Finite Group Databasebeta

← #32990075

Subgroups — #32990075

Order 18688.

364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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#22610084C211yesmaximal, characteristic
2#22608631C212yesmaximal
3#22608443C212yesmaximal
4#22607801C211yesmaximal, characteristic
5C73×#3249C211yesmaximal, characteristic
6#17988644C2212yes—
7C2×C4⋊#10596831C2211yescharacteristic
8C2×#14556520—22no—
9#17988433C2211yescharacteristic
10#17988333—22no—
11#17988333—22no—
12#17988324—24no—
13#533×C73C2212yes—
14#477×C73—22no—
15#467×C73—22no—
16#462×C73—22no—
17C2×C4⋊C8×C73C2211yescharacteristic
18C22×#10596831—21no—
19C2×C4×Dic73—21no—
20C4⋊#10596831—22no—
21C4⋊#10596831—22no—
22#14556520—44no—
23C22⋊#10596831—22no—
24#14556502—22no—
25#14556498—21no—
26#14556498D412yes—
27C2×Q16×C73—22no—
28C22×C8×C73D412yes—
29C4⋊Q8×C73D412yes—
30C4⋊Q8×C73D412yes—
31#125×C73—22no—
32C22⋊Q8×C73—22no—
33C22⋊Q8×C73—22no—
34C4×Q8×C73—22no—
35C4×Q8×C73—22no—
36#117×C73—22no—
37C2×C42×C73C2311yescharacteristic
38#107×C73—22no—
39C4⋊C8×C73—22no—
40#103×C73—24no—
41C22×Dic73—22no—
42C2×#10596831—42no—
43C2×#10596831—41no—
44C2×#10596831—42no—
45C4×Dic73—22no—
46C4×Dic73—22no—
47C2×Q8×C73—22no—
48C2×Q8×C73—22no—
49C22×C4×C73C2×D411yescharacteristic
50C22×C4×C73C2×D411yescharacteristic
51C22×C4×C73#4111yescharacteristic
52Q16×C73—82no—
53C2×C8×C73—22no—
54C2×C8×C73—42no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—22no—
57C4⋊C4×C73—22no—
58C4⋊C4×C73—22no—
59C4⋊C4×C73—42no—
60C4⋊C4×C73—42no—
61C22⋊C4×C73—42no—
62C42×C73—42no—
63C42×C73C2×D412yes—
64C42×C73#4112yes—
65C23×C73#12111yescharacteristic
66Q8×C73—42no—
67Q8×C73—42no—
68Q8×C73—82no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—41no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73#12011yescharacteristic
76C2×C4×C73#12112yes—
77C2×C4×C73#12312yes—
78C2×C4×C73#12411yescharacteristic
79C2×Dic73—24no—
80C2×Dic73—42no—
81C2×Dic73—42no—
82C8×C73—42no—
83#10596831—82no—
84#10596831—81no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73#39411yescharacteristic
88C22×C73#47312yes—
89C4×C73—22no—
90C4×C73—21no—
91C4×C73—22no—
92C4×C73—82no—
93C4×C73—82no—
94C4×C73#45311yescharacteristic
95C4×C73#45611yescharacteristic
96Dic73—44no—
97#10516—731nomaximal, Sylow
98C2×C73—22no—
99C2×C73#203911yescharacteristic
100C2×C73#204711yescharacteristic
101C2×C73#205311yescharacteristic
102#3249D7311yescharacteristic
103#1843—731no—
104#1552—732no—
105#1506—732no—
106#1290—731no—
107C73#1051611yescharacteristic, complemented, Sylow
108#533C2×D7312yes—
109#477—22no—
110#467—22no—
111#462—22no—
112#432—732no—
113C2×C4⋊C8—731no—
114C2×C4⋊C8—1462no—
115C2×C4⋊C8C2×D7311yescharacteristic
116#376—731no—
117#332—1462no—
118#332—1462no—
119#328—1464no—
120C2×Q16—22no—
121C22×C8—1461no—
122C22×C8C22⋊D7312yes—
123C4⋊Q8C22⋊D7312yes—
124C4⋊Q8C22⋊D7312yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—1461no—
132C2×C42C22×D7311yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—2924no—
136C4⋊C8—1462no—
137C4⋊C8—1462no—
138#103—24no—
139C22⋊C8—1462no—
140#97—1462no—
141#95—732no—
142#95—1461no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—1462no—
146C22×C4D4×D7311yescharacteristic
147C22×C4C2×C22⋊D7311yescharacteristic
148C22×C4#1192402711yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—2922no—
153C2×C8—2921no—
154C2×C8—2922no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42—1462no—
164C42—1462no—
165C42C2×C22⋊D7312yes—
166C42#1192402712yes—
167C23#1455656211yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—1464no—
180C2×C4#1455656011yescharacteristic
181C2×C4#1455656312yes—
182C2×C4#1455657212yes—
183C2×C4#1455657811yescharacteristic
184C8—42no—
185C8—5842no—
186C8—5841no—
187C22—21no—
188C22—21no—
189C22#1798850111yescharacteristic
190C22#1798885912yes—
191C4—22no—
192C4—21no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—2924no—
197C4#1798875511yescharacteristic
198C4#1798877011yescharacteristic
199C2—22no—
200C2#2261115211yescharacteristic
201C2#2261119611yescharacteristic
202C2#2261123411yescharacteristic
subgroupG/H
centerC22#17988501
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#3249C2
socleC22×C73#394
prime radicalC23×C73#121
hypercenter#3249D73
hypocenterC73#10516
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
107. C73#10516semidirect

Maximal subgroups

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

subgroupindex
#226100842
#226086312
#226084432
#226078012
C73×#32492
#1051673