Finite Group Databasebeta

← C41×#9716 #23785917

Subgroups — C41×#9716 #23785917

Order 10496.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2850C211yesmaximal, characteristic
2C41×#1797C211yesmaximal, characteristic, complemented
3C2×C41×#328C212yesmaximal, complemented
4C2×C41×#327C212yesmaximal
5C41×#1434C211yesmaximal, characteristic, complemented
6C2×#124×C41C411yescharacteristic, complemented
7C2×C22⋊Q8×C41C2211yescharacteristic
8C2×#121×C41C2211yescharacteristic
9C22×C42×C41C2211yescharacteristic
10C2×C4⋊C8×C41—21no—
11C2×C22⋊C8×C41C2212yes—
12C41×#391C411yescharacteristic, complemented
13C41×#390C411yescharacteristic, complemented
14C41×#388—21no—
15C41×#388—21no—
16C41×#386—21no—
17C41×#386—21no—
18C41×#382C411yescharacteristic, complemented
19C2×#95×C41—21no—
20C2×#95×C41—21no—
21C2×#95×C41C2212yes—
22C41×#336—21no—
23C41×#328—24no—
24C41×#327—24no—
25C22×Q8×C41C2×C411yescharacteristic
26C22×D4×C41—21no—
27C22×D4×C41C2×C411yescharacteristic
28C23×C4×C41—22no—
29C23×C4×C41D411yescharacteristic
30C23×C4×C41D411yescharacteristic
31C23×C4×C41C2311yescharacteristic
32C22×C8×C41—22no—
33#124×C41—42no—
34C22⋊Q8×C41—22no—
35C22⋊Q8×C41—22no—
36#121×C41—22no—
37#121×C41—22no—
38C2×C4⋊C4×C41—21no—
39C2×C4⋊C4×C41C2×C411yescharacteristic
40C2×C4⋊C4×C41C2×C411yescharacteristic
41C2×C22⋊C4×C41—21no—
42C2×C22⋊C4×C41—21no—
43C2×C22⋊C4×C41—21no—
44C2×C22⋊C4×C41—21no—
45C2×C22⋊C4×C41—21no—
46C2×C22⋊C4×C41—21no—
47C2×C42×C41—42no—
48C2×C42×C41C2×C411yescharacteristic
49C2×C42×C41C2×C411yescharacteristic
50C2×C42×C41D411yescharacteristic
51C2×C42×C41D411yescharacteristic
52C4⋊C8×C41—42no—
53C22⋊C8×C41—22no—
54C22⋊C8×C41—22no—
55#95×C41—21no—
56#95×C41—21no—
57#95×C41—21no—
58#95×C41—21no—
59#95×C41—22no—
60#95×C41—42no—
61#95×C41—42no—
62#95×C41D414yes—
63C24×C41—21no—
64C24×C41C2×D411yescharacteristic
65C2×Q8×C41—22no—
66C2×Q8×C41—41no—
67C2×Q8×C41—41no—
68C2×D4×C41—22no—
69C2×D4×C41—41no—
70C2×D4×C41—41no—
71C2×D4×C41—42no—
72C2×D4×C41—42no—
73C2×D4×C41—41no—
74C2×D4×C41—41no—
75C22×C4×C41—22no—
76C22×C4×C41—21no—
77C22×C4×C41—21no—
78C22×C4×C41—22no—
79C22×C4×C41—21no—
80C22×C4×C41—21no—
81C22×C4×C41—21no—
82C22×C4×C41—24no—
83C22×C4×C41—41no—
84C22×C4×C41—41no—
85C22×C4×C41—41no—
86C22×C4×C41—41no—
87C22×C4×C41—41no—
88C22×C4×C41—42no—
89C22×C4×C41—42no—
90C22×C4×C41—42no—
91C22×C4×C41—42no—
92C22×C4×C41—42no—
93C22×C4×C41—42no—
94C22×C4×C41C22⋊C411yescharacteristic
95C22×C4×C41C22⋊C411yescharacteristic
96C22×C4×C41C22⋊C411yescharacteristic
97C22×C4×C41C22⋊C411yescharacteristic
98C22×C4×C41C22×C411yescharacteristic
99C22×C4×C41C2×D411yescharacteristic
100C22×C4×C41C2×D412yes—
101C22×C4×C41#4112yes—
102C2×C8×C41—42no—
103C2×C8×C41—42no—
104C2×C8×C41—42no—
105C4⋊C4×C41—22no—
106C4⋊C4×C41—22no—
107C4⋊C4×C41—41no—
108C4⋊C4×C41—41no—
109C22⋊C4×C41—42no—
110C22⋊C4×C41—42no—
111C22⋊C4×C41—42no—
112C22⋊C4×C41—42no—
113C22⋊C4×C41—42no—
114C22⋊C4×C41—41no—
115C22⋊C4×C41—41no—
116C42×C41—22no—
117C42×C41—22no—
