Finite Group Databasebeta

← #34033040

Subgroups — #34033040

Order 18688.

204 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 31 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#22626967C212yesmaximal
2#22626062C211yesmaximal, characteristic
3#17989673—22no—
4C2×#14556654—22no—
5#17989546C411yescharacteristic
6#17989531C2211yescharacteristic
7C4⋊Q8×D73C411yescharacteristic
8C22⋊#10596842—42no—
9C2×#11924036—21no—
10C2×C4⋊#64408D412yes—
11#14556654—44no—
12#14556646—41no—
13(C2×#64408)⋊C4—41no—
14C2×Q8×D73—21no—
15#14556591C811yescharacteristic, complemented
16#14556590—41no—
17#14556589—21no—
18C4⋊C4×D73—41no—
19C42×D73C2×C411yescharacteristic
20C4⋊Q8×C73C811yescharacteristic, complemented
21C2×#10596842—82no—
22C22×#64408—22no—
23#11924036—22no—
24#11924036—41no—
25C2×#10596833—41no—
26C4⋊#64408—42no—
27C2×Dic146—21no—
28C2×Dic146—41no—
29Q8×D73—42no—
30Q8×D73—42no—
31C2×C4×D73—21no—
32C2×C4×D73—41no—
33C2×C4×D73C22⋊C411yescharacteristic
34C4⋊Dic73—41no—
35#11924007—42no—
36C4×Dic73—21no—
37C4×Dic73M1611yescharacteristic
38C2×Q8×C73—21no—
39C4⋊C4×C73—41no—
40C42×C73C2×C811yescharacteristic
41C22×D73#9911yescharacteristic
42C2×#64408—42no—
43C2×#64408—82no—
44#10596842—162no—
45Q8×C73—42no—
46C2×C4×C73—21no—
47C2×C4×C73—41no—
48C2×C4×C73C22⋊C811yescharacteristic
49C2×Dic73—21no—
50C2×Dic73—41no—
51C2×Dic73#10011yescharacteristic
52C4×D73—21no—
53C4×D73—21no—
54C4×D73—42no—
55C4×D73—81no—
56C4×D73—81no—
57Dic146—42no—
58Dic146—82no—
59#10596833—42no—
60C22×C73#32311yescharacteristic
61C2×D73—22no—
62C2×D73#35311yescharacteristic
63C2×D73#35511yescharacteristic
64#64408—82no—
65C4×C73—21no—
66C4×C73—41no—
67C4×C73—81no—
68Dic73—21no—
69Dic73—41no—
70Dic73—81no—
71#7353—731nomaximal, Sylow
72C2×C73—21no—
73C2×C73#131811yescharacteristic
74D73—21no—
75D73#140712yes—
76#1960—731no—
77#1324—732no—
78C73#735311yescharacteristic, complemented, Sylow
79C2×C4⋊Q8—731no—
80C2×#103—1462no—
81C2×#97—731no—
82#382—731no—
83#324—1462no—
84C22×Q8—1461no—
85C22×C8—1461no—
86C4⋊Q8—2921no—
87C4⋊Q8—731no—
88C4⋊Q8—1461no—
89C4⋊Q8#1059684211yescharacteristic, complemented
90C2×C4⋊C4—2921no—
91C2×C4⋊C4—732no—
92C2×C42—731no—
93#103—2924no—
94C22⋊C8—2922no—
95#97—2921no—
96#95—2921no—
97C2×Q8—21no—
98C2×Q8—2921no—
99C2×Q8—2922no—
100C2×Q8—2922no—
101C2×Q8—1461no—
102C22×C4—2921no—
103C22×C4—731no—
104C22×C4—1461no—
105C22×C4—1462no—
106C2×C8—2921no—
107C2×C8—2921no—
108C2×C8—5842no—
109C2×C8—1462no—
110C4⋊C4—41no—
111C4⋊C4—2921no—
112C4⋊C4—2922no—
113C4⋊C4—2922no—
114C42—731no—
115C42—1461no—
116C42C2×#1059684211yescharacteristic
117C23—731no—
118Q8—42no—
119Q8—2922no—
120Q8—5842no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—2922no—
124C2×C4—2922no—
125C2×C4—2921no—
126C2×C4—5841no—
127C2×C4—5841no—
128C2×C4—5842no—
129C2×C4—731no—
130C2×C4—1461no—
131C2×C4—1461no—
132C2×C4—1461no—
133C2×C4C22⋊#1059684211yescharacteristic
134C8—2922no—
135C8—11682no—
136C22—731no—
137C22—731no—
138C22—1462no—
139C22#1798967211yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—2921no—
144C4—5842no—
145C4—5841no—
146C4—1461no—
147C2—21no—
148C2—732no—
149C2—1461no—
150C2#2262695811yescharacteristic
subgroupG/H
centerC2#22626958
commutatorC42×C73C2×C8
FrattiniC42C2×#10596842
FittingC4⋊Q8×C73C8
socleC2×C73#1318
prime radicalC22×D73#99
cosocle#17989531C22
hypercenterC4⋊Q8#10596842
hypocenterC73#7353
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
15. #14556591C8semidirect
20. C4⋊Q8×C73C8semidirect
78. C73#7353semidirect
89. C4⋊Q8#10596842semidirect

Maximal subgroups

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

subgroupindex
#226269672
#226260622
#735373