋊C8—734no—
109#387—1462no—
110#387—1462no—
111#381—732no—
112#380—731no—
113#380#6440811yescharacteristic
114C4×C22⋊C4—732no—
115#324—1462no—
116#324—1462no—
117C23×C4—731no—
118C23×C4—731no—
119C23×C4C2×#6440811yescharacteristic
120C22×C8—1464no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—1461no—
125C2×C4⋊C4—1464no—
126C2×C22⋊C4—732no—
127C2×C22⋊C4C2×#6440812yes—
128C2×C42—1462no—
129C22⋊C8—1464no—
130C22⋊C8—1464no—
131#95—21no—
132#95—1462no—
133#95—1464no—
134#95—1461no—
135C24C22×#6440811yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—81no—
139C22×C4—5841no—
140C22×C4—732no—
141C22×C4—734no—
142C22×C4—732no—
143C22×C4—1462no—
144C22×C4—1462no—
145C22×C4—1462no—
146C22×C4—1462no—
147C22×C4C22⋊#6440811yescharacteristic
148C22×C4C22⋊#6440811yescharacteristic
149C2×C8—2924no—
150C2×C8—5844no—
151C4⋊C4—81no—
152C4⋊C4—5841no—
153C4⋊C4—1464no—
154C4⋊C4—1464no—
155C22⋊C4—24no—
156C22⋊C4—1464no—
157C42—5842no—
158C23—41no—
159C23—41no—
160C23C2×C22⋊#6440811yescharacteristic
161C23#1455667012yes—
162C23#1455667812yes—
163C23#1455667912yes—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—2924no—
173C2×C4—2922no—
174C2×C4—2922no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2924no—
178C2×C4—734no—
179C2×C4—1462no—
180C2×C4—1462no—
181C2×C4—1462no—
182C8—5844no—
183C22—21no—
184C22—22no—
185C22—21no—
186C22—22no—
187C22—42no—
188C22—42no—
189C22#1798953011yescharacteristic
190C22#1798956111yescharacteristic
191C22#1798956211yescharacteristic
192C22#1798961214yes—
193C4—41no—
194C4—41no—
195C4—82no—
196C4—2922no—
197C4—5842no—
198C4—1464no—
199C2—21no—
200C2—21no—
201C2—24no—
202C2#2262582511yescharacteristic
203C2#2262584211yescharacteristic
204C2#2262584511yescharacteristic
subgroupG/H
centerC22#17989530
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
Fitting#380×C73C4
socleC22×C73#381
cosocleC23×Dic73C23
hypercenter#380#64408
hypocenterC73#8737
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
106. C73#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#179894332
#226247742
#226125332
#873773