Finite Group Databasebeta

← D43×#1272 #24984538

Subgroups — D43×#1272 #24984538

Order 11008.

778 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 169 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#391×D43C211yesmaximal, characteristic
2#336×D43C212yesmaximal
3#19132421C211yesmaximal, characteristic, complemented
4#19132420C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C22×Q8×D43C411yescharacteristic
7C22×C8×D43—22no—
8C2×C4⋊C4×D43C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10#14582806C411yescharacteristic
11#14582805C2211yescharacteristic
12#14582804C411yescharacteristic
13#14582803—22no—
14#95×D43—22no—
15#14582654C2212yes—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86C2×C411yescharacteristic
21C2×Q8×D43—22no—
22C2×Q8×D43—42no—
23C2×Q8×D43—42no—
24C2×Q8×D43C814yescomplemented
25C22×C4×D43—21no—
26C22×C4×D43—21no—
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D412yes—
29C22×C43⋊C8—22no—
30C2×C8×D43—28no—
31C2×C8×D43—44no—
32C2×C8×D43—44no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C4⋊C4×D43—42no—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43D412yes—
38C42×D43—42no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C22×Q8×C43C2×C411yescharacteristic
43C22×C8×C43—22no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C42×C43C2311yescharacteristic
46#95×C43—22no—
47C23×D43C22⋊C411yescharacteristic
48C2×Q8×C43—21no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43C2×C812yescomplemented
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43C22⋊C411yescharacteristic
59C22×Dic43C22⋊C412yes—
60Q8×D43—48no—
61Q8×D43—48no—
62C2×C4×D43—24no—
63C2×C4×D43—24no—
64C2×C4×D43—22no—
65C2×C4×D43—22no—
66C2×C4×D43—24no—
67C2×C4×D43—42no—
68C2×C4×D43—42no—
69C2×C4×D43—42no—
70C2×C4×D43—44no—
71C2×C4×D43C2×C812yes—
72C2×C4×D43M1612yes—
73C2×C4×D43SD1614yes—
74C2×C4×D43Q1614yes—
75C2×Dic86—21no—
76C2×Dic86—24no—
77C2×Dic86—42no—
78C2×Dic86—42no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86C2×C812yescomplemented
82C2×C8×C43—24no—
83C2×C8×C43—42no—
84C2×C8×C43—42no—
85C4⋊C4×C43—41no—
86C42×C43—41no—
87C4⋊Dic43—41no—
88Dic43⋊C4—42no—
89C4×Dic43—41no—
90C4×Dic43—42no—
91C2×C43⋊C8—24no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—42no—
94C8×D43—416no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43C22⋊C812yes—
97C22×D43#9912yes—
98C22×D43#10012yes—
99C22×D43#10314yes—
100C22×D43#10414yes—
101Q8×C43—42no—
102Q8×C43—42no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—42no—
112C2×C4×C43C22×C811yescharacteristic
113C2×C4×C43C2×M1611yescharacteristic
114C2×C4×C43C2×SD1612yes—
115C2×C4×C43C2×Q1612yes—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—21no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43C22⋊C812yes—
126C2×Dic43#10314yes—
127C4×D43—24no—
128C4×D43—24no—
129C4×D43—28no—
130C4×D43—28no—
131C4×D43—48no—
132C4×D43—84no—
133Dic86—48no—
134Dic86—42no—
135Dic86—42no—
136C8×C43—44no—
137C43⋊C8—44no—
138C2×#1272—431nomaximal, Sylow
139C22×C43C2×C22⋊C811yescharacteristic
140C22×C43C2×#9911yescharacteristic
141C22×C43C2×#10011yescharacteristic
142C22×C43C2×#10312yes—
143C22×C43C2×#10412yes—
144C2×D43#32314yes—
145C2×D43Q8⋊C818yes—
146C2×D43#32818yes—
147C2×D43#32914yes—
148C2×D43#33314yes—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—42no—
154C4×C43—81no—
155Dic43—22no—
156Dic43—24no—
157Dic43—42no—
158Dic43—81no—
159C2×#391—431no—
160C2×#336—432no—
161#1272—431no—
162#1272—432no—
163#1272D4311yescharacteristic, direct product factor
164C2×C43C2×#32311yescharacteristic
