Finite Group Databasebeta

← C41×#33022 #23809223

Subgroups — C41×#33022 #23809223

Order 10496.

1528 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#518C211yesmaximal, characteristic
2C41×#2483C212yesmaximal, complemented
3C41×#2405C211yesmaximal, characteristic
4C41×#1890C214yesmaximal, complemented
5C41×#1867C214yesmaximal, complemented
6C41×#1819C212yesmaximal, complemented
7C41×#1781C211yesmaximal, characteristic
8C23×D4×C41C2211yescharacteristic
9C2×#123×C41C2212yes—
10C41×#518—22no—
11C41×#518—24no—
12C41×#518C2214yes—
13C2×C4×D4×C41—22no—
14C2×C4×D4×C41—22no—
15C2×#117×C41—21no—
16C22×C22⋊C4×C41—21no—
17C22×C22⋊C4×C41C2211yescharacteristic
18C22×C22⋊C4×C41C2212yes—
19C2×#99×C41C2214yes—
20C41×#397—24no—
21C41×#394—22no—
22C41×#386C2212yes—
23C41×#385—21no—
24C41×#385—22no—
25C41×#385C2214yescomplemented
26C41×#381—22no—
27C41×#381C2214yescomplemented
28C41×#379—21no—
29C41×#379C2212yes—
30C41×#379C2211yescharacteristic
31C41×#342C2218yescomplemented
32C25×C41D411yescharacteristic
33C25×C41C2311yescharacteristic
34C22×D4×C41—22no—
35C22×D4×C41—22no—
36C22×D4×C41—28no—
37C22×D4×C41D412yes—
38C22×D4×C41C2312yes—
39C23×C4×C41—21no—
40C23×C4×C41—21no—
41C23×C4×C41D411yescharacteristic
42C23×C4×C41D412yes—
43C23×C4×C41D412yes—
44C23×C4×C41C2311yescharacteristic
45C23×C4×C41C2311yescharacteristic
46#123×C41—28no—
47C4×D4×C41—28no—
48C4×D4×C41—28no—
49C4×D4×C41—28no—
50C4×D4×C41—28no—
51#117×C41—24no—
52#117×C41—24no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—21no—
55C2×C4⋊C4×C41—22no—
56C2×C4⋊C4×C41—24no—
57C2×C22⋊C4×C41—22no—
58C2×C22⋊C4×C41—24no—
59C2×C22⋊C4×C41—22no—
60C2×C22⋊C4×C41—24no—
61C2×C22⋊C4×C41—22no—
62C2×C22⋊C4×C41—22no—
63C2×C22⋊C4×C41—22no—
64C2×C22⋊C4×C41—21no—
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—21no—
67C2×C22⋊C4×C41—22no—
68C2×C22⋊C4×C41—22no—
69C2×C22⋊C4×C41—21no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—22no—
72C2×C22⋊C4×C41—21no—
73C2×C22⋊C4×C41—22no—
74C2×C22⋊C4×C41D414yes—
75C2×C22⋊C4×C41C2312yes—
76C2×C22⋊C4×C41C2314yes—
77C2×C22⋊C4×C41C2314yes—
78C2×C42×C41—22no—
79#99×C41—28no—
80#95×C41—24no—
81#95×C41—24no—
82#95×C41—24no—
83#95×C41—22no—
84C24×C41—21no—
85C24×C41—21no—
86C24×C41—24no—
87C24×C41—24no—
88C24×C41—42no—
89C24×C41—42no—
90C24×C41—81no—
91C24×C41—81no—
92C24×C41C2×D411yescharacteristic
93C24×C41C2×D412yes—
94C24×C41C2×D411yescharacteristic
95C24×C41C2×D412yes—
96C24×C41C2×D412yes—
97C24×C41C2411yescharacteristic
98C2×D4×C41—216no—
99C2×D4×C41—216no—
100C2×D4×C41—24no—
101C2×D4×C41—24no—
102C2×D4×C41—24no—
103C2×D4×C41—24no—
104C2×D4×C41—24no—
105C2×D4×C41#4118yes—
106C22×C4×C41—21no—
107C22×C4×C41—21no—
108C22×C4×C41—24no—
109C22×C4×C41—22no—
110C22×C4×C41—22no—
111C22×C4×C41—24no—
112C22×C4×C41—24no—
113C22×C4×C41—22no—
114C22×C4×C41—22no—
115C22×C4×C41—22no—
116C22×C4×C41—24no—
117C22×C4×C41—21no—
118C22×C4×C41—22no—
119C22×C4×C41—22no—
120C22×C4×C41—21no—
121C22×C4×C41—24no—
122C22×C4×C41—44no—
123C22×C4×C41—81no—
124C22×C4×C41—82no—
125C22×C4×C41—82no—
126C22×C4×C41—82no—
127C22×C4×C41C2×D412yes—
128C22×C4×C41C2×D414yes—
129C22×C4×C41C2×D414yes—
130C4⋊C4×C41—24no—
131C4⋊C4×C41—24no—
132C4⋊C4×C41—44no—
133C4⋊C4×C41—84no—
134C22⋊C4×C41—28no—
135C22⋊C4×C41—24no—
136C22⋊C4×C41—24no—
137C22⋊C4×C41—24no—
138C22⋊C4×C41—24no—
139C22⋊C4×C41—28no—
140C22⋊C4×C41—24no—
