Finite Group Databasebeta

← C41×#3316 #19107096

Subgroups — C41×#3316 #19107096

Order 5248.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#554C211yesmaximal, characteristic, complemented
2C41×#548C211yesmaximal, characteristic
3C41×#489C211yesmaximal, characteristic, complemented
4C41×#483C211yesmaximal, characteristic, complemented
5C41×#481C211yesmaximal, characteristic, complemented
6C41×#475C211yesmaximal, characteristic, complemented
7C41×#470C211yesmaximal, characteristic, complemented
8C41×#465C211yesmaximal, characteristic, complemented
9C41×#464C211yesmaximal, characteristic, complemented
10C41×#452C211yesmaximal, characteristic, complemented
11C41×#451C211yesmaximal, characteristic, complemented
12C41×#441C211yesmaximal, characteristic, complemented
13C41×#435C211yesmaximal, characteristic, complemented
14C41×#417C211yesmaximal, characteristic, complemented
15C2×#103×C41C211yesmaximal, characteristic, complemented
16C2×#41×C41C2211yescharacteristic
17C22×Q8×C41C2211yescharacteristic
18C2×Q16×C41C2211yescharacteristic
19C2×Q16×C41C2211yescharacteristic
20C2×SD16×C41C2211yescharacteristic
21C2×M16×C41C2211yescharacteristic
22C22×C8×C41C2211yescharacteristic
23C4⋊Q8×C41C2211yescharacteristic
24#125×C41—21no—
25#124×C41—21no—
26#124×C41C2211yescharacteristic
27C22⋊Q8×C41—21no—
28C22⋊Q8×C41—21no—
29C22⋊Q8×C41—21no—
30C22⋊Q8×C41C2211yescharacteristic
31C22⋊Q8×C41C2211yescharacteristic
32C22⋊Q8×C41C2211yescharacteristic
33#121×C41—21no—
34#121×C41C2211yescharacteristic
35C4×Q8×C41C2211yescharacteristic
36C4×Q8×C41C2211yescharacteristic
37C4×D4×C41—21no—
38C4×D4×C41—21no—
39C4×D4×C41C2211yescharacteristic
40C2×C4⋊C4×C41C2211yescharacteristic
41C2×C4⋊C4×C41C2211yescharacteristic
42#106×C41C2211yescharacteristic
43#106×C41C2211yescharacteristic
44#106×C41C2211yescharacteristic
45C4⋊C8×C41C2211yescharacteristic
46#103×C41C2211yescharacteristic
47#103×C41C2211yescharacteristic
48#103×C41C2211yescharacteristic
49#103×C41C2211yescharacteristic
50#103×C41C2211yescharacteristic
51#103×C41C2211yescharacteristic
52#103×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—
61C2×Q8×C41—21no—
62C2×Q8×C41—21no—
63C2×Q8×C41—22no—
64C2×Q8×C41—41no—
65C2×Q8×C41C2311yescharacteristic
66C2×Q8×C41C2311yescharacteristic
67C2×Q8×C41C2311yescharacteristic
68C2×D4×C41—21no—
69C2×D4×C41—21no—
70C2×D4×C41D411yescharacteristic
71C2×D4×C41C2311yescharacteristic
72C22×C4×C41—21no—
73C22×C4×C41—21no—
74C22×C4×C41—21no—
75C22×C4×C41—21no—
76C22×C4×C41C2311yescharacteristic
77C22×C4×C41C2311yescharacteristic
78Q16×C41—22no—
79Q16×C41—41no—
80SD16×C41—41no—
81M16×C41—41no—
82C2×C8×C41—41no—
83C2×C8×C41C2311yescharacteristic
84C2×C8×C41C2311yescharacteristic
85C2×C8×C41C2311yescharacteristic
86C2×C8×C41C2311yescharacteristic
87C4⋊C4×C41—21no—
88C4⋊C4×C41—21no—
89C4⋊C4×C41—21no—
90C4⋊C4×C41—21no—
91C4⋊C4×C41—21no—
92C4⋊C4×C41—21no—
93C4⋊C4×C41—21no—
94C4⋊C4×C41—21no—
95C4⋊C4×C41D411yescharacteristic
96C4⋊C4×C41C2311yescharacteristic
97C4⋊C4×C41C2311yescharacteristic
98C4⋊C4×C41C2311yescharacteristic
99C4⋊C4×C41C2311yescharacteristic
100C22⋊C4×C41—21no—
101C22⋊C4×C41—21no—
102C22⋊C4×C41—21no—
103C22⋊C4×C41—21no—
104C22⋊C4×C41—21no—
