Finite Group Databasebeta

← C43×#9237 #24929254

Subgroups — C43×#9237 #24929254

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3100C211yesmaximal, characteristic
2C43×#2293C211yesmaximal, characteristic, complemented
3C43×#1962C211yesmaximal, characteristic, complemented
4C43×#1502C211yesmaximal, characteristic, complemented
5C43×#1486C211yesmaximal, characteristic, complemented
6C43×#1303C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C2×C4×D4×C43C2211yescharacteristic
10C2×#117×C43—21no—
11C43×#480—21no—
12C43×#474C412yescomplemented
13C43×#459C412yescomplemented
14C43×#447—21no—
15C4×D8×C43—22no—
16C43×#431C2211yescharacteristic
17C43×#431C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C2×#104×C43—21no—
20C2×#104×C43—21no—
21C43×#390—21no—
22C43×#389—21no—
23C43×#388—22no—
24C4×C4⋊C4×C43C2211yescharacteristic
25C4×C22⋊C4×C43—21no—
26C43×C43C2211yescharacteristic
27C43×#327—22no—
28C43×D4⋊C8—22no—
29C2×#41×C43—21no—
30C22×D4×C43D411yescharacteristic
31C23×C4×C43—21no—
32C2×D8×C43—22no—
33C2×M16×C43—21no—
34C4⋊Q8×C43C2×C411yescharacteristic
35#127×C43C2×C411yescharacteristic
36#124×C43—21no—
37#121×C43—21no—
38#121×C43—21no—
39C4×D4×C43—21no—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C4×D4×C43—21no—
43C4×D4×C43C2×C412yes—
44C4×D4×C43D412yes—
45#117×C43—42no—
46#117×C43—42no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—22no—
53C2×C42×C43—21no—
54C2×C42×C43—21no—
55C2×C42×C43—21no—
56C2×C42×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#107×C43—22no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43C2×C412yes—
64#104×C43—42no—
65#104×C43—42no—
66#102×C43—22no—
67#102×C43—22no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72#95×C43—22no—
73#95×C43D412yes—
74C24×C43—21no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—42no—
85C2×D4×C43—41no—
86C2×D4×C43C22⋊C412yes—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—22no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101D8×C43—44no—
102M16×C43—41no—
103M16×C43—41no—
104C2×C8×C43—22no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—44no—
112C4⋊C4×C43C22⋊C412yes—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—44no—
116C22⋊C4×C43—44no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C42×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—42no—
123C42×C43—42no—
124C42×C43—41no—
125C42×C43—41no—
126C42×C43D812yescomplemented
127C42×C43C22×C411yescharacteristic
128C42×C43C2×D411yescharacteristic
129C42×C43#4111yescharacteristic
130C42×C43#4111yescharacteristic
131C23×C43—22no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43#12011yescharacteristic
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—22no—
141D4×C43—22no—
142D4×C43—42no—
143D4×C43—42no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—81no—
147D4×C43—81no—
148D4×C43—81no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43C4×D411yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12311yescharacteristic
176C2×C4×C43C2×D811yescharacteristic
177C2×C4×C43#13511yescharacteristic
178C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
180C8×C43—42no—
181C8×C43—81no—
182C8×C43—81no—
183#9237C4311yesmaximal, characteristic, direct product factor, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—82no—
190C22×C43—82no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43#38611yescharacteristic
195C22×C43#44711yescharacteristic
196C22×C43#44911yescharacteristic
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—42no—
202C4×C43—42no—
203C4×C43—82no—
204C4×C43—81no—
205C4×C43#42112yes—
206C4×C43C4×D811yescharacteristic
207C4×C43#44211yescharacteristic
208C4×C43#45911yescharacteristic
209C4×C43#46311yescharacteristic
210#3100C2×C4311yescharacteristic
211#2293C2×C4311yescharacteristic, complemented
212#1962C2×C4311yescharacteristic, complemented
213#1502C2×C4311yescharacteristic, complemented
214#1486C2×C4311yescharacteristic, complemented
215#1303C2×C4311yescharacteristic, complemented
216#1276C2×C4311yescharacteristic, complemented
