Finite Group Databasebeta

← #33000390

Subgroups — #33000390

Order 18688.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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#22612174C211yesmaximal, characteristic, complemented
2#22612104C211yesmaximal, characteristic, complemented
3#22612008C211yesmaximal, characteristic
4#22611772C211yesmaximal, characteristic, complemented
5#22607998C211yesmaximal, characteristic, complemented
6#22607967C211yesmaximal, characteristic, complemented
7C73×#1366C211yesmaximal, characteristic, complemented
8#17989025—21no—
9#17989005—21no—
10#17988964C2211yescharacteristic
11#17988705C2211yescharacteristic
12#17988409—21no—
13#17988408C2211yescharacteristic
14#17988401—21no—
15#17988396—21no—
16#17988387—21no—
17#17988387—21no—
18#17988372—21no—
19#17988363C2211yescharacteristic
20#499×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#364×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24C2×D584—21no—
25C2×D584—21no—
26#14556597—21no—
27#14556588—21no—
28#14556536—41no—
29D1168—41no—
30#14556531—21no—
31#14556530—41no—
32C2×#11924003D411yescharacteristic
33C2×#11924003D411yescharacteristic
34C16×D73—41no—
35#14556527D411yescharacteristic
36#14556519—21no—
37#125×C73—21no—
38M32×C73—21no—
39M32×C73—21no—
40#107×C73—21no—
41#106×C73—21no—
42C4×C8×C73C2311yescharacteristic
43#11924028—21no—
44C2×D292—41no—
45C2×D292—81no—
46Dic292SD1611yescharacteristic
47#11924017—21no—
48D584—41no—
49D584—41no—
50D584—41no—
51D584—41no—
52D584SD1611yescharacteristic
53#11924012—21no—
54#11924011—41no—
55C8×D73—41no—
56#11924003—21no—
57#11924003—21no—
58#11924003—41no—
59C2×C8×C73C2×D411yescharacteristic
60C2×C8×C73C2×D411yescharacteristic
61C4⋊C4×C73—41no—
62C4⋊C4×C73—81no—
63C42×C73#4111yescharacteristic
64C16×C73—41no—
65C16×C73—41no—
66C22×D73—81no—
67C2×C4×C73—21no—
68C2×C4×C73—81no—
69C2×C4×C73#12111yescharacteristic
70C22⋊D73—41no—
71D292—21no—
72D292—81no—
73D292—81no—
74D292—162no—
75C4×D73—41no—
76Dic146—21no—
77C8×C73C2×SD1611yescharacteristic
78C8×C73#13511yescharacteristic
79C8×C73#13511yescharacteristic
80C8×C73AGL(1,ℤ/8)11yescharacteristic
81#10596831—41no—
82C22×C73#47211yescharacteristic
83C2×D73—41no—
84C2×D73—162no—
85C2×D73—161no—
86C4×C73—41no—
87C4×C73—161no—
88C4×C73#46311yescharacteristic
89C4×C73#46511yescharacteristic
90Dic73—41no—
91#12465—731nomaximal, Sylow
92C2×C73—21no—
93C2×C73#167711yescharacteristic
94D73—81no—
95D73—321no—
96#2244—731no—
97#2231—731no—
98#2213—731no—
99#2171—731no—
100#1369—731no—
101#1366D7311yescharacteristic, complemented
102#1357—731no—
103C73#1246511yescharacteristic, complemented, Sylow
104#509—1461no—
105#504—1461no—
106#499C2×D7311yescharacteristic
107#493—731no—
108#443—731no—
109#365—1461no—
110#364—731no—
111#364C2×D7311yescharacteristic
112#364C2×D7311yescharacteristic
113#361—1461no—
114#360—1461no—
115#357—1461no—
116#357—1461no—
117#350—1461no—
118#346—731no—
119#135—731no—
120C2×D8—1461no—
121C2×D8—1461no—
122#131—1461no—
123#127—1461no—
124#125—21no—
125SD32—2921no—
126D16—2921no—
127M32—21no—
128M32—21no—
129M32—2921no—
130M32—1461no—
131C2×C16—2921no—
132C2×C16—731no—
133C2×C16—731no—
134#108—731no—
135#107—21no—
136#106—21no—
137#104—1461no—
138C4×C8C22×D7311yescharacteristic
139#41—1461no—
140C2×D4—2921no—
141C2×D4—5841no—
142Q16—731no—
143SD16—1461no—
144D8—2921no—
145D8—2921no—
146D8—2921no—
147D8—2921no—
148D8—731no—
149M16—2921no—
150M16—1461no—
151C2×C8—2921no—
152C2×C8D4×D7311yescharacteristic
153C2×C8D4×D7311yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1192402811yescharacteristic
157C16—41no—
158C16—41no—
159C16—2921no—
160C16—1461no—
161C16—1461no—
162C23—5841no—
163Q8—1461no—
164D4—2921no—
165D4—5841no—
166D4—5841no—
167D4—11682no—
168D4—1461no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—2921no—
172C2×C4#1455656411yescharacteristic
173C8—2921no—
174C8SD16×D7311yescharacteristic
175C8#1455661411yescharacteristic
176C8#1455661411yescharacteristic
177C8#1455661811yescharacteristic
178C22—2921no—
179C22—11682no—
180C22—11681no—
181C22#1798885611yescharacteristic
182C4—41no—
183C4—161no—
184C4—2921no—
185C4#1798880511yescharacteristic
186C4#1798881911yescharacteristic
187C2—21no—
188C2—23361no—
189C2—5841no—
190C2#2260934311yescharacteristic
subgroupG/H
centerC2#22609343
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1366C2
socleC2×C73#1677
prime radical#22612008C2
hypercenter#1366D73
hypocenterC73#12465
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #22612174C2semidirect
2. #22612104C2semidirect
4. #22611772C2semidirect
5. #22607998C2semidirect
6. #22607967C2semidirect
7. C73×#1366C2semidirect
101. #1366D73semidirect
103. C73#12465semidirect

Maximal subgroups

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

subgroupindex
#226121742
#226121042
#226120082
#226117722
#226079982
#226079672
C73×#13662
#1246573