Finite Group Databasebeta

← #32989119

Subgroups — #32989119

Order 18688.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610763C211yesmaximal, characteristic
2#22608425C212yesmaximal
3#22607834C212yesmaximal, complemented
4#22607760C211yesmaximal, characteristic, complemented
5C73×#2402C211yesmaximal, characteristic, complemented
6#17989137C2211yescharacteristic
7#17988640C2212yes—
8#17988611C2211yescharacteristic
9C2×#14556519—22no—
10#17988320—22no—
11#17988320—22no—
12#400×C73—22no—
13#398×C73—22no—
14C4×C4⋊C4×C73—22no—
15C4×C4⋊C4×C73C2212yes—
16#376×C73C2211yescharacteristic
17C2×#11924028—21no—
18C2×#11924012—21no—
19#14556591Q811yescharacteristic
20#14556588Q811yescharacteristic
21#14556579—21no—
22#14556565—22no—
23C4×D292—22no—
24C4⋊#10596831—22no—
25C4⋊#10596831—22no—
26#14556519—44no—
27C22⋊#10596831—22no—
28C4×#10596831—22no—
29C2×C4⋊C4×C73—22no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73—22no—
32C2×C42×C73—22no—
33C2×C42×C73D412yes—
34C2×C42×C73C2311yescharacteristic
35#95×C73—22no—
36#95×C73—22no—
37#95×C73—22no—
38#95×C73D412yes—
39#95×C73D412yes—
40#11924028—42no—
41#11924028—42no—
42C2×Dic146—21no—
43C2×D292—21no—
44C2×D292—22no—
45C2×C22⋊D73—41no—
46C2×C4×D73—41no—
47#11924012—42no—
48C2×#10596831—42no—
49C2×#10596831—41no—
50C4⋊Dic73—22no—
51#11924005—42no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73C2×D412yes—
56C22×C4×C73C2×D411yescharacteristic
57C4⋊C4×C73—44no—
58C4⋊C4×C73—44no—
59C4⋊C4×C73—44no—
60C42×C73—22no—
61C42×C73—22no—
62C42×C73—42no—
63C42×C73—42no—
64C42×C73C2×Q811yescharacteristic
65C42×C73#4112yes—
66C42×C73#4111yescharacteristic
67C23×C73#12011yescharacteristic
68C22×D73—41no—
69C2×C4×C73—24no—
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×C73—42no—
77C2×C4×C73—42no—
78C2×C4×C73—42no—
79C2×C4×C73C22⋊Q812yes—
80C2×C4×C73C22⋊Q811yescharacteristic
81C2×C4×C73#12412yes—
82C2×C4×C73#12411yescharacteristic
83C2×C4×C73#13512yes—
84C2×C4×C73AGL(1,ℤ/8)12yes—
85C22⋊D73—82no—
86C2×Dic73—41no—
87D292—42no—
88D292—82no—
89C4×D73—81no—
90C4×D73—81no—
91Dic146—42no—
92#10596831—82no—
93#10596831—81no—
94C22×C73—22no—
95C22×C73#39311yescharacteristic
96C22×C73#44912yes—
97C2×D73—81no—
98C2×D73—82no—
99C4×C73—22no—
100C4×C73—22no—
101C4×C73—44no—
102C4×C73—82no—
103C4×C73—82no—
104C4×C73#47812yes—
105C4×C73#48811yescharacteristic
106C4×C73#49011yescharacteristic
107Dic73—81no—
108#10372—731nomaximal, Sylow
109C2×C73—22no—
110C2×C73#202511yescharacteristic
111C2×C73#203112yes—
112D73—161no—
113#2402D7311yescharacteristic, complemented
114#1963—731no—
115#1502—732no—
116#1303—732no—
117#1274—731no—
118C73#1037211yescharacteristic, complemented, Sylow
119#532—731no—
120#431—732no—
121#423—731no—
122C2×#104—1462no—
123#400—22no—
124#398—22no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4C2×D7312yes—
127#376C2×D7311yescharacteristic
128#327—1462no—
129#327—1462no—
130C2×#41—1461no—
131C2×M16—1461no—
132C4⋊Q8—731no—
133#127—731no—
134#124—1461no—
135#121—1462no—
136C4×D4—1462no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C42—22no—
141C2×C42C22⋊D7312yes—
142C2×C42C22×D7311yescharacteristic
143C4⋊C8—1462no—
144C4⋊C8—1462no—
145#104—2924no—
146C22⋊C8—1462no—
147C4×C8—1462no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D7312yes—
152#95C22⋊D7312yes—
153#41—2922no—
154#41—2922no—
155C2×Q8—1461no—
156C2×D4—2921no—
157C2×D4—1461no—
158C2×D4—1462no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—2921no—
163C22×C4C2×C22⋊D7312yes—
164C22×C4C2×C22⋊D7311yescharacteristic
165M16—2922no—
166C2×C8—2922no—
167C2×C8—2921no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C4⋊C4—1462no—
172C22⋊C4—2922no—
173C42—22no—
174C42—22no—
175C42—42no—
176C42—42no—
177C42Q8×D7311yescharacteristic
178C42#1192402911yescharacteristic
179C42#1192402912yes—
180C23—2921no—
181C23#1455656011yescharacteristic
182Q8—2922no—
183D4—2922no—
184D4—5842no—
185D4—5842no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—2921no—
197C2×C4—5841no—
198C2×C4—5841no—
199C2×C4#1455656712yes—
200C2×C4#1455656711yescharacteristic
201C2×C4#1455658012yes—
202C2×C4#1455658011yescharacteristic
203C2×C4#1455661112yes—
204C2×C4#1455661612yes—
205C8—5842no—
206C8—5841no—
207C22—22no—
208C22—5841no—
209C22—5842no—
210C22#1798849811yescharacteristic
211C22#1798873212yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—82no—
216C4—82no—
217C4—5841no—
218C4#1798888412yes—
219C4#1798894411yescharacteristic
220C4#1798895311yescharacteristic
221C2—22no—
222C2—11681no—
223C2#2261107411yescharacteristic
224C2#2261110012yes—
subgroupG/H
centerC2×C4#14556580
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2402C2
socleC22×C73#393
prime radical#17989137C22
hypercenter#2402D73
hypocenterC73#10372
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
3. #22607834C2semidirect
4. #22607760C2semidirect
5. C73×#2402C2semidirect
113. #2402D73semidirect
118. C73#10372semidirect

Maximal subgroups

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

subgroupindex
#226107632
#226084252
#226078342
#226077602
C73×#24022
#1037273