Finite Group Databasebeta

← #34014368

Subgroups — #34014368

Order 18688.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#22625072C214yesmaximal, complemented
3#22620332C211yesmaximal, characteristic
4#17989566—22no—
5#17989494—22no—
6#17989492C2214yes—
7#17989137C2211yescharacteristic
8C2×#14556583C411yescharacteristic, complemented
9#17988956C412yescomplemented
10#17988952C2212yes—
11#17988942—22no—
12#17988589—22no—
13C4×M16×C73C411yescharacteristic, complemented
14#14556670—42no—
15#14556650—24no—
16#14556649—42no—
17C2×#11924028D412yes—
18#14556591C2×C411yescharacteristic
19#14556588C2311yescharacteristic
20#14556583—21no—
21#14556583—41no—
22#14556583C2×C412yes—
23#14556579D412yes—
24#14556565—41no—
25C4×D292—41no—
26C2×C4⋊Dic73—21no—
27C2×#11924007—41no—
28#14556516—24no—
29#14556513—24no—
30C2×M16×C73—21no—
31C2×C42×C73C2×C411yescharacteristic
32#97×C73C2×C412yes—
33C4×C8×C73—21no—
34C4⋊#64408—82no—
35C22⋊#64408—44no—
36C4×#64408—82no—
37#11924028—42no—
38#11924028—42no—
39C2×Dic146C22⋊C412yes—
40C2×D292—41no—
41C2×D292C2×D412yes—
42C2×C22⋊D73—22no—
43C22×Dic73—41no—
44C2×C4×D73—22no—
45C4⋊Dic73—22no—
46C4⋊Dic73—41no—
47C4⋊Dic73—41no—
48#11924007—42no—
49#11924007—42no—
50#11924005—42no—
51C22×C4×C73—21no—
52C22×C4×C73C22⋊C411yescharacteristic
53M16×C73—42no—
54C2×C8×C73—22no—
55C42×C73—21no—
56C42×C73C22⋊C411yescharacteristic
57C42×C73C22×C411yescharacteristic
58C23×C73#9911yescharacteristic
59C22×D73—22no—
60C2×#64408—84no—
61C2×C4×C73—22no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—81no—
65C2×C4×C73#9911yescharacteristic
66C2×C4×C73C2×C22⋊C411yescharacteristic
67C22⋊D73—82no—
68C2×Dic73—22no—
69C2×Dic73—42no—
70C2×Dic73—82no—
71D292—42no—
72D292—82no—
73C4×D73—42no—
74C4×D73—42no—
75Dic146—42no—
76C8×C73—42no—
77C22×C73—21no—
78C22×C73—41no—
79C22×C73C2×#9911yescharacteristic
80C2×D73—42no—
81C2×D73—82no—
82#64408—164no—
83C4×C73—21no—
84C4×C73—41no—
85C4×C73—41no—
86C4×C73#35412yes—
87Dic73—42no—
88Dic73—82no—
89#13596—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73—41no—
92C2×C73C2×#35411yescharacteristic
93D73—82no—
94#3142—731no—
95#2126—732no—
96#1412—734no—
97C73#1359611yescharacteristic, complemented, Sylow
98#532—731no—
99C2×#125—731no—
100#491—732no—
101#490—732no—
102#488—1462no—
103#417—1462no—
104#410—1462no—
105C4×M16#6440811yescharacteristic, complemented
106#354—1462no—
107#353—734no—
108C2×#41—732no—
109C2×M16—21no—
110C4⋊Q8—731no—
111#127—731no—
112#125—2921no—
113#125—732no—
114#125—1461no—
115#124—732no—
116#121—2921no—
117C4×D4—2921no—
118#117—2922no—
119C2×C4⋊C4—2921no—
120C2×C4⋊C4—1461no—
121C2×C42C2×#6440811yescharacteristic
122#103—1464no—
123#102—1464no—
124#99—2922no—
125#99—1464no—
126#97C2×#6440812yes—
127C4×C8—21no—
128#41—2922no—
129#41—2922no—
130C2×Q8—732no—
131C2×D4—2921no—
132C2×D4—732no—
133C2×D4—1462no—
134C22×C4—21no—
135C22×C4—2921no—
136C22×C4—1462no—
137C22×C4C22⋊#6440811yescharacteristic
138M16—42no—
139C2×C8—22no—
140C4⋊C4—2922no—
141C4⋊C4—2922no—
142C4⋊C4—2921no—
143C4⋊C4—2921no—
144C4⋊C4—5842no—
145C4⋊C4—1462no—
146C22⋊C4—2922no—
147C22⋊C4—2924no—
148C42—21no—
149C42—5842no—
150C42C22⋊#6440811yescharacteristic
151C42C22×#6440811yescharacteristic
152C23—1462no—
153C23#1455665011yescharacteristic
154Q8—2922no—
155D4—2922no—
156D4—5842no—
157D4—5842no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—81no—
162C2×C4—2922no—
163C2×C4—2922no—
164C2×C4—2922no—
165C2×C4—5842no—
166C2×C4—5844no—
167C2×C4—1462no—
168C2×C4#1455665011yescharacteristic
169C2×C4C2×C22⋊#6440811yescharacteristic
170C8—42no—
171C22—21no—
172C22—41no—
173C22—2922no—
174C22—5842no—
175C22C2×#1455665011yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—2922no—
180C4—5842no—
181C4—11684no—
182C4#1798949412yes—
183C2—21no—
184C2—41no—
185C2—5842no—
186C2C2×#1798949411yescharacteristic
subgroupG/H
centerC2C2×#17989494
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC4×M16×C73C4
socleC2×C73C2×#354
prime radical#17989137C22
cosocle#14556588C23
hypercenterC4×M16#64408
hypocenterC73#13596
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #22625072C2semidirect
8. C2×#14556583C4semidirect
9. #17988956C4semidirect
13. C4×M16×C73C4semidirect
97. C73#13596semidirect
105. C4×M16#64408semidirect

Maximal subgroups

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

subgroupindex
#226262042
#226250722
#226203322
#1359673