Finite Group Databasebeta

← C41×#10402 #23786603

Subgroups — C41×#10402 #23786603

Order 10496.

760 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2656C211yesmaximal, characteristic
2C41×#1874C212yesmaximal, complemented
3C2×C41×#327C212yesmaximal, complemented
4C41×#1444C211yesmaximal, characteristic, complemented
5C41×#1280C211yesmaximal, characteristic, complemented
6C2×#121×C41—21no—
7C2×#121×C41—21no—
8C2×#121×C41C2212yes—
9C22×C4⋊C4×C41—21no—
10C22×C4⋊C4×C41C2211yescharacteristic
11C2×#102×C41—22no—
12C2×C22⋊C8×C41C2212yes—
13C41×#399—22no—
14C41×#392—22no—
15C2×#95×C41—21no—
16C2×#95×C41C2211yescharacteristic
17C2×#95×C41C2211yescharacteristic
18C41×#340—22no—
19C41×#327—24no—
20C22×D4×C41—22no—
21C22×D4×C41—21no—
22C22×D4×C41—21no—
23C22×D4×C41D412yes—
24C23×C4×C41—21no—
25C23×C4×C41—21no—
26C23×C4×C41D411yescharacteristic
27C23×C4×C41D411yescharacteristic
28C23×C4×C41C2311yescharacteristic
29C22×C8×C41—22no—
30#121×C41—22no—
31#121×C41—22no—
32#121×C41—22no—
33#121×C41—22no—
34#121×C41—42no—
35#121×C41—42no—
36#121×C41—42no—
37#121×C41—42no—
38C2×C4⋊C4×C41—22no—
39C2×C4⋊C4×C41—21no—
40C2×C4⋊C4×C41—21no—
41C2×C4⋊C4×C41—42no—
42C2×C4⋊C4×C41—42no—
43C2×C4⋊C4×C41—42no—
44C2×C4⋊C4×C41—42no—
45C2×C4⋊C4×C41D412yes—
46C2×C22⋊C4×C41—22no—
47C2×C22⋊C4×C41—22no—
48C2×C22⋊C4×C41—22no—
49#102×C41—44no—
50C22⋊C8×C41—22no—
51C22⋊C8×C41—22no—
52#95×C41—22no—
53#95×C41—21no—
54#95×C41—42no—
55#95×C41D412yescomplemented
56C24×C41—22no—
57C24×C41C2×D411yescharacteristic
58C2×D4×C41—22no—
59C2×D4×C41—22no—
60C2×D4×C41—42no—
61C2×D4×C41—42no—
62C2×D4×C41—42no—
63C2×D4×C41—42no—
64C2×D4×C41—42no—
65C2×D4×C41—42no—
66C2×D4×C41—42no—
67C2×D4×C41—42no—
68C2×D4×C41—42no—
69C2×D4×C41—42no—
70C2×D4×C41—81no—
71C2×D4×C41—81no—
72C2×D4×C41—81no—
73C2×D4×C41—81no—
74C22×C4×C41—22no—
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—22no—
82C22×C4×C41—22no—
83C22×C4×C41—41no—
84C22×C4×C41—41no—
85C22×C4×C41—41no—
86C22×C4×C41—41no—
87C22×C4×C41—41no—
88C22×C4×C41—41no—
89C22×C4×C41—41no—
90C22×C4×C41—41no—
91C22×C4×C41—41no—
92C22×C4×C41—41no—
93C22×C4×C41—41no—
94C22×C4×C41—41no—
95C22×C4×C41—41no—
96C22×C4×C41—41no—
97C22×C4×C41—41no—
98C22×C4×C41—41no—
99C22×C4×C41D812yes—
100C22×C4×C41SD1612yes—
101C22×C4×C41C2×D412yes—
102C22×C4×C41C2×D411yescharacteristic
103C22×C4×C41#4112yes—
104C22×C4×C41#4111yescharacteristic
105C2×C8×C41—42no—
106C2×C8×C41—42no—
107C2×C8×C41—42no—
108C4⋊C4×C41—24no—
109C4⋊C4×C41—22no—
110C4⋊C4×C41—22no—
111C4⋊C4×C41—42no—
112C4⋊C4×C41—42no—
113C4⋊C4×C41—42no—
114C4⋊C4×C41—48no—
115C22⋊C4×C41—44no—
116C22⋊C4×C41—44no—
117C22⋊C4×C41—42no—
118C22⋊C4×C41—42no—
119C23×C41—21no—
120C23×C41—21no—
121C23×C41—21no—
122C23×C41—21no—
123C23×C41—42no—
124C23×C41—42no—
125C23×C41—42no—
126C23×C41—42no—
127C23×C41—42no—
128C23×C41—42no—
129C23×C41—42no—
