Finite Group Databasebeta

← #25000766

Subgroups — #25000766

Order 11008.

402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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#19134766C211yesmaximal, characteristic, complemented
2#19133330C212yesmaximal, complemented
3#19133046C212yesmaximal, complemented
4C43⋊#1309C211yesmaximal, characteristic, complemented
5C43×#3253C211yesmaximal, characteristic
6C2×#13063260—22no—
7#14582923C2211yescharacteristic
8#14582923C2212yes—
9C2×C4×C43⋊C8C2211yescharacteristic
10#14582648—22no—
11#14582643—22no—
12D4⋊(C43⋊C8)—24no—
13C43×#532C2212yes—
14C43×#476—22no—
15C43×#469—22no—
16C43×#459—22no—
17C43×#423C2211yescharacteristic
18C2×#10621877—21no—
19C2×#10621877—22no—
20C22×C43⋊C8—21no—
21#13063260—44no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)—22no—
25C4×C43⋊C8—21no—
26C4×C43⋊C8D412yes—
27C2×#41×C43—22no—
28C2×D8×C43—22no—
29C2×M16×C43D412yes—
30C4⋊Q8×C43D412yes—
31#127×C43D412yes—
32#124×C43—22no—
33#121×C43—22no—
34#121×C43—22no—
35C4×D4×C43—22no—
36C4×D4×C43—22no—
37C2×C42×C43C2311yescharacteristic
38#106×C43—22no—
39C4⋊C8×C43—22no—
40#102×C43—24no—
41#41×C43—82no—
42#41×C43—82no—
43C2×Q8×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—22no—
46C2×D4×C43—22no—
47C2×D4×C43—42no—
48C22×C4×C43—42no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43#4112yes—
51D8×C43—82no—
52M16×C43—42no—
53C2×C8×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56C22⋊C4×C43—42no—
57C22⋊C4×C43—42no—
58C42×C43C2×D411yescharacteristic
59C42×C43C2×D412yes—
60C42×C43#4111yescharacteristic
61#10621877—42no—
62#10621877—82no—
63C2×C43⋊C8—22no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8—22no—
66C2×C43⋊C8—41no—
67C2×C43⋊C8—42no—
68C23×C43—42no—
69C23×C43#12411yescharacteristic
70Q8×C43—82no—
71D4×C43—42no—
72D4×C43—42no—
73D4×C43—42no—
74D4×C43—42no—
75D4×C43—82no—
76D4×C43—84no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—42no—
82C2×C4×C43—82no—
83C2×C4×C43—82no—
84C2×C4×C43#12011yescharacteristic
85C2×C4×C43#12111yescharacteristic
86C2×C4×C43#12112yes—
87C2×C4×C43#12312yes—
88C8×C43—42no—
89C43⋊C8—24no—
90C43⋊C8—81no—
91C43⋊C8—82no—
92#10530—431nomaximal, Sylow
93C22×C43—22no—
94C22×C43—21no—
95C22×C43—82no—
96C22×C43—82no—
97C22×C43—82no—
98C22×C43#39411yescharacteristic
99C4×C43—22no—
100C4×C43—21no—
101C4×C43—82no—
102C4×C43#45311yescharacteristic
103C4×C43#45611yescharacteristic
104C4×C43#47112yes—
105C4×C43#47212yes—
106#3253D4311yescharacteristic
107#1848—431no—
108#1560—432no—
109#1492—432no—
110#1309—431no—
111C2×C43—41no—
112C2×C43—162no—
113C2×C43#203911yescharacteristic
114C2×C43#205112yes—
115#532C2×D4312yes—
116#476—22no—
117#469—22no—
118#459—22no—
119C2×#108—862no—
120#423—431no—
121#423—432no—
122#423C2×D4311yescharacteristic
123C2×C4×C8—431no—
124#333—862no—
125#331—862no—
126D4⋊C8—864no—
127C43#1053011yescharacteristic, complemented, Sylow
128C2×#41—22no—
129C2×D8—22no—
130C2×M16—862no—
131C2×M16—861no—
132C2×M16C22⋊D4312yes—
133C22×C8—861no—
134C4⋊Q8C22⋊D4312yes—
135#127C22⋊D4312yes—
136#124—22no—
137#121—22no—
138#121—22no—
139C4×D4—22no—
140C4×D4—22no—
141C2×C42C22×D4311yescharacteristic
142#108—1724no—
143#106—22no—
144C4⋊C8—22no—
145C4⋊C8—862no—
146C4⋊C8—862no—
147C4⋊C8—862no—
148#102—24no—
149C4×C8—432no—
150C4×C8—861no—
151#41—82no—
152#41—82no—
153C2×Q8—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—42no—
158C22×C4—42no—
159C22×C4#1062190012yes—
160C22×C4C2×C22⋊D4311yescharacteristic
161D8—82no—
162M16—42no—
163M16—3442no—
164M16—1722no—
165C2×C8—22no—
166C2×C8—862no—
167C2×C8—862no—
168C2×C8—862no—
169C2×C8—1721no—
170C2×C8—1722no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C22⋊C4—42no—
174C22⋊C4—42no—
175C42D4×D4311yescharacteristic
176C42#1062190011yescharacteristic
177C42C2×C22⋊D4312yes—
178C23—42no—
179C23#1306331211yescharacteristic
180Q8—82no—
181D4—42no—
182D4—42no—
183D4—42no—
184D4—42no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4#1306329411yescharacteristic
195C2×C4#1306329611yescharacteristic
196C2×C4#1306329712yes—
197C2×C4#1306330612yes—
198C8—42no—
199C8—864no—
200C8—3441no—
201C8—3442no—
202C22—21no—
203C22—22no—
204C22—82no—
205C22—82no—
206C22—82no—
207C22#1458281311yescharacteristic
208C4—21no—
209C4—22no—
210C4—82no—
211C4#1458306711yescharacteristic
212C4#1458308211yescharacteristic
213C4#1458316012yes—
214C4#1458316712yes—
215C2—41no—
216C2—162no—
217C2#1913581611yescharacteristic
218C2#1913588412yes—
subgroupG/H
centerC22#14582813
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3253C2
socleC22×C43#394
hypercenter#3253D43
hypocenterC43#10530
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #19134766C2semidirect
2. #19133330C2semidirect
3. #19133046C2semidirect
4. C43⋊#1309C2semidirect
127. C43#10530semidirect

Maximal subgroups

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

subgroupindex
#191347662
#191333302
#191330462
C43⋊#13092
C43×#32532
#1053043