Finite Group Databasebeta

← C41×#3308 #19107088

Subgroups — C41×#3308 #19107088

Order 5248.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#548C211yesmaximal, characteristic, complemented
2C41×#547C211yesmaximal, characteristic, complemented
3C41×#489C211yesmaximal, characteristic, complemented
4C41×#484C211yesmaximal, characteristic, complemented
5C41×#480C211yesmaximal, characteristic, complemented
6C41×#477C211yesmaximal, characteristic, complemented
7C41×#468C211yesmaximal, characteristic, complemented
8C41×#466C211yesmaximal, characteristic, complemented
9C41×#463C211yesmaximal, characteristic, complemented
10C41×#449C211yesmaximal, characteristic, complemented
11C41×#448C211yesmaximal, characteristic, complemented
12C41×#440C211yesmaximal, characteristic, complemented
13C41×#435C211yesmaximal, characteristic, complemented
14C41×#417C211yesmaximal, characteristic, complemented
15C2×#103×C41C211yesmaximal, characteristic, complemented
16C2×#41×C41—21no—
17C2×#41×C41C2211yescharacteristic
18C22×Q8×C41C2211yescharacteristic
19C2×SD16×C41C2211yescharacteristic
20C2×SD16×C41C2211yescharacteristic
21C2×D8×C41C2211yescharacteristic
22C2×M16×C41C2211yescharacteristic
23C22×C8×C41C2211yescharacteristic
24C4⋊Q8×C41C2211yescharacteristic
25#124×C41—21no—
26#124×C41C2211yescharacteristic
27#123×C41—21no—
28#123×C41—21no—
29C22⋊Q8×C41—21no—
30C22⋊Q8×C41—21no—
31C22⋊Q8×C41C2211yescharacteristic
32#121×C41—21no—
33#121×C41C2211yescharacteristic
34#121×C41C2211yescharacteristic
35#121×C41C2211yescharacteristic
36C4×Q8×C41C2211yescharacteristic
37C4×D4×C41—21no—
38C4×D4×C41C2211yescharacteristic
39C4×D4×C41C2211yescharacteristic
40C2×C4⋊C4×C41C2211yescharacteristic
41C2×C4⋊C4×C41C2211yescharacteristic
42#107×C41C2211yescharacteristic
43#107×C41C2211yescharacteristic
44#107×C41C2211yescharacteristic
45C4⋊C8×C41C2211yescharacteristic
46#103×C41C2211yescharacteristic
47#103×C41C2211yescharacteristic
48#103×C41C2211yescharacteristic
49#103×C41C2211yescharacteristic
50#103×C41C2211yescharacteristic
51#103×C41C2211yescharacteristic
52#102×C41C2211yescharacteristic
53#102×C41C2211yescharacteristic
54#102×C41C2211yescharacteristic
55#102×C41C2211yescharacteristic
56C22⋊C8×C41C2211yescharacteristic
57C22⋊C8×C41C2211yescharacteristic
58#97×C41C2211yescharacteristic
59#41×C41—22no—
60#41×C41—41no—
61#41×C41—44no—
62C2×Q8×C41—21no—
63C2×Q8×C41—21no—
64C2×Q8×C41—22no—
65C2×Q8×C41—41no—
66C2×Q8×C41C2311yescharacteristic
67C2×Q8×C41C2311yescharacteristic
68C2×D4×C41—21no—
69C2×D4×C41—21no—
70C2×D4×C41—21no—
71C2×D4×C41—21no—
72C2×D4×C41D411yescharacteristic
73C2×D4×C41C2311yescharacteristic
74C2×D4×C41C2311yescharacteristic
75C22×C4×C41—21no—
76C22×C4×C41—21no—
77C22×C4×C41—21no—
78C22×C4×C41—21no—
79C22×C4×C41—21no—
80C22×C4×C41C2311yescharacteristic
81C22×C4×C41C2311yescharacteristic
82SD16×C41—22no—
83SD16×C41—41no—
84D8×C41—41no—
85M16×C41—41no—
86C2×C8×C41—41no—
87C2×C8×C41C2311yescharacteristic
88C2×C8×C41C2311yescharacteristic
89C2×C8×C41C2311yescharacteristic
90C2×C8×C41C2311yescharacteristic
91C4⋊C4×C41—21no—
92C4⋊C4×C41—21no—
93C4⋊C4×C41—21no—
94C4⋊C4×C41—21no—
95C4⋊C4×C41—21no—
96C4⋊C4×C41D411yescharacteristic
97C4⋊C4×C41C2311yescharacteristic
98C4⋊C4×C41C2311yescharacteristic
99C4⋊C4×C41C2311yescharacteristic
100C4⋊C4×C41C2311yescharacteristic
101C22⋊C4×C41—21no—
102C22⋊C4×C41—21no—
103C22⋊C4×C41—21no—
104C22⋊C4×C41—21no—
