Finite Group Databasebeta

← C41×#12943 #23789144

Subgroups — C41×#12943 #23789144

Order 10496.

422 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2943C211yesmaximal, characteristic
2C41×#2159C211yesmaximal, characteristic, complemented
3C2×C41×#360C211yesmaximal, characteristic
4C41×#2139C211yesmaximal, characteristic
5C41×#1944C211yesmaximal, characteristic, complemented
6C41×#1386C211yesmaximal, characteristic, complemented
7C41×#1377C211yesmaximal, characteristic, complemented
8C2×#135×C41C2211yescharacteristic
9C4×#41×C41—21no—
10C2×M32×C41C2211yescharacteristic
11C2×M32×C41C2211yescharacteristic
12C41×#442—21no—
13C41×#441—21no—
14C41×#440—21no—
15C41×#440—21no—
16C41×#427C2211yescharacteristic
17C2×#107×C41C2211yescharacteristic
18C2×#106×C41C2211yescharacteristic
19C41×#416—21no—
20C2×#97×C41C2211yescharacteristic
21C41×#389—21no—
22C41×#367—21no—
23C41×#366—21no—
24C41×#360C414yescomplemented
25C41×#358—21no—
26C41×#357—21no—
27C41×#340—21no—
28C2×#41×C41—21no—
29#135×C41—21no—
30#135×C41—21no—
31#135×C41C2×C412yes—
32#135×C41Q812yes—
33C2×Q16×C41D411yescharacteristic
34C2×SD16×C41—21no—
35C2×D8×C41D411yescharacteristic
36C22×C8×C41D411yescharacteristic
37C22×C8×C41C2311yescharacteristic
38C4×Q8×C41—21no—
39C4×Q8×C41—21no—
40C4×D4×C41—21no—
41C4×D4×C41—21no—
42C4×D4×C41—41no—
43C4×D4×C41—41no—
44#117×C41—21no—
45#117×C41—41no—
46C2×C4⋊C4×C41—21no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41—41no—
49C2×C42×C41—41no—
50C2×C42×C41D411yescharacteristic
51M32×C41—21no—
52M32×C41—21no—
53M32×C41—21no—
54M32×C41C2×C412yescomplemented
55C2×C16×C41—21no—
56C2×C16×C41—21no—
57#107×C41—21no—
58#107×C41—21no—
59#107×C41D411yescharacteristic
60#107×C41D411yescharacteristic
61#106×C41—21no—
62#106×C41—21no—
63#106×C41C2×C412yescomplemented
64#103×C41—21no—
65#103×C41—21no—
66#102×C41—21no—
67#102×C41—21no—
68#97×C41—21no—
69#97×C41—21no—
70#95×C41—41no—
71#41×C41—22no—
72#41×C41—22no—
73#41×C41—41no—
74#41×C41—41no—
75C2×Q8×C41—21no—
76C2×D4×C41—21no—
77C2×D4×C41—41no—
78C22×C4×C41—41no—
79C22×C4×C41—41no—
80C22×C4×C41—41no—
81C22×C4×C41—41no—
82C22×C4×C41—41no—
83C22×C4×C41D811yescharacteristic
84C22×C4×C41D811yescharacteristic
85C22×C4×C41C2×D411yescharacteristic
86Q16×C41—21no—
87Q16×C41C4⋊C412yescomplemented
88SD16×C41—22no—
89SD16×C41—22no—
90D8×C41—21no—
91D8×C41C4⋊C412yescomplemented
92C2×C8×C41—21no—
93C2×C8×C41—21no—
94C2×C8×C41—21no—
95C2×C8×C41C22×C411yescharacteristic
96C2×C8×C41C2×D411yescharacteristic
97C2×C8×C41C2×D411yescharacteristic
98C2×C8×C41C2×Q811yescharacteristic
99C2×C8×C41#4111yescharacteristic
100C2×C8×C41#4111yescharacteristic
101C4⋊C4×C41—22no—
102C4⋊C4×C41—21no—
103C4⋊C4×C41—21no—
104C4⋊C4×C41—41no—
105C4⋊C4×C41—41no—
106C4⋊C4×C41—41no—
107C4⋊C4×C41—41no—
108C4⋊C4×C41—41no—
109C4⋊C4×C41—82no—
110C22⋊C4×C41—41no—
111C22⋊C4×C41—41no—
112C22⋊C4×C41—41no—
113C42×C41—21no—
114C42×C41—21no—
115C42×C41—41no—
116C42×C41—41no—