141C22⋊C4×C41—44no—
142C22⋊C4×C41—42no—
143C22⋊C4×C41—41no—
144C22⋊C4×C41—42no—
145C22⋊C4×C41—41no—
146C22⋊C4×C41—44no—
147C22⋊C4×C41—81no—
148C22⋊C4×C41—82no—
149C22⋊C4×C41—82no—
150C42×C41—28no—
151C23×C41—24no—
152C23×C41—24no—
153C23×C41—22no—
154C23×C41—22no—
155C23×C41—24no—
156C23×C41—24no—
157C23×C41—22no—
158C23×C41—22no—
159C23×C41—22no—
160C23×C41—24no—
161C23×C41—42no—
162C23×C41—41no—
163C23×C41—41no—
164C23×C41—41no—
165C23×C41—42no—
166C23×C41—41no—
167C23×C41—42no—
168C23×C41—41no—
169C23×C41—42no—
170C23×C41—42no—
171C23×C41—42no—
172C23×C41—42no—
173C23×C41—81no—
174C23×C41—81no—
175C23×C41—88no—
176C23×C41—88no—
177C23×C41#12011yescharacteristic
178C23×C41#12012yes—
179C23×C41#12011yescharacteristic
180C23×C41#12314yes—
181C23×C41C22×D411yescharacteristic
182C23×C41C22×D412yes—
183C23×C41C2×#4114yes—
184D4×C41—216no—
185D4×C41—216no—
186C2×C4×C41—24no—
187C2×C4×C41—24no—
188C2×C4×C41—22no—
189C2×C4×C41—22no—
190C2×C4×C41—24no—
191C2×C4×C41—24no—
192C2×C4×C41—44no—
193C2×C4×C41—44no—
194C2×C4×C41—44no—
195C2×C4×C41—44no—
196C2×C4×C41—44no—
197C2×C4×C41—42no—
198C2×C4×C41—42no—
199C2×C4×C41—44no—
200C2×C4×C41—42no—
201C2×C4×C41—44no—
202C2×C4×C41—41no—
203C2×C4×C41—41no—
204C2×C4×C41—42no—
205C2×C4×C41—42no—
206C2×C4×C41—44no—
207C2×C4×C41—44no—
208C2×C4×C41—82no—
209C2×C4×C41—82no—
210C2×C4×C41—84no—
211C2×C4×C41—84no—
212C2×C4×C41#12314yes—
213#33022C4111yesmaximal, characteristic, direct product factor, Sylow
214C22×C41—21no—
215C22×C41—22no—
216C22×C41—21no—
217C22×C41—22no—
218C22×C41—21no—
219C22×C41—21no—
220C22×C41—21no—
221C22×C41—22no—
222C22×C41—24no—
223C22×C41—22no—
224C22×C41—21no—
225C22×C41—22no—
226C22×C41—21no—
227C22×C41—44no—
228C22×C41—48no—
229C22×C41—44no—
230C22×C41—44no—
231C22×C41—48no—
232C22×C41—42no—
233C22×C41—42no—
234C22×C41—82no—
235C22×C41—82no—
236C22×C41—84no—
237C22×C41—84no—
238C22×C41#45812yes—
239C22×C41C2×#12011yescharacteristic
240C22×C41C2×#12312yes—
241C22×C41#52514yes—
242C4×C41—24no—
243C4×C41—44no—
244C4×C41—44no—
245C4×C41—82no—
246C4×C41—84no—
247C4×C41—81no—
248C4×C41—81no—
249C2×#518C2×C4111yescharacteristic
250#2483C2×C4112yescomplemented
251#2405C2×C4111yescharacteristic
252#1890C2×C4114yescomplemented
253#1867C2×C4114yescomplemented
254#1819C2×C4112yescomplemented
255#1781C2×C4111yescharacteristic
256C2×C41—22no—
257C2×C41—24no—
258C2×C41—22no—
259C2×C41—42no—
260C2×C41—41no—
261C2×C41—44no—
262C2×C41#284911yescharacteristic
263C2×C41C2×#45811yescharacteristic
264C2×C41#302611yescharacteristic
265C23×D4C22×C4111yescharacteristic
266C2×#123C22×C4112yes—
267#518—22no—
268#518—24no—
269#518C22×C4114yes—
270C2×C4×D4—22no—
271C2×C4×D4—22no—
272C2×#117—21no—
273C22×C22⋊C4—21no—
274C22×C22⋊C4C22×C4111yescharacteristic
275C22×C22⋊C4C22×C4112yes—
276C2×#99C22×C4114yes—
277#397—24no—
278#394—22no—
279#386C22×C4112yes—
280#385—21no—
281#385—22no—
282#385C22×C4114yescomplemented
283#381—22no—
284#381C22×C4114yescomplemented
285#379—21no—
286#379C22×C4111yescharacteristic
287#379C22×C4112yes—
288#342C22×C4118yescomplemented
289C41#3302211yescharacteristic, direct product factor, Sylow
290C25D4×C4111yescharacteristic
291C25C23×C4111yescharacteristic
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—28no—
295C22×D4D4×C4112yes—
296C22×D4C23×C4112yes—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4D4×C4111yescharacteristic
