Finite Group Databasebeta

← C43×#8560 #24928577

Subgroups — C43×#8560 #24928577

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
2C43×#1797C212yesmaximal
3C2×C43×#324C212yesmaximal
4C43×#1280C212yesmaximal
5C22×C4⋊C4×C43C411yescharacteristic
6C22×C4⋊C4×C43C2211yescharacteristic
7C22×C42×C43C411yescharacteristic
8C22×C42×C43C411yescharacteristic
9C22×C42×C43C2211yescharacteristic
10C2×C4⋊C8×C43—22no—
11C2×C22⋊C8×C43C2214yes—
12C4×C4⋊C4×C43—22no—
13C4×C4⋊C4×C43—22no—
14C2×#95×C43C411yescharacteristic
15C2×#95×C43C2211yescharacteristic
16C43×#336—22no—
17C43×#324—24no—
18C23×C4×C43C2×C411yescharacteristic
19C23×C4×C43C2×C411yescharacteristic
20C23×C4×C43C2×C411yescharacteristic
21C23×C4×C43C2×C411yescharacteristic
22C23×C4×C43C2×C411yescharacteristic
23C23×C4×C43C2×C411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C22×C8×C43—24no—
26C2×C4⋊C4×C43—22no—
27C2×C4⋊C4×C43—22no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43C814yescomplemented
31C2×C4⋊C4×C43D412yes—
32C2×C4⋊C4×C43Q812yes—
33C2×C42×C43—21no—
34C2×C42×C43—21no—
35C2×C42×C43—22no—
36C2×C42×C43—22no—
37C2×C42×C43—21no—
38C2×C42×C43—21no—
39C2×C42×C43—42no—
40C2×C42×C43—42no—
41C2×C42×C43D412yes—
42C2×C42×C43D412yes—
43C4⋊C8×C43—44no—
44C22⋊C8×C43—24no—
45C22⋊C8×C43—24no—
46#95×C43—22no—
47#95×C43—22no—
48C24×C43C22×C411yescharacteristic
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43C22⋊C412yes—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C4⋊C412yes—
77C22×C4×C43C4⋊C412yes—
78C22×C4×C43C2×C812yes—
79C22×C4×C43C2×C812yes—
80C22×C4×C43C2×C812yes—
81C22×C4×C43M1612yes—
82C22×C4×C43M1612yes—
83C22×C4×C43M1612yes—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×Q811yescharacteristic
87C22×C4×C43#4112yes—
88C2×C8×C43—44no—
89C2×C8×C43—44no—
90C2×C8×C43—44no—
91C4⋊C4×C43—28no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43—24no—
94C42×C43—24no—
95C42×C43—24no—
96C42×C43—24no—
97C42×C43—42no—
98C42×C43—42no—
99C42×C43—42no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43C2×C4⋊C411yescharacteristic
106C23×C43#11711yescharacteristic
107C23×C43C22×C811yescharacteristic
108C23×C43C2×M1611yescharacteristic
109C23×C43C2×M1611yescharacteristic
110C23×C43C2×M1611yescharacteristic
111C2×C4×C43—24no—
112C2×C4×C43—24no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43C22⋊C814yes—
148C2×C4×C43#9912yes—
149C2×C4×C43#10112yes—
150C2×C4×C43C4⋊C814yescomplemented
151C2×C4×C43#12112yes—
152C2×C4×C43C22⋊Q812yes—
153C8×C43—84no—
154#8560C4311yesmaximal, characteristic, direct product factor, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#38011yescharacteristic
168C22×C43C2×C22⋊C811yescharacteristic
169C22×C43#40711yescharacteristic
170C22×C43C2×#9911yescharacteristic
171C22×C43#41011yescharacteristic
172C22×C43C2×#10111yescharacteristic
173C22×C43#41311yescharacteristic
174C22×C43C2×C4⋊C811yescharacteristic
175C22×C43#42311yescharacteristic
176C22×C43#43111yescharacteristic
177C22×C43#43211yescharacteristic
178C4×C43—24no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—24no—
182C4×C43—22no—
183C4×C43—22no—
184C4×C43—42no—
185C4×C43—42no—
186C4×C43—42no—
187C2×C4×C4⋊C4C2×C4311yescharacteristic
188#1797C2×C4312yes—
189C2×#324C2×C4312yes—
190#1280C2×C4312yes—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#145911yescharacteristic
196C2×C43#146111yescharacteristic
197C2×C43#146311yescharacteristic
198C2×C43#146411yescharacteristic
199C2×C43#179711yescharacteristic
200C2×C43#179911yescharacteristic
201C2×C43#180111yescharacteristic
