Finite Group Databasebeta

← #34001007

Subgroups — #34001007

Order 18688.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#22624872C211yesmaximal, characteristic
2#22624807C211yesmaximal, characteristic
3#22611282C211yesmaximal, characteristic
4C2×#14556646—21no—
5#17989432—21no—
6#17989218C411yescharacteristic
7#17988629—21no—
8#17988452C2211yescharacteristic
9#17988348—21no—
10#343×C73C411yescharacteristic
11C22×#10596833—41no—
12C22⋊#10596833—41no—
13#14556646—22no—
14#14556646—41no—
15#14556590—41no—
16#14556582—41no—
17#14556570—41no—
18#14556550—21no—
19C2×C4⋊Dic73D411yescharacteristic
20C2×C4×Dic73D411yescharacteristic
21#14556525—41no—
22#14556523—41no—
23#14556498—41no—
24C2×M16×C73—21no—
25C2×C4⋊C4×C73C2×C411yescharacteristic
26C2×#10596833—42no—
27C2×#10596833—42no—
28C2×#10596833—42no—
29C2×#10596833—81no—
30C2×Dic146—41no—
31C22×Dic73—21no—
32C22×Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—41no—
36C4⋊Dic73—41no—
37#11924007—42no—
38C22⋊Dic73—41no—
39C4×Dic73—21no—
40C4×Dic73—41no—
41C4×Dic73SD1611yescharacteristic
42C4×Dic73Q1611yescharacteristic
43C22×C4×C73—21no—
44C22×C4×C73C22⋊C411yescharacteristic
45M16×C73—22no—
46M16×C73—41no—
47C2×C8×C73—41no—
48C4⋊C4×C73—41no—
49C23×C73#9911yescharacteristic
50C2×C4×C73—21no—
51C2×C4×C73—21no—
52C2×C4×C73—41no—
53C2×C4×C73—81no—
54C2×C4×C73#10311yescharacteristic
55C2×C4×C73#10411yescharacteristic
56C2×Dic73—21no—
57C2×Dic73—21no—
58C2×Dic73—41no—
59C2×Dic73—41no—
60C2×Dic73—41no—
61C2×Dic73—41no—
62C2×Dic73—41no—
63C2×Dic73—81no—
64Dic146—161no—
65#10596833—44no—
66#10596833—161no—
67C8×C73—42no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73#32811yescharacteristic
71C22×C73AΣL(1,𝔽16)11yescharacteristic
72C22×C73#35611yescharacteristic
73C4×C73—21no—
74C4×C73—21no—
75C4×C73—81no—
76Dic73—41no—
77Dic73—41no—
78Dic73—81no—
79Dic73—81no—
80Dic73—81no—
81#7442—731nomaximal, Sylow
82C2×C73—21no—
83C2×C73—21no—
84C2×C73#135411yescharacteristic
85C2×C73#140311yescharacteristic
86C2×C73#140411yescharacteristic
87#2061—731no—
88#1324—731no—
89#1295—731no—
90C73#744211yescharacteristic, complemented, Sylow
91#544—731no—
92#428—1461no—
93C2×#97—1461no—
94#382—731no—
95#343#6440811yescharacteristic
96#339—1461no—
97#324—1461no—
98C2×M16—21no—
99C22×C8—2921no—
100C4⋊Q8—2921no—
101#125—2921no—
102C22⋊Q8—2921no—
103#117—1461no—
104C2×C4⋊C4—731no—
105C2×C4⋊C4C2×#6440811yescharacteristic
106C2×C42—731no—
107#107—2921no—
108#106—2921no—
109C22⋊C8—2921no—
110#97—2921no—
111#97—1462no—
112#95—2921no—
113C2×Q8—2921no—
114C22×C4—21no—
115C22×C4—1461no—
116C22×C4—1461no—
117C22×C4C22⋊#6440811yescharacteristic
118M16—22no—
119M16—41no—
120C2×C8—41no—
121C2×C8—2922no—
122C2×C8—2922no—
123C2×C8—2922no—
124C2×C8—5841no—
125C4⋊C4—41no—
126C4⋊C4—2921no—
127C4⋊C4—2921no—
128C4⋊C4—2922no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C22⋊C4—2921no—
132C42—2921no—
133C42—731no—
134C42—731no—
135C42—1461no—
136C23#1455665011yescharacteristic
137Q8—11681no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—81no—
142C2×C4—2921no—
143C2×C4—2921no—
144C2×C4—2921no—
145C2×C4—2921no—
146C2×C4—2921no—
147C2×C4—5841no—
148C2×C4—1461no—
149C2×C4—1461no—
150C2×C4#1455665411yescharacteristic
151C2×C4#1455665511yescharacteristic
152C8—42no—
153C8—2924no—
154C8—11681no—
155C22—21no—
156C22—21no—
157C22#1798944011yescharacteristic
158C22#1798948811yescharacteristic
159C22#1798949811yescharacteristic
160C4—21no—
161C4—21no—
162C4—81no—
163C4—2921no—
164C4—2921no—
165C4—5841no—
166C4—5841no—
167C4—5841no—
168C2—21no—
169C2—21no—
170C2#2262493111yescharacteristic
171C2#2262505311yescharacteristic
172C2#2262505511yescharacteristic
subgroupG/H
centerC22#17989488
commutatorC2×C4⋊C4×C73C2×C4
FrattiniC2×C4⋊C4C2×#64408
Fitting#343×C73C4
socleC22×C73AΣL(1,𝔽16)
prime radicalC23×C73#99
cosocle#17988452C22
hypercenter#343#64408
hypocenterC73#7442
LCSG ▷ C2×C4⋊C4×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
90. C73#7442semidirect

Maximal subgroups

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

subgroupindex
#226248722
#226248072
#226112822
#744273