Finite Group Databasebeta

← #24984344

Subgroups — #24984344

Order 11008.

270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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#19134979C211yesmaximal, characteristic
2#19133257C211yesmaximal, characteristic
3C43×#2132C211yesmaximal, characteristic
4#14583666C411yescharacteristic
5#14582952—21no—
6#14582916—21no—
7#14582873C411yescharacteristic
8#14582659—21no—
9#14582648—21no—
10#14582643C412yescomplemented
11C43×#532C2211yescharacteristic
12C43×#413—21no—
13C43×#356—21no—
14C43×#355C412yescomplemented
15#13063332—42no—
16C2×#10621877—21no—
17C2×#10621877—41no—
18#13063284—21no—
19C4⋊(C43⋊C8)—22no—
20#13063252—42no—
21#13063240—41no—
22C22⋊(C43⋊C8)—41no—
23C4×C43⋊C8—41no—
24C2×#41×C43C2×C411yescharacteristic
25C2×#41×C43D411yescharacteristic
26C2×M16×C43—41no—
27C4⋊Q8×C43D411yescharacteristic
28#127×C43C2×C411yescharacteristic
29#124×C43C2×C411yescharacteristic
30#124×C43Q811yescharacteristic
31#121×C43—41no—
32C4×D4×C43—41no—
33C2×C42×C43D411yescharacteristic
34#101×C43—22no—
35#100×C43—41no—
36#41×C43—41no—
37#41×C43—41no—
38#41×C43—41no—
39#41×C43—41no—
40C2×Q8×C43C22⋊C411yescharacteristic
41C2×Q8×C43C4⋊C411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×D4×C43C4211yescharacteristic
46C2×D4×C43C4⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22⋊C411yescharacteristic
51M16×C43—42no—
52M16×C43—81no—
53C2×C8×C43—81no—
54C4⋊C4×C43—41no—
55C22⋊C4×C43—41no—
56C22⋊C4×C43—41no—
57C42×C43—21no—
58C42×C43C22⋊C411yescharacteristic
59C42×C43C4⋊C411yescharacteristic
60C22⋊Dic43—41no—
61C4⋊Dic43—41no—
62C4×Dic43—41no—
63#10621877—22no—
64#10621877—42no—
65#10621877—41no—
66C2×C43⋊C8—41no—
67C2×C43⋊C8—42no—
68C2×C43⋊C8—42no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43#9911yescharacteristic
72Q8×C43—41no—
73Q8×C43—41no—
74D4×C43—41no—
75D4×C43—41no—
76D4×C43—42no—
77D4×C43—82no—
78D4×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—42no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43#9511yescharacteristic
91C2×C4×C43#9911yescharacteristic
92C2×Dic43—81no—
93C8×C43—82no—
94C43⋊C8—42no—
95C43⋊C8—82no—
96#7488—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—81no—
102C22×C43—81no—
103C22×C43#34211yescharacteristic
104C4×C43—22no—
105C4×C43—21no—
106C4×C43—41no—
107C4×C43—41no—
108C4×C43—41no—
109C4×C43AΣL(1,𝔽16)11yescharacteristic
110C4×C43#35211yescharacteristic
111Dic43—161no—
112#2132D4311yescharacteristic
113#1884—431no—
114#1543—431no—
115C2×C43—21no—
116C2×C43—41no—
117C2×C43—81no—
118C2×C43—81no—
119C2×C43#139011yescharacteristic
120#568—431no—
121#532C2×D4311yescharacteristic
122#431—861no—
123#421—861no—
124#413—21no—
125#410—431no—
126#356—21no—
127#355Dic4312yescomplemented
128#339—861no—
129#333—861no—
130#331—432no—
131C43#748811yescharacteristic, complemented, Sylow
132C2×#41C4×D4311yescharacteristic
133C2×#41C22⋊D4311yescharacteristic
134#131—1722no—
135C2×M16—41no—
136C2×M16—861no—
137C2×M16—1721no—
138C4⋊Q8C22⋊D4311yescharacteristic
139#127C4×D4311yescharacteristic
140#124Dic8611yescharacteristic
141#124C2×Dic4311yescharacteristic
142#121—41no—
143C4×D4—41no—
144#117—861no—
145C2×C42D17211yescharacteristic
146C4⋊C8—862no—
147#104—1722no—
148#101—22no—
149#100—41no—
150#99—1721no—
151C22⋊C8—1721no—
152C4×C8—1721no—
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8Dic43⋊C411yescharacteristic
158C2×Q8C22⋊Dic4311yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4C4×Dic4311yescharacteristic
163C2×D4Dic43⋊C411yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4(C2×D43)⋊C411yescharacteristic
168M16—42no—
169M16—81no—
170M16—862no—
171M16—1722no—
172M16—1721no—
173C2×C8—81no—
174C2×C8—1722no—
175C2×C8—1721no—
176C2×C8—1722no—
177C4⋊C4—41no—
178C4⋊C4—1721no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—1721no—
182C42—21no—
183C42—1721no—
184C42C4⋊Dic4311yescharacteristic
185C42(C2×D43)⋊C411yescharacteristic
186C23—21no—
187C23—21no—
188C23#1306323911yescharacteristic
189Q8—41no—
190Q8—41no—
191D4—41no—
192D4—41no—
193D4—42no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—3441no—
208C2×C4C43⋊#9511yescharacteristic
209C2×C4#1306323911yescharacteristic
210C8—82no—
211C8—3442no—
212C8—1722no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—81no—
219C22#1458266511yescharacteristic
220C4—22no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—6881no—
226C4#1458268511yescharacteristic
227C4#1458268811yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—81no—
232C2#1913271211yescharacteristic
subgroupG/H
centerC4#14582685
commutatorC2×D4×C43C42
Frattini#532C2×D43
FittingC43×#2132C2
socleC2×C43#1390
prime radical, cosocleC43×#532C22
hypercenter#2132D43
hypocenterC43#7488
LCSG ▷ C2×D4×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
10. #14582643C4semidirect
14. C43×#355C4semidirect
127. #355Dic43semidirect
131. C43#7488semidirect

Maximal subgroups

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

subgroupindex
#191349792
#191332572
C43×#21322
#748843