202C22×C4⋊C4C4×C4311yescharacteristic
203C22×C4⋊C4C22×C4311yescharacteristic
204C22×C42C4×C4311yescharacteristic
205C22×C42C4×C4311yescharacteristic
206C22×C42C22×C4311yescharacteristic
207C2×C4⋊C8—22no—
208C2×C22⋊C8C22×C4314yes—
209C4×C4⋊C4—22no—
210C4×C4⋊C4—22no—
211C2×#95C4×C4311yescharacteristic
212C2×#95C22×C4311yescharacteristic
213#336—22no—
214#324—24no—
215C43#856011yescharacteristic, direct product factor, Sylow
216C23×C4C2×C4×C4311yescharacteristic
217C23×C4C2×C4×C4311yescharacteristic
218C23×C4C2×C4×C4311yescharacteristic
219C23×C4C2×C4×C4311yescharacteristic
220C23×C4C2×C4×C4311yescharacteristic
221C23×C4C2×C4×C4311yescharacteristic
222C23×C4C23×C4311yescharacteristic
223C22×C8—24no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4C8×C4314yescomplemented
229C2×C4⋊C4D4×C4312yes—
230C2×C4⋊C4Q8×C4312yes—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—22no—
234C2×C42—22no—
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—42no—
238C2×C42—42no—
239C2×C42D4×C4312yes—
240C2×C42D4×C4312yes—
241C4⋊C8—44no—
242C22⋊C8—24no—
243C22⋊C8—24no—
244#95—22no—
245#95—22no—
246C24C22×C4×C4311yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C22⋊C4×C4312yes—
272C22×C4C22⋊C4×C4311yescharacteristic
273C22×C4C22⋊C4×C4311yescharacteristic
274C22×C4C4⋊C4×C4312yes—
275C22×C4C4⋊C4×C4312yes—
276C22×C4C2×C8×C4312yes—
277C22×C4C2×C8×C4312yes—
278C22×C4C2×C8×C4312yes—
279C22×C4M16×C4312yes—
280C22×C4M16×C4312yes—
281C22×C4M16×C4312yes—
282C22×C4C2×D4×C4312yes—
283C22×C4C2×D4×C4311yescharacteristic
284C22×C4C2×Q8×C4311yescharacteristic
285C22×C4#41×C4312yes—
286C2×C8—44no—
287C2×C8—44no—
288C2×C8—44no—
289C4⋊C4—28no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C42—24no—
293C42—24no—
294C42—24no—
295C42—42no—
296C42—42no—
297C42—42no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊C4×C4311yescharacteristic
303C23C2×C4⋊C4×C4311yescharacteristic
304C23#117×C4311yescharacteristic
305C23C22×C8×C4311yescharacteristic
306C23C2×M16×C4311yescharacteristic
307C23C2×M16×C4311yescharacteristic
308C23C2×M16×C4311yescharacteristic
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4C22⋊C8×C4314yes—
346C2×C4#99×C4312yes—
347C2×C4#101×C4312yes—
348C2×C4C4⋊C8×C4314yescomplemented
349C2×C4#121×C4312yes—
350C2×C4C22⋊Q8×C4312yes—
351C8—84no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22C43×#38011yescharacteristic
365C22C2×C22⋊C8×C4311yescharacteristic
366C22C43×#40711yescharacteristic
367C22C2×#99×C4311yescharacteristic
368C22C43×#41011yescharacteristic
369C22C2×#101×C4311yescharacteristic
370C22C43×#41311yescharacteristic
371C22C2×C4⋊C8×C4311yescharacteristic
372C22C43×#42311yescharacteristic
373C22C43×#43111yescharacteristic
374C22C43×#43211yescharacteristic
375C4—24no—
376C4—22no—
377C4—22no—
378C4—24no—
379C4—22no—
380C4—22no—
381C4—42no—
382C4—42no—
383C4—42no—
384C2—21no—
385C2—21no—
386C2—21no—
387C2—21no—
388C2C43×#145911yescharacteristic
389C2C43×#146111yescharacteristic
390C2C43×#146311yescharacteristic
391C2C43×#146411yescharacteristic
392C2C43×#179711yescharacteristic
393C2C43×#179911yescharacteristic
394C2C43×#180111yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC23C22×C8×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
30. C2×C4⋊C4×C43C8semidirect
150. C2×C4×C43C4⋊C8semidirect
154. #8560C43direct (N × H)
215. C43#8560direct (N × H)
228. C2×C4⋊C4C8×C43semidirect
348. C2×C4C4⋊C8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊C4×C432
C43×#17972
C2×C43×#3242
C43×#12802
#856043