Finite Group Databasebeta

← C41×#3225 #19107005

Subgroups — C41×#3225 #19107005

Order 5248.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#542C211yesmaximal, characteristic, complemented
2C41×#536C211yesmaximal, characteristic, complemented
3C41×#497C211yesmaximal, characteristic, complemented
4C41×#495C211yesmaximal, characteristic, complemented
5C41×#489C211yesmaximal, characteristic, complemented
6C41×#487C211yesmaximal, characteristic, complemented
7C41×#464C211yesmaximal, characteristic, complemented
8C41×#463C211yesmaximal, characteristic, complemented
9C41×#462C211yesmaximal, characteristic, complemented
10C41×#461C211yesmaximal, characteristic, complemented
11C41×#452C211yesmaximal, characteristic, complemented
12C41×#451C211yesmaximal, characteristic, complemented
13C41×#449C211yesmaximal, characteristic
14C41×#448C211yesmaximal, characteristic, complemented
15C41×#433C211yesmaximal, characteristic, complemented
16C2×#41×C41C2211yescharacteristic
17C22×Q8×C41C2211yescharacteristic
18C2×Q16×C41C2211yescharacteristic
19C2×Q16×C41C2211yescharacteristic
20C2×Q16×C41C2211yescharacteristic
21C2×SD16×C41C2211yescharacteristic
22C2×SD16×C41C2211yescharacteristic
23C2×SD16×C41C2211yescharacteristic
24C2×SD16×C41C2211yescharacteristic
25C2×D8×C41C2211yescharacteristic
26C4⋊Q8×C41C2211yescharacteristic
27C4⋊Q8×C41C2211yescharacteristic
28C4⋊Q8×C41C2211yescharacteristic
29#126×C41—21no—
30#124×C41—21no—
31#124×C41C2211yescharacteristic
32#124×C41C2211yescharacteristic
33#124×C41C2211yescharacteristic
34#123×C41—21no—
35#123×C41—21no—
36#123×C41—21no—
37C22⋊Q8×C41—21no—
38C22⋊Q8×C41—21no—
39C22⋊Q8×C41—21no—
40C22⋊Q8×C41C2211yescharacteristic
41#121×C41C2211yescharacteristic
42C4×Q8×C41C2211yescharacteristic
43C4×D4×C41C2211yescharacteristic
44#117×C41C2211yescharacteristic
45C4⋊C8×C41C2211yescharacteristic
46C4⋊C8×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
55C22⋊C8×C41C2211yescharacteristic
56C22⋊C8×C41C2211yescharacteristic
57#97×C41C2211yescharacteristic
58C4×C8×C41C2211yescharacteristic
59#41×C41—41no—
60#41×C41—41no—
61C2×Q8×C41—21no—
62C2×Q8×C41—21no—
63C2×Q8×C41—41no—
64C2×Q8×C41—41no—
65C2×Q8×C41C2311yescharacteristic
66C2×Q8×C41C2311yescharacteristic
67C2×Q8×C41C2311yescharacteristic
68C2×Q8×C41C2311yescharacteristic
69C2×D4×C41—21no—
70C2×D4×C41—21no—
71C2×D4×C41C2311yescharacteristic
72C2×D4×C41C2311yescharacteristic
73C22×C4×C41—21no—
74C22×C4×C41—21no—
75C22×C4×C41—21no—
76C22×C4×C41C2311yescharacteristic
77Q16×C41—41no—
78Q16×C41—41no—
79Q16×C41—41no—
80SD16×C41—41no—
81SD16×C41—41no—
82SD16×C41—41no—
83SD16×C41—41no—
84D8×C41—41no—
85C2×C8×C41C2311yescharacteristic
86C2×C8×C41C2311yescharacteristic
87C2×C8×C41C2311yescharacteristic
88C2×C8×C41C2311yescharacteristic
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×C41—21no—
96C4⋊C4×C41D411yescharacteristic
97C4⋊C4×C41D411yescharacteristic
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×C41—21no—
107C22⋊C4×C41—21no—
108C22⋊C4×C41—21no—
109C22⋊C4×C41D411yescharacteristic
110C22⋊C4×C41D411yescharacteristic
111C42×C41—21no—
112C42×C41C2311yescharacteristic
