Finite Group Databasebeta

← C41×#9245 #23785446

Subgroups — C41×#9245 #23785446

Order 10496.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#478C211yesmaximal, characteristic
2C41×#2974C211yesmaximal, characteristic
3C41×#1528C211yesmaximal, characteristic, complemented
4C41×#1490C211yesmaximal, characteristic
5C41×#1470C211yesmaximal, characteristic, complemented
6C41×#1290C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C2×#125×C41C2211yescharacteristic
9C2×C4×D4×C41C2211yescharacteristic
10C41×#478—21no—
11C41×#478—21no—
12C41×#478—21no—
13C41×#478—21no—
14C41×#436—21no—
15C41×#435—22no—
16C8×D4×C41—21no—
17C41×#432C2211yescharacteristic
18C41×#432C2211yescharacteristic
19C41×#431C2211yescharacteristic
20C2×#107×C41C411yescharacteristic
21C2×#106×C41C411yescharacteristic
22C2×C4⋊C8×C41C2211yescharacteristic
23C2×#102×C41C411yescharacteristic
24C2×#102×C41C411yescharacteristic
25C41×#407—21no—
26C2×C22⋊C8×C41—21no—
27C4×M16×C41C2211yescharacteristic
28C41×#330—22no—
29C41×D4⋊C8—21no—
30C41×D4⋊C8—21no—
31C41×#324—21no—
32C41×#324—21no—
33C22×D4×C41C2×C411yescharacteristic
34C23×C4×C41—21no—
35C2×M16×C41—22no—
36C2×M16×C41—21no—
37C22×C8×C41—22no—
38C22×C8×C41C2×C411yescharacteristic
39C22×C8×C41C2×C411yescharacteristic
40#125×C41—21no—
41#125×C41—21no—
42#125×C41—21no—
43#125×C41—21no—
44C4×D4×C41—21no—
45C4×D4×C41—21no—
46C4×D4×C41D411yescharacteristic
47C4×D4×C41D411yescharacteristic
48C4×D4×C41D411yescharacteristic
49C4×D4×C41D411yescharacteristic
50C2×C4⋊C4×C41—21no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41C2×C411yescharacteristic
53C2×C4⋊C4×C41C2×C411yescharacteristic
54C2×C4⋊C4×C41C2×C411yescharacteristic
55C2×C22⋊C4×C41—21no—
56C2×C42×C41C2311yescharacteristic
57#107×C41—21no—
58#107×C41—21no—
59#106×C41—21no—
60#106×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41—21no—
63C4⋊C8×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66#102×C41—21no—
67#102×C41—21no—
68#102×C41—21no—
69#102×C41—21no—
70C22⋊C8×C41—22no—
71C22⋊C8×C41—22no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41D411yescharacteristic
75C22⋊C8×C41D411yescharacteristic
76#97×C41—21no—
77#97×C41—21no—
78#97×C41D412yes—
79C4×C8×C41—21no—
80C4×C8×C41—21no—
81C24×C41—21no—
82C2×D4×C41—22no—
83C2×D4×C41—21no—
84C2×D4×C41—41no—
85C2×D4×C41C22⋊C411yescharacteristic
86C2×D4×C41C22⋊C411yescharacteristic
87C22×C4×C41—21no—
88C22×C4×C41—21no—
89C22×C4×C41—21no—
90C22×C4×C41—21no—
91C22×C4×C41—21no—
92C22×C4×C41—21no—
93C22×C4×C41—21no—
94C22×C4×C41—82no—
95C22×C4×C41C22×C411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97C22×C4×C41#4111yescharacteristic
98M16×C41—22no—
99M16×C41—41no—
100M16×C41—82no—
101C2×C8×C41—21no—
102C2×C8×C41—21no—
103C2×C8×C41—21no—
104C2×C8×C41—21no—
105C2×C8×C41—22no—
106C2×C8×C41—41no—
107C2×C8×C41—41no—
108C2×C8×C41—41no—
109C2×C8×C41—41no—
110C2×C8×C41—82no—
111C4⋊C4×C41—21no—
112C4⋊C4×C41—21no—
113C4⋊C4×C41—21no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—41no—
