Finite Group Databasebeta

← C43×#19510 #24939527

Subgroups — C43×#19510 #24939527

Order 11008.

636 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3253C211yesmaximal, characteristic, complemented
2C43×#3245C211yesmaximal, characteristic, complemented
3C43×#3207C211yesmaximal, characteristic, complemented
4C43×#2981C211yesmaximal, characteristic, complemented
5C43×#1697C212yesmaximal, complemented
6C43×#1685C212yesmaximal, complemented
7C43×#1683C212yesmaximal, complemented
8C43×#1667C212yesmaximal, complemented
9C43×#1571C211yesmaximal, characteristic, complemented
10C43×#1557C211yesmaximal, characteristic, complemented
11C43×#1551C211yesmaximal, characteristic, complemented
12C43×#532C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C43×#532C2211yescharacteristic
15C43×#493C2211yescharacteristic
16C43×#492C2211yescharacteristic
17C43×#487C2211yescharacteristic
18C43×#486C2211yescharacteristic
19C43×#476—21no—
20C43×#476C2212yes—
21C43×#474—21no—
22C43×#474C2212yes—
23C43×#469—22no—
24C43×#466—22no—
25C43×#463—22no—
26C43×#459—21no—
27C43×#459—21no—
28C43×#459C2212yes—
29C43×#459C2212yes—
30C43×#449—22no—
31C43×#436C2212yes—
32C43×#435—22no—
33C8×D4×C43C2212yes—
34C43×#432C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#423C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C43×#408—22no—
39C43×#335C2212yes—
40C43×#335C2212yes—
41C43×#333C2212yes—
42C43×#332C2212yes—
43C43×#331C2212yes—
44C43×#331C2212yes—
45C2×#41×C43—21no—
46C2×#41×C43—21no—
47C2×#41×C43—21no—
48C2×SD16×C43—22no—
49C2×D8×C43—22no—
50C2×D8×C43—22no—
51C2×D8×C43—22no—
52C2×M16×C43—21no—
53C2×M16×C43—22no—
54C22×C8×C43—21no—
55C22×C8×C43—22no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43C2311yescharacteristic
58C4⋊Q8×C43C2311yescharacteristic
59#127×C43D411yescharacteristic
60#127×C43C2311yescharacteristic
61#127×C43C2311yescharacteristic
62#124×C43—21no—
63#124×C43—21no—
64#124×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69#121×C43—21no—
70#121×C43D412yes—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43C2312yes—
77C2×C42×C43C2311yescharacteristic
78#107×C43—22no—
79#106×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43D412yes—
83C4⋊C8×C43C2312yes—
84C4⋊C8×C43C2312yes—
85C4⋊C8×C43C2312yes—
86#103×C43—22no—
87#102×C43—22no—
88#102×C43—22no—
89#102×C43—22no—
90#102×C43—22no—
91#102×C43—22no—
92C22⋊C8×C43—21no—
93C22⋊C8×C43—22no—
94C22⋊C8×C43—22no—
95C22⋊C8×C43D412yes—
96#97×C43—21no—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99#41×C43—82no—
100#41×C43—82no—
101#41×C43—82no—
102C2×Q8×C43—21no—
103C2×Q8×C43—21no—
104C2×Q8×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43C2×D412yes—
117C22×C4×C43—22no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43#4111yescharacteristic
123SD16×C43—82no—
124D8×C43—82no—
125D8×C43—82no—
126D8×C43—82no—
127M16×C43—82no—
128M16×C43—81no—
129C2×C8×C43—22no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—82no—
133C2×C8×C43—81no—
134C2×C8×C43C2×D412yes—
135C2×C8×C43C2×D412yes—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43C2×D412yes—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43#4111yescharacteristic
151C42×C43C2411yescharacteristic
152C23×C43—22no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43#12111yescharacteristic
156Q8×C43—42no—
157Q8×C43—81no—
158Q8×C43—81no—
159D4×C43—22no—
160D4×C43—22no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—42no—
164D4×C43—42no—
165D4×C43—41no—
166D4×C43—41no—
167D4×C43—81no—
168D4×C43—81no—
169D4×C43—81no—
170D4×C43—81no—
171D4×C43—82no—
172D4×C43—82no—
173D4×C43—82no—
174C2×C4×C43—21no—
175C2×C4×C43—22no—
176C2×C4×C43—21no—
177C2×C4×C43—22no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—82no—
184C2×C4×C43—82no—
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43C22×D411yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C2×#4111yescharacteristic
191C8×C43—22no—
192C8×C43—22no—
193C8×C43—42no—
194C8×C43—42no—
195C8×C43—42no—
196#19510C4311yesmaximal, characteristic, direct product factor, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—42no—
201C22×C43—42no—
202C22×C43—42no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43C2×#12111yescharacteristic
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—42no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43#57612yes—
218C4×C43#57611yescharacteristic
219C4×C43#57811yescharacteristic
220#3253C2×C4311yescharacteristic, complemented
221#3245C2×C4311yescharacteristic, complemented
222#3207C2×C4311yescharacteristic, complemented
223#2981C2×C4311yescharacteristic, complemented
224#1697C2×C4312yescomplemented
225#1685C2×C4312yescomplemented
226#1683C2×C4312yescomplemented
227#1667C2×C4312yescomplemented
