Finite Group Databasebeta

← C43×#25489 #24945506

Subgroups — C43×#25489 #24945506

Order 11008.

664 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×#3165C211yesmaximal, characteristic, complemented
2C43×#3077C211yesmaximal, characteristic
3C2×C43×#474C211yesmaximal, characteristic
4C43×#2962C211yesmaximal, characteristic, complemented
5C43×#2089C212yesmaximal, complemented
6C43×#2063C212yesmaximal
7C43×#1997C211yesmaximal, characteristic, complemented
8C43×#1952C212yesmaximal, complemented
9C43×#1950C211yesmaximal, characteristic, complemented
10C43×#1931C212yesmaximal
11C4×#100×C43C211yesmaximal, characteristic
12C43×#533C2211yescharacteristic
13C2×C4⋊Q8×C43C2211yescharacteristic
14C2×C4×D4×C43C2211yescharacteristic
15C43×#501—22no—
16C43×#500—21no—
17C43×#498—21no—
18C43×#478—22no—
19C43×#476—21no—
20C43×#474—21no—
21C43×#474—21no—
22C43×#474—22no—
23C43×#474—21no—
24C43×#446—22no—
25C43×#446—21no—
26C8×Q8×C43—21no—
27C2×#108×C43C2212yes—
28C43×#428C2212yes—
29C43×#428C2212yes—
30C43×#428C2212yes—
31C2×#107×C43C2212yes—
32C43×#424C2212yes—
33C43×#423C2211yescharacteristic
34C2×C4⋊C8×C43C2211yescharacteristic
35C43×#418C2212yes—
36C2×#102×C43C2212yes—
37C2×#100×C43C2211yescharacteristic
38C2×#100×C43C2211yescharacteristic
39C43×#405C2212yes—
40C4×M16×C43C2211yescharacteristic
41C4×M16×C43C2211yescharacteristic
42C43×#343C2212yes—
43C43×#343C2211yescharacteristic
44C43×#343C2212yes—
45C43×#343C2211yescharacteristic
46C43×#341C2212yes—
47C22×Q8×C43—21no—
48C22×D4×C43C2311yescharacteristic
49C23×C4×C43—21no—
50C2×M16×C43C2312yes—
51C2×M16×C43C2311yescharacteristic
52C2×M16×C43C2311yescharacteristic
53C2×M16×C43C2311yescharacteristic
54C2×M16×C43C2311yescharacteristic
55C22×C8×C43C2312yes—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43D412yes—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71#117×C43C2312yes—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2311yescharacteristic
74C2×C4⋊C4×C43C2312yes—
75C2×C22⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77#108×C43—24no—
78#107×C43—22no—
79#107×C43—22no—
80#107×C43—22no—
81#107×C43—22no—
82#107×C43—22no—
83#106×C43—22no—
84#106×C43—22no—
85#106×C43—22no—
86C4⋊C8×C43—22no—
87C4⋊C8×C43—22no—
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43D411yescharacteristic
91C4⋊C8×C43D411yescharacteristic
92C4⋊C8×C43D412yes—
93#102×C43—22no—
94#102×C43—22no—
95#102×C43—22no—
96#102×C43—22no—
97#100×C43—22no—
98#100×C43Q814yescomplemented
99#97×C43—22no—
100#97×C43—21no—
101#97×C43—21no—
102C4×C8×C43—22no—
103C4×C8×C43—21no—
104C4×C8×C43—21no—
105C24×C43—21no—
106C2×Q8×C43—21no—
107C2×Q8×C43—21no—
108C2×Q8×C43—41no—
109C2×Q8×C43—41no—
110C2×Q8×C43—82no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43C2×Q812yes—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—82no—
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×C4×C43C2411yescharacteristic
125M16×C43—21no—
126M16×C43—21no—
127M16×C43—21no—
128M16×C43—21no—
129M16×C43—22no—
130M16×C43—21no—
131M16×C43—22no—
132M16×C43C2×Q812yes—
133M16×C43C2×Q812yes—
134M16×C43#4112yes—
135C2×C8×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43—22no—
139C2×C8×C43—22no—
140C2×C8×C43—21no—
141C2×C8×C43—22no—
142C2×C8×C43C2×D412yes—