117C4⋊C4×C41—41no—
118C4⋊C4×C41—41no—
119C4⋊C4×C41—41no—
120C4⋊C4×C41C22⋊C411yescharacteristic
121C4⋊C4×C41C22⋊C411yescharacteristic
122C22⋊C4×C41—21no—
123C22⋊C4×C41—21no—
124C22⋊C4×C41—21no—
125C22⋊C4×C41—21no—
126C42×C41C2×D411yescharacteristic
127C42×C41C2×D411yescharacteristic
128C42×C41C2×D411yescharacteristic
129C42×C41#4111yescharacteristic
130C23×C41—21no—
131C23×C41—21no—
132C23×C41—42no—
133C23×C41—41no—
134C23×C41—41no—
135C23×C41—81no—
136C23×C41C4×D411yescharacteristic
137D4×C41—21no—
138D4×C41—21no—
139D4×C41—21no—
140D4×C41—42no—
141D4×C41#10112yes—
142C2×C4×C41—21no—
143C2×C4×C41—21no—
144C2×C4×C41—21no—
145C2×C4×C41—21no—
146C2×C4×C41—21no—
147C2×C4×C41—21no—
148C2×C4×C41—41no—
149C2×C4×C41—42no—
150C2×C4×C41—42no—
151C2×C4×C41—41no—
152C2×C4×C41—41no—
153C2×C4×C41—41no—
154C2×C4×C41—41no—
155C2×C4×C41—81no—
156C2×C4×C41—81no—
157C2×C4×C41—81no—
158C2×C4×C41—81no—
159C2×C4×C41C2×C22⋊C411yescharacteristic
160C2×C4×C41C4×D411yescharacteristic
161C2×C4×C41#12011yescharacteristic
162C2×C4×C41#12111yescharacteristic
163C2×C4×C41#12111yescharacteristic
164C2×C4×C41#12311yescharacteristic
165C8×C41—41no—
166C8×C41—42no—
167C8×C41—41no—
168C8×C41—42no—
169C8×C41—41no—
170C8×C41—41no—
171C8×C41—81no—
172#9245C4111yesmaximal, characteristic, direct product factor, Sylow
173C22×C41—21no—
174C22×C41—21no—
175C22×C41—22no—
176C22×C41—41no—
177C22×C41—41no—
178C22×C41—41no—
179C22×C41—41no—
180C22×C41—41no—
181C22×C41—82no—
182C22×C41—82no—
183C22×C41#38611yescharacteristic
184C22×C41#44311yescharacteristic
185C22×C41#44411yescharacteristic
186C4×C41—21no—
187C4×C41—21no—
188C4×C41—21no—
189C4×C41—21no—
190C4×C41—21no—
191C4×C41—41no—
192C4×C41—41no—
193C4×C41—81no—
194C4×C41—81no—
195C4×C41C2×#10111yescharacteristic
196C4×C41#41311yescharacteristic
197C2×#478C2×C4111yescharacteristic
198#2974C2×C4111yescharacteristic
199#1528C2×C4111yescharacteristic, complemented
200#1490C2×C4111yescharacteristic
201#1470C2×C4111yescharacteristic, complemented
202#1290C2×C4111yescharacteristic, complemented
203#1283C2×C4111yescharacteristic, complemented
204C2×C41—21no—
205C2×C41—21no—
206C2×C41—42no—
207C2×C41—81no—
208C2×C41#187611yescharacteristic
209C2×C41#190111yescharacteristic
210C2×C41#190411yescharacteristic
211C2×#125C22×C4111yescharacteristic
212C2×C4×D4C22×C4111yescharacteristic
213#478—21no—
214#478—21no—
215#478—21no—
216#478—21no—
217#436—21no—
218#435—22no—
219C8×D4—21no—
220#432C22×C4111yescharacteristic
221#432C22×C4111yescharacteristic
222#431C22×C4111yescharacteristic
223C2×#107C4×C4111yescharacteristic
224C2×#106C4×C4111yescharacteristic
225C2×C4⋊C8C22×C4111yescharacteristic
226C2×#102C4×C4111yescharacteristic
227C2×#102C4×C4111yescharacteristic
228#407—21no—
229C2×C22⋊C8—21no—
230C4×M16C22×C4111yescharacteristic
231#330—22no—
232D4⋊C8—21no—
233D4⋊C8—21no—
234#324—21no—
235#324—21no—
236C41#924511yescharacteristic, direct product factor, Sylow
