Finite Group Databasebeta

← #25008470

Subgroups — #25008470

Order 11008.

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

normal subgroups only

This group has 230 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#19136459C211yesmaximal, characteristic
2#19133415C211yesmaximal, characteristic, complemented
3#19132660C211yesmaximal, characteristic, complemented
4#19132564C211yesmaximal, characteristic, complemented
5#19132562C211yesmaximal, characteristic
6#19132516C211yesmaximal, characteristic, complemented
7C43×#1580C211yesmaximal, characteristic
8C2×#13063269C411yescharacteristic
9C8×Dic86—21no—
10C4×Dic172C2211yescharacteristic
11#14582724C411yescharacteristic
12#14582702C411yescharacteristic
13#14582700C411yescharacteristic
14#14582675C2211yescharacteristic
15#14582675C2211yescharacteristic
16#14582650C2211yescharacteristic
17#14582631—21no—
18C4×D8×C43C2211yescharacteristic
19C8×D4×C43—21no—
20C43×#334C2211yescharacteristic
21C43×D4⋊C8—21no—
22C43×#322C2211yescharacteristic
23C2×Dic172C2×C411yescharacteristic
24C4×Dic86—21no—
25#13063269C814yescomplemented
26C2×C43⋊C16—21no—
27C2×C43⋊C16C2×C411yescharacteristic
28C2×C43⋊C16C2×C411yescharacteristic
29#13063259C2×C411yescharacteristic
30C4⋊(C43⋊C8)—21no—
31Dic43⋊C8—41no—
32#13063250—21no—
33C8×Dic43—41no—
34C2×D8×C43C2×C411yescharacteristic
35C22×C8×C43—41no—
36C4×D4×C43—21no—
37#107×C43C2×C411yescharacteristic
38C4⋊C8×C43—21no—
39#102×C43—21no—
40C22⋊C8×C43—41no—
41C4×C8×C43D411yescharacteristic
42C4×C8×C43D411yescharacteristic
43C4×C8×C43C2311yescharacteristic
44C2×D4×C43—21no—
45C22×C4×C43—41no—
46C2×Dic86—21no—
47D8×C43—21no—
48D8×C43C2×C812yes—
49C2×C8×C43—21no—
50C2×C8×C43—21no—
51C2×C8×C43—41no—
52C2×C8×C43—82no—
53C2×C8×C43C22×C411yescharacteristic
54C2×C8×C43#4111yescharacteristic
55C4⋊C4×C43—21no—
56C22⋊C4×C43—41no—
57C42×C43C2×D411yescharacteristic
58C4⋊Dic43—21no—
59Dic43⋊C4—41no—
60C4×Dic43—41no—
61C2×C43⋊C8—41no—
62Dic172—21no—
63Dic172C2×C812yescomplemented
64C43⋊C16—21no—
65C43⋊C16—41no—
66C43⋊C16C2×C812yescomplemented
67C23×C43—41no—
68D4×C43—22no—
69D4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—81no—
72C2×C4×C43—81no—
73C2×C4×C43C4×D411yescharacteristic
74C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
75C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
76C2×Dic43—41no—
77C2×Dic43—41no—
78Dic86—22no—
79Dic86—41no—
80C8×C43—21no—
81C8×C43—41no—
82C8×C43—41no—
83C8×C43—81no—
84C8×C43C22×C811yescharacteristic
85C8×C43#13111yescharacteristic
86C43⋊C8—81no—
87#12065—431nomaximal, Sylow
88C22×C43—42no—
89C22×C43—81no—
90C22×C43—81no—
91C22×C43#44211yescharacteristic
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—81no—
95C4×C43C8×D411yescharacteristic
96C4×C43#44411yescharacteristic
97Dic43—42no—
98Dic43—81no—
99#2175—431no—
100#1580D4311yescharacteristic
101#1579—431no—
102#1368—431no—
103#1334—431no—
104#1333—431no—
105#1313—431no—
106C2×C43—82no—
107C2×C43#158011yescharacteristic
108C2×C43#218011yescharacteristic
109C2×C43AGL(1,ℤ/16)11yescharacteristic
110C2×SD32—431no—
111C8×Q8—861no—
112C4×Q16—431no—
113C4×D8C2×D4311yescharacteristic
114C8×D4—21no—
115#366—431no—
116#358—431no—
117#357—431no—
118#346—431no—
119#346—431no—
120#334—431no—
121#334C2×D4311yescharacteristic
122Q8⋊C8—861no—
123D4⋊C8—21no—
124#322C2×D4311yescharacteristic
125C43#1206511yescharacteristic, complemented, Sylow
126C2×Q16—431no—
127C2×D8C4×D4311yescharacteristic
128C22×C8—41no—
129C4×Q8—861no—
130C4×D4—21no—
131SD32—434no—
132C2×C16—431no—
133C2×C16—431no—
134C2×C16—861no—
135#107—431no—
136#107C4×D4311yescharacteristic
137C4⋊C8—21no—
138C4⋊C8—861no—
139C4⋊C8—1721no—
140#103—861no—
141#102—21no—
142C22⋊C8—41no—
143C4×C8—1721no—
144C4×C8C22⋊D4311yescharacteristic
145C4×C8C22⋊D4311yescharacteristic
146C4×C8C22×D4311yescharacteristic
147C2×Q8—861no—
148C2×D4—21no—
149C22×C4—41no—
150Q16—432no—
151Q16—861no—
152D8—21no—
153D8C8×D4312yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—82no—
158C2×C8—1721no—
159C2×C8C2×C4×D4311yescharacteristic
160C2×C8#1062189811yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—861no—
163C4⋊C4—1721no—
164C22⋊C4—41no—
165C42—1721no—
166C42C2×C22⋊D4311yescharacteristic
167C16—432no—
168C16—861no—
169C16—1721no—
170C23—41no—
171Q8—862no—
172Q8—1721no—
173D4—22no—
174D4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4C4×C22⋊D4311yescharacteristic
181C2×C4#1306335011yescharacteristic
182C2×C4#1306335111yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—81no—
187C8—3441no—
188C8C2×C8×D4311yescharacteristic
189C8#1306333111yescharacteristic
190C22—42no—
191C22—81no—
192C22—81no—
193C22#1458300911yescharacteristic
194C4—21no—
195C4—21no—
196C4—81no—
197C4—3441no—
198C4—1722no—
199C4C8×C22⋊D4311yescharacteristic
200C4#1458301911yescharacteristic
201C2—82no—
202C2#1913341711yescharacteristic
203C2#1913648611yescharacteristic
204C2#1913649111yescharacteristic
subgroupG/H
centerC22#14583009
commutatorC8×C43C22×C8
FrattiniC4×C8C22×D43
FittingC43×#1580C2
socleC22×C43#442
prime radicalC2×D8×C43C2×C4
cosocleC4×C8×C43C23
hypercenter#1580D43
hypocenterC43#12065
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #19133415C2semidirect
3. #19132660C2semidirect
4. #19132564C2semidirect
6. #19132516C2semidirect
25. #13063269C8semidirect
63. Dic172C2×C8semidirect
66. C43⋊C16C2×C8semidirect
125. C43#12065semidirect

Maximal subgroups

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

subgroupindex
#191364592
#191334152
#191326602
#191325642
#191325622
#191325162
C43×#15802
#1206543