Finite Group Databasebeta

← #24984024

Subgroups — #24984024

Order 11008.

228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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#19134804C211yesmaximal, characteristic
2#19132527C211yesmaximal, characteristic
3C43×#1270C211yesmaximal, characteristic
4#14583374C411yescharacteristic
5#14582939—21no—
6C2×#13063242C411yescharacteristic
7#14582659—21no—
8#14582625—21no—
9C43×#390C2211yescharacteristic
10C43×#336—21no—
11C2×#10621877—21no—
12D4×Dic43—41no—
13D4×Dic43—41no—
14#13063284—21no—
15C2×C22⋊Dic43—41no—
16#13063258—41no—
17#13063256—41no—
18#13063242—21no—
19#13063242C812yescomplemented
20C22⋊(C43⋊C8)—41no—
21C22×D4×C43C2×C411yescharacteristic
22C22×C8×C43—41no—
23C2×C4⋊C4×C43D411yescharacteristic
24C2×C22⋊C4×C43—41no—
25C2×C42×C43D411yescharacteristic
26C24×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—41no—
29C2×D4×C43—41no—
30C2×D4×C43C2×C811yescharacteristic
31C2×D4×C43M1611yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43C22⋊C411yescharacteristic
35C22×Dic43—41no—
36C22×Dic43—41no—
37C2×C8×C43—42no—
38C2×C8×C43—81no—
39C2×C8×C43—81no—
40C4⋊C4×C43—41no—
41C22⋊C4×C43—81no—
42C22⋊C4×C43—81no—
43C42×C43—41no—
44C22⋊Dic43—42no—
45C22⋊Dic43—41no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48C4×Dic43—41no—
49#10621877—22no—
50#10621877—41no—
51C2×C43⋊C8—41no—
52C2×C43⋊C8—81no—
53C23×C43—21no—
54C23×C43—21no—
55C23×C43—41no—
56C23×C43—41no—
57C23×C43—81no—
58C23×C43—81no—
59C23×C43#9911yescharacteristic
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—42no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—81no—
71C2×C4×C43C22⋊C811yescharacteristic
72C2×C4×C43#10111yescharacteristic
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—161no—
76C2×Dic43—161no—
77C8×C43—82no—
78C43⋊C8—42no—
79C43⋊C8—161no—
80#7375—431nomaximal, Sylow
81C22×C43—21no—
82C22×C43—21no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—81no—
86C22×C43—81no—
87C22×C43—81no—
88C22×C43—81no—
89C22×C43—161no—
90C22×C43#32411yescharacteristic
91C22×C43AΣL(1,𝔽16)11yescharacteristic
92C22×C43#35211yescharacteristic
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43—41no—
97C4×C43—81no—
98Dic43—81no—
99Dic43—81no—
100#1856—431no—
101#1318—431no—
102#1270D4311yescharacteristic
103C2×C43—21no—
104C2×C43—21no—
105C2×C43—81no—
106C2×C43—81no—
107C2×C43#132611yescharacteristic
108C2×C43#140211yescharacteristic
109C2×C43#140311yescharacteristic
110#518—431no—
111#428—861no—
112C2×#100—431no—
113#390C2×D4311yescharacteristic
114#339—861no—
115#336—21no—
116#324—861no—
117C43#737511yescharacteristic, complemented, Sylow
118C22×D4C4×D4311yescharacteristic
119C2×M16—861no—
120C22×C8—41no—
121C4×D4—1721no—
122C4×D4—1721no—
123#117—861no—
124C2×C4⋊C4D17211yescharacteristic
125C2×C22⋊C4—41no—
126C2×C22⋊C4—1721no—
127C2×C42C22⋊D4311yescharacteristic
128#107—1721no—
129#106—1721no—
130#100—432no—
131#100—861no—
132C22⋊C8—1721no—
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4C8×D4311yescharacteristic
138C2×D4#1062187211yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—1721no—
142C22×C4—1721no—
143C22×C4(C2×D43)⋊C411yescharacteristic
144M16—862no—
145M16—1721no—
146C2×C8—42no—
147C2×C8—81no—
148C2×C8—81no—
149C2×C8—3441no—
150C2×C8—1721no—
151C4⋊C4—41no—
152C4⋊C4—861no—
153C4⋊C4—861no—
154C22⋊C4—81no—
155C22⋊C4—81no—
156C22⋊C4—1722no—
157C22⋊C4—1721no—
158C42—41no—
159C42—1721no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1306323911yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4—6881no—
181C2×C4—6881no—
182C2×C4(C2×D43)⋊C811yescharacteristic
183C2×C4#1306324311yescharacteristic
184C8—82no—
185C8—1722no—
186C8—6881no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1458262411yescharacteristic
197C22#1458268711yescharacteristic
198C22#1458268811yescharacteristic
199C4—21no—
200C4—21no—
201C4—41no—
202C4—41no—
203C4—81no—
204C4—3441no—
205C4—3441no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#1913254411yescharacteristic
211C2#1913274111yescharacteristic
212C2#1913274411yescharacteristic
subgroupG/H
centerC22#14582687
commutatorC2×D4×C43C2×C8
Frattini#390C2×D43
FittingC43×#1270C2
socleC22×C43AΣL(1,𝔽16)
prime radicalC22×D4×C43C2×C4
cosocleC43×#390C22
hypercenter#1270D43
hypocenterC43#7375
LCSG ▷ C2×D4×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1270

Complements

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

NH ≅ G/Ntype
19. #13063242C8semidirect
117. C43#7375semidirect

Maximal subgroups

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

subgroupindex
#191348042
#191325272
C43×#12702
#737543