Finite Group Databasebeta

← #25012882

Subgroups — #25012882

Order 11008.

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

normal subgroups only

This group has 334 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#19143242C211yesmaximal, characteristic
2#19134700C212yesmaximal
3#19132725C212yesmaximal
4#19132716C211yesmaximal, characteristic
5C43×#1392C211yesmaximal, characteristic
6#41×Dic43C2211yescharacteristic
7#14582957—22no—
8#14582953—22no—
9#14582927C411yescharacteristic, complemented
10#14582925C411yescharacteristic, complemented
11#14582873C2212yes—
12#14582866C2211yescharacteristic
13M16×Dic43C411yescharacteristic, complemented
14C2×#13063235C411yescharacteristic, complemented
15#14582660—22no—
16#14582656—22no—
17C43×#413C2212yes—
18C43×#408C2211yescharacteristic
19C2×#10621877C2×C411yescharacteristic
20C22×C43⋊C8C2×C411yescharacteristic
21Q8×Dic43—21no—
22D4×Dic43—22no—
23D4×Dic43—21no—
24#13063284—22no—
25#13063284C2×C411yescharacteristic
26#13063284D412yes—
27C2×C4×Dic43C2×C411yescharacteristic
28C2×C4×Dic43D412yes—
29Dic43⋊C8—22no—
30Dic43⋊C8—22no—
31#13063240—22no—
32#13063240—22no—
33C22⋊(C43⋊C8)—22no—
34#13063235—21no—
35#13063235—21no—
36#13063235—21no—
37C8×Dic43—21no—
38C2×#41×C43C2311yescharacteristic
39C2×M16×C43—22no—
40C2×M16×C43C2×C411yescharacteristic
41C22×C8×C43C2×C411yescharacteristic
42#101×C43—22no—
43#100×C43—22no—
44C22⋊C8×C43—22no—
45#41×C43—41no—
46#41×C43—41no—
47C2×Q8×C43#4111yescharacteristic
48C2×D4×C43#4112yes—
49C2×D4×C43#4111yescharacteristic
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—21no—
53C22×Dic43—22no—
54M16×C43—41no—
55M16×C43—42no—
56M16×C43—42no—
57C2×C8×C43—21no—
58C2×C8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43—42no—
61C22⋊Dic43—21no—
62C22⋊Dic43—22no—
63C22⋊Dic43—42no—
64C4⋊Dic43—21no—
65C4⋊Dic43—22no—
66C4⋊Dic43—42no—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43—42no—
70C4×Dic43C22⋊C411yescharacteristic
71C4×Dic43C22⋊C411yescharacteristic
72C4×Dic43C22⋊C412yes—
73#10621877—41no—
74C2×C43⋊C8—21no—
75C2×C43⋊C8—21no—
76C2×C43⋊C8—41no—
77C23×C43#11711yescharacteristic
78C23×C43#12312yes—
79Q8×C43—41no—
80D4×C43—42no—
81D4×C43—41no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43C2×C22⋊C411yescharacteristic
87C2×C4×C43#11711yescharacteristic
88C2×C4×C43#12312yes—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—81no—
93C2×Dic43—82no—
94C2×Dic43—82no—
95C8×C43—41no—
96C8×C43—41no—
97C8×C43—82no—
98C43⋊C8—41no—
99C43⋊C8—41no—
100#12865—431nomaximal, Sylow
101C22×C43—21no—
102C22×C43—22no—
103C22×C43—41no—
104C22×C43—42no—
105C22×C43#38111yescharacteristic
106C4×C43—22no—
107C4×C43—21no—
108C4×C43#41011yescharacteristic
109C4×C43#41011yescharacteristic
110Dic43—41no—
111Dic43—42no—
112Dic43—41no—
113Dic43—162no—
114#2923—431no—
115#1827—432no—
116#1395—432no—
117#1392D4311yescharacteristic
118#1391—431no—
119C2×C43—21no—
120C2×C43—42no—
121C2×C43—41no—
122C2×C43#182011yescharacteristic
123C4×#41—431no—
124#433—862no—
125#432—862no—
126#424—431no—
127#424—431no—
128#413C2×D4312yes—
129#410—432no—
130#408—431no—
131#408C2×D4311yescharacteristic
132C4×M16—431no—
133C2×#97—431no—
134#339—862no—
135H(3,ℤ/4)—862no—
136C43#1286511yescharacteristic, complemented, Sylow
137C2×#41C22×D4311yescharacteristic
138C2×M16—22no—
139C2×M16—431no—
140C2×M16C4×D4311yescharacteristic
141C22×C8—431no—
142C22×C8C4×D4311yescharacteristic
143C4×Q8—861no—
144C4×D4—862no—
145C4×D4—861no—
146#117—431no—
147#117—432no—
148#117—862no—
149C2×C42—431no—
150C2×C42—432no—
151C4⋊C8—862no—
152C4⋊C8—862no—
153#101—22no—
154#100—22no—
155#99—862no—
156#99—862no—
157C22⋊C8—22no—
158C22⋊C8—862no—
159#97—861no—
160#97—861no—
161#97—861no—
162C4×C8—861no—
163#41—41no—
164#41—41no—
165C2×Q8#1062190011yescharacteristic
166C2×D4#1062189812yes—
167C2×D4#1062190211yescharacteristic
168C22×C4—861no—
169C22×C4—862no—
170C22×C4C2×C4×D4311yescharacteristic
171C22×C4D4×D4312yes—
172M16—41no—
173M16—42no—
174M16—42no—
175M16—1721no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—861no—
181C2×C8—861no—
182C2×C8—1721no—
183C4⋊C4—861no—
184C4⋊C4—862no—
185C4⋊C4—1722no—
186C22⋊C4—861no—
187C22⋊C4—862no—
188C22⋊C4—1722no—
189C42—431no—
190C42—431no—
191C42—432no—
192C42—861no—
193C42—862no—
194C42—1722no—
195C23#1306328211yescharacteristic
196C23#1306331012yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—862no—
207C2×C4—3441no—
208C2×C4—3442no—
209C2×C4—3442no—
210C2×C4C22⋊C4×D4311yescharacteristic
211C2×C4#1306328311yescharacteristic
212C2×C4#1306330712yes—
213C8—41no—
214C8—41no—
215C8—82no—
216C8—1721no—
217C8—1721no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1458276111yescharacteristic
223C4—22no—
224C4—21no—
225C4—1721no—
226C4—1721no—
227C4—1722no—
228C4—6882no—
229C4#1458287111yescharacteristic
230C4#1458287111yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1913467111yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#1392C2
socleC2×C43#1820
prime radical, cosocleC2×#41×C43C23
hypercenter#1392D43
hypocenterC43#12865
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
9. #14582927C4semidirect
10. #14582925C4semidirect
13. M16×Dic43C4semidirect
14. C2×#13063235C4semidirect
136. C43#12865semidirect

Maximal subgroups

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

subgroupindex
#191432422
#191347002
#191327252
#191327162
C43×#13922
#1286543