143C2×C8×C43C2×D412yes—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43C2×D412yes—
155C4⋊C4×C43C2×D412yes—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C42×C43—22no—
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43C2×D411yescharacteristic
164C23×C43—22no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43—81no—
168C23×C43—81no—
169C23×C43C2×#4111yescharacteristic
170Q8×C43—42no—
171Q8×C43—81no—
172Q8×C43—82no—
173Q8×C43—82no—
174D4×C43—22no—
175D4×C43—22no—
176D4×C43—41no—
177D4×C43—41no—
178C2×C4×C43—22no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—42no—
184C2×C4×C43—82no—
185C2×C4×C43—82no—
186C2×C4×C43—81no—
187C2×C4×C43—82no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C22×Q811yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C2×C4×C432−1+411yescharacteristic
197C2×C4×C432−1+411yescharacteristic
198C8×C43—22no—
199C8×C43—22no—
200C8×C43—22no—
201C8×C43—22no—
202C8×C43—22no—
203C8×C43—41no—
204C8×C43—42no—
205#25489C4311yesmaximal, characteristic, direct product factor, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—42no—
209C22×C43—82no—
210C22×C43—82no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43C2×#12111yescharacteristic
214C22×C43#53311yescharacteristic
215C22×C43#54111yescharacteristic
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—42no—
220C4×C43—42no—
221C4×C43—81no—
222C4×C43—82no—
223C4×C43#47212yes—
224C4×C43#54711yescharacteristic
225C4×C43#54811yescharacteristic
226C4×C43D4×Q811yescharacteristic
227C4×C43D4×Q811yescharacteristic
228#3165C2×C4311yescharacteristic, complemented
229#3077C2×C4311yescharacteristic
230C2×#474C2×C4311yescharacteristic
231#2962C2×C4311yescharacteristic, complemented
232#2089C2×C4312yescomplemented
233#2063C2×C4312yes—
234#1997C2×C4311yescharacteristic, complemented
235#1952C2×C4312yescomplemented
236#1950C2×C4311yescharacteristic, complemented
237#1931C2×C4312yes—
238C4×#100C2×C4311yescharacteristic
239C2×C43—21no—
240C2×C43—21no—
241C2×C43—82no—
242C2×C43#242911yescharacteristic
243C2×C43C2×#47211yescharacteristic
244C2×C43#306911yescharacteristic
245#533C22×C4311yescharacteristic
246C2×C4⋊Q8C22×C4311yescharacteristic
247C2×C4×D4C22×C4311yescharacteristic
248#501—22no—
249#500—21no—
250#498—21no—
251#478—22no—
252#476—21no—
253#474—21no—
254#474—21no—
255#474—22no—
256#474—21no—
257#446—22no—
258#446—21no—
259C8×Q8—21no—
260C2×#108C22×C4312yes—
261#428C22×C4312yes—
262#428C22×C4312yes—
263#428C22×C4312yes—
264C2×#107C22×C4312yes—
265#424C22×C4312yes—
266#423C22×C4311yescharacteristic
267C2×C4⋊C8C22×C4311yescharacteristic
268#418C22×C4312yes—
269C2×#102C22×C4312yes—
270C2×#100C22×C4311yescharacteristic
271C2×#100C22×C4311yescharacteristic
272#405C22×C4312yes—
273C4×M16C22×C4311yescharacteristic
274C4×M16C22×C4311yescharacteristic
275#343C22×C4312yes—
276#343C22×C4311yescharacteristic
277#343C22×C4312yes—
278#343C22×C4311yescharacteristic
279#341C22×C4312yes—
280C43#2548911yescharacteristic, direct product factor, Sylow
281C22×Q8—21no—
282C22×D4C23×C4311yescharacteristic
283C23×C4—21no—
284C2×M16C23×C4312yes—
285C2×M16C23×C4311yescharacteristic
286C2×M16C23×C4311yescharacteristic
287C2×M16C23×C4311yescharacteristic
288C2×M16C23×C4311yescharacteristic
