Finite Group Databasebeta

← #25000769

Subgroups — #25000769

Order 11008.

402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145976C211yesmaximal, characteristic
2#19133328C212yesmaximal, complemented
3#19133047C212yesmaximal, complemented
4C43⋊#1309C211yesmaximal, characteristic, complemented
5C43×#1848C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583190—22no—
8#14583152—22no—
9#14583095—22no—
10#14582923C2212yes—
11#14582647—22no—
12#14582642—22no—
13#14582628—24no—
14C2×#108×C43—22no—
15C43×#423C2211yescharacteristic
16C43×#423C2211yescharacteristic
17C2×C4×C8×C43C2211yescharacteristic
18C2×#10621898—22no—
19C2×D344—22no—
20C2×#10621877—22no—
21#13063325D412yes—
22#13063322D412yes—
23#13063313—22no—
24#13063299—22no—
25#13063299—22no—
26C4×D172—22no—
27C4×D172—22no—
28#13063257—22no—
29C4⋊(C43⋊C8)—22no—
30C4⋊(C43⋊C8)—22no—
31#13063247—24no—
32C2×M16×C43—21no—
33C2×M16×C43D412yes—
34C22×C8×C43—21no—
35C2×C42×C43C2311yescharacteristic
36#108×C43—44no—
37C4⋊C8×C43—22no—
38C4⋊C8×C43—22no—
39C4×C8×C43—21no—
40C4×C8×C43D412yes—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43#4112yes—
43C2×C22⋊D43—42no—
44#10621898—82no—
45#10621898—82no—
46C2×D172—22no—
47C2×D172—22no—
48C2×D172—22no—
49C2×C4×D43—42no—
50C2×Dic86—22no—
51M16×C43—42no—
52M16×C43—42no—
53C2×C8×C43—22no—
54C2×C8×C43—22no—
55C2×C8×C43—22no—
56C2×C8×C43—22no—
57C2×C8×C43—41no—
58C42×C43C2×D411yescharacteristic
59C42×C43C2×D412yes—
60C42×C43#4111yescharacteristic
61(C2×D43)⋊C4—42no—
62(C2×D43)⋊C4—42no—
63C4⋊Dic43—22no—
64C4⋊Dic43—22no—
65#10621877—82no—
66C2×C43⋊C8—42no—
67D344—82no—
68C23×C43#12411yescharacteristic
69C22×D43—42no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43#12011yescharacteristic
75C2×C4×C43#12111yescharacteristic
76C2×C4×C43#12112yes—
77C2×C4×C43#12312yes—
78C22⋊D43—84no—
79C2×Dic43—42no—
80D172—42no—
81D172—42no—
82D172—42no—
83D172—42no—
84D172—82no—
85C4×D43—82no—
86C4×D43—82no—
87Dic86—82no—
88C8×C43—24no—
89C8×C43—42no—
90C8×C43—81no—
91C43⋊C8—82no—
92#10530—431nomaximal, Sylow
93C22×C43—22no—
94C22×C43—21no—
95C22×C43#39411yescharacteristic
96C2×D43—82no—
97C2×D43—82no—
98C2×D43—82no—
99C4×C43—22no—
100C4×C43—21no—
101C4×C43#45311yescharacteristic
102C4×C43#45611yescharacteristic
103C4×C43#47112yes—
104C4×C43#47212yes—
105Dic43—82no—
106#3253—431no—
107#1848D4311yescharacteristic, complemented
108#1560—432no—
109#1492—432no—
110#1309—431no—
111C2×C43—41no—
112C2×C43#203911yescharacteristic
113C2×C43#205112yes—
114D43—162no—
115#532—432no—
116#476—862no—
117#469—862no—
118#459—862no—
119C2×#108—22no—
120#423—432no—
121#423C2×D4311yescharacteristic
122#423C2×D4311yescharacteristic
123C2×C4×C8C2×D4311yescharacteristic
124#333—862no—
125#331—862no—
126D4⋊C8—864no—
127C43#1053011yescharacteristic, complemented, Sylow
128C2×#41—862no—
129C2×D8—862no—
130C2×M16—21no—
131C2×M16—862no—
132C2×M16C22⋊D4312yes—
133C22×C8—21no—
134C4⋊Q8—432no—
135#127—432no—
136#124—862no—
137#121—862no—
138#121—862no—
139C4×D4—862no—
140C4×D4—862no—
141C2×C42C22×D4311yescharacteristic
142#108—44no—
143#106—862no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—862no—
147C4⋊C8—862no—
148#102—864no—
149C4×C8—21no—
150C4×C8D17212yes—
151#41—3442no—
152#41—3442no—
153C2×Q8—862no—
154C2×D4—862no—
155C2×D4—862no—
156C2×D4—862no—
157C2×D4—1722no—
158C22×C4—1722no—
159C22×C4#1062190212yes—
160C22×C4C2×C22⋊D4311yescharacteristic
161D8—3442no—
162M16—42no—
163M16—42no—
164M16—3442no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—1722no—
171C4⋊C4—862no—
172C4⋊C4—862no—
173C22⋊C4—1722no—
174C22⋊C4—1722no—
175C42C2×D17211yescharacteristic
176C42#1062189811yescharacteristic
177C42D4×D4312yes—
178C23—1722no—
179C23#1306331411yescharacteristic
180Q8—3442no—
181D4—3442no—
182D4—3444no—
183D4—1722no—
184D4—1722no—
185D4—1722no—
186D4—1722no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—3442no—
192C2×C4—3442no—
193C2×C4—1722no—
194C2×C4#1306329311yescharacteristic
195C2×C4#1306329911yescharacteristic
196C2×C4#1306330012yes—
197C2×C4#1306331012yes—
198C8—24no—
199C8—42no—
200C8—81no—
201C8—3442no—
202C22—21no—
203C22—22no—
204C22—3442no—
205C22—3442no—
206C22—3442no—
207C22#1458281611yescharacteristic
208C4—21no—
209C4—22no—
210C4—3442no—
211C4#1458306611yescharacteristic
212C4#1458308111yescharacteristic
213C4#1458316312yes—
214C4#1458317012yes—
215C2—41no—
216C2—6882no—
217C2#1913581911yescharacteristic
218C2#1913588912yes—
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1848C2
socleC22×C43#394
prime radical#19145976C2
hypercenter#1848D43
hypocenterC43#10530
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. #19133328C2semidirect
3. #19133047C2semidirect
4. C43⋊#1309C2semidirect
5. C43×#1848C2semidirect
107. #1848D43semidirect
127. C43#10530semidirect

Maximal subgroups

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

subgroupindex
#191459762
#191333282
#191330472
C43⋊#13092
C43×#18482
#1053043