Finite Group Databasebeta

← #32980933

Subgroups — #32980933

Order 18688.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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#22620276C211yesmaximal, characteristic
2#22608593C211yesmaximal, characteristic
3#22608403C212yesmaximal, complemented
4#22607829C212yesmaximal, complemented
5C73×#2980C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7#17988955—21no—
8#17988951—21no—
9#17988946C414yes—
10#17988640C2212yes—
11#17988583—22no—
12C2×#14556502C2211yescharacteristic
13#17988336—21no—
14#17988331—21no—
15#17988317—24no—
16#532×C73C2211yescharacteristic
17#435×C73—24no—
18#432×C73C2212yes—
19#408×C73—22no—
20C22×#10596831—21no—
21#14556591C2×C412yes—
22#14556583—21no—
23#14556570—22no—
24C4×Dic146—22no—
25#14556550—21no—
26C4⋊#10596831—22no—
27#14556515—24no—
28#14556512—24no—
29C22⋊#10596831—22no—
30#14556502—21no—
31#14556502C2×C412yes—
32C4×#10596831—22no—
33C2×#41×C73D412yes—
34C2×M16×C73—22no—
35C22×C8×C73—22no—
36C4⋊Q8×C73D411yescharacteristic
37#127×C73D411yescharacteristic
38#124×C73C2×C412yes—
39#121×C73—22no—
40C4×D4×C73—22no—
41C2×C42×C73C2311yescharacteristic
42C4⋊C8×C73D414yes—
43C22⋊C8×C73—24no—
44C22⋊C8×C73—22no—
45#97×C73—22no—
46C2×Dic146—22no—
47C2×#10596831—22no—
48C2×#10596831—42no—
49C2×#10596831—42no—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52#11924007—42no—
53C22⋊Dic73—41no—
54C4×Dic73—41no—
55#41×C73—42no—
56#41×C73—42no—
57C2×Q8×C73C22⋊C412yes—
58C2×D4×C73—22no—
59C2×D4×C73—22no—
60C2×D4×C73C22⋊C412yes—
61C22×C4×C73—22no—
62C22×C4×C73C2×D411yescharacteristic
63C22×C4×C73#4112yes—
64M16×C73—82no—
65C2×C8×C73—24no—
66C2×C8×C73—82no—
67C4⋊C4×C73—22no—
68C22⋊C4×C73—24no—
69C42×C73C22×C411yescharacteristic
70C42×C73C2×D412yes—
71C42×C73C2×D411yescharacteristic
72C23×C73—22no—
73C23×C73#12311yescharacteristic
74Q8×C73—42no—
75D4×C73—42no—
76D4×C73—82no—
77D4×C73—82no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—42no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73C2×C22⋊C411yescharacteristic
84C2×C4×C73C4×D412yes—
85C2×C4×C73#12011yescharacteristic
86C2×C4×C73#12112yes—
87C2×Dic73—42no—
88Dic146—44no—
89C8×C73—44no—
90#10596831—42no—
91#10596831—82no—
92C22×C73—22no—
93C22×C73—21no—
94C22×C73—44no—
95C22×C73—42no—
96C22×C73#38611yescharacteristic
97C4×C73—22no—
98C4×C73—22no—
99C4×C73—21no—
100C4×C73—42no—
101C4×C73#45512yes—
102Dic73—82no—
103#9005—731nomaximal, Sylow
104C2×C73—41no—
105C2×C73—82no—
106C2×C73#188112yes—
107C2×C73#188511yescharacteristic
108#3135—731no—
109#2980D7311yescharacteristic
110#1543—731no—
111#1497—732no—
112#1302—732no—
113C73#900511yescharacteristic, complemented, Sylow
114#533—731no—
115#532C2×D7311yescharacteristic
116#491—1461no—
117#490—1461no—
118#489—734no—
119#435—24no—
120#432C2×D7312yes—
121#431—732no—
122#416—1462no—
123#408—22no—
124C2×#97—731no—
125#333—1461no—
126#331—1461no—
127Q8⋊C8—1464no—
128C2×#41C22⋊D7312yes—
129C2×M16—22no—
130C22×C8—22no—
131C22×C8—1461no—
132C4⋊Q8—732no—
133C4⋊Q8D29211yescharacteristic
134#127D29211yescharacteristic
135#125—1461no—
136#124C4×D7312yes—
137C22⋊Q8—1462no—
138#121—22no—
139C4×Q8—1462no—
140C4×D4—22no—
141#117—1461no—
142C2×C42C22×D7311yescharacteristic
143C4⋊C8—1462no—
144C4⋊C8C22⋊D7314yes—
145#103—1464no—
146#102—1464no—
147C22⋊C8—24no—
148C22⋊C8—22no—
149C22⋊C8—1462no—
150#97—22no—
151#97—732no—
152#97—1461no—
153C4×C8—1462no—
154#41—42no—
155#41—42no—
156C2×Q8—1462no—
157C2×Q8#1192400512yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4#1192400512yes—
161C22×C4—22no—
162C22×C4C2×C22⋊D7311yescharacteristic
163C22×C4#1192402812yes—
164M16—82no—
165C2×C8—24no—
166C2×C8—82no—
167C2×C8—2922no—
168C2×C8—2922no—
169C2×C8—1462no—
170C4⋊C4—22no—
171C4⋊C4—2922no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C22⋊C4—24no—
175C22⋊C4—2921no—
176C42—2921no—
177C42C2×C4×D7311yescharacteristic
178C42C2×C22⋊D7312yes—
179C42C2×D29211yescharacteristic
180C23—22no—
181C23#1455657411yescharacteristic
182Q8—42no—
183Q8—2924no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—2922no—
193C2×C4C2×#1192400511yescharacteristic
194C2×C4C4×C22⋊D7312yes—
195C2×C4#1455656011yescharacteristic
196C2×C4#1455656512yes—
197C8—44no—
198C8—2922no—
199C8—5842no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22#1798846611yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—5842no—
210C4#1798876512yes—
211C2—41no—
212C2—82no—
213C2#2261029312yes—
214C2#2261031911yescharacteristic
subgroupG/H
centerC2×C4#14556560
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2980C2
socleC22×C73#386
prime radical#532×C73C22
cosocleC2×C42×C73C23
hypercenter#2980D73
hypocenterC73#9005
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
3. #22608403C2semidirect
4. #22607829C2semidirect
113. C73#9005semidirect

Maximal subgroups

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

subgroupindex
#226202762
#226085932
#226084032
#226078292
C73×#29802
#900573