237C22×D4C2×C4×C4111yescharacteristic
238C23×C4—21no—
239C2×M16—22no—
240C2×M16—21no—
241C22×C8—22no—
242C22×C8C2×C4×C4111yescharacteristic
243C22×C8C2×C4×C4111yescharacteristic
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4D4×C4111yescharacteristic
251C4×D4D4×C4111yescharacteristic
252C4×D4D4×C4111yescharacteristic
253C4×D4D4×C4111yescharacteristic
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C2×C4×C4111yescharacteristic
257C2×C4⋊C4C2×C4×C4111yescharacteristic
258C2×C4⋊C4C2×C4×C4111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C4111yescharacteristic
261#107—21no—
262#107—21no—
263#106—21no—
264#106—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270#102—21no—
271#102—21no—
272#102—21no—
273#102—21no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8D4×C4111yescharacteristic
279C22⋊C8D4×C4111yescharacteristic
280#97—21no—
281#97—21no—
282#97D4×C4112yes—
283C4×C8—21no—
284C4×C8—21no—
285C24—21no—
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C4111yescharacteristic
290C2×D4C22⋊C4×C4111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—82no—
299C22×C4C22×C4×C4111yescharacteristic
300C22×C4C2×D4×C4111yescharacteristic
301C22×C4#41×C4111yescharacteristic
302M16—22no—
303M16—41no—
304M16—82no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—82no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C22⋊C4×C4111yescharacteristic
325C4⋊C4C22⋊C4×C4111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42C2×D4×C4111yescharacteristic
331C42C2×D4×C4111yescharacteristic
332C42C2×D4×C4111yescharacteristic
333C42#41×C4111yescharacteristic
334C23—21no—
335C23—21no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—81no—
340C23C4×D4×C4111yescharacteristic
341D4—21no—
342D4—21no—
343D4—21no—
344D4—42no—
345D4#101×C4112yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C2×C22⋊C4×C4111yescharacteristic
364C2×C4C4×D4×C4111yescharacteristic
365C2×C4#120×C4111yescharacteristic
366C2×C4#121×C4111yescharacteristic
367C2×C4#121×C4111yescharacteristic
368C2×C4#123×C4111yescharacteristic
369C8—41no—
370C8—42no—
371C8—41no—
372C8—42no—
373C8—41no—
374C8—41no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—82no—
385C22—82no—
386C22C41×#38611yescharacteristic
387C22C41×#44311yescharacteristic
388C22C41×#44411yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4C2×#101×C4111yescharacteristic
399C4C41×#41311yescharacteristic
400C2—21no—
401C2—21no—
402C2—42no—
403C2—81no—
404C2C41×#187611yescharacteristic
405C2C41×#190111yescharacteristic
406C2C41×#190411yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1528C2semidirect
5. C41×#1470C2semidirect
6. C41×#1290C2semidirect
7. C41×#1283C2semidirect
172. #9245C41direct (N × H)
199. #1528C2×C41semidirect
201. #1470C2×C41semidirect
202. #1290C2×C41semidirect
203. #1283C2×C41semidirect
236. C41#9245direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4782
C41×#29742
C41×#15282
C41×#14902
C41×#14702
C41×#12902
C41×#12832
#924541