105C22⋊C4×C41—21no—
106C22⋊C4×C41D411yescharacteristic
107C22⋊C4×C41D411yescharacteristic
108C42×C41—21no—
109C42×C41—21no—
110C42×C41C2311yescharacteristic
111C23×C41—21no—
112C23×C41C2×D411yescharacteristic
113C23×C41C2×D411yescharacteristic
114Q8×C41—21no—
115Q8×C41—21no—
116Q8×C41—21no—
117Q8×C41—21no—
118Q8×C41—21no—
119Q8×C41—42no—
120Q8×C41—81no—
121Q8×C41#4112yes—
122D4×C41—22no—
123D4×C41—21no—
124D4×C41—21no—
125D4×C41—42no—
126D4×C41—42no—
127C2×C4×C41—21no—
128C2×C4×C41—21no—
129C2×C4×C41—21no—
130C2×C4×C41—21no—
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—42no—
139C2×C4×C41—42no—
140C2×C4×C41—81no—
141C2×C4×C41—81no—
142C2×C4×C41C2×D411yescharacteristic
143C2×C4×C41C2×D411yescharacteristic
144C2×C4×C41C2×D411yescharacteristic
145C2×C4×C41C2×D411yescharacteristic
146C2×C4×C41C2411yescharacteristic
147C8×C41—21no—
148C8×C41—21no—
149C8×C41—21no—
150C8×C41—21no—
151C22×C41—21no—
152C22×C41—21no—
153C22×C41—21no—
154C22×C41—21no—
155C22×C41—21no—
156C22×C41—41no—
157C22×C41—41no—
158C22×C41—41no—
159C22×C41#13712yes—
160C22×C41C22×D411yescharacteristic
161C4×C41—21no—
162C4×C41—21no—
163C4×C41—22no—
164C4×C41—21no—
165C4×C41—21no—
166C4×C41—41no—
167C4×C41—41no—
168C4×C41—41no—
169C4×C41—41no—
170C4×C41—41no—
171C4×C41—41no—
172C4×C41C2×#4111yescharacteristic
173C4×C41H(5,𝔽2)11yescharacteristic
174#3316C4111yesmaximal, characteristic, direct product factor, Sylow
175C2×C41—22no—
176C2×C41—41no—
177C2×C41—81no—
178C2×C41#54611yescharacteristic
179C2×C41C2×#13711yescharacteristic
180C2×C41#57711yescharacteristic
181#554C2×C4111yescharacteristic, complemented
182#548C2×C4111yescharacteristic
183#489C2×C4111yescharacteristic, complemented
184#483C2×C4111yescharacteristic, complemented
185#481C2×C4111yescharacteristic, complemented
186#475C2×C4111yescharacteristic, complemented
187#470C2×C4111yescharacteristic, complemented
188#465C2×C4111yescharacteristic, complemented
189#464C2×C4111yescharacteristic, complemented
190#452C2×C4111yescharacteristic, complemented
191#451C2×C4111yescharacteristic, complemented
192#441C2×C4111yescharacteristic, complemented
193#435C2×C4111yescharacteristic, complemented
194#417C2×C4111yescharacteristic, complemented
195C2×#103C2×C4111yescharacteristic, complemented
196C41#331611yescharacteristic, direct product factor, Sylow
197C2×#41C22×C4111yescharacteristic
198C22×Q8C22×C4111yescharacteristic
199C2×Q16C22×C4111yescharacteristic
200C2×Q16C22×C4111yescharacteristic
201C2×SD16C22×C4111yescharacteristic
202C2×M16C22×C4111yescharacteristic
203C22×C8C22×C4111yescharacteristic
204C4⋊Q8C22×C4111yescharacteristic
205#125—21no—
206#124—21no—
207#124C22×C4111yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C22×C4111yescharacteristic
212C22⋊Q8C22×C4111yescharacteristic
213C22⋊Q8C22×C4111yescharacteristic
214#121—21no—
215#121C22×C4111yescharacteristic
216C4×Q8C22×C4111yescharacteristic
217C4×Q8C22×C4111yescharacteristic
218C4×D4—21no—
219C4×D4—21no—
220C4×D4C22×C4111yescharacteristic
221C2×C4⋊C4C22×C4111yescharacteristic
222C2×C4⋊C4C22×C4111yescharacteristic
223#106C22×C4111yescharacteristic
224#106C22×C4111yescharacteristic
225#106C22×C4111yescharacteristic
226C4⋊C8C22×C4111yescharacteristic
