Finite Group Databasebeta

← C43×#10435 #24930452

Subgroups — C43×#10435 #24930452

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2538C211yesmaximal, characteristic
2C43×#1844C211yesmaximal, characteristic, complemented
3C43×#1803C211yesmaximal, characteristic, complemented
4C43×#1802C211yesmaximal, characteristic
5C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C43×D4⋊C8C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C43—21no—
9C2×C4×Q8×C43C2211yescharacteristic
10C2×C4×D4×C43C2211yescharacteristic
11C2×#106×C43—22no—
12C2×C4⋊C8×C43C2211yescharacteristic
13C2×C4⋊C8×C43C2211yescharacteristic
14C2×#103×C43—21no—
15C2×#102×C43—21no—
16C2×C4×C8×C43C2211yescharacteristic
17C43×#396—22no—
18C43×#390—21no—
19C43×#389—21no—
20C43×#384C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C43×#380—21no—
23C43×#340—21no—
24C43×#340—21no—
25C43×Q8⋊C8—22no—
26C43×D4⋊C8—22no—
27C22×Q8×C43D411yescharacteristic
28C22×D4×C43D411yescharacteristic
29C23×C4×C43—21no—
30C22×C8×C43—21no—
31C22×C8×C43—21no—
32C22×C8×C43—21no—
33C22⋊Q8×C43—42no—
34C22⋊Q8×C43—42no—
35C4×Q8×C43—21no—
36C4×Q8×C43—21no—
37C4×Q8×C43—21no—
38C4×Q8×C43—21no—
39C4×D4×C43—21no—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C4×D4×C43—21no—
43C2×C4⋊C4×C43—22no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D412yes—
53C2×C22⋊C4×C43—22no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—22no—
56C2×C42×C43—21no—
57C2×C42×C43C2311yescharacteristic
58#106×C43—44no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63#103×C43—42no—
64#102×C43—42no—
65C4×C8×C43—21no—
66C4×C8×C43D412yes—
67#95×C43—22no—
68C24×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43SD1612yes—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43SD1612yes—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—44no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C22⋊C4×C43—44no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43—82no—
125C42×C43—41no—
126C42×C43—41no—
127C42×C43C2×D411yescharacteristic
128C42×C43#4111yescharacteristic
129C42×C43#4111yescharacteristic
130C42×C43#4111yescharacteristic
131C23×C43—22no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43#12011yescharacteristic
139Q8×C43—22no—
140Q8×C43—22no—
141Q8×C43—41no—
142Q8×C43—41no—
143D4×C43—22no—
144D4×C43—22no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12311yescharacteristic
172C2×C4×C43#12311yescharacteristic
173C2×C4×C43#12411yescharacteristic
174C2×C4×C43C2×SD1611yescharacteristic
175C2×C4×C43C2×SD1611yescharacteristic
176C2×C4×C43#13511yescharacteristic
177C2×C4×C43#13511yescharacteristic
178C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C43#13711yescharacteristic
181C2×C4×C43#13711yescharacteristic
182C8×C43—24no—
183C8×C43—81no—
184C8×C43—81no—
185#10435C4311yesmaximal, characteristic, direct product factor, Sylow
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43#39411yescharacteristic
194C22×C43#44811yescharacteristic
195C22×C43#44911yescharacteristic
196C22×C43#45011yescharacteristic
197C22×C43#45211yescharacteristic
198C22×C43#45311yescharacteristic
199C22×C43#45611yescharacteristic
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—42no—
203C4×C43—82no—
204C4×C43—81no—
205C4×C43—81no—
206C4×C43—161no—
207C4×C43#46511yescharacteristic
208C4×C43#46511yescharacteristic
209C4×C43#46911yescharacteristic
210C4×C43#47011yescharacteristic
211C4×C43#48111yescharacteristic
212C4×C43#48211yescharacteristic
213C4×C43#48311yescharacteristic
214C4×C43#48511yescharacteristic
215#2538C2×C4311yescharacteristic
216#1844C2×C4311yescharacteristic, complemented
217#1803C2×C4311yescharacteristic, complemented
218#1802C2×C4311yescharacteristic
219C2×Q8⋊C8C2×C4311yescharacteristic, complemented
220C2×D4⋊C8C2×C4311yescharacteristic
221#1296C2×C4311yescharacteristic, complemented
