Finite Group Databasebeta

← C43×#13677 #24933694

Subgroups — C43×#13677 #24933694

Order 11008.

420 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3288C211yesmaximal, characteristic, complemented
2C43×#2202C211yesmaximal, characteristic, complemented
3C43×#2199C211yesmaximal, characteristic, complemented
4C43×#1655C211yesmaximal, characteristic, complemented
5C43×#1406C211yesmaximal, characteristic, complemented
6C43×#1404C211yesmaximal, characteristic, complemented
7C43×#1403C211yesmaximal, characteristic, complemented
8C43×#577—21no—
9C43×#576—21no—
10C43×H(3,𝔽4)C2211yescharacteristic, complemented
11C43×#496—21no—
12C43×#496C2211yescharacteristic
13C43×#472—21no—
14C43×#471—21no—
15C43×B(4,𝔽2)—21no—
16C43×#455C2211yescharacteristic
17C43×#454—21no—
18C43×#454C2211yescharacteristic
19C43×#453—21no—
20C43×#444—21no—
21C43×#355—21no—
22C43×#355C2211yescharacteristic, complemented
23C43×#354C2211yescharacteristic, complemented
24C43×AΣL(1,𝔽16)—21no—
25C43×#329—21no—
26C43×#329C2211yescharacteristic, complemented
272−1+4×C43D411yescharacteristic, complemented
28H(5,𝔽2)×C43—21no—
29H(5,𝔽2)×C43D411yescharacteristic
30#137×C43—21no—
31#137×C43—41no—
32AGL(1,ℤ/8)×C43—21no—
33AGL(1,ℤ/8)×C43—21no—
34AGL(1,ℤ/8)×C43—21no—
35AGL(1,ℤ/8)×C43—41no—
36AGL(1,ℤ/8)×C43—41no—
37AGL(1,ℤ/8)×C43—41no—
38AGL(1,ℤ/8)×C43—41no—
39#135×C43—21no—
40#135×C43—41no—
41#135×C43—41no—
42C2×SD16×C43—21no—
43C2×SD16×C43—41no—
44C2×SD16×C43—41no—
45C2×D8×C43—21no—
46C2×D8×C43—41no—
47C2×D8×C43—41no—
48#131×C43—21no—
49#131×C43—21no—
50#127×C43D411yescharacteristic, complemented
51#124×C43—21no—
52#124×C43—21no—
53#124×C43—41no—
54#124×C43C2311yescharacteristic
55#120×C43—21no—
56#120×C43—41no—
57#120×C43—41no—
58#108×C43—21no—
59#104×C43—21no—
60#104×C43—21no—
61#104×C43—41no—
62#101×C43—21no—
63#101×C43D411yescharacteristic, complemented
64#100×C43—21no—
65#100×C43D411yescharacteristic
66#99×C43—21no—
67#99×C43—41no—
68#97×C43—21no—
69#97×C43D411yescharacteristic, complemented
70C24×C43—21no—
71#41×C43—21no—
72#41×C43—21no—
73#41×C43—41no—
74#41×C43—41no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43—21no—
79C2×Q8×C43—41no—
80C2×Q8×C43C2×D411yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—81no—
91C2×D4×C43—81no—
92C2×D4×C43C2×D411yescharacteristic
93Q16×C43—21no—
94Q16×C43—41no—
95SD16×C43—21no—
96SD16×C43—21no—
97SD16×C43—41no—
98SD16×C43—41no—
99SD16×C43—41no—
100SD16×C43—41no—
101SD16×C43—41no—
102SD16×C43—41no—
103SD16×C43—82no—
104SD16×C43—81no—
105D8×C43—21no—
106D8×C43—41no—
107D8×C43—41no—
108D8×C43—41no—
109D8×C43—41no—
110D8×C43—41no—
111D8×C43—82no—
112D8×C43—81no—
113M16×C43—21no—
114M16×C43—21no—
115M16×C43—41no—
116M16×C43—41no—
117M16×C43—41no—
118C2×C8×C43—21no—
119C2×C8×C43—41no—
120C2×C8×C43—41no—
121C2×C8×C43—41no—
122C22⋊C4×C43—21no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—81no—
129C42×C43—21no—
130C42×C43C2×D411yescharacteristic
131C23×C43—21no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—81no—
136C23×C43—81no—
137C23×C43—161no—
138Q8×C43—21no—
139Q8×C43—21no—
140Q8×C43—41no—
141Q8×C43—41no—
142Q8×C43—81no—
143D4×C43—21no—
144D4×C43—21no—
145D4×C43—41no—
146D4×C43—41no—
147D4×C43—41no—
148D4×C43—41no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—81no—
152D4×C43—81no—
153D4×C43—81no—
154D4×C43—81no—
155D4×C43—81no—
156D4×C43—81no—
157D4×C43—81no—
158D4×C43—161no—
159D4×C43—162no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43#12011yescharacteristic
170C8×C43—21no—
171C8×C43—21no—
172C8×C43—41no—
173C8×C43—41no—
174C8×C43—42no—
175C8×C43—81no—
176#13677C4311yesmaximal, characteristic, direct product factor, Sylow
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—82no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—161no—
187C22×C43—161no—
188C22×C43—161no—
189C22×C43—321no—
190C22×C43B(4,𝔽2)11yescharacteristic
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43—41no—
196C4×C43—81no—
197C4×C43—161no—
198#3288C2×C4311yescharacteristic, complemented
199#2202C2×C4311yescharacteristic, complemented
200#2199C2×C4311yescharacteristic, complemented
201#1655C2×C4311yescharacteristic, complemented
202#1406C2×C4311yescharacteristic, complemented