130C23×C41#12011yescharacteristic
131C23×C41#12111yescharacteristic
132C23×C41#12411yescharacteristic
133C23×C41C2×D811yescharacteristic
134C23×C41C2×SD1611yescharacteristic
135C23×C41AGL(1,ℤ/8)11yescharacteristic
136C23×C41AGL(1,ℤ/8)11yescharacteristic
137D4×C41—44no—
138D4×C41—82no—
139D4×C41—84no—
140D4×C41—84no—
141D4×C41—82no—
142D4×C41—82no—
143D4×C41—82no—
144D4×C41—82no—
145C2×C4×C41—22no—
146C2×C4×C41—22no—
147C2×C4×C41—24no—
148C2×C4×C41—22no—
149C2×C4×C41—22no—
150C2×C4×C41—41no—
151C2×C4×C41—42no—
152C2×C4×C41—41no—
153C2×C4×C41—42no—
154C2×C4×C41—42no—
155C2×C4×C41—42no—
156C2×C4×C41—42no—
157C2×C4×C41—42no—
158C2×C4×C41—41no—
159C2×C4×C41—41no—
160C2×C4×C41—41no—
161C2×C4×C41—41no—
162C2×C4×C41—42no—
163C2×C4×C41—42no—
164C2×C4×C41—42no—
165C2×C4×C41—42no—
166C2×C4×C41—42no—
167C2×C4×C41—42no—
168C2×C4×C41—42no—
169C2×C4×C41—42no—
170C2×C4×C41—42no—
171C2×C4×C41—81no—
172C2×C4×C41—81no—
173C2×C4×C41—81no—
174C2×C4×C41—81no—
175C2×C4×C41—81no—
176C2×C4×C41—81no—
177C2×C4×C41#12112yes—
178C2×C4×C41#12312yes—
179C8×C41—82no—
180#10402C4111yesmaximal, characteristic, direct product factor, Sylow
181C22×C41—21no—
182C22×C41—21no—
183C22×C41—21no—
184C22×C41—21no—
185C22×C41—21no—
186C22×C41—21no—
187C22×C41—21no—
188C22×C41—21no—
189C22×C41—21no—
190C22×C41—21no—
191C22×C41—21no—
192C22×C41—21no—
193C22×C41—82no—
194C22×C41—82no—
195C22×C41—82no—
196C22×C41—82no—
197C22×C41—82no—
198C22×C41—82no—
199C22×C41—82no—
200C22×C41#39411yescharacteristic
201C22×C41#44711yescharacteristic
202C22×C41#45011yescharacteristic
203C22×C41#45311yescharacteristic
204C22×C41#45611yescharacteristic
205C22×C41B(4,𝔽2)11yescharacteristic
206C22×C41#45811yescharacteristic
207C22×C41#45911yescharacteristic
208C22×C41#46011yescharacteristic
209C22×C41#48611yescharacteristic
210C22×C41#49011yescharacteristic
211C4×C41—22no—
212C4×C41—22no—
213C4×C41—44no—
214C4×C41—42no—
215C4×C41—42no—
216C4×C41—82no—
217C4×C41—82no—
218#2656C2×C4111yescharacteristic
219#1874C2×C4112yescomplemented
220C2×#327C2×C4112yescomplemented
221#1444C2×C4111yescharacteristic, complemented
222#1280C2×C4111yescharacteristic, complemented
223C2×C41—21no—
224C2×C41—21no—
225C2×C41—21no—
226C2×C41—21no—
227C2×C41—162no—
228C2×C41#159511yescharacteristic
229C2×C41#160411yescharacteristic
230C2×C41#161011yescharacteristic
231C2×C41#161311yescharacteristic
232C2×C41#203911yescharacteristic
233C2×C41#204111yescharacteristic
234C2×C41#204411yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C22×C4112yes—
238C22×C4⋊C4—21no—
239C22×C4⋊C4C22×C4111yescharacteristic
240C2×#102—22no—
241C2×C22⋊C8C22×C4112yes—
242#399—22no—
243#392—22no—
244C2×#95—21no—
245C2×#95C22×C4111yescharacteristic
246C2×#95C22×C4111yescharacteristic
247#340—22no—
248#327—24no—
249C41#1040211yescharacteristic, direct product factor, Sylow