113C42×C41C2311yescharacteristic
114C23×C41—21no—
115C23×C41—21no—
116C23×C41C2×D411yescharacteristic
117Q8×C41—21no—
118Q8×C41—21no—
119Q8×C41—21no—
120Q8×C41—21no—
121Q8×C41—21no—
122Q8×C41—21no—
123Q8×C41—21no—
124Q8×C41—21no—
125Q8×C41—42no—
126Q8×C41—81no—
127D4×C41—21no—
128D4×C41—21no—
129D4×C41—21no—
130D4×C41—21no—
131D4×C41—42no—
132D4×C41—81no—
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—81no—
144C2×C4×C41C2×D411yescharacteristic
145C2×C4×C41C2×D411yescharacteristic
146C2×C4×C41C2×D411yescharacteristic
147C2×C4×C41C2×D411yescharacteristic
148C2×C4×C41C2×D411yescharacteristic
149C2×C4×C41C2411yescharacteristic
150C8×C41—21no—
151C8×C41—21no—
152C8×C41—21no—
153C8×C41—21no—
154C22×C41—21no—
155C22×C41—21no—
156C22×C41—21no—
157C22×C41—41no—
158C22×C41—41no—
159C22×C41—41no—
160C22×C41—41no—
161C22×C41—41no—
162C22×C41—41no—
163C22×C41C22×D411yescharacteristic
164C4×C41—21no—
165C4×C41—21no—
166C4×C41—21no—
167C4×C41—21no—
168C4×C41—21no—
169C4×C41—41no—
170C4×C41—41no—
171C4×C41—41no—
172C4×C41—41no—
173C4×C41—41no—
174C4×C41—41no—
175C4×C41H(5,𝔽2)11yescharacteristic
176C4×C41H(5,𝔽2)11yescharacteristic
177#3225C4111yesmaximal, characteristic, direct product factor, Sylow
178C2×C41—41no—
179C2×C41—81no—
180C2×C41—81no—
181C2×C41#53511yescharacteristic
182C2×C41#57711yescharacteristic
183C2×C41#57811yescharacteristic
184#542C2×C4111yescharacteristic, complemented
185#536C2×C4111yescharacteristic, complemented
186#497C2×C4111yescharacteristic, complemented
187#495C2×C4111yescharacteristic, complemented
188#489C2×C4111yescharacteristic, complemented
189#487C2×C4111yescharacteristic, complemented
190#464C2×C4111yescharacteristic, complemented
191#463C2×C4111yescharacteristic, complemented
192#462C2×C4111yescharacteristic, complemented
193#461C2×C4111yescharacteristic, complemented
194#452C2×C4111yescharacteristic, complemented
195#451C2×C4111yescharacteristic, complemented
196#449C2×C4111yescharacteristic
197#448C2×C4111yescharacteristic, complemented
198#433C2×C4111yescharacteristic, complemented
199C41#322511yescharacteristic, direct product factor, Sylow
200C2×#41C22×C4111yescharacteristic
201C22×Q8C22×C4111yescharacteristic
202C2×Q16C22×C4111yescharacteristic
203C2×Q16C22×C4111yescharacteristic
204C2×Q16C22×C4111yescharacteristic
205C2×SD16C22×C4111yescharacteristic
206C2×SD16C22×C4111yescharacteristic
207C2×SD16C22×C4111yescharacteristic
208C2×SD16C22×C4111yescharacteristic
209C2×D8C22×C4111yescharacteristic
210C4⋊Q8C22×C4111yescharacteristic
211C4⋊Q8C22×C4111yescharacteristic
212C4⋊Q8C22×C4111yescharacteristic
213#126—21no—
214#124—21no—
215#124C22×C4111yescharacteristic
216#124C22×C4111yescharacteristic
217#124C22×C4111yescharacteristic
218#123—21no—
219#123—21no—
220#123—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8C22×C4111yescharacteristic
225#121C22×C4111yescharacteristic
226C4×Q8C22×C4111yescharacteristic
227C4×D4C22×C4111yescharacteristic
228#117C22×C4111yescharacteristic
229C4⋊C8C22×C4111yescharacteristic
230C4⋊C8C22×C4111yescharacteristic
231#103C22×C4111yescharacteristic
232#103C22×C4111yescharacteristic