227#103C22×C4111yescharacteristic
228#103C22×C4111yescharacteristic
229#103C22×C4111yescharacteristic
230#103C22×C4111yescharacteristic
231#103C22×C4111yescharacteristic
232#103C22×C4111yescharacteristic
233#103C22×C4111yescharacteristic
234#102C22×C4111yescharacteristic
235#102C22×C4111yescharacteristic
236#102C22×C4111yescharacteristic
237C22⋊C8C22×C4111yescharacteristic
238C22⋊C8C22×C4111yescharacteristic
239#97C22×C4111yescharacteristic
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8C23×C4111yescharacteristic
247C2×Q8C23×C4111yescharacteristic
248C2×Q8C23×C4111yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4D4×C4111yescharacteristic
252C2×D4C23×C4111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4C23×C4111yescharacteristic
258C22×C4C23×C4111yescharacteristic
259Q16—22no—
260Q16—41no—
261SD16—41no—
262M16—41no—
263C2×C8—41no—
264C2×C8C23×C4111yescharacteristic
265C2×C8C23×C4111yescharacteristic
266C2×C8C23×C4111yescharacteristic
267C2×C8C23×C4111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4D4×C4111yescharacteristic
277C4⋊C4C23×C4111yescharacteristic
278C4⋊C4C23×C4111yescharacteristic
279C4⋊C4C23×C4111yescharacteristic
280C4⋊C4C23×C4111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4D4×C4111yescharacteristic
288C22⋊C4D4×C4111yescharacteristic
289C42—21no—
290C42—21no—
291C42C23×C4111yescharacteristic
292C23—21no—
293C23C2×D4×C4111yescharacteristic
294C23C2×D4×C4111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—81no—
302Q8#41×C4112yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×D4×C4111yescharacteristic
324C2×C4C2×D4×C4111yescharacteristic
325C2×C4C2×D4×C4111yescharacteristic
326C2×C4C2×D4×C4111yescharacteristic
327C2×C4C24×C4111yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#137×C4112yes—
341C22C22×D4×C4111yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4C2×#41×C4111yescharacteristic
354C4H(5,𝔽2)×C4111yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2C41×#54611yescharacteristic
359C2C2×#137×C4111yescharacteristic
360C2C41×#57711yescharacteristic
subgroupG/H
center, socleC22×C41C22×D4
commutator, Frattini, cosocleC2×C4C24×C41
prime radicalC41×#548C2
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×#554C2semidirect
3. C41×#489C2semidirect
4. C41×#483C2semidirect
5. C41×#481C2semidirect
6. C41×#475C2semidirect
7. C41×#470C2semidirect
8. C41×#465C2semidirect
9. C41×#464C2semidirect
10. C41×#452C2semidirect
11. C41×#451C2semidirect
12. C41×#441C2semidirect
13. C41×#435C2semidirect
14. C41×#417C2semidirect
15. C2×#103×C41C2semidirect
174. #3316C41direct (N × H)
181. #554C2×C41semidirect
183. #489C2×C41semidirect
184. #483C2×C41semidirect
185. #481C2×C41semidirect
186. #475C2×C41semidirect
187. #470C2×C41semidirect
188. #465C2×C41semidirect
189. #464C2×C41semidirect
190. #452C2×C41semidirect
191. #451C2×C41semidirect
192. #441C2×C41semidirect
193. #435C2×C41semidirect
194. #417C2×C41semidirect
195. C2×#103C2×C41semidirect
196. C41#3316direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#5542
C41×#5482
C41×#4892
C41×#4832
C41×#4812
C41×#4752
C41×#4702
C41×#4652
C41×#4642
C41×#4522
C41×#4512
C41×#4412
C41×#4352
C41×#4172
C2×#103×C412
#331641