105C22⋊C4×C41—21no—
106C22⋊C4×C41—21no—
107C22⋊C4×C41—21no—
108C22⋊C4×C41D411yescharacteristic
109C22⋊C4×C41D411yescharacteristic
110C42×C41—21no—
111C42×C41C2311yescharacteristic
112C23×C41—21no—
113C23×C41—21no—
114C23×C41C2×D411yescharacteristic
115C23×C41C2×D411yescharacteristic
116Q8×C41—21no—
117Q8×C41—21no—
118Q8×C41—21no—
119Q8×C41—42no—
120Q8×C41—42no—
121Q8×C41#4112yescomplemented
122D4×C41—22no—
123D4×C41—21no—
124D4×C41—21no—
125D4×C41—21no—
126D4×C41—21no—
127D4×C41—42no—
128D4×C41—42no—
129D4×C41—42no—
130D4×C41—42no—
131C2×C4×C41—21no—
132C2×C4×C41—21no—
133C2×C4×C41—21no—
134C2×C4×C41—21no—
135C2×C4×C41—21no—
136C2×C4×C41—21no—
137C2×C4×C41—21no—
138C2×C4×C41—21no—
139C2×C4×C41—21no—
140C2×C4×C41—21no—
141C2×C4×C41—42no—
142C2×C4×C41—42no—
143C2×C4×C41—42no—
144C2×C4×C41—42no—
145C2×C4×C41—42no—
146C2×C4×C41C2×D411yescharacteristic
147C2×C4×C41C2×D411yescharacteristic
148C2×C4×C41C2×D411yescharacteristic
149C2×C4×C41C2×D411yescharacteristic
150C2×C4×C41C2411yescharacteristic
151C8×C41—21no—
152C8×C41—21no—
153C8×C41—21no—
154C8×C41—21no—
155C22×C41—21no—
156C22×C41—21no—
157C22×C41—21no—
158C22×C41—21no—
159C22×C41—21no—
160C22×C41—41no—
161C22×C41—41no—
162C22×C41—41no—
163C22×C41—41no—
164C22×C41—41no—
165C22×C41—41no—
166C22×C41AGL(1,ℤ/8)12yes—
167C22×C41C22×D411yescharacteristic
168C4×C41—21no—
169C4×C41—21no—
170C4×C41—22no—
171C4×C41—21no—
172C4×C41—21no—
173C4×C41—41no—
174C4×C41—41no—
175C4×C41—41no—
176C4×C41—41no—
177C4×C41—41no—
178C4×C41C2×#4111yescharacteristic
179C4×C41H(5,𝔽2)11yescharacteristic
180#3308C4111yesmaximal, characteristic, direct product factor, Sylow
181C2×C41—22no—
182C2×C41—41no—
183C2×C41—81no—
184C2×C41—81no—
185C2×C41#54611yescharacteristic
186C2×C41C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C41#57811yescharacteristic
188#548C2×C4111yescharacteristic, complemented
189#547C2×C4111yescharacteristic, complemented
190#489C2×C4111yescharacteristic, complemented
191#484C2×C4111yescharacteristic, complemented
192#480C2×C4111yescharacteristic, complemented
193#477C2×C4111yescharacteristic, complemented
194#468C2×C4111yescharacteristic, complemented
195#466C2×C4111yescharacteristic, complemented
196#463C2×C4111yescharacteristic, complemented
197#449C2×C4111yescharacteristic, complemented
198#448C2×C4111yescharacteristic, complemented
199#440C2×C4111yescharacteristic, complemented
200#435C2×C4111yescharacteristic, complemented
201#417C2×C4111yescharacteristic, complemented
202C2×#103C2×C4111yescharacteristic, complemented
203C41#330811yescharacteristic, direct product factor, Sylow
204C2×#41—21no—
205C2×#41C22×C4111yescharacteristic
206C22×Q8C22×C4111yescharacteristic
207C2×SD16C22×C4111yescharacteristic
208C2×SD16C22×C4111yescharacteristic
209C2×D8C22×C4111yescharacteristic
210C2×M16C22×C4111yescharacteristic
211C22×C8C22×C4111yescharacteristic
212C4⋊Q8C22×C4111yescharacteristic
213#124—21no—
214#124C22×C4111yescharacteristic
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8C22×C4111yescharacteristic
220#121—21no—
221#121C22×C4111yescharacteristic
222#121C22×C4111yescharacteristic
223#121C22×C4111yescharacteristic
224C4×Q8C22×C4111yescharacteristic
225C4×D4—21no—
226C4×D4C22×C4111yescharacteristic
227C4×D4C22×C4111yescharacteristic
228C2×C4⋊C4C22×C4111yescharacteristic
229C2×C4⋊C4C22×C4111yescharacteristic
230#107C22×C4111yescharacteristic
231#107C22×C4111yescharacteristic