233#103C22×C4111yescharacteristic
234#103C22×C4111yescharacteristic
235#103C22×C4111yescharacteristic
236#103C22×C4111yescharacteristic
237#102C22×C4111yescharacteristic
238#102C22×C4111yescharacteristic
239C22⋊C8C22×C4111yescharacteristic
240C22⋊C8C22×C4111yescharacteristic
241#97C22×C4111yescharacteristic
242C4×C8C22×C4111yescharacteristic
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C23×C4111yescharacteristic
250C2×Q8C23×C4111yescharacteristic
251C2×Q8C23×C4111yescharacteristic
252C2×Q8C23×C4111yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C23×C4111yescharacteristic
256C2×D4C23×C4111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C23×C4111yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—41no—
264SD16—41no—
265SD16—41no—
266SD16—41no—
267SD16—41no—
268D8—41no—
269C2×C8C23×C4111yescharacteristic
270C2×C8C23×C4111yescharacteristic
271C2×C8C23×C4111yescharacteristic
272C2×C8C23×C4111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4D4×C4111yescharacteristic
281C4⋊C4D4×C4111yescharacteristic
282C4⋊C4C23×C4111yescharacteristic
283C4⋊C4C23×C4111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4D4×C4111yescharacteristic
294C22⋊C4D4×C4111yescharacteristic
295C42—21no—
296C42C23×C4111yescharacteristic
297C42C23×C4111yescharacteristic
298C23—21no—
299C23—21no—
300C23C2×D4×C4111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—81no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4C2×D4×C4111yescharacteristic
329C2×C4C2×D4×C4111yescharacteristic
330C2×C4C2×D4×C4111yescharacteristic
331C2×C4C2×D4×C4111yescharacteristic
332C2×C4C2×D4×C4111yescharacteristic
333C2×C4C24×C4111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C22×D4×C4111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4H(5,𝔽2)×C4111yescharacteristic
360C4H(5,𝔽2)×C4111yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2C41×#53511yescharacteristic
365C2C41×#57711yescharacteristic
366C2C41×#57811yescharacteristic
subgroupG/H
center, socleC22×C41C22×D4
commutator, Frattini, cosocleC2×C4C24×C41
prime radicalC41×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ #117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#542C2semidirect
2. C41×#536C2semidirect
3. C41×#497C2semidirect
4. C41×#495C2semidirect
5. C41×#489C2semidirect
6. C41×#487C2semidirect
7. C41×#464C2semidirect
8. C41×#463C2semidirect
9. C41×#462C2semidirect
10. C41×#461C2semidirect
11. C41×#452C2semidirect
12. C41×#451C2semidirect
14. C41×#448C2semidirect
15. C41×#433C2semidirect
177. #3225C41direct (N × H)
184. #542C2×C41semidirect
185. #536C2×C41semidirect
186. #497C2×C41semidirect
187. #495C2×C41semidirect
188. #489C2×C41semidirect
189. #487C2×C41semidirect
190. #464C2×C41semidirect
191. #463C2×C41semidirect
192. #462C2×C41semidirect
193. #461C2×C41semidirect
194. #452C2×C41semidirect
195. #451C2×C41semidirect
197. #448C2×C41semidirect
198. #433C2×C41semidirect
199. C41#3225direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#5422
C41×#5362
C41×#4972
C41×#4952
C41×#4892
C41×#4872
C41×#4642
C41×#4632
C41×#4622
C41×#4612
C41×#4522
C41×#4512
C41×#4492
C41×#4482
C41×#4332
#322541