289C22×C8C23×C4312yes—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8D4×C4311yescharacteristic
295C4⋊Q8D4×C4311yescharacteristic
296#125D4×C4312yes—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305#117C23×C4312yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C23×C4311yescharacteristic
308C2×C4⋊C4C23×C4312yes—
309C2×C22⋊C4—21no—
310C2×C42C23×C4311yescharacteristic
311#108—24no—
312#107—22no—
313#107—22no—
314#107—22no—
315#107—22no—
316#107—22no—
317#106—22no—
318#106—22no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—22no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8D4×C4311yescharacteristic
325C4⋊C8D4×C4311yescharacteristic
326C4⋊C8D4×C4312yes—
327#102—22no—
328#102—22no—
329#102—22no—
330#102—22no—
331#100—22no—
332#100Q8×C4314yescomplemented
333#97—22no—
334#97—21no—
335#97—21no—
336C4×C8—22no—
337C4×C8—21no—
338C4×C8—21no—
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×Q8×C4312yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—82no—
356C22×C4#41×C4311yescharacteristic
357C22×C4#41×C4311yescharacteristic
358C22×C4C24×C4311yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—22no—
364M16—21no—
365M16—22no—
366M16C2×Q8×C4312yes—
367M16C2×Q8×C4312yes—
368M16#41×C4312yes—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C2×D4×C4312yes—
377C2×C8C2×D4×C4312yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C2×D4×C4312yes—
389C4⋊C4C2×D4×C4312yes—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C42—22no—
394C42C2×D4×C4311yescharacteristic
395C42C2×D4×C4311yescharacteristic
396C42C2×D4×C4311yescharacteristic
397C42C2×D4×C4311yescharacteristic
398C23—22no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C2×#41×C4311yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8—82no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4#121×C4311yescharacteristic
423C2×C4#121×C4311yescharacteristic
424C2×C4#121×C4311yescharacteristic
425C2×C4#121×C4311yescharacteristic
426C2×C4C22×D4×C4311yescharacteristic
427C2×C4C22×D4×C4311yescharacteristic
428C2×C4C22×Q8×C4311yescharacteristic
429C2×C4C2×#41×C4311yescharacteristic
430C2×C42−1+4×C4311yescharacteristic
431C2×C42−1+4×C4311yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22—81no—
445C22—81no—
446C22C2×#121×C4311yescharacteristic
447C22C43×#53311yescharacteristic
448C22C43×#54111yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—81no—
455C4—82no—
456C4C43×#47212yes—
457C4C43×#54711yescharacteristic
458C4C43×#54811yescharacteristic
459C4D4×Q8×C4311yescharacteristic
460C4D4×Q8×C4311yescharacteristic
461C2—21no—
462C2—21no—
463C2—82no—
464C2C43×#242911yescharacteristic
465C2C2×C43×#47211yescharacteristic
466C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3165C2semidirect
4. C43×#2962C2semidirect
5. C43×#2089C2semidirect
7. C43×#1997C2semidirect
8. C43×#1952C2semidirect
9. C43×#1950C2semidirect
98. #100×C43Q8semidirect
205. #25489C43direct (N × H)
228. #3165C2×C43semidirect
231. #2962C2×C43semidirect
232. #2089C2×C43semidirect
234. #1997C2×C43semidirect
235. #1952C2×C43semidirect
236. #1950C2×C43semidirect
280. C43#25489direct (N × H)
332. #100Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31652
C43×#30772
C2×C43×#4742
C43×#29622
C43×#20892
C43×#20632
C43×#19972
C43×#19522
C43×#19502
C43×#19312
C4×#100×C432
#2548943