Finite Group Databasebeta

← #34001457

Subgroups — #34001457

Order 18688.

608 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 110 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#22625858C212yesmaximal, complemented
2#22624748C214yesmaximal, complemented
3#22612493C211yesmaximal, characteristic
4#17989453—22no—
5#17989453—22no—
6#17989453C2214yes—
7C2×#14556588C411yescharacteristic
8C2×#14556553—22no—
9C2×#14556553C412yes—
10#17988488—22no—
11#17988488C2212yes—
12C42×Dic73C2211yescharacteristic
13#384×C73C411yescharacteristic
14C22×#10596833—24no—
15C22×D292—22no—
16C22×D292C2×C412yes—
17C22×C4×D73—22no—
18#14556588—22no—
19#14556588C814yescomplemented
20#14556553—48no—
21#14556553—44no—
22C2×#11924005—22no—
23C2×#11924005—24no—
24C2×C4×Dic73C2×C411yescharacteristic
25C2×C4×Dic73D412yes—
26C2×C4×Dic73D412yes—
27C2×C4×Dic73C2311yescharacteristic
28C2×C4⋊C4×C73—22no—
29C2×C4⋊C4×C73C2×C412yes—
30C2×C42×C73C2×C411yescharacteristic
31C2×#10596833—44no—
32C2×#10596833—44no—
33C2×#10596833—44no—
34C23×D73—22no—
35C2×D292—28no—
36C2×D292—22no—
37C2×D292—42no—
38C2×D292—42no—
39C2×D292—44no—
40C2×D292—44no—
41C2×D292C2×C814yes—
42C22×Dic73C22⋊C411yescharacteristic
43C22×Dic73C22⋊C411yescharacteristic
44C22×Dic73C2×D412yes—
45C2×C4×D73—48no—
46C2×C4×D73—44no—
47#11924005—44no—
48#11924005—48no—
49C4×Dic73—22no—
50C4×Dic73—24no—
51C4×Dic73—42no—
52C4×Dic73—41no—
53C22×C4×C73—22no—
54C22×C4×C73C22⋊C412yes—
55C22×C4×C73C22×C411yescharacteristic
56C4⋊C4×C73—42no—
57C4⋊C4×C73—44no—
58C42×C73C2×C812yes—
59C42×C73M1612yes—
60C23×C73C2×C22⋊C411yescharacteristic
61C22×D73—24no—
62C22×D73—42no—
63C22×D73—42no—
64C22×D73—44no—
65C22×D73—44no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—42no—
71C2×C4×C73—44no—
72C2×C4×C73C22⋊C814yes—
73C2×C4×C73C22×C811yescharacteristic
74C2×C4×C73C2×M1611yescharacteristic
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—21no—
79C2×Dic73—22no—
80C2×Dic73#10012yes—
81C2×Dic73AGL(1,ℤ/8)14yes—
82D292—44no—
83D292—44no—
84D292—416no—
85C4×D73—88no—
86#10596833—84no—
87C22×C73C2×C22⋊C811yescharacteristic
88C22×C73#41011yescharacteristic
89C22×C73C2×#10011yescharacteristic
90C22×C73#41812yes—
91C22×C73#42112yes—
92C2×D73—44no—
93C2×D73—48no—
94C2×D73—82no—
95C2×D73—82no—
96C2×D73—84no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—24no—
100C4×C73—82no—
101Dic73—22no—
102Dic73—24no—
103Dic73—41no—
104#7603—731nomaximal, Sylow
105C2×C73#146011yescharacteristic
106C2×C73#147812yes—
107C2×C73#151412yes—
108C2×C73#153611yescharacteristic
109C2×C73#155511yescharacteristic
110D73—84no—
111C4×#127—731no—
112#1839—732no—
113#1270—734no—
114C73#760311yescharacteristic, complemented, Sylow
115C2×#127—731no—
116C2×C4×D4—732no—
117C2×C4×D4—1462no—
118#390—732no—
119#390—1462no—
120#384#6440811yescharacteristic
121C43—731no—
122#336—734no—
123#336—1462no—
124#336—1462no—
125C22×D4—732no—
126C22×D4—1462no—
127C23×C4—1462no—
128C22×C8—1464no—
129#127—734no—
130#127—1462no—
131C4×D4—2928no—
132C4×D4—2924no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4C2×#6440812yes—
135C2×C22⋊C4—1462no—
136C2×C22⋊C4—1464no—
137C2×C42—732no—
138C2×C42—731no—
139C2×C42—732no—
140C2×C42—731no—
141C2×C42C2×#6440811yescharacteristic
142C24—1462no—
143C2×D4—2922no—
144C2×D4—2922no—
145C2×D4—2924no—
146C2×D4—2924no—
147C2×D4—734no—
148C2×D4—1462no—
149C2×D4—1468no—
150C22×C4—22no—
151C22×C4—2924no—
152C22×C4—2928no—
153C22×C4—731no—
154C22×C4—732no—
155C22×C4—731no—
156C22×C4C22⋊#6440812yes—
157C22×C4C22×#6440811yescharacteristic
158C2×C8—2924no—
159C2×C8—2924no—
160C2×C8—2924no—
161C4⋊C4—42no—
162C4⋊C4—44no—
163C22⋊C4—2928no—
164C22⋊C4—2924no—
165C42—2921no—
166C42—2922no—
167C42—1462no—
168C42—1464no—
169C42#1192403612yes—
170C42#1192403812yes—
171C23—2922no—
172C23—2922no—
173C23—2924no—
174C23—2924no—
175C23—1464no—
176C23C2×C22⋊#6440811yescharacteristic
177D4—2924no—
178D4—2924no—
179D4—29216no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—44no—
186C2×C4—5848no—
187C2×C4—732no—
188C2×C4—734no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4#1455664814yes—
195C2×C4C2×#1192403611yescharacteristic
196C2×C4C2×#1192403811yescharacteristic
197C8—5844no—
198C22—2924no—
199C22—2928no—
200C22—5844no—
201C22—5842no—
202C22—5842no—
203C22C2×#1455664811yescharacteristic
204C22#1798956811yescharacteristic
205C22D73⋊#10011yescharacteristic
206C22#1798957912yes—
207C22#1798958612yes—
208C4—21no—
209C4—21no—
210C4—24no—
211C4—82no—
212C4—2921no—
213C4—1464no—
214C4—1462no—
215C2—5844no—
216C2#2262517211yescharacteristic
217C2#2262523212yes—
218C2#2262535212yes—
219C2#2262542111yescharacteristic
220C2#2262545911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556588C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#7603
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #22625858C2semidirect
2. #22624748C2semidirect
19. #14556588C8semidirect
114. C73#7603semidirect

Maximal subgroups

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

subgroupindex
#226258582
#226247482
#226124932
#760373