Finite Group Databasebeta

← #24984351

Subgroups — #24984351

Order 11008.

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

normal subgroups only

This group has 274 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#19136260C211yesmaximal, characteristic
2#19133257C211yesmaximal, characteristic
3C43×#1884C211yesmaximal, characteristic
4#14582952—21no—
5#14582873—21no—
6#14582694C412yescomplemented
7#14582692—21no—
8#14582648C412yescomplemented
9#14582643—21no—
10C43×#568C411yescharacteristic, complemented
11C43×#532C2211yescharacteristic
12C43×#421—21no—
13C43×#410C411yescharacteristic, complemented
14C43×#339—21no—
15#13063284—41no—
16C4⋊(C43⋊C8)—22no—
17#13063240—22no—
18#13063240—41no—
19C22⋊(C43⋊C8)—41no—
20C4×C43⋊C8—41no—
21C2×#41×C43C2×C411yescharacteristic
22C2×#41×C43D411yescharacteristic
23#131×C43—42no—
24C2×M16×C43—21no—
25C2×M16×C43—41no—
26C4⋊Q8×C43C2×C411yescharacteristic
27#127×C43D411yescharacteristic
28#124×C43C2×C411yescharacteristic
29#124×C43Q811yescharacteristic
30#121×C43—41no—
31C4×D4×C43—41no—
32#117×C43—21no—
33C2×C42×C43D411yescharacteristic
34#104×C43—42no—
35#99×C43—41no—
36#41×C43—41no—
37#41×C43—41no—
38#41×C43—41no—
39#41×C43—41no—
40C2×Q8×C43C4211yescharacteristic
41C2×Q8×C43C4⋊C411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×D4×C43C22⋊C411yescharacteristic
46C2×D4×C43C4⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22⋊C411yescharacteristic
51M16×C43—22no—
52M16×C43—41no—
53M16×C43—42no—
54C2×C8×C43—41no—
55C2×C8×C43—42no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C22⋊C4×C43—41no—
59C22⋊C4×C43—41no—
60C22⋊C4×C43—41no—
61C42×C43—21no—
62C42×C43—41no—
63C42×C43C22⋊C411yescharacteristic
64C42×C43C4⋊C411yescharacteristic
65C22⋊Dic43—42no—
66C4⋊Dic43—81no—
67C4×Dic43—81no—
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—81no—
91C2×C4×C43#9511yescharacteristic
92C2×C4×C43#9911yescharacteristic
93C2×Dic43—82no—
94C8×C43—42no—
95C43⋊C8—82no—
96#7490—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×C43—161no—
110C4×C43AΣL(1,𝔽16)11yescharacteristic
111C4×C43#35211yescharacteristic
112Dic43—162no—
113#2126—431no—
114#1884D4311yescharacteristic
115#1543—431no—
116C2×C43—21no—
117C2×C43—41no—
118C2×C43—81no—
119C2×C43—81no—
120C2×C43#139011yescharacteristic
121#568Dic4311yescharacteristic, complemented
122#532C2×D4311yescharacteristic
123#431—861no—
124#421—21no—
125#410—861no—
126#410Dic4311yescharacteristic, complemented
127#354—432no—
128#353—861no—
129#339—21no—
130#333—432no—
131#331—861no—
132C43#749011yescharacteristic, complemented, Sylow
133C2×#41C2×Dic4311yescharacteristic
134C2×#41C22⋊D4311yescharacteristic
135#131—42no—
136C2×M16—21no—
137C2×M16—41no—
138C4⋊Q8C4×D4311yescharacteristic
139#127D17211yescharacteristic
140#124Dic8611yescharacteristic
141#124C4×D4311yescharacteristic
142#121—41no—
143C4×D4—41no—
144#117—21no—
145#117—1721no—
146C2×C42C22⋊D4311yescharacteristic
147C4⋊C8—862no—
148#104—42no—
149#99—41no—
150#99—862no—
151#99—1721no—
152C22⋊C8—1721no—
153C4×C8—1721no—
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8C4×Dic4311yescharacteristic
159C2×Q8Dic43⋊C411yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4C4⋊Dic4311yescharacteristic
164C2×D4(C2×D43)⋊C411yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4C22⋊Dic4311yescharacteristic
169M16—22no—
170M16—41no—
171M16—42no—
172C2×C8—41no—
173C2×C8—42no—
174C2×C8—1722no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—3441no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—1722no—
182C42—21no—
183C42—41no—
184C42—3441no—
185C42Dic43⋊C411yescharacteristic
186C42(C2×D43)⋊C411yescharacteristic
187C23—21no—
188C23—21no—
189C23#1306324011yescharacteristic
190Q8—41no—
191Q8—41no—
192D4—41no—
193D4—41no—
194D4—42no—
195D4—82no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—3442no—
210C2×C4C43⋊#9511yescharacteristic
211C2×C4#1306324011yescharacteristic
212C8—42no—
213C8—3442no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—81no—
219C22—81no—
220C22#1458266611yescharacteristic
221C4—22no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—161no—
227C4—6882no—
228C4#1458268611yescharacteristic
229C4#1458268911yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—81no—
234C2#1913271311yescharacteristic
subgroupG/H
centerC4#14582686
commutatorC2×Q8×C43C42
Frattini#532C2×D43
FittingC43×#1884C2
socleC2×C43#1390
prime radical, cosocleC43×#532C22
hypercenter#1884D43
hypocenterC43#7490
LCSG ▷ C2×Q8×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1884

Complements

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

NH ≅ G/Ntype
6. #14582694C4semidirect
8. #14582648C4semidirect
10. C43×#568C4semidirect
13. C43×#410C4semidirect
121. #568Dic43semidirect
126. #410Dic43semidirect
132. C43#7490semidirect

Maximal subgroups

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

subgroupindex
#191362602
#191332572
C43×#18842
#749043