203#1404C2×C4311yescharacteristic, complemented
204#1403C2×C4311yescharacteristic, complemented
205C2×C43—21no—
206C2×C43—81no—
207C2×C43—81no—
208C2×C43—81no—
209C2×C43—161no—
210C2×C43—161no—
211C2×C43#219611yescharacteristic
212#577—21no—
213#576—21no—
214H(3,𝔽4)C22×C4311yescharacteristic, complemented
215#496—21no—
216#496C22×C4311yescharacteristic
217#472—21no—
218#471—21no—
219B(4,𝔽2)—21no—
220#455C22×C4311yescharacteristic
221#454—21no—
222#454C22×C4311yescharacteristic
223#453—21no—
224#444—21no—
225#355—21no—
226#355C22×C4311yescharacteristic, complemented
227#354C22×C4311yescharacteristic, complemented
228AΣL(1,𝔽16)—21no—
229#329—21no—
230#329C22×C4311yescharacteristic, complemented
231C43#1367711yescharacteristic, direct product factor, Sylow
2322−1+4D4×C4311yescharacteristic, complemented
233H(5,𝔽2)—21no—
234H(5,𝔽2)D4×C4311yescharacteristic
235#137—21no—
236#137—41no—
237AGL(1,ℤ/8)—21no—
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)—21no—
240AGL(1,ℤ/8)—41no—
241AGL(1,ℤ/8)—41no—
242AGL(1,ℤ/8)—41no—
243AGL(1,ℤ/8)—41no—
244#135—21no—
245#135—41no—
246#135—41no—
247C2×SD16—21no—
248C2×SD16—41no—
249C2×SD16—41no—
250C2×D8—21no—
251C2×D8—41no—
252C2×D8—41no—
253#131—21no—
254#131—21no—
255#127D4×C4311yescharacteristic, complemented
256#124—21no—
257#124—21no—
258#124—41no—
259#124C23×C4311yescharacteristic
260#120—21no—
261#120—41no—
262#120—41no—
263#108—21no—
264#104—21no—
265#104—21no—
266#104—41no—
267#101—21no—
268#101D4×C4311yescharacteristic, complemented
269#100—21no—
270#100D4×C4311yescharacteristic
271#99—21no—
272#99—41no—
273#97—21no—
274#97D4×C4311yescharacteristic, complemented
275C24—21no—
276#41—21no—
277#41—21no—
278#41—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8C2×D4×C4311yescharacteristic
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4C2×D4×C4311yescharacteristic
298Q16—21no—
299Q16—41no—
300SD16—21no—
301SD16—21no—
302SD16—41no—
303SD16—41no—
304SD16—41no—
305SD16—41no—
306SD16—41no—
307SD16—41no—
308SD16—82no—
309SD16—81no—
310D8—21no—
311D8—41no—
312D8—41no—
313D8—41no—
314D8—41no—
315D8—41no—
316D8—82no—
317D8—81no—
318M16—21no—
319M16—21no—
320M16—41no—
321M16—41no—
322M16—41no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C42—21no—
335C42C2×D4×C4311yescharacteristic
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—161no—
343Q8—21no—
344Q8—21no—
345Q8—41no—
346Q8—41no—
347Q8—81no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—161no—
364D4—162no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4#120×C4311yescharacteristic
375C8—21no—
376C8—21no—
377C8—41no—
378C8—41no—
379C8—42no—
380C8—81no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—82no—
388C22—81no—
389C22—81no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22—321no—
394C22C43×B(4,𝔽2)11yescharacteristic
395C4—21no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—81no—
401C4—161no—
402C2—21no—
403C2—81no—
404C2—81no—
405C2—81no—
406C2—161no—
407C2—161no—
408C2C43×#219611yescharacteristic
subgroupG/H
center, socleC2×C43#2196
commutator, Frattini, cosocle#124C23×C43
LCSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C43 ◁ C2×C4×C43 ◁ #124×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3288C2semidirect
2. C43×#2202C2semidirect
3. C43×#2199C2semidirect
4. C43×#1655C2semidirect
5. C43×#1406C2semidirect
6. C43×#1404C2semidirect
7. C43×#1403C2semidirect
10. C43×H(3,𝔽4)C22semidirect
22. C43×#355C22semidirect
23. C43×#354C22semidirect
26. C43×#329C22semidirect
27. 2−1+4×C43D4semidirect
50. #127×C43D4semidirect
63. #101×C43D4semidirect
69. #97×C43D4semidirect
176. #13677C43direct (N × H)
198. #3288C2×C43semidirect
199. #2202C2×C43semidirect
200. #2199C2×C43semidirect
201. #1655C2×C43semidirect
202. #1406C2×C43semidirect
203. #1404C2×C43semidirect
204. #1403C2×C43semidirect
214. H(3,𝔽4)C22×C43semidirect
226. #355C22×C43semidirect
227. #354C22×C43semidirect
230. #329C22×C43semidirect
231. C43#13677direct (N × H)
232. 2−1+4D4×C43semidirect
255. #127D4×C43semidirect
268. #101D4×C43semidirect
274. #97D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#32882
C43×#22022
C43×#21992
C43×#16552
C43×#14062
C43×#14042
C43×#14032
#1367743