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—82no—
220C2×C43—161no—
221C2×C43#187911yescharacteristic
222C2×C43#189711yescharacteristic
223C2×C43#190611yescharacteristic
224#532C22×C4311yescharacteristic
225C2×C4×D4C22×C4311yescharacteristic
226C2×#117—21no—
227#480—21no—
228#474C4×C4312yescomplemented
229#459C4×C4312yescomplemented
230#447—21no—
231C4×D8—22no—
232#431C22×C4311yescharacteristic
233#431C22×C4311yescharacteristic
234#423C22×C4311yescharacteristic
235C2×#104—21no—
236C2×#104—21no—
237#390—21no—
238#389—21no—
239#388—22no—
240C4×C4⋊C4C22×C4311yescharacteristic
241C4×C22⋊C4—21no—
242C43C22×C4311yescharacteristic
243#327—22no—
244D4⋊C8—22no—
245C43#923711yescharacteristic, direct product factor, Sylow
246C2×#41—21no—
247C22×D4D4×C4311yescharacteristic
248C23×C4—21no—
249C2×D8—22no—
250C2×M16—21no—
251C4⋊Q8C2×C4×C4311yescharacteristic
252#127C2×C4×C4311yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C2×C4×C4312yes—
261C4×D4D4×C4312yes—
262#117—42no—
263#117—42no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C4311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42D4×C4311yescharacteristic
274C2×C42D4×C4311yescharacteristic
275C2×C42C23×C4311yescharacteristic
276#107—22no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8C2×C4×C4312yes—
281#104—42no—
282#104—42no—
283#102—22no—
284#102—22no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C4×C8—21no—
288C4×C8—21no—
289#95—22no—
290#95D4×C4312yes—
291C24—21no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4C22⋊C4×C4312yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
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
318D8—44no—
319M16—41no—
320M16—41no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—44no—
328C4⋊C4—42no—
329C4⋊C4C22⋊C4×C4312yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—42no—
340C42—42no—
341C42—41no—
342C42—41no—
343C42D8×C4312yescomplemented
344C42C22×C4×C4311yescharacteristic
345C42C2×D4×C4311yescharacteristic
346C42#41×C4311yescharacteristic
347C42#41×C4311yescharacteristic
348C23—22no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23#120×C4311yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—22no—
358D4—22no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4C2×C22⋊C4×C4311yescharacteristic
388C2×C4C4×D4×C4311yescharacteristic
389C2×C4C4×D4×C4311yescharacteristic
390C2×C4#121×C4311yescharacteristic
391C2×C4#121×C4311yescharacteristic
392C2×C4#123×C4311yescharacteristic
393C2×C4C2×D8×C4311yescharacteristic
394C2×C4#135×C4311yescharacteristic
395C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
396C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
397C8—42no—
398C8—81no—
399C8—81no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—82no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22C43×#38611yescharacteristic
411C22C43×#44711yescharacteristic
412C22C43×#44911yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—42no—
419C4—82no—
420C4—81no—
421C4C43×#42112yes—
422C4C4×D8×C4311yescharacteristic
423C4C43×#44211yescharacteristic
424C4C43×#45911yescharacteristic
425C4C43×#46311yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2C43×#187911yescharacteristic
431C2C43×#189711yescharacteristic
432C2C43×#190611yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radicalC43×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2293C2semidirect
3. C43×#1962C2semidirect
4. C43×#1502C2semidirect
5. C43×#1486C2semidirect
6. C43×#1303C2semidirect
7. C43×#1276C2semidirect
12. C43×#474C4semidirect
13. C43×#459C4semidirect
126. C42×C43D8semidirect
183. #9237C43direct (N × H)
211. #2293C2×C43semidirect
212. #1962C2×C43semidirect
213. #1502C2×C43semidirect
214. #1486C2×C43semidirect
215. #1303C2×C43semidirect
216. #1276C2×C43semidirect
228. #474C4×C43semidirect
229. #459C4×C43semidirect
245. C43#9237direct (N × H)
343. C42D8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31002
C43×#22932
C43×#19622
C43×#15022
C43×#14862
C43×#13032
C43×#12762
#923743