118C42×C41—41no—
119C42×C41—41no—
120C23×C41—21no—
121C23×C41—21no—
122C23×C41—21no—
123C23×C41—21no—
124C23×C41—41no—
125C23×C41—41no—
126C23×C41—41no—
127C23×C41—41no—
128C23×C41—41no—
129C23×C41—41no—
130C23×C41—41no—
131C23×C41C2×C22⋊C411yescharacteristic
132C23×C41#12112yes—
133C23×C41#13512yes—
134C23×C41AGL(1,ℤ/8)11yescharacteristic
135C23×C41#13711yescharacteristic
136Q8×C41—82no—
137D4×C41—82no—
138D4×C41—82no—
139D4×C41—82no—
140C2×C4×C41—21no—
141C2×C4×C41—21no—
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—21no—
149C2×C4×C41—21no—
150C2×C4×C41—21no—
151C2×C4×C41—21no—
152C2×C4×C41—21no—
153C2×C4×C41—21no—
154C2×C4×C41—21no—
155C2×C4×C41—42no—
156C2×C4×C41—42no—
157C2×C4×C41—44no—
158C2×C4×C41—42no—
159C2×C4×C41—42no—
160C2×C4×C41—44no—
161C2×C4×C41—44no—
162C2×C4×C41—41no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—41no—
168C2×C4×C41—41no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—44no—
172C2×C4×C41—82no—
173C2×C4×C41—82no—
174C2×C4×C41—82no—
175C2×C4×C41—82no—
176C2×C4×C41#9912yes—
177C2×C4×C41C4×D412yes—
178C2×C4×C41#12411yescharacteristic
179C2×C4×C41#12711yescharacteristic
180C8×C41—82no—
181#9716C4111yesmaximal, characteristic, direct product factor, Sylow
182C22×C41—22no—
183C22×C41—22no—
184C22×C41—21no—
185C22×C41—21no—
186C22×C41—21no—
187C22×C41—21no—
188C22×C41—22no—
189C22×C41—22no—
190C22×C41—81no—
191C22×C41—81no—
192C22×C41—81no—
193C22×C41—81no—
194C22×C41—81no—
195C22×C41—81no—
196C22×C41—81no—
197C22×C41#39011yescharacteristic
198C22×C41C2×#9911yescharacteristic
199C22×C41#41011yescharacteristic
200C22×C41#41611yescharacteristic
201C22×C41#41711yescharacteristic
202C22×C41#42111yescharacteristic
203C22×C41#42111yescharacteristic
204C22×C41#46312yes—
205C22×C41#46412yes—
206C4×C41—21no—
207C4×C41—22no—
208C4×C41—21no—
209C4×C41—22no—
210C4×C41—41no—
211C4×C41—41no—
212C4×C41—41no—
213C4×C41—84no—
214C4×C41—81no—
215C4×C41—81no—
216C4×C41—81no—
217#2850C2×C4111yescharacteristic
218#1797C2×C4111yescharacteristic, complemented
219C2×#328C2×C4112yescomplemented
220C2×#327C2×C4112yes—
221#1434C2×C4111yescharacteristic, complemented
222C2×C41—22no—
223C2×C41—22no—
224C2×C41—161no—
225C2×C41#151211yescharacteristic
226C2×C41#151311yescharacteristic
227C2×C41#151611yescharacteristic
228C2×C41#152111yescharacteristic
229C2×C41#196311yescharacteristic
230C2×C41#196411yescharacteristic
231C2×C41#198311yescharacteristic
232C2×#124C4×C4111yescharacteristic, complemented
233C2×C22⋊Q8C22×C4111yescharacteristic
234C2×#121C22×C4111yescharacteristic
235C22×C42C22×C4111yescharacteristic
236C2×C4⋊C8—21no—
237C2×C22⋊C8C22×C4112yes—
238#391C4×C4111yescharacteristic, complemented
239#390C4×C4111yescharacteristic, complemented
240#388—21no—
241#388—21no—
242#386—21no—
243#386—21no—
244#382C4×C4111yescharacteristic, complemented
245C2×#95—21no—
246C2×#95—21no—
247C2×#95C22×C4112yes—
248#336—21no—
249#328—24no—
250#327—24no—
251C41#971611yescharacteristic, direct product factor, Sylow
