Finite Group Databasebeta

← #33000395

Subgroups — #33000395

Order 18688.

186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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#22612177C211yesmaximal, characteristic, complemented
2#22612108C211yesmaximal, characteristic
3#22612013C211yesmaximal, characteristic
4#22611774C211yesmaximal, characteristic
5#22607991C211yesmaximal, characteristic, complemented
6#22607969C211yesmaximal, characteristic, complemented
7C73×#1369C211yesmaximal, characteristic, complemented
8#17989030—21no—
9#17989003—21no—
10#17988989C2211yescharacteristic
11#17988967C2211yescharacteristic
12#17988705C2211yescharacteristic
13#17988410—21no—
14#17988408C2211yescharacteristic
15#17988404—21no—
16#17988398—21no—
17#17988392—21no—
18#17988392—21no—
19#17988370—21no—
20#364×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#346×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24C2×Dic292—21no—
25C2×Dic292—21no—
26#14556597—21no—
27#14556591—21no—
28#14556583—21no—
29Dic584—41no—
30#14556536—41no—
31#14556531—21no—
32#14556530—41no—
33C16×D73—41no—
34#14556527D411yescharacteristic
35#14556525—21no—
36#14556523—21no—
37#14556519—21no—
38M32×C73—21no—
39M32×C73—21no—
40C2×C16×C73D411yescharacteristic
41C2×C16×C73D411yescharacteristic
42C4×C8×C73C2311yescharacteristic
43#11924028—21no—
44C2×Dic146—41no—
45Dic292—41no—
46Dic292—41no—
47Dic292—41no—
48Dic292—41no—
49Dic292SD1611yescharacteristic
50#11924017—21no—
51D584SD1611yescharacteristic
52#11924012—21no—
53#11924011—41no—
54C8×D73—41no—
55C4⋊Dic73—41no—
56C4⋊Dic73—81no—
57#11924007—81no—
58#11924003—41no—
59C2×C8×C73C2×D411yescharacteristic
60C2×C8×C73C2×D411yescharacteristic
61C42×C73#4111yescharacteristic
62C16×C73—21no—
63C16×C73—21no—
64C16×C73—41no—
65C16×C73—41no—
66C2×C4×C73—21no—
67C2×C4×C73#12111yescharacteristic
68C22⋊D73—41no—
69C2×Dic73—81no—
70C2×Dic73—81no—
71D292—21no—
72C4×D73—41no—
73Dic146—21no—
74Dic146—81no—
75Dic146—81no—
76C8×C73C2×SD1611yescharacteristic
77C8×C73#13511yescharacteristic
78C8×C73#13511yescharacteristic
79C8×C73AGL(1,ℤ/8)11yescharacteristic
80#10596831—41no—
81C22×C73#47211yescharacteristic
82C2×D73—41no—
83C4×C73—41no—
84C4×C73#46311yescharacteristic
85C4×C73#46511yescharacteristic
86Dic73—41no—
87Dic73—161no—
88Dic73—161no—
89#12466—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73#167711yescharacteristic
92D73—81no—
93#2245—731no—
94#2231—731no—
95#2214—731no—
96#2171—731no—
97#1369D7311yescharacteristic, complemented
98#1366—731no—
99#1358—731no—
100C73#1246611yescharacteristic, complemented, Sylow
101#510—1461no—
102#504—1461no—
103#499—731no—
104#494—731no—
105#443—731no—
106#365—1461no—
107#364—731no—
108#364C2×D7311yescharacteristic
109#364C2×D7311yescharacteristic
110#362—1461no—
111#360—1461no—
112#358—1461no—
113#358—1461no—
114#350—1461no—
115#346C2×D7311yescharacteristic
116#135—731no—
117C2×Q16—1461no—
118C2×Q16—1461no—
119#131—1461no—
120C4⋊Q8—1461no—
121#125—1461no—
122Q32—2921no—
123SD32—2921no—
124M32—21no—
125M32—21no—
126M32—2921no—
127M32—1461no—
128C2×C16—2921no—
129C2×C16D29211yescharacteristic
130C2×C16D29211yescharacteristic
131#108—731no—
132#107—1461no—
133#106—1461no—
134#104—1461no—
135C4×C8C22×D7311yescharacteristic
136#41—1461no—
137C2×Q8—2921no—
138Q16—2921no—
139Q16—2921no—
140Q16—2921no—
141Q16—2921no—
142Q16—731no—
143SD16—1461no—
144D8—731no—
145M16—2921no—
146M16—1461no—
147C2×C8—2921no—
148C2×C8D4×D7311yescharacteristic
149C2×C8C2×D29211yescharacteristic
150C4⋊C4—2921no—
151C4⋊C4—5841no—
152C4⋊C4—5841no—
153C42#1192402911yescharacteristic
154C16—21no—
155C16—21no—
156C16—41no—
157C16—41no—
158C16—2921no—
159Q8—5841no—
160Q8—5841no—
161Q8—1461no—
162D4—2921no—
163D4—1461no—
164C2×C4—21no—
165C2×C4—2921no—
166C2×C4—5841no—
167C2×C4—5841no—
168C2×C4#1455656611yescharacteristic
169C8—2921no—
170C8SD16×D7311yescharacteristic
171C8#1455661211yescharacteristic
172C8#1455661311yescharacteristic
173C8#1455661911yescharacteristic
174C22—2921no—
175C22#1798885811yescharacteristic
176C4—41no—
177C4—2921no—
178C4—11681no—
179C4—11681no—
180C4#1798880311yescharacteristic
181C4#1798881711yescharacteristic
182C2—21no—
183C2—5841no—
184C2#2260934111yescharacteristic
subgroupG/H
centerC2#22609341
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1369C2
socleC2×C73#1677
prime radical#14556613D4
hypercenter#1369D73
hypocenterC73#12466
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1369

Complements

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

NH ≅ G/Ntype
1. #22612177C2semidirect
5. #22607991C2semidirect
6. #22607969C2semidirect
7. C73×#1369C2semidirect
97. #1369D73semidirect
100. C73#12466semidirect

Maximal subgroups

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

subgroupindex
#226121772
#226121082
#226120132
#226117742
#226079912
#226079692
C73×#13692
#1246673