Finite Group Databasebeta

← #34033042

Subgroups — #34033042

Order 18688.

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

normal subgroups only

This group has 216 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#22626968C212yesmaximal
2#22626058C211yesmaximal, characteristic
3#17989673—22no—
4C2×#14556654—22no—
5C4×#11924036C411yescharacteristic
6#17989533C2211yescharacteristic
7C4⋊Q8×D73C411yescharacteristic
8C22⋊#10596842—42no—
9C2×#11924036—21no—
10C2×C4⋊#64408—41no—
11C2×C4⋊#64408D412yes—
12#14556654—44no—
13C4×#10596833—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—
27C4⋊#64408—82no—
28C2×Dic146—21no—
29C2×Dic146—41no—
30Q8×D73—42no—
31Q8×D73—42no—
32C2×C4×D73—21no—
33C2×C4×D73—41no—
34C2×C4×D73C22⋊C411yescharacteristic
35C4⋊Dic73—41no—
36#11924007—42no—
37C4×Dic73—21no—
38C4×Dic73M1611yescharacteristic
39C2×Q8×C73—21no—
40C4⋊C4×C73—41no—
41C42×C73C2×C811yescharacteristic
42C22×D73#9911yescharacteristic
43C2×#64408—42no—
44C2×#64408—82no—
45#10596842—162no—
46Q8×C73—42no—
47C2×C4×C73—21no—
48C2×C4×C73—41no—
49C2×C4×C73C22⋊C811yescharacteristic
50C2×Dic73—21no—
51C2×Dic73—41no—
52C2×Dic73#10011yescharacteristic
53C4×D73—22no—
54C4×D73—22no—
55C4×D73—21no—
56C4×D73—21no—
57C4×D73—81no—
58C4×D73—81no—
59Dic146—42no—
60Dic146—82no—
61#10596833—42no—
62C22×C73#32311yescharacteristic
63C2×D73—21no—
64C2×D73—21no—
65C2×D73#35311yescharacteristic
66C2×D73#35511yescharacteristic
67#64408—82no—
68C4×C73—22no—
69C4×C73—21no—
70C4×C73—81no—
71Dic73—22no—
72Dic73—21no—
73Dic73—81no—
74#7355—731nomaximal, Sylow
75C2×C73—21no—
76C2×C73#131811yescharacteristic
77D73—21no—
78D73#140911yescharacteristic
79D73#141111yescharacteristic
80#1956—731no—
81#1325—732no—
82C73#735511yescharacteristic, complemented, Sylow
83C2×C4⋊Q8—731no—
84C2×#103—1462no—
85C2×C4×C8—731no—
86#384—731no—
87#324—1462no—
88C22×Q8—1461no—
89C22×C8—1461no—
90C4⋊Q8—2921no—
91C4⋊Q8—731no—
92C4⋊Q8—1461no—
93C4⋊Q8#1059684211yescharacteristic, complemented
94C2×C4⋊C4—2921no—
95C2×C4⋊C4—2921no—
96C2×C4⋊C4—732no—
97C2×C42—731no—
98#103—2924no—
99C22⋊C8—2922no—
100C4×C8—2921no—
101C2×Q8—21no—
102C2×Q8—2921no—
103C2×Q8—2922no—
104C2×Q8—2922no—
105C2×Q8—1461no—
106C22×C4—2921no—
107C22×C4—731no—
108C22×C4—1461no—
109C22×C4—1462no—
110C2×C8—2921no—
111C2×C8—2921no—
112C2×C8—5842no—
113C2×C8—1462no—
114C4⋊C4—41no—
115C4⋊C4—2921no—
116C4⋊C4—2922no—
117C4⋊C4—2922no—
118C4⋊C4—5842no—
119C42—731no—
120C42—1461no—
121C42C2×#1059684211yescharacteristic
122C23—731no—
123Q8—42no—
124Q8—2922no—
125Q8—5842no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—2922no—
129C2×C4—2921no—
130C2×C4—5841no—
131C2×C4—5841no—
132C2×C4—5842no—
133C2×C4—731no—
134C2×C4—1461no—
135C2×C4—1461no—
136C2×C4—1462no—
137C2×C4—1462no—
138C2×C4—1461no—
139C2×C4C22⋊#1059684211yescharacteristic
140C8—2922no—
141C8—11682no—
142C22—731no—
143C22—731no—
144C22—1461no—
145C22—1461no—
146C22#1798967211yescharacteristic
147C4—22no—
148C4—21no—
149C4—81no—
150C4—5842no—
151C4—5841no—
152C4—1462no—
153C4—1461no—
154C2—21no—
155C2—731no—
156C2—731no—
157C2—1461no—
158C2#2262695811yescharacteristic
subgroupG/H
centerC2#22626958
commutatorC42×C73C2×C8
FrattiniC42C2×#10596842
FittingC4⋊Q8×C73C8
socleC2×C73#1318
prime radicalC22×D73#99
cosocle#17989533C22
hypercenterC4⋊Q8#10596842
hypocenterC73#7355
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
82. C73#7355semidirect
93. C4⋊Q8#10596842semidirect

Maximal subgroups

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

subgroupindex
#226269682
#226260582
#735573