Finite Group Databasebeta

← D43×#1411 #25016923

Subgroups — D43×#1411 #25016923

Order 11008.

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

normal subgroups only

This group has 398 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#494×D43C211yesmaximal, characteristic
2#356×D43C212yesmaximal
3#19132764C211yesmaximal, characteristic, complemented
4#19132763C212yesmaximal, complemented
5C43×#1411C211yesmaximal, characteristic, complemented
6C2×Q16×D43—22no—
7C4⋊Q8×D43C411yescharacteristic
8C4⋊Q8×D43C2211yescharacteristic
9#14583279C411yescharacteristic
10#14583278C411yescharacteristic
11#14583278C2211yescharacteristic
12#14583277—22no—
13#101×D43—22no—
14C4×C8×D43C411yescharacteristic
15#14582698C2212yes—
16#14582697—22no—
17C43×#494C2211yescharacteristic
18C43×#356C2212yes—
19C2×Q8×D43—21no—
20C2×Q8×D43D412yes—
21C2×Dic172—22no—
22C2×#10621885—22no—
23C2×#10621885—22no—
24Q16×D43—44no—
25Q16×D43—44no—
26M16×D43—42no—
27C2×C8×D43—21no—
28#13063325C2×C411yescharacteristic
29#13063325C2×C411yescharacteristic
30#13063324—41no—
31#13063324—41no—
32#13063323—21no—
33#13063323D412yes—
34C4⋊C4×D43—41no—
35C4⋊C4×D43—41no—
36C42×D43C2×C411yescharacteristic
37#13063244—22no—
38#13063243—42no—
39C4×C43⋊C8C2×C411yescharacteristic
40C8×Dic43—21no—
41C2×Q16×C43—22no—
42C4⋊Q8×C43C2×C411yescharacteristic
43C4⋊Q8×C43C2311yescharacteristic
44#101×C43—22no—
45C4×C8×C43C2×C411yescharacteristic
46C2×Q8×C43—21no—
47C2×Q8×C43C2×D412yes—
48Q8×D43—42no—
49Q8×D43—42no—
50Q8×D43—42no—
51Q8×D43—42no—
52C2×C4×D43—21no—
53C2×C4×D43—22no—
54C2×C4×D43—41no—
55C2×C4×D43C22⋊C411yescharacteristic
56C2×Dic86—21no—
57C2×Dic86—22no—
58C2×Dic86—41no—
59C2×Dic86C22⋊C412yes—
60Q16×C43—44no—
61M16×C43—42no—
62C2×C8×C43—21no—
63C4⋊C4×C43—41no—
64C4⋊C4×C43—41no—
65C42×C43C22×C411yescharacteristic
66#10621885—44no—
67#10621885—44no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72C4×Dic43—21no—
73C4×Dic43C22⋊C411yescharacteristic
74#10621877—42no—
75C2×C43⋊C8—21no—
76Dic172—44no—
77#10621872—82no—
78C8×D43—22no—
79C8×D43—22no—
80C8×D43—82no—
81C22×D43#9911yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—41no—
87C2×C4×C43C2×C22⋊C411yescharacteristic
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—41no—
91C2×Dic43#9911yescharacteristic
92C4×D43—24no—
93C4×D43—21no—
94C4×D43—21no—
95C4×D43—42no—
96C4×D43—42no—
97C4×D43—81no—
98C4×D43—81no—
99Dic86—42no—
100Dic86—42no—
101Dic86—82no—
102Dic86—82no—
103C8×C43—22no—
104C8×C43—82no—
105C43⋊C8—22no—
106C43⋊C8—82no—
107C2×#1411—431nomaximal, Sylow
108C22×C43C2×#9911yescharacteristic
109C2×D43—22no—
110C2×D43#35311yescharacteristic
111C2×D43#35311yescharacteristic
112C4×C43—22no—
113C4×C43—21no—
114C4×C43—42no—
115C4×C43—81no—
116Dic43—22no—
117Dic43—21no—
118Dic43—42no—
119Dic43—81no—
120C2×#494—431no—
121C2×#356—432no—
122#1411—431no—
123#1411—432no—
