Finite Group Databasebeta

← #32989084

Subgroups — #32989084

Order 18688.

400 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 101 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#22610908C211yesmaximal, characteristic
2#22608494C212yesmaximal
3#22607789C212yesmaximal
4#22607764C211yesmaximal, characteristic
5C73×#2859C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7#17988640C2212yes—
8#17988611C2211yescharacteristic
9#17988347—21no—
10#17988347—21no—
11#17988323—24no—
12C2×#125×C73—21no—
13#389×C73—24no—
14#384×C73—21no—
15#382×C73C2212yes—
16C43×C73C2211yescharacteristic
17C2×#11924012—21no—
18#14556591Q812yes—
19#14556583—21no—
20#14556570—22no—
21C4×Dic146—22no—
22#14556550—21no—
23C4⋊#10596831—22no—
24C4⋊#10596831—22no—
25C22⋊#10596831—22no—
26C4×#10596831—22no—
27#125×C73—42no—
28#125×C73—42no—
29C2×C4⋊C4×C73—24no—
30C2×C4⋊C4×C73—24no—
31C2×C4⋊C4×C73—22no—
32C2×C42×C73—22no—
33C2×C42×C73D411yescharacteristic
34C2×C42×C73D411yescharacteristic
35C2×C42×C73C2311yescharacteristic
36#95×C73—22no—
37#95×C73D414yes—
38C2×Dic146—22no—
39#11924012—41no—
40#11924012—41no—
41C2×#10596831—42no—
42C2×#10596831—41no—
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45#11924007—42no—
46C22⋊Dic73—41no—
47C4×Dic73—41no—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73—24no—
51C22×C4×C73C2×D412yes—
52C22×C4×C73C2×D411yescharacteristic
53C4⋊C4×C73—48no—
54C4⋊C4×C73—48no—
55C4⋊C4×C73—42no—
56C4⋊C4×C73—42no—
57C42×C73—21no—
58C42×C73—21no—
59C42×C73—44no—
60C42×C73SD1612yes—
61C42×C73Q1612yes—
62C42×C73C2×Q811yescharacteristic
63C42×C73#4111yescharacteristic
64C42×C73#4112yes—
65C23×C73#12011yescharacteristic
66C2×C4×C73—24no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—42no—
70C2×C4×C73—42no—
71C2×C4×C73—48no—
72C2×C4×C73—44no—
73C2×C4×C73C22⋊Q812yes—
74C2×C4×C73C22⋊Q811yescharacteristic
75C2×C4×C73#12412yes—
76C2×C4×C73#12411yescharacteristic
77C2×C4×C73C2×SD1611yescharacteristic
78C2×C4×C73C2×Q1611yescharacteristic
79C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C73#13711yescharacteristic
81C2×Dic73—42no—
82Dic146—82no—
83#10596831—82no—
84#10596831—81no—
85C22×C73—22no—
86C22×C73#39311yescharacteristic
87C22×C73#45011yescharacteristic
88C22×C73#45111yescharacteristic
89C4×C73—24no—
90C4×C73—22no—
91C4×C73—22no—
92C4×C73—42no—
93C4×C73—84no—
94C4×C73#47511yescharacteristic
95C4×C73#47711yescharacteristic
96C4×C73#48711yescharacteristic
97C4×C73#48911yescharacteristic
98Dic73—82no—
99#10365—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—21no—
102C2×C73#202411yescharacteristic
103C2×C73#203112yes—
104#2859D7311yescharacteristic
105#1994—731no—
106#1518—732no—
107#1286—732no—
108#1276—731no—
109C73#1036511yescharacteristic, complemented, Sylow
110#533—731no—
111C2×#125—21no—
112#431—732no—
113#423—731no—
114#389—24no—
115#384—21no—
116#382C2×D7312yes—
117C43C2×D7311yescharacteristic
118#339—1461no—
119#339—1461no—
120#328—1464no—
121C2×M16—1461no—
122C4⋊Q8—732no—
123#125—42no—
124#125—42no—
125#125—1461no—
126C22⋊Q8—1462no—
127C4×Q8—1462no—
128#117—1461no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C42—22no—
133C2×C42C22⋊D7311yescharacteristic
134C2×C42C22⋊D7311yescharacteristic
135C2×C42C22×D7311yescharacteristic
136C4⋊C8—1462no—
137C4⋊C8—1462no—
138C22⋊C8—1462no—
139C4×C8—1462no—
140#95—22no—
141#95C22⋊D7314yes—
142C2×Q8—1462no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—24no—
146C22×C4C2×C22⋊D7312yes—
147C22×C4C2×C22⋊D7311yescharacteristic
148M16—2921no—
149M16—2921no—
150C2×C8—2922no—
151C2×C8—2921no—
152C4⋊C4—48no—
153C4⋊C4—48no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—2922no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C22⋊C4—2921no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—2921no—
164C42#1192401612yes—
165C42#1192401812yes—
166C42Q8×D7311yescharacteristic
167C42#1192402911yescharacteristic
168C42#1192402912yes—
169C23#1455656011yescharacteristic
170Q8—5842no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—2922no—
179C2×C4#1455656712yes—
180C2×C4#1455656711yescharacteristic
181C2×C4#1455658012yes—
182C2×C4#1455658011yescharacteristic
183C2×C4C2×#1192401611yescharacteristic
184C2×C4C2×#1192401811yescharacteristic
185C2×C4#1455661711yescharacteristic
186C2×C4#1455662211yescharacteristic
187C8—5842no—
188C8—5841no—
189C22—22no—
190C22#1798849811yescharacteristic
191C22#1798873811yescharacteristic
192C22#1798874311yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—5842no—
199C4#1798886911yescharacteristic
200C4#1798887911yescharacteristic
201C4#1798893911yescharacteristic
202C4#1798894911yescharacteristic
203C2—21no—
204C2—21no—
205C2#2261106911yescharacteristic
206C2#2261110012yes—
subgroupG/H
centerC22#17988498
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2859C2
socleC22×C73#393
prime radicalC23×C73#120
hypercenter#2859D73
hypocenterC73#10365
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2859

Complements

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

NH ≅ G/Ntype
109. C73#10365semidirect

Maximal subgroups

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

subgroupindex
#226109082
#226084942
#226077892
#226077642
C73×#28592
#1036573