Finite Group Databasebeta

← #32990488

Subgroups — #32990488

Order 18688.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#22610100C212yesmaximal
2#22610064C211yesmaximal, characteristic
3#22607812C211yesmaximal, characteristic
4#22607812C212yesmaximal
5C73×#2845C211yesmaximal, characteristic
6C2×#14556524—22no—
7C2×#14556522—22no—
8C2×#14556502C2211yescharacteristic
9C2×#14556502C2212yes—
10#17988457C2211yescharacteristic
11#17988349—22no—
12#398×C73—22no—
13#398×C73—22no—
14#398×C73—22no—
15#382×C73C2211yescharacteristic
16#382×C73C2212yes—
17C22×#10596831—22no—
18C22×#10596831—21no—
19C2×C4⋊Dic73—22no—
20C2×C4⋊Dic73—21no—
21#14556524—44no—
22#14556522—44no—
23#14556502—22no—
24#14556502—21no—
25#14556502Q814yes—
26#14556502Q812yes—
27C2×C4⋊C4×C73—22no—
28C2×C4⋊C4×C73—22no—
29C2×C4⋊C4×C73—22no—
30C2×C4⋊C4×C73D412yes—
31C2×C4⋊C4×C73D412yes—
32C2×C4⋊C4×C73D412yes—
33C2×C42×C73C2311yescharacteristic
34#95×C73—22no—
35#95×C73—22no—
36#95×C73—22no—
37#95×C73—22no—
38C22×Dic73—41no—
39C2×#10596831—24no—
40C2×#10596831—24no—
41C2×#10596831—24no—
42C2×#10596831—22no—
43C2×#10596831—41no—
44C2×#10596831—41no—
45C4⋊Dic73—42no—
46C4⋊Dic73—42no—
47C4⋊Dic73—42no—
48C22×C4×C73—22no—
49C22×C4×C73—22no—
50C22×C4×C73—22no—
51C22×C4×C73C2×D412yes—
52C22×C4×C73C2×D411yescharacteristic
53C4⋊C4×C73—42no—
54C4⋊C4×C73—42no—
55C4⋊C4×C73—42no—
56C4⋊C4×C73—82no—
57C4⋊C4×C73—82no—
58C4⋊C4×C73—82no—
59C42×C73C2×Q812yes—
60C42×C73C2×Q811yescharacteristic
61C42×C73#4111yescharacteristic
62C23×C73#12011yescharacteristic
63C2×C4×C73—22no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—42no—
68C2×C4×C73—42no—
69C2×C4×C73—42no—
70C2×C4×C73—42no—
71C2×C4×C73—42no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73—42no—
76C2×C4×C73C22⋊Q812yes—
77C2×C4×C73C22⋊Q811yescharacteristic
78C2×C4×C73C4⋊Q812yes—
79C2×C4×C73C4⋊Q811yescharacteristic
80C2×Dic73—82no—
81C2×Dic73—81no—
82#10596831—28no—
83#10596831—42no—
84C22×C73#39511yescharacteristic
85C22×C73#45312yes—
86C22×C73#45411yescharacteristic
87C22×C73#45511yescharacteristic
88C22×C73#45612yes—
89C4×C73—22no—
90C4×C73—22no—
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—82no—
94C4×C73—82no—
95C4×C73—82no—
96Dic73—161no—
97#10585—731nomaximal, Sylow
98C2×C73#165611yescharacteristic
99C2×C73#166112yes—
100C2×C73#166311yescharacteristic
101C2×C73#206012yes—
102C2×C73#206111yescharacteristic
103#2845D7311yescharacteristic
104#1847—732no—
105#1836—731no—
106#1295—731no—
107#1295—732no—
108C73#1058511yescharacteristic, complemented, Sylow
109C2×#107—1462no—
110C2×#106—1462no—
111C2×#97—731no—
112C2×#97—732no—
113#398—22no—
114#398—22no—
115#398—22no—
116#384—731no—
117#382C2×D7311yescharacteristic
118#382C2×D7312yes—
119#340—1462no—
120C22×C8—1461no—
121C22×C8—1462no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—1461no—
126C2×C4⋊C4—1462no—
127C2×C4⋊C4C22⋊D7312yes—
128C2×C4⋊C4C22⋊D7312yes—
129C2×C4⋊C4C22⋊D7312yes—
130C2×C42C22×D7311yescharacteristic
131#107—2924no—
132#106—2924no—
133#97—732no—
134#97—734no—
135#97—1461no—
136#97—1462no—
137#95—22no—
138#95—22no—
139#95—22no—
140#95—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—2921no—
145C22×C4C2×C22⋊D7312yes—
146C22×C4C2×C22⋊D7311yescharacteristic
147C2×C8—2921no—
148C2×C8—2921no—
149C2×C8—1462no—
150C2×C8—1464no—
151C2×C8—1464no—
152C2×C8—1464no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—2922no—
160C4⋊C4—2922no—
161C4⋊C4—2922no—
162C42Q8×D7312yes—
163C42Q8×D7311yescharacteristic
164C42#1192402911yescharacteristic
165C23#1455656011yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—5842no—
180C2×C4—5841no—
181C2×C4#1455656712yes—
182C2×C4#1455656711yescharacteristic
183C2×C4#1455658912yes—
184C2×C4#1455658911yescharacteristic
185C8—2922no—
186C8—1468no—
187C22#1798850611yescharacteristic
188C22#1798875512yes—
189C22#1798876011yescharacteristic
190C22#1798876511yescharacteristic
191C22#1798877012yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—11681no—
200C2#2260922411yescharacteristic
201C2#2260924812yes—
202C2#2260925911yescharacteristic
203C2#2261127312yes—
204C2#2261127811yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2845C2
socle, prime radicalC23×C73#120
hypercenter#2845D73
hypocenterC73#10585
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
108. C73#10585semidirect

Maximal subgroups

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

subgroupindex
#226101002
#226100642
#226078122
C73×#28452
#1058573