Finite Group Databasebeta

← D43×#1319 #25005697

Subgroups — D43×#1319 #25005697

Order 11008.

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

normal subgroups only

This group has 618 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#391×D43C211yesmaximal, characteristic
2#324×D43C212yesmaximal
3#19132529C211yesmaximal, characteristic, complemented
4#19132528C212yesmaximal, complemented
5C43×#1319C211yesmaximal, characteristic, complemented
6C22×Q8×D43C411yescharacteristic
7C2×C4⋊C4×D43C2211yescharacteristic
8C2×C42×D43C411yescharacteristic
9C22⋊C8×D43—22no—
10#14582806C411yescharacteristic
11#14582805C411yescharacteristic
12#14582804C2211yescharacteristic
13#14582803—22no—
14#95×D43—22no—
15#14582625C2212yes—
16#14582624—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C22×Dic86C2×C411yescharacteristic
21C2×Q8×D43—22no—
22C2×Q8×D43—41no—
23C2×Q8×D43—41no—
24C2×Q8×D43—42no—
25C2×Q8×D43C814yescomplemented
26C22×C4×D43—21no—
27C22×C4×D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D412yes—
30C2×C8×D43—42no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4D412yes—
33C4⋊C4×D43—41no—
34C4⋊C4×D43—41no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C42×D43—42no—
38C22⋊(C43⋊C8)—22no—
39(C2×D43)⋊C8—42no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C22×Q8×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46C22⋊C8×C43—22no—
47#95×C43—22no—
48C23×D43C22⋊C411yescharacteristic
49C2×Q8×C43—21no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C2×C812yescomplemented
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D412yes—
57C22×Dic43—21no—
58C22×Dic43—21no—
59C22×Dic43C22⋊C411yescharacteristic
60C22×Dic43C22⋊C412yes—
61Q8×D43—44no—
62Q8×D43—44no—
63Q8×D43—44no—
64Q8×D43—44no—
65C2×C4×D43—24no—
66C2×C4×D43—24no—
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—42no—
73C2×C4×D43—44no—
74C2×C4×D43—41no—
75C2×C4×D43—41no—
76C2×C4×D43—42no—
77C2×C4×D43—42no—
78C2×C4×D43C2×C812yes—
79C2×C4×D43M1612yes—
80C2×Dic86—21no—
81C2×Dic86—24no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86C2×C812yescomplemented
87C2×C8×C43—42no—
88C4⋊C4×C43—41no—
89C42×C43—41no—
90C4⋊Dic43—41no—
91Dic43⋊C4—42no—
92C4×Dic43—42no—
93C4×Dic43—41no—
94C2×C43⋊C8—42no—
95C8×D43—84no—
96C23×C43C2×C22⋊C411yescharacteristic
97C22×D43—22no—
98C22×D43—22no—
99C22×D43C22⋊C812yes—
100C22×D43#9911yescharacteristic
101C22×D43#9911yescharacteristic
102C22×D43#10012yes—
103Q8×C43—42no—
104Q8×C43—42no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—42no—
115C2×C4×C43C22×C811yescharacteristic
116C2×C4×C43C2×M1611yescharacteristic
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—42no—
127C2×Dic43C22⋊C812yes—
128C4×D43—22no—
129C4×D43—22no—
130C4×D43—22no—
131C4×D43—22no—
132C4×D43—48no—
133C4×D43—44no—
134C4×D43—44no—
135C4×D43—44no—
136C4×D43—82no—
137Dic86—48no—
138Dic86—42no—
139Dic86—42no—
140C8×C43—82no—
141C43⋊C8—82no—
142C2×#1319—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43C2×C22⋊C811yescharacteristic
146C22×C43C2×#9911yescharacteristic
147C22×C43C2×#10011yescharacteristic
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—24no—
151C2×D43—24no—
152C2×D43#32312yes—
153C2×D43#32312yes—
154C2×D43#35412yes—
155C2×D43#35612yes—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—42no—
159C4×C43—42no—
160C4×C43—42no—
161Dic43—22no—
162Dic43—42no—
163Dic43—42no—
164Dic43—42no—
165C2×#391—431no—
166C2×#324—432no—
167#1319—431no—
168#1319—432no—
