Finite Group Databasebeta

← #25000691

Subgroups — #25000691

Order 11008.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#19145940C211yesmaximal, characteristic
2#19133293C212yesmaximal
3#19133106C212yesmaximal
4#19132465C211yesmaximal, characteristic
5C43×#1843C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583195—22no—
8#14583140—22no—
9#14583110—22no—
10#14582956C2212yes—
11#14582646—22no—
12#14582644—22no—
13#14582635—24no—
14C2×C4⋊C8×C43—22no—
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×C4⋊C8×C43C2211yescharacteristic
17C43×#376C2211yescharacteristic
18C2×Dic172—22no—
19#13063325D412yes—
20#13063325D412yes—
21#13063317—22no—
22#13063304—22no—
23#13063304—22no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26#13063284—22no—
27#13063259—22no—
28C4⋊(C43⋊C8)—22no—
29#13063250—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32C22×C8×C43—21no—
33C22×C8×C43D412yes—
34C2×C42×C43—21no—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38C4⋊C8×C43—44no—
39#95×C43—21no—
40#95×C43D412yes—
41C22×C4×C43—22no—
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43C2×D411yescharacteristic
44C22×C4×C43#4111yescharacteristic
45C2×Dic86—22no—
46C2×Dic86—22no—
47C2×C8×C43—22no—
48C2×C8×C43—42no—
49C2×C8×C43—42no—
50C2×C8×C43—41no—
51C42×C43—22no—
52C42×C43—22no—
53C42×C43C2×D412yes—
54C42×C43#4112yes—
55C22⋊Dic43—42no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60Dic43⋊C4—42no—
61Dic43⋊C4—42no—
62C4×Dic43—42no—
63C2×C43⋊C8—42no—
64Dic172—82no—
65C23×C43#12111yescharacteristic
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—24no—
70C2×C4×C43—41no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43#12011yescharacteristic
74C2×C4×C43#12112yes—
75C2×C4×C43#12312yes—
76C2×C4×C43#12411yescharacteristic
77C2×Dic43—42no—
78C2×Dic43—42no—
79Dic86—42no—
80Dic86—42no—
81Dic86—82no—
82C8×C43—42no—
83C8×C43—81no—
84C43⋊C8—82no—
85#10516—431nomaximal, Sylow
86C22×C43—21no—
87C22×C43—21no—
88C22×C43#39411yescharacteristic
89C22×C43#47312yes—
90C4×C43—22no—
91C4×C43—21no—
92C4×C43—22no—
93C4×C43—44no—
94C4×C43#45311yescharacteristic
95C4×C43#45611yescharacteristic
96Dic43—82no—
97Dic43—82no—
98#3249—431no—
99#1843D4311yescharacteristic
100#1552—432no—
101#1506—432no—
102#1290—431no—
103C2×C43—22no—
104C2×C43#203911yescharacteristic
105C2×C43#204711yescharacteristic
106C2×C43#205311yescharacteristic
107#533—432no—
108#477—862no—
109#467—862no—
110#462—862no—
111#432—432no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8C2×D4311yescharacteristic
114C2×C4⋊C8C2×D4311yescharacteristic
115#376C2×D4311yescharacteristic
116#332—862no—
117#332—862no—
118#328—864no—
119C43#1051611yescharacteristic, complemented, Sylow
120C2×Q16—862no—
121C22×C8—21no—
122C22×C8C22⋊D4312yes—
123C4⋊Q8—432no—
124C4⋊Q8—432no—
125#125—862no—
126C22⋊Q8—862no—
127C22⋊Q8—862no—
128C4×Q8—862no—
129C4×Q8—862no—
130#117—862no—
131C2×C42—21no—
132C2×C42C22×D4311yescharacteristic
133#107—862no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—862no—
138#103—864no—
139C22⋊C8—862no—
140#97—862no—
141#95—21no—
142#95D17212yes—
143C2×Q8—862no—
144C2×Q8—862no—
145C22×C4—22no—
146C22×C4C2×D17211yescharacteristic
147C22×C4#1062189811yescharacteristic
148C22×C4C2×C22⋊D4311yescharacteristic
149Q16—3442no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—1722no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—862no—
158C4⋊C4—862no—
159C4⋊C4—1722no—
160C4⋊C4—1722no—
161C22⋊C4—1722no—
162C42—22no—
163C42—22no—
164C42—1722no—
165C42D4×D4312yes—
166C42#1062190212yes—
167C23#1306329911yescharacteristic
168Q8—3442no—
169Q8—1722no—
170Q8—1722no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—1722no—
179C2×C4—1722no—
180C2×C4#1306329311yescharacteristic
181C2×C4#1306330012yes—
182C2×C4#1306331012yes—
183C2×C4#1306331411yescharacteristic
184C8—42no—
185C8—81no—
186C8—3442no—
187C22—21no—
188C22—21no—
189C22#1458281611yescharacteristic
190C22#1458317412yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—3442no—
196C4—3442no—
197C4#1458306611yescharacteristic
198C4#1458308111yescharacteristic
199C2—22no—
200C2#1913581911yescharacteristic
201C2#1913586311yescharacteristic
202C2#1913590111yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1843C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1843D43
hypocenterC43#10516
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
119. C43#10516semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191332932
#191331062
#191324652
C43×#18432
#1051643