Finite Group Databasebeta

← D43×#1306 #24986957

Subgroups — D43×#1306 #24986957

Order 11008.

942 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 159 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#407×D43C212yesmaximal
2#381×D43C211yesmaximal, characteristic
3#19132504C212yesmaximal, complemented
4#19132503C211yesmaximal, characteristic, complemented
5C43×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D43C2211yescharacteristic
7C2×M16×D43—22no—
8C2×C22⋊C4×D43C412yes—
9#14582863C2212yes—
10#14582862—22no—
11#14582861—22no—
12#14582861C414yescomplemented
13C22⋊C8×D43—22no—
14C22⋊C8×D43C414yescomplemented
15#14582762C2211yescharacteristic
16#14582761—22no—
17#14582760C412yes—
18#95×D43—22no—
19C43×#407C2212yes—
20C43×#381C2211yescharacteristic
21C24×D43C2×C411yescharacteristic
22C23×Dic43C2×C411yescharacteristic
23C22×C4×D43—22no—
24C22×C4×D43—44no—
25C22×C4×D43C2×C412yes—
26C22×C4×D43C2×C412yes—
27C22×C4×D43D412yes—
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D412yes—
31C22×C4×D43Q811yescharacteristic
32C22×C4×D43Q811yescharacteristic
33C2×#10621877—22no—
34C2×#10621872—24no—
35M16×D43—48no—
36C2×C8×D43—24no—
37C2×C22⋊Dic43C2×C412yes—
38C2×(C2×D43)⋊C4—22no—
39C22⋊C4×D43—44no—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)C2×C414yescomplemented
42(C2×D43)⋊C8—24no—
43(C2×D43)⋊C8—24no—
44C43⋊#95—22no—
45C43⋊#95—24no—
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C2×C22⋊C4×C43C2×C412yes—
49C22⋊C8×C43—22no—
50C22⋊C8×C43C2×C414yescomplemented
51#95×C43—22no—
52C24×C43C22×C411yescharacteristic
53C23×D43—24no—
54C23×D43—44no—
55C23×D43C4211yescharacteristic
56C23×D43C4211yescharacteristic
57C23×D43C22⋊C411yescharacteristic
58C23×D43C22⋊C411yescharacteristic
59C23×D43C4⋊C411yescharacteristic
60C23×D43C4⋊C411yescharacteristic
61C22×C4×C43—22no—
62C22×C4×C43—42no—
63C22×C4×C43C22×C412yes—
64C22×C4×C43C2×D412yes—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×Q811yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—42no—
69C22×Dic43C4212yes—
70C22×Dic43C22⋊C412yes—
71C22×Dic43C4⋊C411yescharacteristic
72C22×Dic43C4⋊C411yescharacteristic
73C2×C4×D43—28no—
74C2×C4×D43—44no—
75C2×C4×D43—44no—
76C2×C4×D43—42no—
77C2×C4×D43—42no—
78C2×C4×D43—42no—
79C2×C4×D43—42no—
80C2×C4×D43—44no—
81C2×C4×D43—48no—
82C2×C4×D43—44no—
83C2×C4×D43C22⋊C412yes—
84C2×C4×D43C22⋊C412yes—
85C2×C4×D43C22⋊C412yes—
86C2×C4×D43C22⋊C412yes—
87C2×C4×D43C4⋊C412yes—
88C2×C4×D43C4⋊C412yes—
89C2×C4×D43C4⋊C412yes—
90C2×C4×D43C4⋊C412yes—
91M16×C43—44no—
92C2×C8×C43—24no—
93C22⋊C4×C43—42no—
94C22⋊Dic43—42no—
95(C2×D43)⋊C4—44no—
96#10621877—44no—
97C2×C43⋊C8—24no—
98#10621872—48no—
99C8×D43—48no—
100C23×C43—22no—
101C23×C43—42no—
102C23×C43C2×C4211yescharacteristic
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43C2×C4⋊C411yescharacteristic
105C22×D43—24no—
106C22×D43—22no—
107C22×D43—22no—
108C22×D43—22no—
109C22×D43—22no—
110C22×D43—22no—
111C22×D43—24no—
112C22×D43—24no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—416no—
117C22×D43#9511yescharacteristic
118C22×D43#9511yescharacteristic
119C22×D43#9511yescharacteristic
120C22×D43#9511yescharacteristic
121C22×D43#9914yes—
122C2×C4×C43—24no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—44no—
127C2×C4×C43—42no—
128C2×C4×C43C2×C22⋊C412yes—
129C2×C4×C43C2×C4⋊C412yes—
130C2×Dic43—24no—
131C2×Dic43—42no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—44no—
135C2×Dic43—42no—
136C2×Dic43#9512yes—
137C2×Dic43#9512yes—
138C4×D43—24no—
139C4×D43—24no—
140C4×D43—24no—
141C4×D43—24no—
142C4×D43—42no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—88no—
147C8×C43—44no—
148C43⋊C8—44no—
149C2×#1306—431nomaximal, Sylow
150C22×C43—22no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—44no—
156C22×C43C2×#9511yescharacteristic
157C22×C43C2×#9912yes—
158C2×D43—22no—
159C2×D43—28no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—22no—
163C2×D43—22no—
164C2×D43—44no—
165C2×D43—44no—
166C2×D43—44no—
167C2×D43—44no—
168C2×D43—44no—
169C2×D43#34212yes—
170C2×D43#34212yes—
