Finite Group Databasebeta

← C41×#13012 #23789213

Subgroups — C41×#13012 #23789213

Order 10496.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D16×C41C211yesmaximal, characteristic
2C2×C4×D8×C41C211yesmaximal, characteristic, complemented
3C2×C41×#357C211yesmaximal, characteristic, complemented
4C2×C41×#357C211yesmaximal, characteristic, complemented
5C41×#1970C211yesmaximal, characteristic, complemented
6C41×#1380C211yesmaximal, characteristic, complemented
7C41×#1374C211yesmaximal, characteristic, complemented
8C22×D8×C41C2211yescharacteristic
9C22×D8×C41C2211yescharacteristic
10C2×C4×D4×C41—21no—
11C2×D16×C41—22no—
12C2×D16×C41—22no—
13C2×D16×C41C414yescomplemented
14C22×C16×C41C2211yescharacteristic
15C22×C16×C41C2211yescharacteristic
16C4×D8×C41—22no—
17C4×D8×C41—22no—
18C2×#107×C41C2211yescharacteristic
19C2×#107×C41C2211yescharacteristic
20C2×#102×C41—21no—
21C2×#102×C41—21no—
22C2×C4×C8×C41C2211yescharacteristic
23C41×#390—21no—
24C41×#357—22no—
25C41×#357—22no—
26C22×D4×C41—21no—
27C22×D4×C41—21no—
28C23×C4×C41—41no—
29C2×D8×C41—21no—
30C2×D8×C41—21no—
31C2×D8×C41—21no—
32C2×D8×C41—21no—
33C2×D8×C41—21no—
34C2×D8×C41—21no—
35C2×D8×C41—21no—
36C2×D8×C41—21no—
37C2×D8×C41C2×C412yes—
38C2×D8×C41C2×C412yescomplemented
39C2×D8×C41D412yes—
40C2×D8×C41D412yes—
41C22×C8×C41D411yescharacteristic
42C22×C8×C41C2311yescharacteristic
43C4×D4×C41—24no—
44C4×D4×C41—42no—
45C2×C4⋊C4×C41—21no—
46C2×C4⋊C4×C41—21no—
47C2×C22⋊C4×C41—41no—
48C2×C22⋊C4×C41—41no—
49C2×C22⋊C4×C41—41no—
50C2×C42×C41D411yescharacteristic
51D16×C41—28no—
52C2×C16×C41—21no—
53C2×C16×C41—21no—
54C2×C16×C41—21no—
55C2×C16×C41—21no—
56C2×C16×C41—21no—
57C2×C16×C41C2×C412yescomplemented
58#107×C41—21no—
59#107×C41—21no—
60#107×C41—21no—
61#107×C41D412yes—
62#102×C41—24no—
63#102×C41—42no—
64C4×C8×C41—21no—
65C4×C8×C41—21no—
66C24×C41—41no—
67C24×C41—41no—
68C2×D4×C41—22no—
69C2×D4×C41—22no—
70C2×D4×C41—22no—
71C2×D4×C41—22no—
72C2×D4×C41—41no—
73C2×D4×C41—41no—
74C2×D4×C41—41no—
75C2×D4×C41—41no—
76C2×D4×C41—41no—
77C2×D4×C41—41no—
78C2×D4×C41—41no—
79C2×D4×C41—41no—
80C22×C4×C41—44no—
81C22×C4×C41—41no—
82C22×C4×C41—41no—
83C22×C4×C41—82no—
84C22×C4×C41—82no—
85C22×C4×C41D811yescharacteristic
86C22×C4×C41D811yescharacteristic
87C22×C4×C41C2×D411yescharacteristic
88D8×C41—22no—
89D8×C41—22no—
90D8×C41—22no—
91D8×C41—22no—
92D8×C41—22no—
93D8×C41—41no—
94D8×C41—41no—
95D8×C41C22⋊C414yescomplemented
96C2×C8×C41—21no—
97C2×C8×C41—21no—
98C2×C8×C41—21no—
99C2×C8×C41C22×C411yescharacteristic
100C2×C8×C41C2×D411yescharacteristic
101C2×C8×C41C2×D411yescharacteristic
102C2×C8×C41C2×D411yescharacteristic
103C2×C8×C41#4111yescharacteristic
104C2×C8×C41#4111yescharacteristic
105C4⋊C4×C41—22no—
106C4⋊C4×C41—41no—
107C4⋊C4×C41—41no—
108C4⋊C4×C41—41no—
109C22⋊C4×C41—44no—
110C22⋊C4×C41—82no—
111C22⋊C4×C41—82no—
112C42×C41—21no—
113C42×C41—21no—
114C16×C41—22no—
115C16×C41—41no—
116C23×C41—42no—
117C23×C41—42no—
118C23×C41—42no—
119C23×C41—42no—
120C23×C41—81no—
121C23×C41—81no—
122C23×C41—81no—
123C23×C41—81no—
124C23×C41—81no—
125C23×C41—81no—
126C23×C41—81no—
127C23×C41—81no—
128C23×C41—81no—
129C23×C41—81no—
130C23×C41C2×D811yescharacteristic
