Finite Group Databasebeta

← #32973615

Subgroups — #32973615

Order 18688.

198 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 41 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#22611276C211yesmaximal, characteristic
2#22607814C211yesmaximal, characteristic
3C73×#1325C211yesmaximal, characteristic
4#17989218C411yescharacteristic
5#17988627—21no—
6C2×C4⋊#10596831—21no—
7#17988356C411yescharacteristic
8#17988347—21no—
9#384×C73C2211yescharacteristic
10#324×C73—21no—
11C2×#11924012—21no—
12C22×#10596831—41no—
13#14556590—41no—
14#14556582—41no—
15#14556570—41no—
16#14556550—21no—
17#14556524—41no—
18#14556522—41no—
19C4⋊#10596831—22no—
20C4⋊#10596831—41no—
21C2×C4⋊C4×C73—41no—
22C2×C4⋊C4×C73C2×C411yescharacteristic
23C2×C4⋊C4×C73D411yescharacteristic
24C2×C42×C73D411yescharacteristic
25C22⋊C8×C73—41no—
26C2×Dic146—41no—
27#11924012—22no—
28#11924012—41no—
29C2×#10596831—41no—
30C2×#10596831—42no—
31C2×#10596831—81no—
32C2×#10596831—81no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—41no—
36#11924007—42no—
37C22⋊Dic73—41no—
38C4×Dic73—41no—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73—21no—
42C22×C4×C73C22⋊C411yescharacteristic
43C2×C8×C73—81no—
44C4⋊C4×C73—41no—
45C4⋊C4×C73—41no—
46C4⋊C4×C73—81no—
47C4⋊C4×C73—81no—
48C42×C73—21no—
49C42×C73SD1611yescharacteristic
50C42×C73Q1611yescharacteristic
51C23×C73#9911yescharacteristic
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73—81no—
63C2×C4×C73—81no—
64C2×C4×C73#10311yescharacteristic
65C2×C4×C73#10411yescharacteristic
66C2×Dic73—41no—
67C2×Dic73—41no—
68Dic146—161no—
69C8×C73—161no—
70#10596831—42no—
71#10596831—82no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73#32811yescharacteristic
75C22×C73AΣL(1,𝔽16)11yescharacteristic
76C22×C73#35611yescharacteristic
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—21no—
83C4×C73—81no—
84C4×C73—81no—
85Dic73—81no—
86Dic73—81no—
87#7443—731nomaximal, Sylow
88C2×C73—21no—
89C2×C73—21no—
90C2×C73#135411yescharacteristic
91C2×C73#140211yescharacteristic
92C2×C73#140511yescharacteristic
93#2060—731no—
94#1325D7311yescharacteristic
95#1296—731no—
96C73#744311yescharacteristic, complemented, Sylow
97#544—731no—
98#428—1461no—
99C2×C4⋊C8—1461no—
100#384C2×D7311yescharacteristic
101#343—731no—
102#339—1461no—
103#324—21no—
104C2×M16—1461no—
105C22×C8—2921no—
106C4⋊Q8—2921no—
107#125—2921no—
108C22⋊Q8—2921no—
109#117—1461no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C4×D7311yescharacteristic
112C2×C4⋊C4C22⋊D7311yescharacteristic
113C2×C42D29211yescharacteristic
114#107—2921no—
115#106—2921no—
116C4⋊C8—2921no—
117C4⋊C8—1462no—
118C22⋊C8—41no—
119C2×Q8—2921no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4#1192400511yescharacteristic
124M16—2921no—
125M16—1462no—
126C2×C8—81no—
127C2×C8—2921no—
128C2×C8—2922no—
129C2×C8—5841no—
130C2×C8—5841no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—2921no—
136C4⋊C4—2922no—
137C4⋊C4—1461no—
138C4⋊C4—1461no—
139C22⋊C4—2921no—
140C42—21no—
141C42—2921no—
142C42#1192401711yescharacteristic
143C42Dic29211yescharacteristic
144C23#1455650511yescharacteristic
145Q8—11681no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—2921no—
159C2×C4—2921no—
160C2×C4#1455651611yescharacteristic
161C2×C4#1455651711yescharacteristic
162C8—161no—
163C8—2922no—
164C8—5842no—
165C22—21no—
166C22—21no—
167C22#1798832511yescharacteristic
168C22#1798837311yescharacteristic
169C22#1798838511yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—5841no—
179C4—5841no—
180C2—21no—
181C2—21no—
182C2#2260796211yescharacteristic
183C2#2260807511yescharacteristic
184C2#2260808411yescharacteristic
subgroupG/H
centerC22#17988373
commutatorC2×C4⋊C4×C73C2×C4
Frattini#384C2×D73
FittingC73×#1325C2
socleC22×C73AΣL(1,𝔽16)
prime radicalC23×C73#99
cosocle#384×C73C22
hypercenter#1325D73
hypocenterC73#7443
LCSG ▷ C2×C4⋊C4×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
96. C73#7443semidirect

Maximal subgroups

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

subgroupindex
#226112762
#226078142
C73×#13252
#744373