Finite Group Databasebeta

← #25010371

Subgroups — #25010371

Order 11008.

336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136766C212yesmaximal, complemented
2#19134226C211yesmaximal, characteristic, complemented
3#19132634C211yesmaximal, characteristic, complemented
4#19132571C212yesmaximal, complemented
5C43×#3293C211yesmaximal, characteristic
6#14583297C2211yescharacteristic
7#14583295—21no—
8#14583251—21no—
9#14582723—22no—
10#14582720C2212yes—
11#14582709—22no—
12#14582620C2211yescharacteristic
13C43×#578—22no—
14C43×#494C2211yescharacteristic
15C43×#473—22no—
16C43×#456—21no—
17C43×#456—21no—
18C43×#443C2212yes—
19#13063325—21no—
20#13063265—22no—
21#13063257—22no—
22#13063256—42no—
23#13063248—42no—
24C4×C43⋊C8—21no—
252−1+4×C43—21no—
262−1+4×C43—21no—
27#137×C43—22no—
28#137×C43—22no—
29#137×C43—42no—
30#137×C43—42no—
31#135×C43—42no—
32#135×C43D412yes—
33C2×Q16×C43—22no—
34C2×Q16×C43—42no—
35#131×C43—22no—
36C4⋊Q8×C43D411yescharacteristic
37C4⋊Q8×C43D411yescharacteristic
38#108×C43D412yes—
39#104×C43—22no—
40#101×C43—21no—
41#101×C43—21no—
42C4×C8×C43C2311yescharacteristic
43#41×C43—22no—
44#41×C43—42no—
45#41×C43—42no—
46#41×C43—81no—
47#41×C43—81no—
48C2×Q8×C43—21no—
49C2×Q8×C43—21no—
50C2×Q8×C43—42no—
51C2×Q8×C43—42no—
52C2×Dic86—41no—
53Q16×C43—42no—
54Q16×C43—42no—
55Q16×C43—42no—
56Q16×C43—42no—
57Q16×C43SD1612yes—
58SD16×C43—22no—
59SD16×C43—42no—
60SD16×C43—42no—
61D8×C43SD1612yes—
62M16×C43—22no—
63M16×C43—42no—
64C2×C8×C43—42no—
65C2×C8×C43C2×D412yes—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C42×C43C2×D411yescharacteristic
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71C2×C43⋊C8—22no—
72C43⋊C16—42no—
73Q8×C43—22no—
74Q8×C43—42no—
75Q8×C43—42no—
76Q8×C43—81no—
77Q8×C43—81no—
78D4×C43—22no—
79D4×C43—42no—
80D4×C43—81no—
81D4×C43—81no—
82C2×C4×C43—21no—
83C2×C4×C43—42no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—82no—
87C2×C4×C43—82no—
88C2×C4×C43#12011yescharacteristic
89C2×Dic43—81no—
90Dic86—82no—
91C8×C43—42no—
92C8×C43C2×SD1612yes—
93C8×C43AGL(1,ℤ/8)12yes—
94C43⋊C8—42no—
95#12367—431nomaximal, Sylow
96C22×C43—42no—
97C22×C43#45311yescharacteristic
98C4×C43—22no—
99C4×C43—42no—
100C4×C43—81no—
101C4×C43—81no—
102C4×C43#45012yes—
103Dic43—161no—
104#3293D4311yescharacteristic
105#2230—432no—
106#1716—431no—
107#1358—431no—
108#1336—432no—
109C2×C43—21no—
110C2×C43—82no—
111C2×C43#162911yescharacteristic
112#578—22no—
113#498—431no—
114#498—861no—
115#494C2×D4311yescharacteristic
116#487—861no—
117#473—22no—
118#456—21no—
119#456—21no—
120#443C2×D4312yes—
121#365—862no—
122#364—432no—
123#360—862no—
124#322—431no—
125C43#1236711yescharacteristic, complemented, Sylow
1262−1+4—21no—
1272−1+4—21no—
128#137—22no—
129#137—22no—
130#137—42no—
131#137—42no—
132#135—42no—
133#135C22⋊D4312yes—
134C2×Q16—22no—
135C2×Q16—42no—
136#131—22no—
137C4⋊Q8—861no—
138C4⋊Q8C22⋊D4311yescharacteristic
139C4⋊Q8C22⋊D4311yescharacteristic
140M32—862no—
141#108C22⋊D4312yes—
142#106—862no—
143#106—1722no—
144#104—22no—
145#103—1722no—
146#101—21no—
147#101—21no—
148C4×C8—861no—
149C4×C8C22×D4311yescharacteristic
150#41—22no—
151#41—42no—
152#41—42no—
153#41—81no—
154#41—81no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—1721no—
160Q16—42no—
161Q16—42no—
162Q16—42no—
163Q16—42no—
164Q16#1062188312yes—
165SD16—22no—
166SD16—42no—
167SD16—42no—
168D8#1062188312yes—
169M16—22no—
170M16—42no—
171C2×C8—42no—
172C2×C8—862no—
173C2×C8C2×C22⋊D4312yes—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—1721no—
177C4⋊C4—1721no—
178C42C2×C22⋊D4311yescharacteristic
179C16—1722no—
180Q8—22no—
181Q8—42no—
182Q8—42no—
183Q8—81no—
184Q8—81no—
185Q8—3442no—
186D4—22no—
187D4—42no—
188D4—81no—
189D4—81no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—3441no—
197C2×C4#1306329411yescharacteristic
198C8—42no—
199C8—1722no—
200C8C2×#1062188312yes—
201C8#1306335112yes—
202C22—42no—
203C22#1458306711yescharacteristic
204C4—22no—
205C4—42no—
206C4—81no—
207C4—81no—
208C4—6881no—
209C4#1458305012yes—
210C2—21no—
211C2—82no—
212C2#1913371111yescharacteristic
subgroupG/H
centerC2#19133711
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3293C2
socleC2×C43#1629
hypercenter#3293D43
hypocenterC43#12367
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #19136766C2semidirect
2. #19134226C2semidirect
3. #19132634C2semidirect
4. #19132571C2semidirect
125. C43#12367semidirect

Maximal subgroups

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

subgroupindex
#191367662
#191342262
#191326342
#191325712
C43×#32932
#1236743