Finite Group Databasebeta

← D43×#1413 #25016952

Subgroups — D43×#1413 #25016952

Order 11008.

314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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#491×D43C211yesmaximal, characteristic
2#356×D43C212yesmaximal
3#19132768C211yesmaximal, characteristic, complemented
4#19132767C212yesmaximal, complemented
5C43×#1413C211yesmaximal, characteristic, complemented
6C4⋊Q8×D43C2211yescharacteristic
7#125×D43C411yescharacteristic
8#14583269C411yescharacteristic
9#14583268C411yescharacteristic
10#14583267C2211yescharacteristic
11#14583266—22no—
12#103×D43—22no—
13#101×D43—22no—
14#97×D43C411yescharacteristic
15#14582698C2212yes—
16#14582697—22no—
17C43×#491C2211yescharacteristic
18C43×#356C2212yes—
19C2×Q8×D43D412yes—
20M16×D43—42no—
21C2×C8×D43—21no—
22#13063325C2×C411yescharacteristic
23#13063324—41no—
24#13063323D412yes—
25#13063317C2×C411yescharacteristic
26#13063316—21no—
27#13063315—41no—
28C4⋊C4×D43—21no—
29C4⋊C4×D43—41no—
30C4⋊C4×D43—41no—
31C42×D43C2×C411yescharacteristic
32#13063250—22no—
33#13063249—22no—
34#13063248—22no—
35#13063244—22no—
36#13063243—42no—
37#13063236C2×C411yescharacteristic
38#13063235—21no—
39C4⋊Q8×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic
41#103×C43—22no—
42#101×C43—22no—
43#97×C43C2×C411yescharacteristic
44C2×Q8×C43C2×D412yes—
45Q8×D43—42no—
46Q8×D43—42no—
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×C4×D43—41no—
50C2×C4×D43C22⋊C411yescharacteristic
51C2×Dic86—22no—
52C2×Dic86C22⋊C412yes—
53M16×C43—42no—
54C2×C8×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C42×C43C22×C411yescharacteristic
59C4⋊Dic43—21no—
60C4⋊Dic43—41no—
61C4⋊Dic43—41no—
62Dic43⋊C4—42no—
63Dic43⋊C4—41no—
64Dic43⋊C4—41no—
65Dic43⋊C4—41no—
66C4×Dic43—21no—
67C4×Dic43C22⋊C411yescharacteristic
68#10621877—42no—
69C2×C43⋊C8—21no—
70#10621872—82no—
71C8×D43—41no—
72C8×D43—41no—
73C8×D43—82no—
74C22×D43#9911yescharacteristic
75Q8×C43—42no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—41no—
79C2×C4×C43C2×C22⋊C411yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—22no—
82C2×Dic43—41no—
83C2×Dic43#9911yescharacteristic
84C4×D43—21no—
85C4×D43—21no—
86C4×D43—42no—
87C4×D43—42no—
88C4×D43—42no—
89C4×D43—82no—
90Dic86—42no—
91Dic86—82no—
92C8×C43—41no—
93C8×C43—82no—
94C43⋊C8—41no—
95C43⋊C8—82no—
96C2×#1413—431nomaximal, Sylow
97C22×C43C2×#9911yescharacteristic
98C2×D43—22no—
99C2×D43#35411yescharacteristic
100C2×D43#35411yescharacteristic
101C4×C43—21no—
102C4×C43—41no—
103C4×C43—42no—
104C4×C43—81no—
105Dic43—21no—
106Dic43—41no—
107Dic43—42no—
108Dic43—81no—
109C2×#491—431no—
110C2×#356—432no—
111#1413—431no—
112#1413—432no—
113#1413D4311yescharacteristic, direct product factor
114C2×C43—21no—
115C2×C43C2×#35411yescharacteristic
116D43—21no—
117D43#141312yesdirect product factor
118C2×C4⋊Q8—431no—
119C2×#125—431no—
120#491—431no—
121#491—431no—
122#491—431no—
123#491—862no—
124#491C2×D4311yescharacteristic
125C2×#103—862no—
126C2×#101—862no—
127C2×#97—431no—
128#356—432no—
129#356—862no—
130#356C2×D4312yes—
131C43C2×#141311yescharacteristic, complemented, Sylow
132C22×Q8—432no—
133C2×M16—1722no—
134C22×C8—861no—
135C4⋊Q8—432no—
136C4⋊Q8—431no—
137C4⋊Q8—1721no—
138C4⋊Q8C22×D4311yescharacteristic
139#125—431no—
140#125—861no—
141#125—1721no—
142#125C4×D4311yescharacteristic
143C2×C4⋊C4—861no—
144C2×C4⋊C4—1721no—
145C2×C4⋊C4—1721no—
146C2×C42—431no—
147#103—22no—
148#103—862no—
149#103—862no—
150#103—862no—
151#101—22no—
152#101—862no—
153#101—1722no—
154#97—431no—
155#97—861no—
156#97C4×D4311yescharacteristic
157C2×Q8—432no—
158C2×Q8—862no—
159C2×Q8—1722no—
160C2×Q8—1722no—
161C2×Q8D4×D4312yes—
162C22×C4—431no—
163C22×C4—861no—
164C22×C4—862no—
165C22×C4—1721no—
166M16—42no—
167M16—3442no—
168M16—1722no—
169C2×C8—21no—
170C2×C8—861no—
171C2×C8—3442no—
172C2×C8—1721no—
173C2×C8—1721no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—861no—
178C4⋊C4—1722no—
179C4⋊C4—1721no—
180C4⋊C4—1721no—
181C4⋊C4—1721no—
182C4⋊C4—1721no—
183C4⋊C4—1721no—
184C42—431no—
185C42—861no—
186C42C2×C4×D4311yescharacteristic
187C23—431no—
188Q8—42no—
189Q8—3442no—
190Q8—1722no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—431no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—862no—
199C2×C4—3442no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4—1722no—
203C2×C4—1721no—
204C2×C4C22⋊C4×D4311yescharacteristic
205C8—41no—
206C8—82no—
207C8—3442no—
208C8—1721no—
209C22—431no—
210C22—431no—
211C22—862no—
212C22#99×D4311yescharacteristic
213C4—21no—
214C4—41no—
215C4—42no—
216C4—81no—
217C4—861no—
218C4—3441no—
219C4—1721no—
220C4—1722no—
221C2—21no—
222C2—432no—
223C2—861no—
224C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#1413C2
socleC2×C43C2×#354
prime radicalC22×D43#99
cosocleC4⋊Q8×C43C23
hypercenter#1413D43
hypocenterC43C2×#1413
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
3. #19132768C2semidirect
4. #19132767C2semidirect
5. C43×#1413C2semidirect
113. #1413D43direct (N × H)
117. D43#1413direct (N × H)
131. C43C2×#1413semidirect

Maximal subgroups

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

subgroupindex
#491×D432
#356×D432
#191327682
#191327672
C43×#14132
C2×#141343