131D4×C41—24no—
132D4×C41—42no—
133D4×C41—42no—
134D4×C41—42no—
135D4×C41—42no—
136D4×C41—42no—
137D4×C41—81no—
138D4×C41—81no—
139C2×C4×C41—21no—
140C2×C4×C41—21no—
141C2×C4×C41—21no—
142C2×C4×C41—21no—
143C2×C4×C41—21no—
144C2×C4×C41—42no—
145C2×C4×C41—88no—
146C2×C4×C41—81no—
147C2×C4×C41—81no—
148C2×C4×C41—81no—
149C2×C4×C41—81no—
150C2×C4×C41—81no—
151C2×C4×C41D1612yescomplemented
152C2×C4×C41C4×D411yescharacteristic
153C2×C4×C41#12011yescharacteristic
154C2×C4×C41#12111yescharacteristic
155C2×C4×C41#13511yescharacteristic
156C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
158C8×C41—41no—
159C8×C41C2×C22⋊C411yescharacteristic
160C8×C41C4×D411yescharacteristic
161C8×C41#12111yescharacteristic
162C8×C41#12311yescharacteristic
163#13012C4111yesmaximal, characteristic, direct product factor, Sylow
164C22×C41—44no—
165C22×C41—82no—
166C22×C41—82no—
167C22×C41—82no—
168C22×C41—82no—
169C22×C41—82no—
170C22×C41—82no—
171C22×C41—82no—
172C22×C41—82no—
173C22×C41—82no—
174C22×C41—161no—
175C22×C41—161no—
176C22×C41—161no—
177C22×C41—161no—
178C22×C41C4×D811yescharacteristic
179C22×C41#44711yescharacteristic
180C22×C41#45911yescharacteristic
181C22×C41C2×D1611yescharacteristic
182C22×C41#50811yescharacteristic
183C22×C41#50911yescharacteristic
184C22×C41#50911yescharacteristic
185C4×C41—22no—
186C4×C41—41no—
187C4×C41—82no—
188C4×C41—161no—
189C4×C41#38611yescharacteristic
190C4×C41#44211yescharacteristic
191C4×C41#44911yescharacteristic
192C4×C41#46311yescharacteristic
193C22×D16C2×C4111yescharacteristic
194C2×C4×D8C2×C4111yescharacteristic, complemented
195C2×#357C2×C4111yescharacteristic, complemented
196C2×#357C2×C4111yescharacteristic, complemented
197#1970C2×C4111yescharacteristic, complemented
198#1380C2×C4111yescharacteristic, complemented
199#1374C2×C4111yescharacteristic, complemented
200C2×C41—84no—
201C2×C41—162no—
202C2×C41#187911yescharacteristic
203C2×C41C4×D1611yescharacteristic
204C2×C41#217711yescharacteristic
205C2×C41#218411yescharacteristic
206C2×C41#218611yescharacteristic
207C2×C41#220611yescharacteristic
208C2×C41#221011yescharacteristic
209C22×D8C22×C4111yescharacteristic
210C22×D8C22×C4111yescharacteristic
211C2×C4×D4—21no—
212C2×D16—22no—
213C2×D16—22no—
214C2×D16C4×C4114yescomplemented
215C22×C16C22×C4111yescharacteristic
216C22×C16C22×C4111yescharacteristic
217C4×D8—22no—
218C4×D8—22no—
219C2×#107C22×C4111yescharacteristic
220C2×#107C22×C4111yescharacteristic
221C2×#102—21no—
222C2×#102—21no—
223C2×C4×C8C22×C4111yescharacteristic
224#390—21no—
225#357—22no—
226#357—22no—
227C41#1301211yescharacteristic, direct product factor, Sylow
228C22×D4—21no—
229C22×D4—21no—
230C23×C4—41no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8C2×C4×C4112yes—
240C2×D8C2×C4×C4112yescomplemented
241C2×D8D4×C4112yes—
242C2×D8D4×C4112yes—
243C22×C8D4×C4111yescharacteristic
244C22×C8C23×C4111yescharacteristic
245C4×D4—24no—
246C4×D4—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—41no—
252C2×C42D4×C4111yescharacteristic
253D16—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16C2×C4×C4112yescomplemented
260#107—21no—
261#107—21no—
262#107—21no—
263#107D4×C4112yes—