252C22×Q8C2×C4×C4111yescharacteristic
253C22×D4—21no—
254C22×D4C2×C4×C4111yescharacteristic
255C23×C4—22no—
256C23×C4D4×C4111yescharacteristic
257C23×C4D4×C4111yescharacteristic
258C23×C4C23×C4111yescharacteristic
259C22×C8—22no—
260#124—42no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263#121—22no—
264#121—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C4111yescharacteristic
267C2×C4⋊C4C2×C4×C4111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C42—42no—
275C2×C42C2×C4×C4111yescharacteristic
276C2×C42C2×C4×C4111yescharacteristic
277C2×C42D4×C4111yescharacteristic
278C2×C42D4×C4111yescharacteristic
279C4⋊C8—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—42no—
288#95—42no—
289#95D4×C4114yes—
290C24—21no—
291C24C2×D4×C4111yescharacteristic
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4C22⋊C4×C4111yescharacteristic
322C22×C4C22⋊C4×C4111yescharacteristic
323C22×C4C22⋊C4×C4111yescharacteristic
324C22×C4C22⋊C4×C4111yescharacteristic
325C22×C4C22×C4×C4111yescharacteristic
326C22×C4C2×D4×C4111yescharacteristic
327C22×C4C2×D4×C4112yes—
328C22×C4#41×C4112yes—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C2×C22⋊C4×C4111yescharacteristic
359C23#121×C4112yes—
360C23#135×C4112yes—
361C23AGL(1,ℤ/8)×C4111yescharacteristic
362C23#137×C4111yescharacteristic
363Q8—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—44no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#99×C4112yes—
404C2×C4C4×D4×C4112yes—
405C2×C4#124×C4111yescharacteristic
406C2×C4#127×C4111yescharacteristic
407C8—82no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C41×#39011yescharacteristic
424C22C2×#99×C4111yescharacteristic
425C22C41×#41011yescharacteristic
426C22C41×#41611yescharacteristic
427C22C41×#41711yescharacteristic
428C22C41×#42111yescharacteristic
429C22C41×#42111yescharacteristic
430C22C41×#46312yes—
431C22C41×#46412yes—
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—81no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2C41×#151211yescharacteristic
447C2C41×#151311yescharacteristic
448C2C41×#151611yescharacteristic
449C2C41×#152111yescharacteristic
450C2C41×#196311yescharacteristic
451C2C41×#196411yescharacteristic
452C2C41×#198311yescharacteristic
subgroupG/H
center, socleC23×C41C2×C22⋊C4
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC2×#121×C41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C22×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1797C2semidirect
3. C2×C41×#328C2semidirect
5. C41×#1434C2semidirect
6. C2×#124×C41C4semidirect
12. C41×#391C4semidirect
13. C41×#390C4semidirect
18. C41×#382C4semidirect
181. #9716C41direct (N × H)
218. #1797C2×C41semidirect
219. C2×#328C2×C41semidirect
221. #1434C2×C41semidirect
232. C2×#124C4×C41semidirect
238. #391C4×C41semidirect
239. #390C4×C41semidirect
244. #382C4×C41semidirect
251. C41#9716direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#28502
C41×#17972
C2×C41×#3282
C2×C41×#3272
C41×#14342
#971641