171C2×D43#34414yes—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—82no—
175Dic43—22no—
176Dic43—22no—
177Dic43—82no—
178C2×#407—432no—
179C2×#381—431no—
180#1306—432no—
181#1306—431no—
182#1306D4311yescharacteristic, direct product factor
183C2×C43—22no—
184C2×C43—41no—
185C2×C43—41no—
186C2×C43C2×#34211yescharacteristic
187C2×C43C2×#34412yes—
188D43—22no—
189D43—41no—
190D43—41no—
191D43#130614yesdirect product factor
192C24×C4—431no—
193C22×M16—862no—
194C22×C22⋊C4—432no—
195#407—432no—
196#407—434no—
197#407—862no—
198#407—862no—
199#407C2×D4312yes—
200C2×C22⋊C8—434no—
201C2×C22⋊C8—862no—
202#381—431no—
203#381—432no—
204#381—862no—
205#381C2×D4311yescharacteristic
206C2×#95—862no—
207C43C2×#130611yescharacteristic, complemented, Sylow
208C25—431no—
209C23×C4—431no—
210C23×C4—432no—
211C23×C4—432no—
212C23×C4—432no—
213C23×C4—432no—
214C23×C4—431no—
215C23×C4—431no—
216C23×C4—431no—
217C23×C4—431no—
218C23×C4—862no—
219C23×C4—1724no—
220C23×C4C22×D4311yescharacteristic
221C2×M16—22no—
222C2×M16—864no—
223C2×M16—862no—
224C2×M16—1728no—
225C22×C8—864no—
226C2×C22⋊C4—432no—
227C2×C22⋊C4—862no—
228C2×C22⋊C4—1724no—
229C2×C22⋊C4C4×D4312yes—
230C22⋊C8—22no—
231C22⋊C8—434no—
232C22⋊C8—864no—
233C22⋊C8—864no—
234C22⋊C8—862no—
235C22⋊C8C4×D4314yescomplemented
236#95—22no—
237#95—864no—
238#95—862no—
239C24—431no—
240C24—431no—
241C24—431no—
242C24—431no—
243C24—431no—
244C24—431no—
245C24—864no—
246C24—1724no—
247C24C2×C4×D4311yescharacteristic
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—432no—
251C22×C4—432no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—432no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4—432no—
259C22×C4—432no—
260C22×C4—432no—
261C22×C4—432no—
262C22×C4—868no—
263C22×C4—862no—
264C22×C4—1724no—
265C22×C4—1724no—
266C22×C4—1724no—
267C22×C4—1722no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4—1722no—
271C22×C4—1724no—
272C22×C4—1728no—
273C22×C4—1722no—
274C22×C4C2×C4×D4312yes—
275C22×C4D4×D4312yes—
276C22×C4D4×D4311yescharacteristic
277C22×C4Q8×D4311yescharacteristic
278M16—44no—
279M16—1728no—
280M16—1724no—
281C2×C8—24no—
282C2×C8—864no—
283C2×C8—1728no—
284C22⋊C4—42no—
285C22⋊C4—1724no—
286C22⋊C4—1722no—
287C23—22no—
288C23—42no—
289C23—431no—
290C23—434no—
291C23—431no—
292C23—431no—
293C23—431no—
294C23—864no—
295C23—862no—
296C23—862no—
297C23—862no—
298C23—862no—
299C23—864no—
300C23—864no—
301C23—862no—
302C23—1722no—
303C23—1722no—
304C23—1722no—
305C23—17216no—
306C23C42×D4311yescharacteristic
307C23C22⋊C4×D4311yescharacteristic
308C23C4⋊C4×D4311yescharacteristic
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—432no—
316C2×C4—432no—
317C2×C4—864no—
318C2×C4—864no—
319C2×C4—864no—
320C2×C4—864no—
321C2×C4—864no—
322C2×C4—3448no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1724no—
331C2×C4—1722no—
332C2×C4C22⋊C4×D4312yes—
333C2×C4C4⋊C4×D4312yes—
334C8—44no—
335C8—1724no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—44no—
342C22—432no—
343C22—434no—
344C22—432no—
345C22—868no—
346C22—862no—
347C22—861no—
348C22—861no—
349C22—862no—
350C22—862no—
351C22—1724no—
352C22—1724no—
353C22—1724no—
354C22—1724no—
355C22—1724no—
356C22#95×D4311yescharacteristic
357C22#99×D4312yes—
358C4—22no—
359C4—22no—
360C4—82no—
361C4—862no—
362C4—862no—
363C4—3442no—
364C2—22no—
365C2—41no—
366C2—41no—
367C2—434no—
368C2—862no—
369C2—1721no—
370C2—1721no—
371C2#342×D4311yescharacteristic
372C2#344×D4312yes—
subgroupG/H
centerC22#95×D43
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43C2×#95
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1306D43
hypocenterC43C2×#1306
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #19132504C2semidirect
4. #19132503C2semidirect
5. C43×#1306C2semidirect
12. #14582861C4semidirect
14. C22⋊C8×D43C4semidirect
41. C22⋊(C43⋊C8)C2×C4semidirect
50. C22⋊C8×C43C2×C4semidirect
182. #1306D43direct (N × H)
191. D43#1306direct (N × H)
207. C43C2×#1306semidirect
235. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#407×D432
#381×D432
#191325042
#191325032
C43×#13062
C2×#130643