Finite Group Databasebeta

← #32989128

Subgroups — #32989128

Order 18688.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#22613236C211yesmaximal, characteristic
2#22610912C211yesmaximal, characteristic
3#22608431C212yesmaximal
4#22607833C212yesmaximal
5C73×#1274C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7#17988611C2211yescharacteristic
8#17988529—22no—
9#17988521—22no—
10C4×#11924007—22no—
11C4×C4⋊Dic73C2212yes—
12#17988347—22no—
13#17988325—22no—
14#17988325—22no—
15#431×C73C2212yes—
16#376×C73C2211yescharacteristic
17C2×#11924012—21no—
18#14556591Q812yes—
19#14556583—21no—
20#14556570—22no—
21C4×Dic146—22no—
22#14556550—21no—
23C2×C4⋊Dic73—22no—
24C2×#11924007—22no—
25C2×#11924007—22no—
26C2×C4×Dic73—22no—
27C4⋊#10596831—22no—
28#14556498—22no—
29#14556498—22no—
30#14556498D412yes—
31#14556498D412yes—
32C2×C42×C73D412yes—
33C2×C42×C73C2311yescharacteristic
34C4⋊C8×C73—22no—
35C22⋊C8×C73—22no—
36C4×C8×C73—22no—
37#95×C73—22no—
38C2×Dic146—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41#11924012—42no—
42C2×#10596831—41no—
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45C4⋊Dic73—44no—
46#11924007—44no—
47#11924007—44no—
48#11924007—42no—
49C22⋊Dic73—41no—
50C4×Dic73—41no—
51C4×Dic73—42no—
52C4×Dic73—42no—
53C22×C4×C73—22no—
54C22×C4×C73C2×D412yes—
55C22×C4×C73C2×D411yescharacteristic
56C2×C8×C73—42no—
57C42×C73—22no—
58C42×C73—22no—
59C42×C73C2×Q811yescharacteristic
60C42×C73#4111yescharacteristic
61C42×C73#4112yes—
62C23×C73#12011yescharacteristic
63C2×C4×C73—42no—
64C2×C4×C73—42no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×C4×C73C22⋊Q812yes—
68C2×C4×C73C22⋊Q811yescharacteristic
69C2×C4×C73#12412yes—
70C2×C4×C73#12411yescharacteristic
71C2×C4×C73#13512yes—
72C2×C4×C73#13712yes—
73C2×Dic73—24no—
74C2×Dic73—42no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73—42no—
79C2×Dic73—42no—
80Dic146—82no—
81C8×C73—82no—
82#10596831—81no—
83C22×C73—22no—
84C22×C73#39311yescharacteristic
85C22×C73#45212yes—
86C4×C73—22no—
87C4×C73—22no—
88C4×C73—82no—
89C4×C73#47912yes—
90C4×C73#48811yescharacteristic
91C4×C73#49111yescharacteristic
92Dic73—44no—
93Dic73—82no—
94Dic73—82no—
95#10373—731nomaximal, Sylow
96C2×C73—22no—
97C2×C73#202611yescharacteristic
98C2×C73#203112yes—
99#2402—731no—
100#1995—731no—
101#1503—732no—
102#1303—732no—
103#1274D7311yescharacteristic
104C73#1037311yescharacteristic, complemented, Sylow
105#533—731no—
106#431C2×D7312yes—
107#423—731no—
108#400—1462no—
109#398—1462no—
110C4×C4⋊C4—732no—
111C4×C4⋊C4—1462no—
112#376C2×D7311yescharacteristic
113#339—1462no—
114#328—1462no—
115#328—1462no—
116C2×M16—1461no—
117C4⋊Q8—732no—
118#125—1461no—
119C22⋊Q8—1462no—
120C4×Q8—1462no—
121#117—1461no—
122C2×C4⋊C4—1462no—
123C2×C4⋊C4—1462no—
124C2×C4⋊C4—1462no—
125C2×C42—1462no—
126C2×C42D29212yes—
127C2×C42C22×D7311yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1462no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—732no—
134#95—732no—
135#95—1462no—
136#95—1462no—
137C2×Q8—1462no—
138C22×C4—22no—
139C22×C4—1462no—
140C22×C4—1462no—
141C22×C4D4×D7312yes—
142C22×C4C2×D29211yescharacteristic
143M16—2922no—
144C2×C8—42no—
145C2×C8—2921no—
146C4⋊C4—2924no—
147C4⋊C4—2924no—
148C4⋊C4—2924no—
149C4⋊C4—2922no—
150C4⋊C4—1462no—
151C4⋊C4—1462no—
152C22⋊C4—2921no—
153C42—22no—
154C42—22no—
155C42—2921no—
156C42—2922no—
157C42—2922no—
158C42Q8×D7311yescharacteristic
159C42#1192402711yescharacteristic
160C42#1192402812yes—
161C23#1455656111yescharacteristic
162Q8—5842no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—2922no—
170C2×C4—2922no—
171C2×C4—2922no—
172C2×C4—2922no—
173C2×C4—1464no—
174C2×C4#1455656912yes—
175C2×C4#1455657111yescharacteristic
176C2×C4#1455657712yes—
177C2×C4#1455657911yescharacteristic
178C2×C4#1455661312yes—
179C2×C4#1455662412yes—
180C8—82no—
181C8—5841no—
182C22—22no—
183C22#1798850011yescharacteristic
184C22#1798875112yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—2924no—
189C4—5842no—
190C4—5842no—
191C4#1798889512yes—
192C4#1798894211yescharacteristic
193C4#1798895611yescharacteristic
194C2—22no—
195C2#2261108311yescharacteristic
196C2#2261110212yes—
subgroupG/H
centerC2×C4#14556579
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1274C2
socleC22×C73#393
prime radicalC23×C73#120
hypercenter#1274D73
hypocenterC73#10373
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
104. C73#10373semidirect

Maximal subgroups

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

subgroupindex
#226132362
#226109122
#226084312
#226078332
C73×#12742
#1037373