Finite Group Databasebeta

← D43×#1325 #25005749

Subgroups — D43×#1325 #25005749

Order 11008.

598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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#384×D43C211yesmaximal, characteristic
2#324×D43C212yesmaximal
3#19132541C211yesmaximal, characteristic, complemented
4#19132540C212yesmaximal, complemented
5C43×#1325C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D43—22no—
7C2×C4⋊C4×D43C411yescharacteristic
8C2×C4⋊C4×D43C2211yescharacteristic
9C2×C42×D43C411yescharacteristic
10C22⋊C8×D43—22no—
11#14582769C411yescharacteristic
12#14582768—22no—
13#14582768C411yescharacteristic
14#14582768C2211yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×C4×D43—21no—
20C22×C4×D43—21no—
21C22×C4×D43C2×C411yescharacteristic
22C22×C4×D43D412yes—
23C2×C8×D43—42no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4D412yes—
31C4⋊C4×D43—41no—
32C4⋊C4×D43—41no—
33C4⋊C4×D43—41no—
34C4⋊C4×D43—41no—
35C4⋊C4×D43—48no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C42×D43—22no—
39C42×D43C814yescomplemented
40C22⋊(C43⋊C8)—22no—
41(C2×D43)⋊C8—42no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46C22⋊C8×C43—22no—
47C23×D43C22⋊C411yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—21no—
53C22×Dic43—21no—
54C22×Dic43C22⋊C411yescharacteristic
55C22×Dic43C22⋊C412yes—
56C2×C4×D43—24no—
57C2×C4×D43—24no—
58C2×C4×D43—24no—
59C2×C4×D43—21no—
60C2×C4×D43—21no—
61C2×C4×D43—22no—
62C2×C4×D43—22no—
63C2×C4×D43—22no—
64C2×C4×D43—44no—
65C2×C4×D43—44no—
66C2×C4×D43—41no—
67C2×C4×D43—41no—
68C2×C4×D43C2×C812yes—
69C2×C4×D43M1612yes—
70C2×C8×C43—42no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—44no—
74C42×C43—21no—
75C42×C43C2×C812yescomplemented
76C4⋊Dic43—41no—
77C4⋊Dic43—44no—
78C4⋊Dic43—41no—
79Dic43⋊C4—42no—
80Dic43⋊C4—44no—
81Dic43⋊C4—44no—
82Dic43⋊C4—42no—
83C4×Dic43—21no—
84C4×Dic43—24no—
85C4×Dic43C2×C812yescomplemented
86C2×C43⋊C8—42no—
87C8×D43—84no—
88C23×C43C2×C22⋊C411yescharacteristic
89C22×D43—22no—
90C22×D43—22no—
91C22×D43C22⋊C812yes—
92C22×D43#9911yescharacteristic
93C22×D43#9911yescharacteristic
94C22×D43#10112yes—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43C22×C811yescharacteristic
105C2×C4×C43C2×M1611yescharacteristic
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—41no—
115C2×Dic43C22⋊C812yes—
116C4×D43—216no—
117C4×D43—22no—
118C4×D43—22no—
119C4×D43—22no—
120C4×D43—22no—
121C4×D43—44no—
122C4×D43—82no—
123C4×D43—82no—
124C4×D43—82no—
125C8×C43—82no—
126C43⋊C8—82no—
127C2×#1325—431nomaximal, Sylow
128C22×C43—21no—
129C22×C43—21no—
130C22×C43C2×C22⋊C811yescharacteristic
131C22×C43C2×#9911yescharacteristic
132C22×C43C2×#10111yescharacteristic
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—24no—
136C2×D43—24no—
137C2×D43#32412yes—
138C2×D43#32412yes—
139C2×D43#35312yes—
140C2×D43#35612yes—
141C4×C43—24no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—42no—
145C4×C43—81no—
146Dic43—24no—
147Dic43—22no—
148Dic43—42no—
149Dic43—81no—
150C2×#384—431no—
151C2×#324—432no—
152#1325—431no—
153#1325—432no—
154#1325D4311yescharacteristic, direct product factor
155C2×C43—21no—
156C2×C43—21no—
157C2×C43C2×#32411yescharacteristic
158C2×C43C2×#35311yescharacteristic
159C2×C43C2×#35611yescharacteristic
160D43—22no—