228#1571C2×C4311yescharacteristic, complemented
229#1557C2×C4311yescharacteristic, complemented
230#1551C2×C4311yescharacteristic, complemented
231C2×C43—41no—
232C2×C43—82no—
233C2×C43—161no—
234C2×C43—161no—
235C2×C43#304111yescharacteristic
236C2×C43#306111yescharacteristic
237C2×C43#306811yescharacteristic
238#532C22×C4311yescharacteristic
239#532C22×C4311yescharacteristic
240#532C22×C4311yescharacteristic
241#493C22×C4311yescharacteristic
242#492C22×C4311yescharacteristic
243#487C22×C4311yescharacteristic
244#486C22×C4311yescharacteristic
245#476—21no—
246#476C22×C4312yes—
247#474—21no—
248#474C22×C4312yes—
249#469—22no—
250#466—22no—
251#463—22no—
252#459—21no—
253#459—21no—
254#459C22×C4312yes—
255#459C22×C4312yes—
256#449—22no—
257#436C22×C4312yes—
258#435—22no—
259C8×D4C22×C4312yes—
260#432C22×C4311yescharacteristic
261#431C22×C4311yescharacteristic
262#423C22×C4311yescharacteristic
263C2×C4⋊C8C22×C4311yescharacteristic
264#408—22no—
265#335C22×C4312yes—
266#335C22×C4312yes—
267#333C22×C4312yes—
268#332C22×C4312yes—
269#331C22×C4312yes—
270#331C22×C4312yes—
271C43#1951011yescharacteristic, direct product factor, Sylow
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×SD16—22no—
276C2×D8—22no—
277C2×D8—22no—
278C2×D8—22no—
279C2×M16—21no—
280C2×M16—22no—
281C22×C8—21no—
282C22×C8—22no—
283C4⋊Q8D4×C4311yescharacteristic
284C4⋊Q8C23×C4311yescharacteristic
285C4⋊Q8C23×C4311yescharacteristic
286#127D4×C4311yescharacteristic
287#127C23×C4311yescharacteristic
288#127C23×C4311yescharacteristic
289#124—21no—
290#124—21no—
291#124—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—21no—
297#121D4×C4312yes—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4C23×C4312yes—
304C2×C42C23×C4311yescharacteristic
305#107—22no—
306#106—22no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8D4×C4312yes—
310C4⋊C8C23×C4312yes—
311C4⋊C8C23×C4312yes—
312C4⋊C8C23×C4312yes—
313#103—22no—
314#102—22no—
315#102—22no—
316#102—22no—
317#102—22no—
318#102—22no—
319C22⋊C8—21no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322C22⋊C8D4×C4312yes—
323#97—21no—
324C4×C8C23×C4311yescharacteristic
325C4×C8C23×C4311yescharacteristic
326#41—82no—
327#41—82no—
328#41—82no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4C2×D4×C4312yes—
344C22×C4—22no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4C2×D4×C4311yescharacteristic
348C22×C4C2×D4×C4311yescharacteristic
349C22×C4#41×C4311yescharacteristic
350SD16—82no—
351D8—82no—
352D8—82no—
353D8—82no—
354M16—82no—
355M16—81no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—82no—
360C2×C8—81no—
361C2×C8C2×D4×C4312yes—
362C2×C8C2×D4×C4312yes—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4C2×D4×C4312yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C42C2×D4×C4311yescharacteristic
376C42C2×D4×C4311yescharacteristic
377C42#41×C4311yescharacteristic
378C42C24×C4311yescharacteristic
379C23—22no—
380C23—41no—
381C23—41no—
382C23#121×C4311yescharacteristic
383Q8—42no—
384Q8—81no—
385Q8—81no—
386D4—22no—
387D4—22no—
388D4—41no—
389D4—41no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—41no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—81no—
398D4—82no—
399D4—82no—
400D4—82no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4#121×C4311yescharacteristic
413C2×C4#121×C4311yescharacteristic
414C2×C4#121×C4311yescharacteristic
415C2×C4C22×D4×C4311yescharacteristic
416C2×C4C22×D4×C4311yescharacteristic
417C2×C4C2×#41×C4311yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C8—42no—
422C8—42no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22C2×#121×C4311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—81no—
442C4—81no—
443C4C43×#57612yes—
444C4C43×#57611yescharacteristic
445C4C43×#57811yescharacteristic
446C2—41no—
447C2—82no—
448C2—161no—
449C2—161no—
450C2C43×#304111yescharacteristic
451C2C43×#306111yescharacteristic
452C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3253C2semidirect
2. C43×#3245C2semidirect
3. C43×#3207C2semidirect
4. C43×#2981C2semidirect
5. C43×#1697C2semidirect
6. C43×#1685C2semidirect
7. C43×#1683C2semidirect
8. C43×#1667C2semidirect
9. C43×#1571C2semidirect
10. C43×#1557C2semidirect
11. C43×#1551C2semidirect
196. #19510C43direct (N × H)
220. #3253C2×C43semidirect
221. #3245C2×C43semidirect
222. #3207C2×C43semidirect
223. #2981C2×C43semidirect
224. #1697C2×C43semidirect
225. #1685C2×C43semidirect
226. #1683C2×C43semidirect
227. #1667C2×C43semidirect
228. #1571C2×C43semidirect
229. #1557C2×C43semidirect
230. #1551C2×C43semidirect
271. C43#19510direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32532
C43×#32452
C43×#32072
C43×#29812
C43×#16972
C43×#16852
C43×#16832
C43×#16672
C43×#15712
C43×#15572
C43×#15512
#1951043