165C2×C43C2×Q8⋊C812yes—
166C2×C43C2×#32812yes—
167C2×C43C2×#32911yescharacteristic
168C2×C43C2×#33311yescharacteristic
169D43#127218yesdirect product factor
170C23×Q8—431no—
171C23×C8—862no—
172C22×C4⋊C4—431no—
173C22×C42—431no—
174#391—431no—
175#391—431no—
176#391—431no—
177#391—862no—
178#391C2×D4311yescharacteristic
179C2×#95—862no—
180#336—432no—
181#336—862no—
182#336C2×D4312yes—
183C43C2×#127211yescharacteristic, complemented, Sylow
184C22×Q8—434no—
185C22×Q8—431no—
186C22×Q8—861no—
187C22×Q8—862no—
188C22×Q8—1722no—
189C22×Q8—1722no—
190C22×Q8C4×D4311yescharacteristic
191C23×C4—431no—
192C23×C4—432no—
193C23×C4—861no—
194C23×C4—861no—
195C22×C8—22no—
196C22×C8—868no—
197C22×C8—862no—
198C22×C8—1724no—
199C22×C8—1724no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—1722no—
203C2×C4⋊C4C4×D4311yescharacteristic
204C2×C42—431no—
205C2×C42—432no—
206C2×C42—1722no—
207C2×C42C22×D4311yescharacteristic
208#95—22no—
209#95—862no—
210#95—862no—
211#95—862no—
212C24—431no—
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8—432no—
217C2×Q8—864no—
218C2×Q8—861no—
219C2×Q8—1721no—
220C2×Q8—1721no—
221C2×Q8—1722no—
222C2×Q8—1722no—
223C2×Q8—1728no—
224C2×Q8—1728no—
225C2×Q8C8×D4312yescomplemented
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—432no—
229C22×C4—431no—
230C22×C4—432no—
231C22×C4—432no—
232C22×C4—434no—
233C22×C4—434no—
234C22×C4—864no—
235C22×C4—862no—
236C22×C4—862no—
237C22×C4—864no—
238C22×C4—864no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1722no—
242C22×C4—1724no—
243C22×C4—1722no—
244C22×C4—1722no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4D4×D4312yes—
247C2×C8—24no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—864no—
251C2×C8—17216no—
252C2×C8—1722no—
253C2×C8—1722no—
254C4⋊C4—41no—
255C4⋊C4—1721no—
256C4⋊C4—1722no—
257C42—41no—
258C42—1722no—
259C42—1721no—
260C23—432no—
261C23—432no—
262C23—432no—
263C23—434no—
264C23—434no—
265C23C22⋊C4×D4311yescharacteristic
266Q8—42no—
267Q8—42no—
268Q8—1722no—
269Q8—1722no—
270Q8—1728no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—432no—
281C2×C4—434no—
282C2×C4—868no—
283C2×C4—864no—
284C2×C4—864no—
285C2×C4—868no—
286C2×C4—861no—
287C2×C4—862no—
288C2×C4—861no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—3444no—
292C2×C4—1728no—
293C2×C4—1721no—
294C2×C4—1722no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4C2×C8×D4311yescharacteristic
298C2×C4M16×D4311yescharacteristic
299C2×C4SD16×D4312yes—
300C2×C4Q16×D4312yes—
301C8—44no—
302C8—1724no—
303C22—438no—
304C22—434no—
305C22—438no—
306C22—434no—
307C22—434no—
308C22C22⋊C8×D4311yescharacteristic
309C22#99×D4311yescharacteristic
310C22#100×D4311yescharacteristic
311C22#103×D4312yes—
312C22#104×D4312yes—
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—864no—
320C4—862no—
321C4—3441no—
322C4—1722no—
323C2—438no—
324C2#323×D4311yescharacteristic
325C2Q8⋊C8×D4312yes—
326C2#328×D4312yes—
327C2#329×D4311yescharacteristic
328C2#333×D4311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43C2×#1272
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
3. #19132421C2semidirect
4. #19132420C2semidirect
5. C43×#1272C2semidirect
24. C2×Q8×D43C8semidirect
51. C2×Q8×C43C2×C8semidirect
81. C2×Dic86C2×C8semidirect
163. #1272D43direct (N × H)
169. D43#1272direct (N × H)
183. C43C2×#1272semidirect
225. C2×Q8C8×D43semidirect

Maximal subgroups

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

subgroupindex
#391×D432
#336×D432
#191324212
#191324202
C43×#12722
C2×#127243