117C42×C41—41no—
118C16×C41—22no—
119C16×C41—41no—
120C23×C41—41no—
121C23×C41C2×D811yescharacteristic
122Q8×C41—22no—
123Q8×C41—41no—
124D4×C41—22no—
125D4×C41—42no—
126D4×C41—42no—
127D4×C41—41no—
128C2×C4×C41—21no—
129C2×C4×C41—21no—
130C2×C4×C41—41no—
131C2×C4×C41—42no—
132C2×C4×C41—42no—
133C2×C4×C41—41no—
134C2×C4×C41—41no—
135C2×C4×C41—42no—
136C2×C4×C41—41no—
137C2×C4×C41—41no—
138C2×C4×C41—82no—
139C2×C4×C41—82no—
140C2×C4×C41—81no—
141C2×C4×C41—81no—
142C2×C4×C41—81no—
143C2×C4×C41—81no—
144C2×C4×C41—81no—
145C2×C4×C41C4×D411yescharacteristic
146C2×C4×C41#12011yescharacteristic
147C2×C4×C41C22⋊Q811yescharacteristic
148C2×C4×C41#13511yescharacteristic
149C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C41#13711yescharacteristic
151C8×C41—41no—
152C8×C41C2×C4⋊C411yescharacteristic
153C8×C41C4×D411yescharacteristic
154C8×C41C22⋊Q811yescharacteristic
155C8×C41#12311yescharacteristic
156#12943C4111yesmaximal, characteristic, direct product factor, Sylow
157C22×C41—21no—
158C22×C41—21no—
159C22×C41—42no—
160C22×C41—81no—
161C22×C41—81no—
162C22×C41C4×D811yescharacteristic
163C22×C41#44711yescharacteristic
164C22×C41#47411yescharacteristic
165C4×C41—42no—
166C4×C41—41no—
167C4×C41—41no—
168C4×C41—82no—
169C4×C41—81no—
170C4×C41—81no—
171C4×C41—161no—
172C4×C41#38511yescharacteristic
173C4×C41#44011yescharacteristic
174C4×C41#45211yescharacteristic
175C4×C41#47811yescharacteristic
176#2943C2×C4111yescharacteristic
177#2159C2×C4111yescharacteristic, complemented
178C2×#360C2×C4111yescharacteristic
179#2139C2×C4111yescharacteristic
180#1944C2×C4111yescharacteristic, complemented
181#1386C2×C4111yescharacteristic, complemented
182#1377C2×C4111yescharacteristic, complemented
183C2×C41—21no—
184C2×C41—21no—
185C2×C41—82no—
186C2×C41#186211yescharacteristic
187C2×C41#219011yescharacteristic
188C2×C41#219111yescharacteristic
189C2×#135C22×C4111yescharacteristic
190C4×#41—21no—
191C2×M32C22×C4111yescharacteristic
192C2×M32C22×C4111yescharacteristic
193#442—21no—
194#441—21no—
195#440—21no—
196#440—21no—
197#427C22×C4111yescharacteristic
198C2×#107C22×C4111yescharacteristic
199C2×#106C22×C4111yescharacteristic
200#416—21no—
201C2×#97C22×C4111yescharacteristic
202#389—21no—
203#367—21no—
204#366—21no—
205#360C4×C4114yescomplemented
206#358—21no—
207#357—21no—
208#340—21no—
209C41#1294311yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211#135—21no—
212#135—21no—
213#135C2×C4×C4112yes—
214#135Q8×C4112yes—
215C2×Q16D4×C4111yescharacteristic
216C2×SD16—21no—
217C2×D8D4×C4111yescharacteristic
218C22×C8D4×C4111yescharacteristic
219C22×C8C23×C4111yescharacteristic
220C4×Q8—21no—
221C4×Q8—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—41no—
225C4×D4—41no—
226#117—21no—
227#117—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—41no—
231C2×C42—41no—
232C2×C42D4×C4111yescharacteristic
233M32—21no—
234M32—21no—
235M32—21no—
236M32C2×C4×C4112yescomplemented
