Finite Group Databasebeta

← #34014366

Subgroups — #34014366

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#22625071C214yesmaximal, complemented
3#22620334C211yesmaximal, characteristic
4#17989566—22no—
5#17989494—22no—
6#17989492C2214yes—
7#17989137C2211yescharacteristic
8#17988957C412yescomplemented
9#17988953C2212yes—
10#17988944—22no—
11#17988586—22no—
12C4×#11924012C411yescharacteristic, complemented
13C2×#125×C73C411yescharacteristic, complemented
14#14556670—42no—
15#14556650—24no—
16#14556649—42no—
17C2×#11924028D412yes—
18C2×#11924012—21no—
19#14556591C2×C411yescharacteristic
20#14556588C2311yescharacteristic
21#14556579D412yes—
22#14556565—41no—
23C4×D292—41no—
24#14556514—24no—
25#14556511—24no—
26#14556502C2×C412yes—
27C4×#10596831—21no—
28#125×C73—21no—
29#125×C73—41no—
30#125×C73C2×C412yes—
31C2×C4⋊C4×C73—21no—
32C2×C4⋊C4×C73—41no—
33C2×C42×C73C2×C411yescharacteristic
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—
43C2×C4×D73—22no—
44#11924012—42no—
45C2×#10596831—22no—
46C4⋊Dic73—41no—
47#11924005—42no—
48C22×C4×C73—21no—
49C22×C4×C73—41no—
50C22×C4×C73C22⋊C411yescharacteristic
51C4⋊C4×C73—22no—
52C4⋊C4×C73—42no—
53C4⋊C4×C73—42no—
54C4⋊C4×C73—41no—
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—42no—
65C2×C4×C73—81no—
66C2×C4×C73—82no—
67C2×C4×C73#9911yescharacteristic
68C2×C4×C73C2×C22⋊C411yescharacteristic
69C22⋊D73—82no—
70C2×Dic73—22no—
71D292—42no—
72D292—82no—
73C4×D73—42no—
74C4×D73—42no—
75Dic146—42no—
76#10596831—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—82no—
87C4×C73#35412yes—
88Dic73—42no—
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#6440811yescharacteristic, complemented
100#491—732no—
101#490—732no—
102#488—1462no—
103#417—1462no—
104#410—1462no—
105C4×M16—731no—
106#354—1462no—
107#353—734no—
108C2×#41—732no—
109C2×M16—1461no—
110C4⋊Q8—731no—
111#127—731no—
112#125—21no—
113#125—41no—
114#125C2×#6440812yes—
115#124—732no—
116#121—2921no—
117C4×D4—2921no—
118#117—2922no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C42C2×#6440811yescharacteristic
122#103—1464no—
123#102—1464no—
124#99—2922no—
125#99—1464no—
126#97—732no—
127C4×C8—1461no—
128#41—2922no—
129#41—2922no—
130C2×Q8—732no—
131C2×D4—2921no—
132C2×D4—732no—
133C2×D4—1462no—
134C22×C4—21no—
135C22×C4—41no—
136C22×C4—1462no—
137C22×C4C22⋊#6440811yescharacteristic
138M16—2922no—
139C2×C8—1462no—
140C4⋊C4—22no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C4⋊C4—2921no—
145C4⋊C4—5842no—
146C22⋊C4—2922no—
147C22⋊C4—2924no—
148C42—21no—
149C42—5842no—
150C42C22⋊#6440811yescharacteristic
151C42C22×#6440811yescharacteristic
152C23—1462no—
153C23#1455664911yescharacteristic
154Q8—2922no—
155D4—2922no—
156D4—5842no—
157D4—5842no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—2922no—
165C2×C4—2922no—
166C2×C4—5844no—
167C2×C4—1462no—
168C2×C4#1455664911yescharacteristic
169C2×C4C2×C22⋊#6440811yescharacteristic
170C8—2922no—
171C22—21no—
172C22—41no—
173C22—2922no—
174C22—5842no—
175C22C2×#1455664911yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—82no—
180C4—2922no—
181C4—11684no—
182C4#1798949312yes—
183C2—21no—
184C2—41no—
185C2—5842no—
186C2C2×#1798949311yescharacteristic
subgroupG/H
centerC2C2×#17989493
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×#125×C73C4
socleC2×C73C2×#354
prime radical#17989137C22
cosocle#14556588C23
hypercenterC2×#125#64408
hypocenterC73#13596
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #22625071C2semidirect
8. #17988957C4semidirect
12. C4×#11924012C4semidirect
13. C2×#125×C73C4semidirect
97. C73#13596semidirect
99. C2×#125#64408semidirect

Maximal subgroups

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

subgroupindex
#226262042
#226250712
#226203342
#1359673