232#107C22×C4111yescharacteristic
233C4⋊C8C22×C4111yescharacteristic
234#103C22×C4111yescharacteristic
235#103C22×C4111yescharacteristic
236#103C22×C4111yescharacteristic
237#103C22×C4111yescharacteristic
238#103C22×C4111yescharacteristic
239#103C22×C4111yescharacteristic
240#102C22×C4111yescharacteristic
241#102C22×C4111yescharacteristic
242#102C22×C4111yescharacteristic
243#102C22×C4111yescharacteristic
244C22⋊C8C22×C4111yescharacteristic
245C22⋊C8C22×C4111yescharacteristic
246#97C22×C4111yescharacteristic
247#41—22no—
248#41—41no—
249#41—44no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8C23×C4111yescharacteristic
255C2×Q8C23×C4111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4D4×C4111yescharacteristic
261C2×D4C23×C4111yescharacteristic
262C2×D4C23×C4111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C23×C4111yescharacteristic
269C22×C4C23×C4111yescharacteristic
270SD16—22no—
271SD16—41no—
272D8—41no—
273M16—41no—
274C2×C8—41no—
275C2×C8C23×C4111yescharacteristic
276C2×C8C23×C4111yescharacteristic
277C2×C8C23×C4111yescharacteristic
278C2×C8C23×C4111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4D4×C4111yescharacteristic
285C4⋊C4C23×C4111yescharacteristic
286C4⋊C4C23×C4111yescharacteristic
287C4⋊C4C23×C4111yescharacteristic
288C4⋊C4C23×C4111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4D4×C4111yescharacteristic
297C22⋊C4D4×C4111yescharacteristic
298C42—21no—
299C42C23×C4111yescharacteristic
300C23—21no—
301C23—21no—
302C23C2×D4×C4111yescharacteristic
303C23C2×D4×C4111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—42no—
309Q8#41×C4112yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4C2×D4×C4111yescharacteristic
335C2×C4C2×D4×C4111yescharacteristic
336C2×C4C2×D4×C4111yescharacteristic
337C2×C4C2×D4×C4111yescharacteristic
338C2×C4C24×C4111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22AGL(1,ℤ/8)×C4112yes—
355C22C22×D4×C4111yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C2×#41×C4111yescharacteristic
367C4H(5,𝔽2)×C4111yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—81no—
372C2C41×#54611yescharacteristic
373C2C2×AGL(1,ℤ/8)×C4111yescharacteristic
374C2C41×#57811yescharacteristic
subgroupG/H
center, socleC22×C41C22×D4
commutator, Frattini, cosocleC2×C4C24×C41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#548C2semidirect
2. C41×#547C2semidirect
3. C41×#489C2semidirect
4. C41×#484C2semidirect
5. C41×#480C2semidirect
6. C41×#477C2semidirect
7. C41×#468C2semidirect
8. C41×#466C2semidirect
9. C41×#463C2semidirect
10. C41×#449C2semidirect
11. C41×#448C2semidirect
12. C41×#440C2semidirect
13. C41×#435C2semidirect
14. C41×#417C2semidirect
15. C2×#103×C41C2semidirect
121. Q8×C41#41semidirect
180. #3308C41direct (N × H)
188. #548C2×C41semidirect
189. #547C2×C41semidirect
190. #489C2×C41semidirect
191. #484C2×C41semidirect
192. #480C2×C41semidirect
193. #477C2×C41semidirect
194. #468C2×C41semidirect
195. #466C2×C41semidirect
196. #463C2×C41semidirect
197. #449C2×C41semidirect
198. #448C2×C41semidirect
199. #440C2×C41semidirect
200. #435C2×C41semidirect
201. #417C2×C41semidirect
202. C2×#103C2×C41semidirect
203. C41#3308direct (N × H)
309. Q8#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#5482
C41×#5472
C41×#4892
C41×#4842
C41×#4802
C41×#4772
C41×#4682
C41×#4662
C41×#4632
C41×#4492
C41×#4482
C41×#4402
C41×#4352
C41×#4172
C2×#103×C412
#330841