237C2×C16—21no—
238C2×C16—21no—
239#107—21no—
240#107—21no—
241#107D4×C4111yescharacteristic
242#107D4×C4111yescharacteristic
243#106—21no—
244#106—21no—
245#106C2×C4×C4112yescomplemented
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250#97—21no—
251#97—21no—
252#95—41no—
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4D8×C4111yescharacteristic
266C22×C4D8×C4111yescharacteristic
267C22×C4C2×D4×C4111yescharacteristic
268Q16—21no—
269Q16C4⋊C4×C4112yescomplemented
270SD16—22no—
271SD16—22no—
272D8—21no—
273D8C4⋊C4×C4112yescomplemented
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8C22×C4×C4111yescharacteristic
278C2×C8C2×D4×C4111yescharacteristic
279C2×C8C2×D4×C4111yescharacteristic
280C2×C8C2×Q8×C4111yescharacteristic
281C2×C8#41×C4111yescharacteristic
282C2×C8#41×C4111yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—82no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—21no—
296C42—21no—
297C42—41no—
298C42—41no—
299C42—41no—
300C16—22no—
301C16—41no—
302C23—41no—
303C23C2×D8×C4111yescharacteristic
304Q8—22no—
305Q8—41no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C4×D4×C4111yescharacteristic
328C2×C4#120×C4111yescharacteristic
329C2×C4C22⋊Q8×C4111yescharacteristic
330C2×C4#135×C4111yescharacteristic
331C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
332C2×C4#137×C4111yescharacteristic
333C8—41no—
334C8C2×C4⋊C4×C4111yescharacteristic
335C8C4×D4×C4111yescharacteristic
336C8C22⋊Q8×C4111yescharacteristic
337C8#123×C4111yescharacteristic
338C22—21no—
339C22—21no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22C4×D8×C4111yescharacteristic
344C22C41×#44711yescharacteristic
345C22C41×#47411yescharacteristic
346C4—42no—
347C4—41no—
348C4—41no—
349C4—82no—
350C4—81no—
351C4—81no—
352C4—161no—
353C4C41×#38511yescharacteristic
354C4C41×#44011yescharacteristic
355C4C41×#45211yescharacteristic
356C4C41×#47811yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C41×#186211yescharacteristic
361C2C41×#219011yescharacteristic
362C2C41×#219111yescharacteristic
subgroupG/H
center, socleC22×C41#447
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
prime radicalC2×#135×C41C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#97×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2159C2semidirect
5. C41×#1944C2semidirect
6. C41×#1386C2semidirect
7. C41×#1377C2semidirect
24. C41×#360C4semidirect
54. M32×C41C2×C4semidirect
63. #106×C41C2×C4semidirect
87. Q16×C41C4⋊C4semidirect
91. D8×C41C4⋊C4semidirect
156. #12943C41direct (N × H)
177. #2159C2×C41semidirect
180. #1944C2×C41semidirect
181. #1386C2×C41semidirect
182. #1377C2×C41semidirect
205. #360C4×C41semidirect
209. C41#12943direct (N × H)
236. M32C2×C4×C41semidirect
245. #106C2×C4×C41semidirect
269. Q16C4⋊C4×C41semidirect
273. D8C4⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#29432
C41×#21592
C2×C41×#3602
C41×#21392
C41×#19442
C41×#13862
C41×#13772
#1294341