Finite Group Databasebeta

← C43×#9263 #24929280

Subgroups — C43×#9263 #24929280

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3190C211yesmaximal, characteristic
2C43×#2977C211yesmaximal, characteristic
3C43×#1504C211yesmaximal, characteristic
4C2×C43×#328C211yesmaximal, characteristic, complemented
5C43×#1472C211yesmaximal, characteristic, complemented
6C43×#1298C211yesmaximal, characteristic, complemented
7C43×#1280C211yesmaximal, characteristic, complemented
8C43×#525C2211yescharacteristic
9C2×C22⋊Q8×C43C2211yescharacteristic
10C43×#485—21no—
11C43×#483C411yescharacteristic, complemented
12C43×#480C411yescharacteristic, complemented
13C43×#467—21no—
14C43×#465—21no—
15C43×#452—21no—
16C43×#451C411yescharacteristic, complemented
17C43×#448C411yescharacteristic, complemented
18C43×#435—21no—
19C43×#435—21no—
20C8×D4×C43—21no—
21C8×D4×C43—21no—
22C43×#433—21no—
23C43×#408—21no—
24C43×#407C2211yescharacteristic
25C2×C22⋊C8×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C43×#328—21no—
30C43×#328—21no—
31C43×#328—21no—
32C43×#327—21no—
33C43×#324—21no—
34C43×#324—21no—
35C2×#41×C43D411yescharacteristic
36C22×Q8×C43C2×C411yescharacteristic
37C23×C4×C43—21no—
38C23×C4×C43C2311yescharacteristic
39C2×Q16×C43—21no—
40C2×SD16×C43—21no—
41C2×M16×C43—21no—
42C2×M16×C43—21no—
43C22×C8×C43—21no—
44C22×C8×C43—21no—
45C22×C8×C43—21no—
46C22×C8×C43—21no—
47#123×C43—21no—
48C22⋊Q8×C43—21no—
49C22⋊Q8×C43—21no—
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43C2×C411yescharacteristic
53C22⋊Q8×C43D411yescharacteristic
54#121×C43C2×C411yescharacteristic
55#121×C43D411yescharacteristic
56#120×C43—21no—
57C4×D4×C43—21no—
58C4×D4×C43—21no—
59#117×C43D411yescharacteristic
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43—21no—
63#107×C43—21no—
64#106×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67#103×C43—21no—
68#103×C43—21no—
69#103×C43—21no—
70#102×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43C2×C411yescharacteristic
79C22⋊C8×C43C2×C411yescharacteristic
80C22⋊C8×C43D411yescharacteristic
81C22⋊C8×C43D411yescharacteristic
82C22⋊C8×C43D411yescharacteristic
83C22⋊C8×C43D411yescharacteristic
84#97×C43—21no—
85C4×C8×C43—21no—
86#95×C43—21no—
87#95×C43—21no—
88C24×C43#4111yescharacteristic
89#41×C43—81no—
90C2×Q8×C43—21no—
91C2×Q8×C43—21no—
92C2×Q8×C43—81no—
93C2×Q8×C43C22⋊C411yescharacteristic
94C2×D4×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43—21no—
97C2×D4×C43C22⋊C411yescharacteristic
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—81no—
105C22×C4×C43—81no—
106C22×C4×C43—81no—
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113Q16×C43—81no—
114SD16×C43—81no—
115M16×C43—81no—
116M16×C43—81no—
117C2×C8×C43—21no—
118C2×C8×C43—21no—
119C2×C8×C43—21no—
120C2×C8×C43—21no—
121C2×C8×C43—21no—
122C2×C8×C43—21no—
123C2×C8×C43—41no—
124C2×C8×C43—81no—
125C2×C8×C43—81no—
126C2×C8×C43—81no—
127C2×C8×C43—81no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43C22⋊C411yescharacteristic
135C4⋊C4×C43C22⋊C411yescharacteristic
136C22⋊C4×C43—21no—
137C22⋊C4×C43—21no—
138C22⋊C4×C43—21no—
139C22⋊C4×C43—21no—
140C22⋊C4×C43—21no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43C4×D411yescharacteristic
151C23×C43#12111yescharacteristic
152C23×C43#12311yescharacteristic
153Q8×C43—41no—
154Q8×C43—41no—
155Q8×C43—41no—
156Q8×C43—81no—
157D4×C43—41no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43—41no—
161D4×C43—41no—
162D4×C43—81no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—81no—
180C2×C4×C43—82no—
181C2×C4×C43—81no—
182C2×C4×C43—81no—
183C2×C4×C43—82no—
184C2×C4×C43C2×C22⋊C411yescharacteristic
185C2×C4×C43C4×D411yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C8×C43—41no—
189C8×C43—41no—
190C8×C43—41no—
191C8×C43—41no—
192C8×C43—41no—
193C8×C43—41no—
194C8×C43—81no—
195#9263C4311yesmaximal, characteristic, direct product factor, Sylow
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43#38611yescharacteristic
211C22×C43#44311yescharacteristic
212C22×C43#44411yescharacteristic
213C22×C43#47111yescharacteristic
214C22×C43#47311yescharacteristic
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—41no—
220C4×C43—41no—
221C4×C43—41no—
222C4×C43—82no—
223C4×C43—81no—
224C4×C43—81no—
225#3190C2×C4311yescharacteristic
226#2977C2×C4311yescharacteristic
227#1504C2×C4311yescharacteristic
228C2×#328C2×C4311yescharacteristic, complemented
229#1472C2×C4311yescharacteristic, complemented