161D43#132514yesdirect product factor
162C22×C4⋊C4—431no—
163C22×C4⋊C4—431no—
164C22×C4⋊C4—862no—
165C22×C42—431no—
166C2×C22⋊C8—862no—
167#384—431no—
168#384—431no—
169#384—431no—
170#384—862no—
171#384C2×D4311yescharacteristic
172#324—432no—
173#324—862no—
174#324C2×D4312yes—
175C43C2×#132511yescharacteristic, complemented, Sylow
176C23×C4—431no—
177C23×C4—432no—
178C23×C4—861no—
179C23×C4—861no—
180C22×C8—1722no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—431no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—431no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—862no—
187C2×C4⋊C4—862no—
188C2×C4⋊C4—862no—
189C2×C4⋊C4—1721no—
190C2×C4⋊C4—1721no—
191C2×C4⋊C4—1721no—
192C2×C4⋊C4—1721no—
193C2×C4⋊C4—1728no—
194C2×C4⋊C4C4×D4311yescharacteristic
195C2×C4⋊C4C22×D4311yescharacteristic
196C2×C42—431no—
197C2×C42—434no—
198C2×C42—862no—
199C2×C42—861no—
200C2×C42C4×D4311yescharacteristic
201C22⋊C8—22no—
202C22⋊C8—862no—
203C22⋊C8—1722no—
204C24—431no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—431no—
208C22×C4—432no—
209C22×C4—432no—
210C22×C4—432no—
211C22×C4—864no—
212C22×C4—861no—
213C22×C4—861no—
214C22×C4—862no—
215C22×C4—864no—
216C22×C4—864no—
217C22×C4—862no—
218C22×C4—862no—
219C22×C4—861no—
220C22×C4—861no—
221C22×C4—1721no—
222C22×C4—1721no—
223C22×C4—1724no—
224C22×C4—1724no—
225C22×C4C2×C4×D4311yescharacteristic
226C22×C4D4×D4312yes—
227C2×C8—42no—
228C2×C8—3444no—
229C2×C8—1722no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—44no—
233C4⋊C4—1722no—
234C4⋊C4—1721no—
235C4⋊C4—1721no—
236C4⋊C4—1724no—
237C4⋊C4—1724no—
238C4⋊C4—1724no—
239C4⋊C4—1722no—
240C42—21no—
241C42—432no—
242C42—864no—
243C42—861no—
244C42C8×D4312yescomplemented
245C23—431no—
246C23—432no—
247C23—431no—
248C23—432no—
249C23—862no—
250C23—862no—
251C23C22⋊C4×D4311yescharacteristic
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—432no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—8616no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4—862no—
273C2×C4—3442no—
274C2×C4—3442no—
275C2×C4—3442no—
276C2×C4—1724no—
277C2×C4—1722no—
278C2×C4—1721no—
279C2×C4—1722no—
280C2×C4C2×C8×D4311yescharacteristic
281C2×C4M16×D4311yescharacteristic
282C8—82no—
283C8—3442no—
284C22—21no—
285C22—21no—
286C22—432no—
287C22—432no—
288C22—432no—
289C22—432no—
290C22—864no—
291C22—864no—
292C22—861no—
293C22—861no—
294C22C22⋊C8×D4311yescharacteristic
295C22#99×D4311yescharacteristic
296C22#101×D4311yescharacteristic
297C4—24no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—81no—
302C4—864no—
303C4—862no—
304C4—3441no—
305C4—1722no—
306C2—21no—
307C2—21no—
308C2—434no—
309C2—862no—
310C2#324×D4311yescharacteristic
311C2#353×D4311yescharacteristic
312C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1325D43
hypocenterC43C2×#1325
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #19132541C2semidirect
4. #19132540C2semidirect
5. C43×#1325C2semidirect
39. C42×D43C8semidirect
75. C42×C43C2×C8semidirect
85. C4×Dic43C2×C8semidirect
154. #1325D43direct (N × H)
161. D43#1325direct (N × H)
175. C43C2×#1325semidirect
244. C42C8×D43semidirect

Maximal subgroups

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

subgroupindex
#384×D432
#324×D432
#191325412
#191325402
C43×#13252
C2×#132543