300C23×C4D4×C4112yes—
301C23×C4D4×C4112yes—
302C23×C4C23×C4111yescharacteristic
303C23×C4C23×C4111yescharacteristic
304#123—28no—
305C4×D4—28no—
306C4×D4—28no—
307C4×D4—28no—
308C4×D4—28no—
309#117—24no—
310#117—24no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4D4×C4114yes—
333C2×C22⋊C4C23×C4112yes—
334C2×C22⋊C4C23×C4114yes—
335C2×C22⋊C4C23×C4114yes—
336C2×C42—22no—
337#99—28no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—22no—
342C24—21no—
343C24—21no—
344C24—24no—
345C24—24no—
346C24—42no—
347C24—42no—
348C24—81no—
349C24—81no—
350C24C2×D4×C4111yescharacteristic
351C24C2×D4×C4112yes—
352C24C2×D4×C4111yescharacteristic
353C24C2×D4×C4112yes—
354C24C2×D4×C4112yes—
355C24C24×C4111yescharacteristic
356C2×D4—216no—
357C2×D4—216no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4#41×C4118yes—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—24no—
380C22×C4—44no—
381C22×C4—81no—
382C22×C4—82no—
383C22×C4—82no—
384C22×C4—82no—
385C22×C4C2×D4×C4112yes—
386C22×C4C2×D4×C4114yes—
387C22×C4C2×D4×C4114yes—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—44no—
391C4⋊C4—84no—
392C22⋊C4—28no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—28no—
398C22⋊C4—24no—
399C22⋊C4—44no—
400C22⋊C4—42no—
401C22⋊C4—41no—
402C22⋊C4—42no—
403C22⋊C4—41no—
404C22⋊C4—44no—
405C22⋊C4—81no—
406C22⋊C4—82no—
407C22⋊C4—82no—
408C42—28no—
409C23—24no—
410C23—24no—
411C23—22no—
412C23—22no—
413C23—24no—
414C23—24no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—24no—
419C23—42no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—42no—
424C23—41no—
425C23—42no—
426C23—41no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—81no—
432C23—81no—
433C23—88no—
434C23—88no—
435C23#120×C4111yescharacteristic
436C23#120×C4112yes—
437C23#120×C4111yescharacteristic
438C23#123×C4114yes—
439C23C22×D4×C4111yescharacteristic
440C23C22×D4×C4112yes—
441C23C2×#41×C4114yes—
442D4—216no—
443D4—216no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4#123×C4114yes—
471C22—21no—
472C22—22no—
473C22—21no—
474C22—22no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—22no—
479C22—24no—
480C22—22no—
481C22—21no—
482C22—22no—
483C22—21no—
484C22—44no—
485C22—44no—
486C22—48no—
487C22—44no—
488C22—48no—
489C22—42no—
490C22—42no—
491C22—82no—
492C22—82no—
493C22—84no—
494C22—84no—
495C22C41×#45812yes—
496C22C2×#120×C4111yescharacteristic
497C22C2×#123×C4112yes—
498C22C41×#52514yes—
499C4—24no—
500C4—44no—
501C4—44no—
502C4—82no—
503C4—84no—
504C4—81no—
505C4—81no—
506C2—22no—
507C2—24no—
508C2—22no—
509C2—41no—
510C2—42no—
511C2—44no—
512C2C41×#284911yescharacteristic
513C2C2×C41×#45811yescharacteristic
514C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC23×D4×C41C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2483C2semidirect
4. C41×#1890C2semidirect
5. C41×#1867C2semidirect
6. C41×#1819C2semidirect
25. C41×#385C22semidirect
27. C41×#381C22semidirect
31. C41×#342C22semidirect
213. #33022C41direct (N × H)
250. #2483C2×C41semidirect
252. #1890C2×C41semidirect
253. #1867C2×C41semidirect
254. #1819C2×C41semidirect
282. #385C22×C41semidirect
284. #381C22×C41semidirect
288. #342C22×C41semidirect
289. C41#33022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5182
C41×#24832
C41×#24052
C41×#18902
C41×#18672
C41×#18192
C41×#17812
#3302241