Finite Group Databasebeta

← #33000384

Subgroups — #33000384

Order 18688.

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

normal subgroups only

This group has 196 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#22612104C211yesmaximal, characteristic, complemented
2#22612004C211yesmaximal, characteristic
3#22611774C211yesmaximal, characteristic, complemented
4#22607999C211yesmaximal, characteristic, complemented
5#22607992C211yesmaximal, characteristic, complemented
6#22607968C211yesmaximal, characteristic, complemented
7C73×#2244C211yesmaximal, characteristic, complemented
8#17989023—21no—
9#17989003—21no—
10#17988705C2211yescharacteristic
11#17988409—21no—
12#17988408C2211yescharacteristic
13#17988408C2211yescharacteristic
14#17988408C2211yescharacteristic
15#17988400—21no—
16#17988396—21no—
17#17988370—21no—
18#499×C73C2211yescharacteristic
19#493×C73C2211yescharacteristic
20#357×C73—21no—
21#357×C73—21no—
22#346×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24#14556597—21no—
25#14556535—41no—
26#14556532—41no—
27#14556531—21no—
28#14556531—21no—
29#14556531—21no—
30#14556530—41no—
31C16×D73—41no—
32#14556527D411yescharacteristic
33#14556519—21no—
34C2×D8×C73—21no—
35C2×D8×C73—21no—
36#127×C73—21no—
37#125×C73—21no—
38C2×C16×C73D411yescharacteristic
39C2×C16×C73D411yescharacteristic
40#107×C73—21no—
41#106×C73—21no—
42C4×C8×C73C2311yescharacteristic
43#11924028—21no—
44Dic292SD1611yescharacteristic
45#11924017—21no—
46D584SD1611yescharacteristic
47#11924012—21no—
48#11924011—41no—
49C8×D73—41no—
50#11924003—41no—
51#11924003—41no—
52#11924003—41no—
53C2×D4×C73—41no—
54C2×D4×C73—81no—
55D8×C73—41no—
56D8×C73—41no—
57D8×C73—41no—
58D8×C73—41no—
59C2×C8×C73C2×D411yescharacteristic
60C2×C8×C73C2×D411yescharacteristic
61C4⋊C4×C73—41no—
62C4⋊C4×C73—81no—
63C42×C73#4111yescharacteristic
64C16×C73—21no—
65C16×C73—21no—
66C23×C73—81no—
67D4×C73—81no—
68D4×C73—81no—
69D4×C73—162no—
70C2×C4×C73—21no—
71C2×C4×C73—81no—
72C2×C4×C73#12111yescharacteristic
73C22⋊D73—41no—
74D292—21no—
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—162no—
83C22×C73—161no—
84C22×C73#47211yescharacteristic
85C2×D73—41no—
86C4×C73—41no—
87C4×C73—161no—
88C4×C73#46311yescharacteristic
89C4×C73#46511yescharacteristic
90Dic73—41no—
91#12465—731nomaximal, Sylow
92C2×C73—21no—
93C2×C73—321no—
94C2×C73#167711yescharacteristic
95D73—81no—
96#2244D7311yescharacteristic, complemented
97#2231—731no—
98#2213—731no—
99#2171—731no—
100#1369—731no—
101#1366—731no—
102#1357—731no—
103C73#1246511yescharacteristic, complemented, Sylow
104#509—1461no—
105#504—1461no—
106#499C2×D7311yescharacteristic
107#493C2×D7311yescharacteristic
108#443—731no—
109#365—1461no—
110#364—731no—
111#364—731no—
112#364—731no—
113#361—1461no—
114#360—1461no—
115#357—21no—
116#357—21no—
117#350—1461no—
118#346C2×D7311yescharacteristic
119#135—731no—
120C2×D8—21no—
121C2×D8—21no—
122#131—1461no—
123#127—21no—
124#125—21no—
125SD32—2921no—
126D16—2921no—
127M32—2921no—
128M32—1461no—
129M32—1461no—
130M32—1461no—
131C2×C16—2921no—
132C2×C16C22⋊D7311yescharacteristic
133C2×C16C22⋊D7311yescharacteristic
134#108—731no—
135#107—21no—
136#106—21no—
137#104—1461no—
138C4×C8C22×D7311yescharacteristic
139#41—1461no—
140C2×D4—41no—
141C2×D4—81no—
142Q16—731no—
143SD16—1461no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8—731no—
149M16—2921no—
150M16—1461no—
151C2×C8—2921no—
152C2×C8D4×D7311yescharacteristic
153C2×C8C2×C22⋊D7311yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1192402711yescharacteristic
157C16—21no—
158C16—21no—
159C16—2921no—
160C16—2921no—
161C16—2921no—
162C23—81no—
163Q8—1461no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—2921no—
168D4—1461no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—2921no—
172C2×C4#1455656211yescharacteristic
173C8—2921no—
174C8SD16×D7311yescharacteristic
175C8#1455661111yescharacteristic
176C8#1455661211yescharacteristic
177C8#1455661611yescharacteristic
178C22—162no—
179C22—161no—
180C22—2921no—
181C22#1798885411yescharacteristic
182C4—41no—
183C4—161no—
184C4—2921no—
185C4#1798879911yescharacteristic
186C4#1798881311yescharacteristic
187C2—21no—
188C2—321no—
189C2—5841no—
190C2#2260933711yescharacteristic
subgroupG/H
centerC2#22609337
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2244C2
socleC2×C73#1677
prime radical#22612004C2
hypercenter#2244D73
hypocenterC73#12465
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #22612104C2semidirect
3. #22611774C2semidirect
4. #22607999C2semidirect
5. #22607992C2semidirect
6. #22607968C2semidirect
7. C73×#2244C2semidirect
96. #2244D73semidirect
103. C73#12465semidirect

Maximal subgroups

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

subgroupindex
#226121042
#226120042
#226117742
#226079992
#226079922
#226079682
C73×#22442
#1246573