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4D4×C4112yes—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4D4×C4111yescharacteristic
257C23×C4D4×C4111yescharacteristic
258C23×C4C23×C4111yescharacteristic
259C22×C8—22no—
260#121—22no—
261#121—22no—
262#121—22no—
263#121—22no—
264#121—42no—
265#121—42no—
266#121—42no—
267#121—42no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4D4×C4112yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279#102—44no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—22no—
283#95—21no—
284#95—42no—
285#95D4×C4112yescomplemented
286C24—22no—
287C24C2×D4×C4111yescharacteristic
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—81no—
301C2×D4—81no—
302C2×D4—81no—
303C2×D4—81no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4D8×C4112yes—
330C22×C4SD16×C4112yes—
331C22×C4C2×D4×C4112yes—
332C22×C4C2×D4×C4111yescharacteristic
333C22×C4#41×C4112yes—
334C22×C4#41×C4111yescharacteristic
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—48no—
345C22⋊C4—44no—
346C22⋊C4—44no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23#120×C4111yescharacteristic
361C23#121×C4111yescharacteristic
362C23#124×C4111yescharacteristic
363C23C2×D8×C4111yescharacteristic
364C23C2×SD16×C4111yescharacteristic
365C23AGL(1,ℤ/8)×C4111yescharacteristic
366C23AGL(1,ℤ/8)×C4111yescharacteristic
367D4—44no—
368D4—82no—
369D4—84no—
370D4—84no—
371D4—82no—
372D4—82no—
373D4—82no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4#121×C4112yes—
408C2×C4#123×C4112yes—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22C41×#39411yescharacteristic
430C22C41×#44711yescharacteristic
431C22C41×#45011yescharacteristic
432C22C41×#45311yescharacteristic
433C22C41×#45611yescharacteristic
434C22C41×B(4,𝔽2)11yescharacteristic
435C22C41×#45811yescharacteristic
436C22C41×#45911yescharacteristic
437C22C41×#46011yescharacteristic
438C22C41×#48611yescharacteristic
439C22C41×#49011yescharacteristic
440C4—22no—
441C4—22no—
442C4—44no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—162no—
452C2C41×#159511yescharacteristic
453C2C41×#160411yescharacteristic
454C2C41×#161011yescharacteristic
455C2C41×#161311yescharacteristic
456C2C41×#203911yescharacteristic
457C2C41×#204111yescharacteristic
458C2C41×#204411yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC41×#2656C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1874C2semidirect
3. C2×C41×#327C2semidirect
4. C41×#1444C2semidirect
5. C41×#1280C2semidirect
55. #95×C41D4semidirect
180. #10402C41direct (N × H)
219. #1874C2×C41semidirect
220. C2×#327C2×C41semidirect
221. #1444C2×C41semidirect
222. #1280C2×C41semidirect
249. C41#10402direct (N × H)
285. #95D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#26562
C41×#18742
C2×C41×#3272
C41×#14442
C41×#12802
#1040241