169#1319D4311yescharacteristic, direct product factor
170C2×C43—21no—
171C2×C43—21no—
172C2×C43C2×#32311yescharacteristic
173C2×C43C2×#35411yescharacteristic
174C2×C43C2×#35611yescharacteristic
175D43—22no—
176D43#131914yesdirect product factor
177C23×Q8—431no—
178C22×C4⋊C4—431no—
179C22×C42—431no—
180C2×C22⋊C8—862no—
181#391—431no—
182#391—431no—
183#391—431no—
184#391—862no—
185#391C2×D4311yescharacteristic
186C2×#95—862no—
187#324—432no—
188#324—862no—
189#324C2×D4312yes—
190C43C2×#131911yescharacteristic, complemented, Sylow
191C22×Q8—434no—
192C22×Q8—431no—
193C22×Q8—861no—
194C22×Q8—862no—
195C22×Q8—1722no—
196C22×Q8—1721no—
197C22×Q8—1721no—
198C22×Q8C4×D4311yescharacteristic
199C23×C4—431no—
200C23×C4—432no—
201C23×C4—861no—
202C23×C4—861no—
203C22×C8—1722no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—432no—
206C2×C4⋊C4—1721no—
207C2×C4⋊C4—1721no—
208C2×C4⋊C4C22×D4311yescharacteristic
209C2×C42—431no—
210C2×C42—861no—
211C2×C42—1722no—
212C2×C42C4×D4311yescharacteristic
213C22⋊C8—22no—
214C22⋊C8—862no—
215C22⋊C8—1722no—
216#95—22no—
217#95—862no—
218#95—862no—
219#95—862no—
220C24—431no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—432no—
225C2×Q8—864no—
226C2×Q8—861no—
227C2×Q8—1721no—
228C2×Q8—1721no—
229C2×Q8—1722no—
230C2×Q8—1722no—
231C2×Q8—1724no—
232C2×Q8—1724no—
233C2×Q8—1724no—
234C2×Q8—1724no—
235C2×Q8C8×D4312yescomplemented
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—431no—
239C22×C4—432no—
240C22×C4—432no—
241C22×C4—432no—
242C22×C4—862no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—862no—
246C22×C4—862no—
247C22×C4—864no—
248C22×C4—864no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—1724no—
252C22×C4—1722no—
253C22×C4—1721no—
254C22×C4—1721no—
255C22×C4—1722no—
256C22×C4—1722no—
257C22×C4C2×C4×D4311yescharacteristic
258C22×C4D4×D4312yes—
259C2×C8—42no—
260C2×C8—3444no—
261C2×C8—1722no—
262C4⋊C4—41no—
263C4⋊C4—1722no—
264C4⋊C4—1721no—
265C42—41no—
266C42—1721no—
267C42—1722no—
268C23—431no—
269C23—432no—
270C23—431no—
271C23—432no—
272C23—862no—
273C23—862no—
274C23C22⋊C4×D4311yescharacteristic
275Q8—42no—
276Q8—42no—
277Q8—1722no—
278Q8—1722no—
279Q8—1728no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—432no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—3442no—
301C2×C4—1724no—
302C2×C4—1724no—
303C2×C4—1724no—
304C2×C4—1728no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1722no—
310C2×C4C2×C8×D4311yescharacteristic
311C2×C4M16×D4311yescharacteristic
312C8—82no—
313C8—3442no—
314C22—21no—
315C22—21no—
316C22—432no—
317C22—432no—
318C22—432no—
319C22—432no—
320C22—864no—
321C22—864no—
322C22—861no—
323C22—861no—
324C22C22⋊C8×D4311yescharacteristic
325C22#99×D4311yescharacteristic
326C22#100×D4311yescharacteristic
327C4—21no—
328C4—21no—
329C4—42no—
330C4—42no—
331C4—42no—
332C4—862no—
333C4—1722no—
334C4—1722no—
335C4—1722no—
336C2—21no—
337C2—21no—
338C2—434no—
339C2—862no—
340C2#323×D4311yescharacteristic
341C2#354×D4311yescharacteristic
342C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43C2×#1319
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #19132529C2semidirect
4. #19132528C2semidirect
5. C43×#1319C2semidirect
25. C2×Q8×D43C8semidirect
52. C2×Q8×C43C2×C8semidirect
86. C2×Dic86C2×C8semidirect
169. #1319D43direct (N × H)
176. D43#1319direct (N × H)
190. C43C2×#1319semidirect
235. 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
#324×D432
#191325292
#191325282
C43×#13192
C2×#131943