124#1411D4311yescharacteristic, direct product factor
125C2×C43—21no—
126C2×C43C2×#35311yescharacteristic
127D43—21no—
128D43#141112yesdirect product factor
129C22×Q16—862no—
130C2×C4⋊Q8—431no—
131C2×C4⋊Q8—431no—
132#494—431no—
133#494—431no—
134#494—431no—
135#494—862no—
136#494C2×D4311yescharacteristic
137C2×#101—862no—
138C2×C4×C8—431no—
139#356—432no—
140#356—862no—
141#356C2×D4312yes—
142C43C2×#141111yescharacteristic, complemented, Sylow
143C22×Q8—432no—
144C22×Q8—861no—
145C2×Q16—22no—
146C2×Q16—862no—
147C2×Q16—862no—
148C2×Q16—862no—
149C2×Q16—1724no—
150C2×Q16—1724no—
151C2×M16—1722no—
152C22×C8—861no—
153C4⋊Q8—432no—
154C4⋊Q8—431no—
155C4⋊Q8—431no—
156C4⋊Q8—861no—
157C4⋊Q8—1721no—
158C4⋊Q8—1721no—
159C4⋊Q8C4×D4311yescharacteristic
160C4⋊Q8C22×D4311yescharacteristic
161C2×C4⋊C4—1721no—
162C2×C4⋊C4—1721no—
163C2×C42—431no—
164#101—22no—
165#101—862no—
166#101—1722no—
167C4×C8—431no—
168C4×C8—861no—
169C4×C8C4×D4311yescharacteristic
170C2×Q8—21no—
171C2×Q8—432no—
172C2×Q8—862no—
173C2×Q8—861no—
174C2×Q8—1721no—
175C2×Q8—1722no—
176C2×Q8—1722no—
177C2×Q8—1722no—
178C2×Q8—1722no—
179C2×Q8D4×D4312yes—
180C22×C4—431no—
181C22×C4—861no—
182C22×C4—862no—
183C22×C4—1721no—
184Q16—44no—
185Q16—1724no—
186Q16—1724no—
187Q16—1724no—
188M16—42no—
189M16—3442no—
190M16—1722no—
191C2×C8—21no—
192C2×C8—862no—
193C2×C8—862no—
194C2×C8—861no—
195C2×C8—3442no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—1722no—
199C4⋊C4—1721no—
200C4⋊C4—1721no—
201C4⋊C4—1722no—
202C42—431no—
203C42—861no—
204C42C2×C4×D4311yescharacteristic
205C23—431no—
206Q8—42no—
207Q8—42no—
208Q8—3442no—
209Q8—3442no—
210Q8—1722no—
211Q8—1722no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—431no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—864no—
219C2×C4—861no—
220C2×C4—862no—
221C2×C4—3441no—
222C2×C4—3441no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1721no—
226C2×C4C22⋊C4×D4311yescharacteristic
227C8—22no—
228C8—82no—
229C8—862no—
230C8—3442no—
231C22—431no—
232C22—431no—
233C22—862no—
234C22#99×D4311yescharacteristic
235C4—22no—
236C4—21no—
237C4—42no—
238C4—81no—
239C4—862no—
240C4—861no—
241C4—3441no—
242C4—1722no—
243C2—21no—
244C2—432no—
245C2—861no—
246C2#353×D4311yescharacteristic
subgroupG/H
centerC2#353×D43
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#1411C2
socleC2×C43C2×#353
prime radicalC22×D43#99
cosocleC4⋊Q8×C43C23
hypercenter#1411D43
hypocenterC43C2×#1411
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1411

Complements

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

NH ≅ G/Ntype
3. #19132764C2semidirect
4. #19132763C2semidirect
5. C43×#1411C2semidirect
124. #1411D43direct (N × H)
128. D43#1411direct (N × H)
142. C43C2×#1411semidirect

Maximal subgroups

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

subgroupindex
#494×D432
#356×D432
#191327642
#191327632
C43×#14112
C2×#141143