230#1298C2×C4311yescharacteristic, complemented
231#1280C2×C4311yescharacteristic, complemented
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43—41no—
237C2×C43—81no—
238C2×C43#187611yescharacteristic
239C2×C43#190811yescharacteristic
240C2×C43#191311yescharacteristic
241#525C22×C4311yescharacteristic
242C2×C22⋊Q8C22×C4311yescharacteristic
243#485—21no—
244#483C4×C4311yescharacteristic, complemented
245#480C4×C4311yescharacteristic, complemented
246#467—21no—
247#465—21no—
248#452—21no—
249#451C4×C4311yescharacteristic, complemented
250#448C4×C4311yescharacteristic, complemented
251#435—21no—
252#435—21no—
253C8×D4—21no—
254C8×D4—21no—
255#433—21no—
256#408—21no—
257#407C22×C4311yescharacteristic
258C2×C22⋊C8C22×C4311yescharacteristic
259C2×C22⋊C8C22×C4311yescharacteristic
260C2×C22⋊C8C22×C4311yescharacteristic
261C2×#95C22×C4311yescharacteristic
262#328—21no—
263#328—21no—
264#328—21no—
265#327—21no—
266#324—21no—
267#324—21no—
268C43#926311yescharacteristic, direct product factor, Sylow
269C2×#41D4×C4311yescharacteristic
270C22×Q8C2×C4×C4311yescharacteristic
271C23×C4—21no—
272C23×C4C23×C4311yescharacteristic
273C2×Q16—21no—
274C2×SD16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281#123—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8C2×C4×C4311yescharacteristic
287C22⋊Q8D4×C4311yescharacteristic
288#121C2×C4×C4311yescharacteristic
289#121D4×C4311yescharacteristic
290#120—21no—
291C4×D4—21no—
292C4×D4—21no—
293#117D4×C4311yescharacteristic
294C2×C4⋊C4—21no—
295C2×C4⋊C4C2×C4×C4311yescharacteristic
296C2×C22⋊C4—21no—
297#107—21no—
298#106—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301#103—21no—
302#103—21no—
303#103—21no—
304#102—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8C2×C4×C4311yescharacteristic
313C22⋊C8C2×C4×C4311yescharacteristic
314C22⋊C8D4×C4311yescharacteristic
315C22⋊C8D4×C4311yescharacteristic
316C22⋊C8D4×C4311yescharacteristic
317C22⋊C8D4×C4311yescharacteristic
318#97—21no—
319C4×C8—21no—
320#95—21no—
321#95—21no—
322C24#41×C4311yescharacteristic
323#41—81no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8C22⋊C4×C4311yescharacteristic
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4C22⋊C4×C4311yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4—81no—
341C22×C4C22×C4×C4311yescharacteristic
342C22×C4C2×D4×C4311yescharacteristic
343C22×C4C2×D4×C4311yescharacteristic
344C22×C4C2×D4×C4311yescharacteristic
345C22×C4C2×D4×C4311yescharacteristic
346C22×C4#41×C4311yescharacteristic
347Q16—81no—
348SD16—81no—
349M16—81no—
350M16—81no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—41no—
358C2×C8—81no—
359C2×C8—81no—
360C2×C8—81no—
361C2×C8—81no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4C22⋊C4×C4311yescharacteristic
369C4⋊C4C22⋊C4×C4311yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C42—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23C4×D4×C4311yescharacteristic
385C23#121×C4311yescharacteristic
386C23#123×C4311yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—81no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4C2×C22⋊C4×C4311yescharacteristic
419C2×C4C4×D4×C4311yescharacteristic
420C2×C4#120×C4311yescharacteristic
421C2×C4#121×C4311yescharacteristic
422C8—41no—
423C8—41no—
424C8—41no—
425C8—41no—
426C8—41no—
427C8—41no—
428C8—81no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22C43×#38611yescharacteristic
444C22C43×#44311yescharacteristic
445C22C43×#44411yescharacteristic
446C22C43×#47111yescharacteristic
447C22C43×#47311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—82no—
456C4—81no—
457C4—81no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—81no—
464C2C43×#187611yescharacteristic
465C2C43×#190811yescharacteristic
466C2C43×#191311yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC43×#525C22
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. C2×C43×#328C2semidirect
5. C43×#1472C2semidirect
6. C43×#1298C2semidirect
7. C43×#1280C2semidirect
11. C43×#483C4semidirect
12. C43×#480C4semidirect
16. C43×#451C4semidirect
17. C43×#448C4semidirect
195. #9263C43direct (N × H)
228. C2×#328C2×C43semidirect
229. #1472C2×C43semidirect
230. #1298C2×C43semidirect
231. #1280C2×C43semidirect
244. #483C4×C43semidirect
245. #480C4×C43semidirect
249. #451C4×C43semidirect
250. #448C4×C43semidirect
268. C43#9263direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31902
C43×#29772
C43×#15042
C2×C43×#3282
C43×#14722
C43×#12982
C43×#12802
#926343