Finite Group Databasebeta

← #34001192

Subgroups — #34001192

Order 18688.

274 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 46 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#22626204C212yesmaximal
2#22610762C211yesmaximal, characteristic
3#17989566—22no—
4#17989494C414yescomplemented
5#17989492—22no—
6#17989137C2211yescharacteristic
7C2×#14556517—22no—
8#17988433C411yescharacteristic, complemented
9#423×C73C411yescharacteristic, complemented
10#14556670—42no—
11#14556650—24no—
12#14556649—42no—
13C2×#11924028D412yes—
14#14556591Q811yescharacteristic
15#14556588D411yescharacteristic
16#14556579C2×C412yes—
17#14556565—41no—
18C4×D292—41no—
19C2×C4×Dic73—21no—
20#14556517—44no—
21#14556498—41no—
22C2×M16×C73—21no—
23C2×C42×C73C2×C411yescharacteristic
24C4⋊C8×C73—41no—
25C4⋊#64408—82no—
26C22⋊#64408—44no—
27C4×#64408—82no—
28#11924028—42no—
29#11924028—42no—
30C2×Dic146C4⋊C412yes—
31C2×D292—41no—
32C2×D292C22⋊C412yes—
33C2×C22⋊D73—22no—
34C22×Dic73—41no—
35C2×C4×D73—22no—
36C4⋊Dic73—41no—
37#11924005—42no—
38C4×Dic73—22no—
39C4×Dic73—41no—
40C22×C4×C73—21no—
41C22×C4×C73C22⋊C411yescharacteristic
42M16×C73—42no—
43C2×C8×C73—41no—
44C42×C73—21no—
45C42×C73C4211yescharacteristic
46C42×C73C4⋊C411yescharacteristic
47C23×C73#9911yescharacteristic
48C22×D73—22no—
49C2×#64408—84no—
50C2×C4×C73—21no—
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—81no—
55C2×C4×C73#9511yescharacteristic
56C2×C4×C73#9911yescharacteristic
57C22⋊D73—82no—
58C2×Dic73—22no—
59C2×Dic73—42no—
60C2×Dic73—82no—
61D292—42no—
62D292—82no—
63C4×D73—42no—
64C4×D73—42no—
65Dic146—42no—
66C8×C73—81no—
67C22×C73—21no—
68C22×C73—41no—
69C22×C73#34211yescharacteristic
70C2×D73—42no—
71C2×D73—82no—
72#64408—164no—
73C4×C73—21no—
74C4×C73—41no—
75C4×C73—41no—
76C4×C73#35311yescharacteristic
77C4×C73#35411yescharacteristic
78Dic73—42no—
79Dic73—82no—
80#7506—731nomaximal, Sylow
81C2×C73—21no—
82C2×C73—41no—
83C2×C73#139311yescharacteristic
84D73—82no—
85#2126—732no—
86#1963—731no—
87C73#750611yescharacteristic, complemented, Sylow
88#532—731no—
89#423#6440811yescharacteristic, complemented
90C2×#104—1462no—
91#410—1462no—
92#376—731no—
93#354—734no—
94#353—1462no—
95C2×#41—732no—
96C2×M16—21no—
97C4⋊Q8—731no—
98#127—731no—
99#124—732no—
100#121—2921no—
101C4×D4—2921no—
102#117—2922no—
103C2×C42—1461no—
104C2×C42C2×#6440811yescharacteristic
105C4⋊C8—41no—
106#104—2924no—
107#99—2922no—
108#99—1464no—
109#95—2921no—
110#41—2922no—
111#41—2922no—
112C2×Q8—732no—
113C2×D4—2921no—
114C2×D4—732no—
115C2×D4—1462no—
116C22×C4—21no—
117C22×C4—2921no—
118C22×C4—1462no—
119C22×C4C22⋊#6440811yescharacteristic
120M16—42no—
121C2×C8—41no—
122C4⋊C4—2921no—
123C4⋊C4—5842no—
124C22⋊C4—2922no—
125C22⋊C4—2924no—
126C42—21no—
127C42—2921no—
128C42—5842no—
129C42—1462no—
130C42C4×#6440811yescharacteristic
131C42C4⋊#6440811yescharacteristic
132C23—1462no—
133C23#1455665011yescharacteristic
134Q8—2922no—
135D4—2922no—
136D4—5842no—
137D4—5842no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—81no—
143C2×C4—2922no—
144C2×C4—2922no—
145C2×C4—2922no—
146C2×C4—5842no—
147C2×C4—5844no—
148C2×C4—1462no—
149C2×C4(C2×#64408)⋊C411yescharacteristic
150C2×C4#1455664911yescharacteristic
151C8—81no—
152C22—21no—
153C22—41no—
154C22—2922no—
155C22—5842no—
156C22#1798946511yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—2922no—
161C4—5842no—
162C4—11684no—
163C4#1798949111yescharacteristic
164C4#1798949311yescharacteristic
165C2—21no—
166C2—41no—
167C2—5842no—
168C2#2262502611yescharacteristic
subgroupG/H
centerC4#17989491
commutatorC42×C73C42
FrattiniC2×C42C2×#64408
Fitting#423×C73C4
socleC2×C73#1393
prime radical, cosocle#17989137C22
hypercenter#423#64408
hypocenterC73#7506
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
4. #17989494C4semidirect
8. #17988433C4semidirect
9. #423×C73C4semidirect
87. C73#7506semidirect
89. #423#64408semidirect

Maximal subgroups

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

subgroupindex
#226262042
#226107622
#750673