Finite Group Databasebeta

← C43×#9184 #24929201

Subgroups — C43×#9184 #24929201

Order 11008.

530 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C43×#2975C211yesmaximal, characteristic
2C43×#2638C211yesmaximal, characteristic
3C4×#99×C43C211yesmaximal, characteristic
4C43×#1508C212yesmaximal, complemented
5C43×#1284C212yesmaximal, complemented
6C2×C22⋊Q8×C43C2211yescharacteristic
7C2×C4×D4×C43C2211yescharacteristic
8C43×#436—24no—
9C43×#431—21no—
10C2×#99×C43—21no—
11C43×#407—21no—
12C43×#407C2212yes—
13C43×#398C411yescharacteristic, complemented
14C43×#397—21no—
15C43×#397C411yescharacteristic, complemented
16C43×#395C411yescharacteristic, complemented
17C43×#394—21no—
18C43×#393C411yescharacteristic, complemented
19C43×#387—21no—
20C43×#385—21no—
21C43×#381C2211yescharacteristic
22C4×C22⋊C4×C43C2212yes—
23C43×#342—21no—
24C43×#328—24no—
25C22×Q8×C43C2×C411yescharacteristic
26C22×D4×C43D411yescharacteristic
27C23×C4×C43D411yescharacteristic
28C23×C4×C43C2311yescharacteristic
29C2×M16×C43—22no—
30C2×M16×C43—22no—
31C22⋊Q8×C43—22no—
32C22⋊Q8×C43—22no—
33C4×D4×C43—22no—
34C4×D4×C43—22no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C42×C43—22no—
48C2×C42×C43D411yescharacteristic
49C4⋊C8×C43—22no—
50#99×C43—24no—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C22⋊C8×C43D414yes—
54C4×C8×C43—22no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—22no—
61#95×C43C2×C411yescharacteristic
62#95×C43C2×C411yescharacteristic
63C24×C43C22⋊C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C2×Q8×C43—22no—
66C2×Q8×C43—81no—
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—42no—
77C22×C4×C43—81no—
78C22×C4×C43—81no—
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D412yes—
85C22×C4×C43#4112yes—
86M16×C43—82no—
87M16×C43—82no—
88C2×C8×C43—24no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—81no—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—24no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—42no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—81no—
102C22⋊C4×C43—81no—
103C42×C43—21no—
104C42×C43—21no—
105C42×C43—82no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43#12112yes—
117Q8×C43—82no—
118D4×C43—44no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—44no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—81no—
144C2×C4×C43—82no—
145C2×C4×C43—82no—
146C2×C4×C43#10412yes—
147C2×C4×C43C4×D412yes—
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C8×C43—44no—
151#9184C4311yesmaximal, characteristic, direct product factor, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—42no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43#38611yescharacteristic
165C22×C43C2×#10411yescharacteristic
166C22×C43#42111yescharacteristic
167C4×C43—22no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—22no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—81no—
174C4×C43—81no—
175C4×C43—84no—
176C4×C43—81no—
177C4×C43—81no—
178#2975C2×C4311yescharacteristic
179#2638C2×C4311yescharacteristic
180C4×#99C2×C4311yescharacteristic
181#1508C2×C4312yescomplemented
182#1284C2×C4312yescomplemented
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—42no—
186C2×C43—81no—
187C2×C43#187111yescharacteristic
188C2×C43#190911yescharacteristic
189C2×C43#191311yescharacteristic
190C2×C22⋊Q8C22×C4311yescharacteristic
191C2×C4×D4C22×C4311yescharacteristic
192#436—24no—
193#431—21no—
194C2×#99—21no—
195#407—21no—
196#407C22×C4312yes—
197#398C4×C4311yescharacteristic, complemented
198#397—21no—
199#397C4×C4311yescharacteristic, complemented
200#395C4×C4311yescharacteristic, complemented
201#394—21no—
202#393C4×C4311yescharacteristic, complemented
203#387—21no—
204#385—21no—
205#381C22×C4311yescharacteristic
206C4×C22⋊C4C22×C4312yes—
207#342—21no—
208#328—24no—
209C43#918411yescharacteristic, direct product factor, Sylow
210C22×Q8C2×C4×C4311yescharacteristic
211C22×D4D4×C4311yescharacteristic
212C23×C4D4×C4311yescharacteristic
213C23×C4C23×C4311yescharacteristic
214C2×M16—22no—
215C2×M16—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C4×D4—22no—
219C4×D4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×C4×C4311yescharacteristic
224C2×C4⋊C4C2×C4×C4311yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4C2×C4×C4311yescharacteristic
231C2×C22⋊C4D4×C4311yescharacteristic
232C2×C42—22no—
233C2×C42D4×C4311yescharacteristic
234C4⋊C8—22no—
235#99—24no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8D4×C4314yes—
239C4×C8—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—22no—
246#95C2×C4×C4311yescharacteristic
247#95C2×C4×C4311yescharacteristic
248C24C22⋊C4×C4311yescharacteristic
249C24C2×D4×C4311yescharacteristic
250C2×Q8—22no—
251C2×Q8—81no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4C22⋊C4×C4311yescharacteristic
265C22×C4C22⋊C4×C4311yescharacteristic
266C22×C4C22⋊C4×C4311yescharacteristic
267C22×C4C22×C4×C4311yescharacteristic
268C22×C4C2×D4×C4312yes—
269C22×C4C2×D4×C4311yescharacteristic
270C22×C4#41×C4312yes—
271M16—82no—
272M16—82no—
273C2×C8—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—24no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C42—21no—
289C42—21no—
290C42—82no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×C22⋊C4×C4311yescharacteristic
301C23#121×C4312yes—
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4#104×C4312yes—
332C2×C4C4×D4×C4312yes—
333C2×C4#120×C4311yescharacteristic
334C2×C4#123×C4311yescharacteristic
335C8—44no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C43×#38611yescharacteristic
349C22C2×#104×C4311yescharacteristic
350C22C43×#42111yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—84no—
360C4—81no—
361C4—81no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2C43×#187111yescharacteristic
367C2C43×#190911yescharacteristic
368C2C43×#191311yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1508C2semidirect
5. C43×#1284C2semidirect
13. C43×#398C4semidirect
15. C43×#397C4semidirect
16. C43×#395C4semidirect
18. C43×#393C4semidirect
151. #9184C43direct (N × H)
181. #1508C2×C43semidirect
182. #1284C2×C43semidirect
197. #398C4×C43semidirect
199. #397C4×C43semidirect
200. #395C4×C43semidirect
202. #393C4×C43semidirect
209. C43#9184direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29752
C43×#26382
C4×#99×C432
C43×#15082
C43×#12842
#918443