264#102—24no—
265#102—42no—
266C4×C8—21no—
267C4×C8—21no—
268C24—41no—
269C24—41no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—44no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4D8×C4111yescharacteristic
288C22×C4D8×C4111yescharacteristic
289C22×C4C2×D4×C4111yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297D8C22⋊C4×C4114yescomplemented
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8C22×C4×C4111yescharacteristic
302C2×C8C2×D4×C4111yescharacteristic
303C2×C8C2×D4×C4111yescharacteristic
304C2×C8C2×D4×C4111yescharacteristic
305C2×C8#41×C4111yescharacteristic
306C2×C8#41×C4111yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—44no—
312C22⋊C4—82no—
313C22⋊C4—82no—
314C42—21no—
315C42—21no—
316C16—22no—
317C16—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23C2×D8×C4111yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—88no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4D16×C4112yescomplemented
354C2×C4C4×D4×C4111yescharacteristic
355C2×C4#120×C4111yescharacteristic
356C2×C4#121×C4111yescharacteristic
357C2×C4#135×C4111yescharacteristic
358C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
359C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
360C8—41no—
361C8C2×C22⋊C4×C4111yescharacteristic
362C8C4×D4×C4111yescharacteristic
363C8#121×C4111yescharacteristic
364C8#123×C4111yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22C4×D8×C4111yescharacteristic
380C22C41×#44711yescharacteristic
381C22C41×#45911yescharacteristic
382C22C2×D16×C4111yescharacteristic
383C22C41×#50811yescharacteristic
384C22C41×#50911yescharacteristic
385C22C41×#50911yescharacteristic
386C4—22no—
387C4—41no—
388C4—82no—
389C4—161no—
390C4C41×#38611yescharacteristic
391C4C41×#44211yescharacteristic
392C4C41×#44911yescharacteristic
393C4C41×#46311yescharacteristic
394C2—84no—
395C2—162no—
396C2C41×#187911yescharacteristic
397C2C4×D16×C4111yescharacteristic
398C2C41×#217711yescharacteristic
399C2C41×#218411yescharacteristic
400C2C41×#218611yescharacteristic
401C2C41×#220611yescharacteristic
402C2C41×#221011yescharacteristic
subgroupG/H
center, socleC23×C41C2×D8
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
prime radicalC22×D16×C41C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ C2×C4×C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C41C2semidirect
3. C2×C41×#357C2semidirect
4. C2×C41×#357C2semidirect
5. C41×#1970C2semidirect
6. C41×#1380C2semidirect
7. C41×#1374C2semidirect
13. C2×D16×C41C4semidirect
38. C2×D8×C41C2×C4semidirect
57. C2×C16×C41C2×C4semidirect
95. D8×C41C22⋊C4semidirect
151. C2×C4×C41D16semidirect
163. #13012C41direct (N × H)
194. C2×C4×D8C2×C41semidirect
195. C2×#357C2×C41semidirect
196. C2×#357C2×C41semidirect
197. #1970C2×C41semidirect
198. #1380C2×C41semidirect
199. #1374C2×C41semidirect
214. C2×D16C4×C41semidirect
227. C41#13012direct (N × H)
240. C2×D8C2×C4×C41semidirect
259. C2×C16C2×C4×C41semidirect
297. D8C22⋊C4×C41semidirect
353. C2×C4D16×C41semidirect

Maximal subgroups

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

subgroupindex
C22×D16×C412
C2×C4×D8×C412
C2×C41×#3572
C41×#19702
C41×#13802
C41×#13742
#1301241