Finite Group Databasebeta

← C41×#13677 #23789878

Subgroups — C41×#13677 #23789878

Order 10496.

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
1C41×#3288C211yesmaximal, characteristic, complemented
2C41×#2202C211yesmaximal, characteristic, complemented
3C41×#2199C211yesmaximal, characteristic, complemented
4C41×#1655C211yesmaximal, characteristic, complemented
5C41×#1406C211yesmaximal, characteristic, complemented
6C41×#1404C211yesmaximal, characteristic, complemented
7C41×#1403C211yesmaximal, characteristic, complemented
8C41×#577—21no—
9C41×#576—21no—
10C41×H(3,𝔽4)C2211yescharacteristic, complemented
11C41×#496—21no—
12C41×#496C2211yescharacteristic
13C41×#472—21no—
14C41×#471—21no—
15C41×B(4,𝔽2)—21no—
16C41×#455C2211yescharacteristic
17C41×#454—21no—
18C41×#454C2211yescharacteristic
19C41×#453—21no—
20C41×#444—21no—
21C41×#355—21no—
22C41×#355C2211yescharacteristic, complemented
23C41×#354C2211yescharacteristic, complemented
24C41×AΣL(1,𝔽16)—21no—
25C41×#329—21no—
26C41×#329C2211yescharacteristic, complemented
272−1+4×C41D411yescharacteristic, complemented
28H(5,𝔽2)×C41—21no—
29H(5,𝔽2)×C41D411yescharacteristic
30#137×C41—21no—
31#137×C41—41no—
32AGL(1,ℤ/8)×C41—21no—
33AGL(1,ℤ/8)×C41—21no—
34AGL(1,ℤ/8)×C41—21no—
35AGL(1,ℤ/8)×C41—41no—
36AGL(1,ℤ/8)×C41—41no—
37AGL(1,ℤ/8)×C41—41no—
38AGL(1,ℤ/8)×C41—41no—
39#135×C41—21no—
40#135×C41—41no—
41#135×C41—41no—
42C2×SD16×C41—21no—
43C2×SD16×C41—41no—
44C2×SD16×C41—41no—
45C2×D8×C41—21no—
46C2×D8×C41—41no—
47C2×D8×C41—41no—
48#131×C41—21no—
49#131×C41—21no—
50#127×C41D411yescharacteristic, complemented
51#124×C41—21no—
52#124×C41—21no—
53#124×C41—41no—
54#124×C41C2311yescharacteristic
55#120×C41—21no—
56#120×C41—41no—
57#120×C41—41no—
58#108×C41—21no—
59#104×C41—21no—
60#104×C41—21no—
61#104×C41—41no—
62#101×C41—21no—
63#101×C41D411yescharacteristic, complemented
64#100×C41—21no—
65#100×C41D411yescharacteristic
66#99×C41—21no—
67#99×C41—41no—
68#97×C41—21no—
69#97×C41D411yescharacteristic, complemented
70C24×C41—21no—
71#41×C41—21no—
72#41×C41—21no—
73#41×C41—41no—
74#41×C41—41no—
75#41×C41—41no—
76#41×C41—41no—
77#41×C41—41no—
78C2×Q8×C41—21no—
79C2×Q8×C41—41no—
80C2×Q8×C41C2×D411yescharacteristic
81C2×D4×C41—21no—
82C2×D4×C41—21no—
83C2×D4×C41—21no—
84C2×D4×C41—41no—
85C2×D4×C41—41no—
86C2×D4×C41—41no—
87C2×D4×C41—41no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C2×D4×C41—81no—
91C2×D4×C41—81no—
92C2×D4×C41C2×D411yescharacteristic
93Q16×C41—21no—
94Q16×C41—41no—
95SD16×C41—21no—
96SD16×C41—21no—
97SD16×C41—41no—
98SD16×C41—41no—
99SD16×C41—41no—
100SD16×C41—41no—
101SD16×C41—41no—
102SD16×C41—41no—
103SD16×C41—82no—
104SD16×C41—81no—
105D8×C41—21no—
106D8×C41—41no—
107D8×C41—41no—
108D8×C41—41no—
109D8×C41—41no—
110D8×C41—41no—
111D8×C41—82no—
112D8×C41—81no—
113M16×C41—21no—
114M16×C41—21no—
115M16×C41—41no—
116M16×C41—41no—
117M16×C41—41no—
118C2×C8×C41—21no—
119C2×C8×C41—41no—
120C2×C8×C41—41no—
121C2×C8×C41—41no—
122C22⋊C4×C41—21no—
123C22⋊C4×C41—41no—
124C22⋊C4×C41—41no—
125C22⋊C4×C41—41no—
126C22⋊C4×C41—41no—
127C22⋊C4×C41—41no—
128C22⋊C4×C41—81no—
129C42×C41—21no—
130C42×C41C2×D411yescharacteristic
131C23×C41—21no—
132C23×C41—41no—
133C23×C41—41no—
134C23×C41—41no—
135C23×C41—81no—
136C23×C41—81no—
137C23×C41—161no—
138Q8×C41—21no—
139Q8×C41—21no—
140Q8×C41—41no—
141Q8×C41—41no—
142Q8×C41—81no—
143D4×C41—21no—
144D4×C41—21no—
145D4×C41—41no—
146D4×C41—41no—
147D4×C41—41no—
148D4×C41—41no—
149D4×C41—41no—
150D4×C41—41no—
151D4×C41—81no—
152D4×C41—81no—
153D4×C41—81no—
154D4×C41—81no—
155D4×C41—81no—
156D4×C41—81no—
157D4×C41—81no—
158D4×C41—161no—
159D4×C41—162no—
160C2×C4×C41—21no—
161C2×C4×C41—21no—
162C2×C4×C41—41no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—81no—