222C2×C43—82no—
223C2×C43#162211yescharacteristic
224C2×C43#163111yescharacteristic
225C2×C43#165111yescharacteristic
226C2×C43#165211yescharacteristic
227C2×C43#203411yescharacteristic
228C2×C43#203511yescharacteristic
229C2×C43#203911yescharacteristic
230C2×C22⋊Q8—21no—
231C2×C4×Q8C22×C4311yescharacteristic
232C2×C4×D4C22×C4311yescharacteristic
233C2×#106—22no—
234C2×C4⋊C8C22×C4311yescharacteristic
235C2×C4⋊C8C22×C4311yescharacteristic
236C2×#103—21no—
237C2×#102—21no—
238C2×C4×C8C22×C4311yescharacteristic
239#396—22no—
240#390—21no—
241#389—21no—
242#384C22×C4311yescharacteristic
243#384C22×C4311yescharacteristic
244#380—21no—
245#340—21no—
246#340—21no—
247Q8⋊C8—22no—
248D4⋊C8—22no—
249C43#1043511yescharacteristic, direct product factor, Sylow
250C22×Q8D4×C4311yescharacteristic
251C22×D4D4×C4311yescharacteristic
252C23×C4—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22⋊Q8—42no—
257C22⋊Q8—42no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C4311yescharacteristic
274C2×C4⋊C4D4×C4311yescharacteristic
275C2×C4⋊C4D4×C4312yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42—21no—
280C2×C42C23×C4311yescharacteristic
281#106—44no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286#103—42no—
287#102—42no—
288C4×C8—21no—
289C4×C8D4×C4312yes—
290#95—22no—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8SD16×C4312yes—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4SD16×C4312yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C2×D4×C4311yescharacteristic
316C22×C4C2×D4×C4311yescharacteristic
317C22×C4C2×D4×C4311yescharacteristic
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—82no—
348C42—41no—
349C42—41no—
350C42C2×D4×C4311yescharacteristic
351C42#41×C4311yescharacteristic
352C42#41×C4311yescharacteristic
353C42#41×C4311yescharacteristic
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#120×C4311yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4#121×C4311yescharacteristic
392C2×C4#121×C4311yescharacteristic
393C2×C4#121×C4311yescharacteristic
394C2×C4#123×C4311yescharacteristic
395C2×C4#123×C4311yescharacteristic
396C2×C4#124×C4311yescharacteristic
397C2×C4C2×SD16×C4311yescharacteristic
398C2×C4C2×SD16×C4311yescharacteristic
399C2×C4#135×C4311yescharacteristic
400C2×C4#135×C4311yescharacteristic
401C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
402C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
403C2×C4#137×C4311yescharacteristic
404C2×C4#137×C4311yescharacteristic
405C8—24no—
406C8—81no—
407C8—81no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C43×#39411yescharacteristic
416C22C43×#44811yescharacteristic
417C22C43×#44911yescharacteristic
418C22C43×#45011yescharacteristic
419C22C43×#45211yescharacteristic
420C22C43×#45311yescharacteristic
421C22C43×#45611yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—161no—
429C4C43×#46511yescharacteristic
430C4C43×#46511yescharacteristic
431C4C43×#46911yescharacteristic
432C4C43×#47011yescharacteristic
433C4C43×#48111yescharacteristic
434C4C43×#48211yescharacteristic
435C4C43×#48311yescharacteristic
436C4C43×#48511yescharacteristic
437C2—82no—
438C2C43×#162211yescharacteristic
439C2C43×#163111yescharacteristic
440C2C43×#165111yescharacteristic
441C2C43×#165211yescharacteristic
442C2C43×#203411yescharacteristic
443C2C43×#203511yescharacteristic
444C2C43×#203911yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1844C2semidirect
3. C43×#1803C2semidirect
5. C2×C43×Q8⋊C8C2semidirect
7. C43×#1296C2semidirect
185. #10435C43direct (N × H)
216. #1844C2×C43semidirect
217. #1803C2×C43semidirect
219. C2×Q8⋊C8C2×C43semidirect
221. #1296C2×C43semidirect
249. C43#10435direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25382
C43×#18442
C43×#18032
C43×#18022
C2×C43×Q8⋊C82
C2×C43×D4⋊C82
C43×#12962
#1043543