Finite Group Databasebeta

← #34005242

Subgroups — #34005242

Order 18688.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 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#22625658C212yesmaximal
2#22624807C214yesmaximal, complemented
3#382×D73C211yesmaximal, characteristic
4C2×#14556648—22no—
5C2×#14556646C2214yes—
6#17989453—22no—
7C2×C4⋊C4×D73C412yes—
8C2×C42×D73C2211yescharacteristic
9#17988453C411yescharacteristic
10#17988452C2212yes—
11#17988451—22no—
12#95×D73—22no—
13#382×C73C411yescharacteristic
14C22×#10596833—24no—
15#14556648—28no—
16#14556646—28no—
17C22×C4×D73—22no—
18C22×C4×D73C2×C411yescharacteristic
19C22×C4×D73D412yes—
20C2×C4⋊Dic73C2×C412yes—
21C2×#11924007—22no—
22C4⋊C4×D73—44no—
23C2×C4×Dic73D412yes—
24C2×C4×Dic73C2311yescharacteristic
25C42×D73—24no—
26#14556498—24no—
27#14556498—22no—
28C2×C4⋊C4×C73C2×C412yes—
29C2×C42×C73C2×C411yescharacteristic
30#95×C73—22no—
31C2×#10596833—28no—
32C2×#10596833—44no—
33C2×#10596833—44no—
34C23×D73C22⋊C411yescharacteristic
35C22×Dic73—22no—
36C22×Dic73C22⋊C411yescharacteristic
37C22×Dic73C2×D412yes—
38C2×C4×D73—22no—
39C2×C4×D73—22no—
40C2×C4×D73—22no—
41C2×C4×D73—24no—
42C2×C4×D73—24no—
43C2×C4×D73—42no—
44C2×C4×D73—44no—
45C2×C4×D73—44no—
46C2×C4×D73—44no—
47C4⋊Dic73—42no—
48#11924007—44no—
49C4×Dic73—24no—
50C4×Dic73#4114yes—
51C22×C4×C73—22no—
52C22×C4×C73C22⋊C412yes—
53C22×C4×C73C22×C411yescharacteristic
54C4⋊C4×C73—42no—
55C42×C73—22no—
56C23×C73C2×C22⋊C411yescharacteristic
57C22×D73—21no—
58C22×D73—21no—
59C22×D73—22no—
60C22×D73#10112yes—
61C22×D73#10414yes—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—42no—
68C2×C4×C73—42no—
69C2×C4×C73—42no—
70C2×C4×C73#11712yes—
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73#10012yes—
79C2×Dic73#12314yes—
80C4×D73—28no—
81C4×D73—48no—
82C4×D73—88no—
83#10596833—48no—
84C22×C73#38111yescharacteristic
85C22×C73C2×#10011yescharacteristic
86C22×C73C2×#10111yescharacteristic
87C22×C73C2×#10412yes—
88C22×C73#42112yes—
89C2×D73—22no—
90C2×D73—24no—
91C2×D73—24no—
92C2×D73—22no—
93C2×D73#33014yes—
94C4×C73—22no—
95C4×C73—42no—
96C4×C73—82no—
97Dic73—22no—
98Dic73—24no—
99Dic73—82no—
100#8719—731nomaximal, Sylow
101C2×C73C2×#33011yescharacteristic
102C2×C73#152712yes—
103C2×C73#153411yescharacteristic
104C2×C73#182111yescharacteristic
105C2×C73#182612yes—
106D73—24no—
107C2×#382—731no—
108#1749—732no—
109#1295—734no—
110C73#871911yescharacteristic, complemented, Sylow
111C22×C4⋊C4—732no—
112C22×C42—731no—
113C2×C22⋊C8—1462no—
114C2×#97—734no—
115#382—732no—
116#382—731no—
117#382—1462no—
118#382#6440811yescharacteristic
119C2×#95—1462no—
120#336—1462no—
121C23×C4—732no—
122C23×C4—731no—
123C23×C4—1462no—
124C22×C8—1464no—
125C2×C4⋊C4—2924no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—1462no—
128C2×C4⋊C4C2×#6440812yes—
129C2×C42—731no—
130C2×C42—732no—
131C2×C42—1464no—
132C2×C42C2×#6440811yescharacteristic
133C22⋊C8—1468no—
134#97—1468no—
135#95—22no—
136#95—1464no—
137#95—1462no—
138C24—731no—
139C22×C4—22no—
140C22×C4—2922no—
141C22×C4—2924no—
142C22×C4—2924no—
143C22×C4—2924no—
144C22×C4—731no—
145C22×C4—732no—
146C22×C4—1464no—
147C22×C4—1464no—
148C22×C4—1462no—
149C22×C4—1462no—
150C22×C4—1462no—
151C22×C4—1462no—
152C22×C4C22⋊#6440812yes—
153C22×C4C22×#6440811yescharacteristic
154C2×C8—2924no—
155C2×C8—2924no—
156C2×C8—1468no—
157C4⋊C4—42no—
158C4⋊C4—2922no—
159C4⋊C4—2924no—
160C42—22no—
161C42—734no—
162C42—1464no—
163C23—732no—
164C23—734no—
165C23—1461no—
166C23—1461no—
167C23—1462no—
168C23C2×C22⋊#6440811yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—2928no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4—2922no—
181C2×C4—5848no—
182C2×C4—734no—
183C2×C4—732no—
184C2×C4—1468no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4#1455667012yes—
190C8—2928no—
191C22—734no—
192C22—1462no—
193C22—1464no—
194C22—1464no—
195C22—1462no—
196C22#1798953011yescharacteristic
197C22D73⋊#10011yescharacteristic
198C22D73⋊#10111yescharacteristic
199C22D73⋊#10412yes—
200C22#1798958412yes—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—5842no—
205C4—1462no—
206C4—1464no—
207C2—1464no—
208C2D73⋊#33011yescharacteristic
209C2#2262539112yes—
210C2#2262541411yescharacteristic
211C2#2262583111yescharacteristic
212C2#2262583912yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#382×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#382#64408
hypocenterC73#8719
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #22624807C2semidirect
110. C73#8719semidirect

Maximal subgroups

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

subgroupindex
#226256582
#226248072
#382×D732
#871973