167C2×C4×C41—81no—
168C2×C4×C41—81no—
169C2×C4×C41#12011yescharacteristic
170C8×C41—21no—
171C8×C41—21no—
172C8×C41—41no—
173C8×C41—41no—
174C8×C41—42no—
175C8×C41—81no—
176#13677C4111yesmaximal, characteristic, direct product factor, Sylow
177C22×C41—41no—
178C22×C41—41no—
179C22×C41—41no—
180C22×C41—81no—
181C22×C41—81no—
182C22×C41—81no—
183C22×C41—82no—
184C22×C41—81no—
185C22×C41—81no—
186C22×C41—161no—
187C22×C41—161no—
188C22×C41—161no—
189C22×C41—321no—
190C22×C41B(4,𝔽2)11yescharacteristic
191C4×C41—21no—
192C4×C41—41no—
193C4×C41—41no—
194C4×C41—41no—
195C4×C41—41no—
196C4×C41—81no—
197C4×C41—161no—
198#3288C2×C4111yescharacteristic, complemented
199#2202C2×C4111yescharacteristic, complemented
200#2199C2×C4111yescharacteristic, complemented
201#1655C2×C4111yescharacteristic, complemented
202#1406C2×C4111yescharacteristic, complemented
203#1404C2×C4111yescharacteristic, complemented
204#1403C2×C4111yescharacteristic, complemented
205C2×C41—21no—
206C2×C41—81no—
207C2×C41—81no—
208C2×C41—81no—
209C2×C41—161no—
210C2×C41—161no—
211C2×C41#219611yescharacteristic
212#577—21no—
213#576—21no—
214H(3,𝔽4)C22×C4111yescharacteristic, complemented
215#496—21no—
216#496C22×C4111yescharacteristic
217#472—21no—
218#471—21no—
219B(4,𝔽2)—21no—
220#455C22×C4111yescharacteristic
221#454—21no—
222#454C22×C4111yescharacteristic
223#453—21no—
224#444—21no—
225#355—21no—
226#355C22×C4111yescharacteristic, complemented
227#354C22×C4111yescharacteristic, complemented
228AΣL(1,𝔽16)—21no—
229#329—21no—
230#329C22×C4111yescharacteristic, complemented
231C41#1367711yescharacteristic, direct product factor, Sylow
2322−1+4D4×C4111yescharacteristic, complemented
233H(5,𝔽2)—21no—
234H(5,𝔽2)D4×C4111yescharacteristic
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×C4111yescharacteristic, complemented
256#124—21no—
257#124—21no—
258#124—41no—
259#124C23×C4111yescharacteristic
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×C4111yescharacteristic, complemented
269#100—21no—
270#100D4×C4111yescharacteristic
271#99—21no—
272#99—41no—
273#97—21no—
274#97D4×C4111yescharacteristic, 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×C4111yescharacteristic
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×C4111yescharacteristic
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×C4111yescharacteristic
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×C4111yescharacteristic
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—
394C22C41×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—
408C2C41×#219611yescharacteristic
subgroupG/H
center, socleC2×C41#2196
commutator, Frattini, cosocle#124C23×C41
LCSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C22×C41 ◁ C2×C4×C41 ◁ #124×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3288C2semidirect
2. C41×#2202C2semidirect
3. C41×#2199C2semidirect
4. C41×#1655C2semidirect
5. C41×#1406C2semidirect
6. C41×#1404C2semidirect
7. C41×#1403C2semidirect
10. C41×H(3,𝔽4)C22semidirect
22. C41×#355C22semidirect
23. C41×#354C22semidirect
26. C41×#329C22semidirect
27. 2−1+4×C41D4semidirect
50. #127×C41D4semidirect
63. #101×C41D4semidirect
69. #97×C41D4semidirect
176. #13677C41direct (N × H)
198. #3288C2×C41semidirect
199. #2202C2×C41semidirect
200. #2199C2×C41semidirect
201. #1655C2×C41semidirect
202. #1406C2×C41semidirect
203. #1404C2×C41semidirect
204. #1403C2×C41semidirect
214. H(3,𝔽4)C22×C41semidirect
226. #355C22×C41semidirect
227. #354C22×C41semidirect
230. #329C22×C41semidirect
231. C41#13677direct (N × H)
232. 2−1+4D4×C41semidirect
255. #127D4×C41semidirect
268. #101D4×C41semidirect
274. #97D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#32882
C41×#22022
C41×#21992
C41×#16552
C41×#14062
C41×#14042
C41×#14032
#1367741